Nelson Goodman
Philosophy Now Series Editor: John Shand This is a fresh and vital series of new introductions to today’s most read, discussed and important philosophers. Combining rigorous analysis with authoritative exposition, each book gives a clear, comprehensive and enthralling access to the ideas of those philosophers who have made a truly fundamental and original contribution to the subject. Together the volumes comprise a remarkable gallery of the thinkers who have been at the forefront of philosophical ideas. Published Donald Davidson Marc Joseph
Hilary Putnam Maximilian de Gaynesford
Michael Dummett Bernhard Weiss
W. V. Quine Alex Orenstein
Nelson Goodman Daniel Cohnitz & Marcus Rossberg
Richard Rorty Alan Malachowski
Saul Kripke G. W. Fitch
John Searle Nick Fotion
Thomas Kuhn Alexander Bird
Wilfrid Sellars Willem A. deVries
David Lewis Daniel Nolan
Charles Taylor Ruth Abbey
John McDowell Tim Thornton
Peter Winch Colin Lyas
Robert Nozick A. R. Lacey Forthcoming David Armstrong Stephen Mumford
Peter Strawson Clifford Brown
Thomas Nagel Alan Thomas
Bernard Williams Mark Jenkins
John Rawls Catherine Audard
Nelson Goodman Daniel Cohnitz & Marcus Rossberg
In memoriam Lothar Ridder, teacher and friend
© Daniel Cohnitz & Marcus Rossberg, 2006 This book is copyright under the Berne Convention. No reproduction without permission. All rights reserved. First published in 2006 by Acumen Acumen Publishing Limited 15a Lewins Yard East Street Chesham Bucks HP5 1HQ www.acumenpublishing.co.uk ISBN: ISBN:
1-84465-036-7 (hardcover) 1-84465-037-5 (paperback)
British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Designed and typeset in Century Schoolbook by Kate Williams, Swansea. Printed and bound by Cromwell Press, Trowbridge.
Contents
Acknowledgements Abbreviations 1 The worldmaker’s universe
vii viii 1
2 If this were an emerald it would be grue: problems and riddles of induction
28
3 The big picture
54
4 Particulars and parts
75
5 From Vienna Station to Boston Terminus
99
6 Follow the sign
140
7 Diagnosing art
164
8 Starmaking
191
9 Never mind mind, essence is not essential, and matter does not matter
204
List of symbols Glossary of technical terms Further reading Notes Bibliography Index
229 230 237 240 261 277
v
Acknowledgements
We should like to thank the following colleagues for helpful comments on earlier versions of parts of this book, and various kinds of support ranging from technical help to philosophical discussions that lasted many hours: Stefan Bagusche, Elizabeth Barnes, Aislinn Batstone, Dieter Birnbacher, Mike Bishop, Manuel Bremer, Marc Breuer, Ross Cameron, Curtis Carter, Roy Cook, Lindsay Duffield, Philip Ebert, Catherine Elgin, Gerhard Ernst, Steven Gerrard, Patrick Greenough, Bob Hale, Sune Holm, Carrie Jenkins, Lisa Jones, Andrew Jorgensen, Christoph Kann, Tanja Kosubek, Hannes Leitgeb, Darren McDonald, Brian McElwee, Aidan McGlynn, Thomas Mormann, Daniel Nolan, John Norton, Nikolaj Pedersen, Oliver Petersen, Simon Robertson, Raffaele Rodogno, Oliver Scholz, John Shand, Peter Simons, Barry Smith, Axel Spree, Jakob Steinbrenner, Chiara Tabet, Myung Hee Theuer, R. K. B. Vaas, Michael Weh, Robert Williams, Crispin Wright, the members of the seminar that was held on an earlier version of this book at the University of St Andrews, and two anonymous referees. We dedicate this book to the memory of Lothar Ridder, our friend and teacher, who died 31 January 2004, aged 51, after a long battle with cancer. Lothar had been our teacher since our undergraduate studies. He received his PhD for a thesis on the ontology of logical atomism (1989) and we first met him when he was writing his “Habilitation” on mereology. Lothar discussed Goodman’s and Leonard’s work in detail in his Mereologie (2003). In Chapter 4 of our book, which deals with Goodman’s mereology and nominalism, you will find some of his ideas and results. Lothar impressed everyone who was privileged to know him with his sharp analytic mind, his meticulous precision in philosophy, his gentleness and immense modesty. He embodied the qualities to which we aspire. We miss him greatly. vii
Abbreviations
BA Basic Abilities Required for Understanding and Creation in the Arts: Final Report (with David Perkins, Howard Gardner, and the assistance of Jeanne Bamberger et al.) (Cambridge, MA: Harvard University, Graduate School of Education, 1972). FFF Fact, Fiction, and Forecast, 4th edn (Cambridge, MA: Harvard University Press, [1954] 1983). LA Languages of Art: An Approach to a Theory of Symbols (Brighton: Harvester, [1968] 1981). MM Of Mind and Other Matters (Cambridge, MA: Harvard University Press, 1984). PP Problems and Projects (Indianapolis, IN: Bobbs-Merrill, 1972). RP Reconceptions in Philosophy and other Arts and Sciences (with Catherine Z. Elgin) (London: Routledge, 1990). SA The Structure of Appearance, 3rd edn (Boston, MA: Reidel, 1977 [1951]). SQ A Study of Qualities (New York: Garland, [1941] 1990). WW Ways of Worldmaking (Indianapolis, IN: Hackett, [1978] 1985).
viii
Chapter 1
The worldmaker’s universe
The whole and its parts Nelson Goodman was a philosopher of enormous breadth. He made important and highly original contributions to epistemology, logic and the philosophy of science, but is also a famous figure in the analytic philosophy of art and in metaphysics. Unlike many other philosophers of the twentieth century, Goodman was not a puzzle-solver who wrote in an almost inaccessible technical style on unrelated highly specialized problems; on the contrary, he worked on the most fundamental problems, contributing original and provocative insights, and his writing was always brilliant in both precision and style. As his students and/or co-authors Catherine Elgin, Israel Scheffler and Robert Schwartz have remarked in retrospect, he: delighted in making points in the most provocative way possible. There is some controversy over what is the most outrageous thing he ever said. Among the more obvious contenders are the repudiation of sets, the grue paradox, the contention that one wrong note disqualifies a performance as an instance of a musical work, and the claim that there are many worlds if any. In such remarks, Goodman threw down the gauntlet. If you disagree with one (or more) of the above, you need to show what is wrong with the argument that leads to it. All too frequently the initial irritation is compounded as we begin to appreciate the difficulty of evading his conclusions without begging the question, or committing ourselves to claims that seem even more dubious than his. (Elgin et al. 1999: 207) 1
Nelson Goodman
Goodman clearly ranks among the most important philosophers of the twentieth century. Full appreciation of the value of his work, however, has barely begun. One might go as far as saying that of the most influential philosophers of the twentieth century, Goodman is today the most neglected. This book, for example, is, as far as we know, the first attempt to introduce Goodman’s philosophy as the coherent, interconnected system of ideas it is. Thus one of our major aims here is to show by way of example that studying Goodman systematically and in some detail is worthwhile. What we also hope to achieve is to put some of Goodman’s better known contributions into the right context. Goodman’s Languages of Art (1968) brought him to the attention of postmodern thinkers, who tend to interpret him (with approval) as a culture relativist with leanings towards irrationalism.1 This is a much distorted picture of Goodman’s philosophy, based on a misunderstanding of his constructionalism. Unlike philosophers such as Paul Feyerabend or Richard Rorty, who worked in a certain analytic tradition for a part of their lives and then converted to some sort of non-analytic philosophy in later years, Goodman’s whole work is within one and the same tradition of analytic philosophy. Of course, Goodman’s views have developed over the years (it would be sad if this was not so), but we want to demonstrate that his early work in logic and epistemology and his later work on art and constructionalism actually form a coherent whole, methodologically as well as in their content. This enterprise might be doomed from the start. In what we believe to be Goodman’s last publication he writes: There is no such thing as the philosophy of Nelson Goodman any more than there is such a thing as the finger of Nelson Goodman. There are many philosophies, but on the other hand there is no nice neat order of different complete philosophies: there are lots of ideas, conjectures about various fields. A few months ago, at the Technische Universität in Berlin, … I gave an impromptu talk called “Untangling Nelson Goodman” and I said, ‘Well, here’s all this mess and can I do anything about untangling these things?’. The answer was that I couldn’t do very much. I mean, for instance, I had dealt with certain topics many different times and in many different contexts; but it is not always clear how these relate to one another. And so perhaps I should try to make it clear. All I could do is suggest some of the different attacks that I made on some of the problems at different times and at least note that these were not all part of a well organized 2
The worldmaker’s universe
scheme. They were all different attempts to deal with different aspects of the problem. And then it occurred to me that untangling this mess might entail a good deal of loss, the kind of loss you get if you try to untangle a plate of spaghetti: you would end up with some rather uninspiring strings of dough which would not have anything of the central quality of the whole meal. (Goodman 1997: 16–17) Despite Goodman’s pessimism, we hope to have achieved an introduction to Goodman’s philosophies that points out the coherence and unity that Goodman denies in the quote above. We hope to have “untangled” Goodman a bit, or to have at least provided a startingpoint for further studies. The most systematic presentation of Goodman’s work would start with his PhD thesis A Study of Qualities (SQ) and develop everything else from there. A Study of Qualities, however, is one of the the most complicated books he ever wrote, which is why we have decided to sacrifice some systematicity on the altar of didactics. Instead, after some remarks about Goodman’s life, personality and historical background in this chapter, we shall introduce Goodman’s so-called “new riddle of induction” – one of Goodman’s major contributions to the philosophy of science – in Chapter 2. Presumably, readers are already familiar with the “new riddle” or have already heard about ‘grue’ and kindred predicates. We hope that learning by way of example how Goodman approaches a philosophical problem is a useful start for understanding his philosophy. Having introduced Goodman’s way of doing philosophy in a specific area of epistemology, we turn to the broader perspectives. In Chapter 3 we reconstruct Goodman’s view on the purpose and aim of philosophy as a professional activity. We will see that Goodman’s philosophy aims at elucidation and understanding in a very specific sense. Philosophically problematic notions are clarified by way of rational reconstructions. In the ideal language tradition, the philosophical tradition Goodman belongs to, this gets done by explicating problematic concepts. What explication is, and how it differs from other forms of definition, is explained in the second half of the chapter. In Chapter 4, with a few broad brushstrokes, we introduce the formal basis for Goodman’s nominalism. In 1940 Goodman and Henry S. Leonard published a mereological system called the calculus of individuals, departing from work that Leonard had already done for his PhD (1930). Goodman and Leonard demonstrate that this apparatus is able to make precise, and hence elucidate, important 3
Nelson Goodman
philosophical concepts with the aid of relations such as ‘overlapping’, ‘part’ or ‘mereological sum’, which are definable in the calculus. This powerful formal tool was brought to use in Goodman’s chief work, The Structure of Appearance (1951), a considerably revised version of A Study of Qualities. This book is a thorough analysis and further elaboration of the work of Rudolf Carnap, his most famous predecessor in the ideal-language tradition. In Chapter 5 we characterize Carnap’s project in Der logische Aufbau der Welt (the Aufbau) ([1928] 1961) and also review Carnap’s early conventionalism (of the early 1930s), which arose from Carnap’s collaboration and discussions with Otto Neurath. Goodman’s work is usually classified as being an anti-foundationalist version of Carnap’s project, but Carnap himself endorsed most of Goodman’s later results shortly after the Aufbau (in the period including The Logical Syntax of Language ([1934] 1937), with its principle of tolerance). The main characteristics of this period of Carnap’s are also characteristics of Goodman’s Structure of Appearance and his later work. Since much in The Structure of Appearance is in direct confrontation with Carnap’s Aufbau, it is best, and probably solely, understood on the basis of a firm knowledge of the key issues of the Aufbau. We therefore take the space to dedicate a good part of this chapter to the pre-Goodman philosophy, from which his own work arises as a criticism and further development. The second formal basis for Goodman’s philosophy, his theory of symbols, will be introduced in Chapter 6. All of our cognitive access to the world, Goodman insists, is governed by the use of symbols of all sorts. In Languages of Art he develops a taxonomy of symbol systems that contribute in different ways to our different cognitive enterprises. All kinds of symbol systems and all ways of reference have nevertheless one thing in common: they facilitate our understanding. Chapter 7 will finally take us to Goodman’s philosophy of art. Taking a work of art as a complex symbol, Goodman has a good part of what he needs for his “epistemic turn” in aesthetics (Elgin 1997a: ch. 3). Goodman sees art as an essentially cognitive endeavour, and so the most important thing is to recognize a work of art as promoting our understanding (or making) of a world version. Along with this comes a relocation of what was traditionally taken to be essential to art. After having placed Goodman in a certain branch of analytic philosophy and having already noted the constructionist nature of his solution for the new riddle of induction, in Chapter 8 we shall explain Goodman’s constructionalism and relativism. According to Goodman, worlds and the objects in them are made rather than found. 4
The worldmaker’s universe
The enterprise of cognition is to construct symbol systems, so-called versions. True versions constitute a world. So in choosing a symbol system that, for example, categorizes the celestial bodies, we, in a sense, make the stars. In this chapter we shall present the worldmaking that Goodman describes, for example, in Ways of Worldmaking (1978), and in doing so demonstrate why for Goodman art, philosophy and science are all “ways of worldmaking”. These ways are on a par, but construct different worlds, each appropriate for different epistemic purposes. In order to help the understanding of the unity of Goodman’s thought, most of the book is conceived as a rather affirmative reconstruction of Goodman’s views. Chapter 9, however, will deal mainly with critical remarks. One group of Goodman’s publications that are often forgotten are the highly technical papers he wrote, most of which have been published in the Journal of Symbolic Logic. Ullian (1999) gives an overview of them; this book is not the place to introduce them. Another area of Goodman’s work that we cannot adequately treat here is his non-philosophical engagement with the arts and art education, although we shall say something about that in the next section.
Nelson Goodman (1906–1998)2 Henry Nelson Goodman was born on 7 August 1906 in Summerville , Massachusetts, USA, the son of Sarah Elizabeth (Woodbury) Goodman and Henry L. Goodman. In the 1920s he enrolled at Harvard University. As a student, Goodman was interested in philosophy, as well as in mathematics and creative writing; in fact, at the very beginning of his studies he wanted to become a novelist. However, at the end of the first semester, after a seminar on the pre-Socratics, he knew that philosophy was right for him (Scholz 2005). At that time, Harvard was a good place to study philosophy. Alfred North Whitehead, Clarence Irving Lewis and Henry Maurice Sheffer were prominent members of the faculty, as were William Ernst Hocking, Ralph Barton Perry, and James Haughton Woods. Looking back on his early years of study, Goodman wrote: Our introduction to philosophy included the historic running debate over idealism versus realism between W. E. Hocking and Ralph Barton Perry, and over monism and pluralism in logic between C. I. Lewis and Harry Sheffer. We were absorbed by 5
Nelson Goodman
Lewis’ courses in the theory of knowledge, based on the just published Mind and the World Order; and we were first exasperated and then enthralled by the nearly incoherent but inspired and profound lectures of James Haughton Woods on Plato. We sharpened our philosophical teeth in almost daily discussions of such matters as Berkeley’s idealism, Plato’s theory of ideas, Whitehead’s extensive abstraction, and problems in logic. (1969b: ix) Goodman graduated from Harvard with a BS (Phi Beta Kappa,3 magna cum laude) in 1928, his PhD, however, which he received in 1941 for A Study of Qualities, took him more than 12 years to complete. There are several possible reasons for the lateness of his PhD. Maybe the most important was that Goodman was Jewish, and therefore not eligible for a graduate fellowship at Harvard (Schwartz 1999, Elgin 2000a, Scholz 2005). He had to work outside the university to finance his studies. This, however, leads to the more often recognized reason for the lateness of his PhD: Goodman’s interest and activity in the art world. In 1937, the German philosopher Rudolf Carnap had just accepted a permanent post at the University of Chicago. Carnap was offered the leadership of a research group with several assistantships. He wrote to his friend Willard Van Orman Quine at Harvard for advice on whom to hire. Quine responded with a list of recommendations, naming J. C. C. McKinsey, Leonard and Goodman: My next recommendation would be H. Nelson Goodman … Candidate for PhD. Age about 30. Very competent and industrious. An authority on the Logischer Aufbau, and conversant with your later work. Well grounded in philosophy and logic. As you know, he is in business – which accounts for the lateness of his PhD. I am not sure that he would not be interested in the assistantship. Teaching experience and pul’ns [publications], none. (Creath 1990: 233) ‘In business’ here refers to Goodman’s activities as the director of an art gallery. As Oliver Scholz (2005) reports, Goodman started extensive studies in practical and theoretical aspects of art. In the seminars and colloquia of the collector and connoisseur Paul Joseph Sachs (1878–1965), Goodman learnt about the basics of art history as well as about practical matters of art presentation and art appreciation. In particular he learnt to see the difference between the cursory perception of artworks in a museum or a catalogue and the intensive 6
The worldmaker’s universe
appreciation of an original. Sachs’s seminars and lectures created many an art collector and Goodman was one of them. It was a passion that Goodman kept throughout his life: Goodman’s professional role as a gallery director and his private art collecting were sources of great satisfaction. His life-long pursuit of collecting art began in his student days. He was well known in the art world for his discriminating aesthetic perception and equally for his astuteness in negotiating the price of an object. A visit to his home in Weston, Massachusetts would reveal a collector with enthusiasm and in-depth knowledge over a wide range of art. Virtually every corner and closet held yet another group of art treasures. It was not unusual to see hanging on opposite walls an important Flemish Old Master by Jan Van Kessel and an exquisite naïve work by an unknown twentieth century Italian immigrant farmer, Peter Petronzio. His collections included seventeenth century Old Master paintings and drawings, modern art from Picasso to Demuth, ancient Asian sculptures, and Native American arts of the Northwest Coast and the Southwest, even Pre-Columbian. (Carter 2000: 252–3) From 1928 until 1941 Goodman was Director of the Walker-Goodman Art Gallery at Copley Square, Boston. Here he met his later wife Katharine (“Kay”) Sturgis, who came to the gallery in order to exhibit her watercolours and ink drawings.4 From this time on, Goodman would constantly be travelling between the art world and the world of academic philosophy, as at home in museums, at art exhibitions and in auction houses as at congresses and conferences on logic and epistemology. Working as the director of an art gallery at least provided Goodman with a bigger car than teaching at Harvard did for contemporaries such as Quine. When Carnap visited the US in 1935, Quine organized a trip5 to the annual philosophy convention at Baltimore. To Carnap he wrote: “Everything is in order for our trip to Baltimore. A man by the name of Goodman, who is busy with your [Aufbau], will take us in his large car” (Creath 1990: 194). Although he was successfully running an art gallery, Goodman still found time for philosophy. During the early 1930s Goodman belonged, with David Prall, Leonard, Charles Stevenson and John Cooley, to the privileged few who attended Quine’s early lectures on Carnap.6 A Study of Qualities, now regarded by some (see Elgin 2000a, Scholz 2005) to be the best and most ambitious philosophical PhD 7
Nelson Goodman
thesis ever submitted at Harvard, was presumably reworked considerably after 1930. (We shall come to that in some detail in Chapter 5.) However, the idea of a calculus of individuals, one of the main technical innovations in Goodman’s thesis, first appeared in Leonard’s doctoral thesis Singular Terms (1930). Leonard’s thesis probably gives a good impression of what Goodman was up to in 1930. It seems easily conceivable that Goodman only drew the connection to Carnap’s work later (we know that even Quine did not know much about the Aufbau until 1932 or so, when he heard about it from Cooley; see Quine 1985: 86). It might also have been surprising for Goodman to learn from Quine in 1935 that Leśniewski had already provided a full theory of parthood relations (see Quine 1985: 122). All of these factors might have forced Goodman to enlarge his project into new directions during the early 1930s to render his PhD thesis an original contribution, since the basic ideas for the calculus of individuals were already in his hands in 1930 (SA: XVII) and a “finished version” of his dissertation was ready by 1933 (SQ: i).7 As Scholz (2005) points out, Goodman’s perfectionism might also have caused some delay. The subsequent delay in publication, however, was mainly due to the Second World War. From 1942 to 1945 Goodman performed military service in the US Army, conducting psychological tests (Scholz 2005, Carter 2000). It then took until 1951 for The Structure of Appearance to appear in print (A Study of Qualities was not published until 1990). After his military service, Goodman taught briefly as “instructor in philosophy” at Tufts College, and was then hired as associate professor (1946–51) and later as full professor (1951–64) at the University of Pennsylvania. He served briefly as Harry Austryn Wolfson Professor of Philosophy at Brandeis University (1964–67), finally returning to Harvard in 1968, where he taught philosophy until 1977. In 1967 Goodman founded Project Zero at Harvard: a centre to study and improve education in the arts. Goodman believed that arts learning should be studied as a serious cognitive activity, but that nothing, or “zero”, had been firmly established in the field, hence the name of the project. At Harvard, Goodman was also involved in establishing the Dance Center and the Institute for Arts Administration. Goodman chaired the Arts Orientation Series (1969–71) and was advisor of the Arts for Summer School for seven years (1971–77). In these activities Goodman could combine his interests in the arts with his work as a philosophy professor. Besides art administration, Goodman actively participated as a producer in the art world. Goodman conceived altogether three 8
The worldmaker’s universe
multimedia-performance events. Inspired by paintings by his wife, Katharine Sturgis, Goodman first produced Hockey Seen together with composer John Adams and choreographer Martha Armstrong Gray. Hockey Seen was shown in 1972 at Harvard and in 1980 in the Belgian town Knokke-le-Zoute; in 1984 it was recorded on film at Harvard. John Updike’s novel Rabbit, Run served as the template for Goodman’s same-titled second work, which was realized again with choreographer Gray and composer Joel Kabakov. Goodman’s last work was Variations: An Illustrated Lecture Concert, featuring twenty-one of Pablo Picasso’s variations on Diego Velázquez’s painting Las Meninas. The original painting and its variations were displayed with the help of slide projections, while a musical theme and analogous twenty-one variations composed by David Alpher were played. Variations was performed at a number of places, including Helsinki University, Wayne State University, the Rockport (Massachusetts) Chamber Music Festival, Harvard University and Trinity University Texas (Carter 2000). In 1986 the Gloucester Daily Times (Massachusetts) praised it in a review as “a serious and original work. It succeeds in at least two ways: it forces the audience to think about how each section is a variation on what precedes it, and about the relationship between [visual] art and music.”8 Nelson Goodman’s personality is often described as unapproachable and demanding. Indeed, Goodman – a perfectionist – demanded a great deal from himself and others. W. J. T. Mitchell, now Gaylord Donnelley Distinguished Service Professor in the departments of English and art history at the University of Chicago, remembers his respect for this aspect of Goodman’s reputation at their first meeting: I first met Goodman in the mid-’80s, having made the pilgrimage to Cambridge to discuss with him the chapter of Iconology that deals with his work. I was scared to death. Goodman’s own writing, and his reputation as one of the most demanding, formidable characters in the Harvard philosophy department, was intimidating enough. Then there were the stories of how notoriously difficult he was on doctoral exams. I knew that he did not suffer fools gladly, and I was pretty sure at that moment that I had been a fool to take on the task of expounding his relation to the traditional problem of word and image. His appearance – bald, a massively sculpted head with prominent nose and jaw – and his gruff, peremptory tone of voice only reinforced my terror. (Mitchell 1999)
9
Nelson Goodman
However, people who knew him well were also acquainted with Goodman’s gentler side.9 As his friend and colleague Hilary Putnam remarked, “he affected to be a sourpuss, but he was really enormously cheerful” (Harvard University Gazette 1998).10 His gentleness extended beyond his fellow human beings. Goodman and his wife were animal-lovers and dedicated animal-welfare activists. Both were members of the World Society for the Protection of Animals and supported campaigns to help animals that were endangered due to wars or natural disasters. Elgin recalls the following story, which nicely combines the two aspect of Goodman’s personality. It was summer in the early ’80s. Nelson Goodman and I were working on Reconceptions. As always, Nelson adamantly insisted that what he was working on was to be given the highest priority. All other matters were to be shelved until his project, whatever it happened to be, was done. He spent his summers in a cottage in Rockport, Massachusetts, but arranged to meet me in Cambridge to confer about the book. When I arrived, I found a message. Owing to an emergency, he would not be in. Naturally, I was alarmed. He was, after all, an old man. Was he sick? Was he injured? When I telephoned him in Rockport, he seemed surprisingly unruffled. Evidently my view of what qualifies as an emergency and his diverged considerably. He told me that a robin had built her nest and laid her eggs in an apple tree outside his window. This, he remarked in an aside, enabled him to realize the objective, first bruited in Fact, Fiction, and Forecast, of doing ornithology without going out in the rain. That morning the eggs had hatched. This all sounded rather pleasant in a bucolic sort of way, but what, I demanded, was the emergency? “Cats have been sighted,” he replied. That said it all. He stayed at his cottage and patrolled the perimeter until the nestlings flew away. Then he returned to work, insisting as adamantly as ever that all other matters had to be shelved until our project was done. (Elgin 1999) Goodman was not fond of looking back on his achievements, but was always looking forward to the next philosophical problem to tackle. As he once advised Elgin: “When you finish one project, ask yourself what is the most difficult outstanding problem in philosophy. Then work on that” (Elgin 2000: 2). 10
The worldmaker’s universe
This might well be the reason why there is nothing like an autobiography and only two interviews with Goodman (see Scholz 2005). He even refused the offer to be honoured with a volume in the prestigious Schilpp Library of Living Philosophers (Elgin 2000a: 2). However, he was revered in other ways (see Carter 2000). He served as President of the American Philosophical Association, Eastern Division, in 1967 and as Vice President of the Association for Symbolic Logic, 1950–52. Goodman was a Fellow of the American Academy of Arts and Sciences and a corresponding Fellow of the British Academy. In 1946 and 1947 he received the Guggenheim Award. His many distinguished lectures and lecture series included: the Sherman Lecture (1953) at the University of London; the Alfred North Whitehead Lecture (1962) at Harvard University; the John Locke Lectures (1962) at the University of Oxford; the Miller Lectures (1974) at the University of Illinois; the Immanuel Kant Lectures (1976) at Stanford University; and the Howison Lecture (1985) at the University of California, Berkeley. His honorary doctoral degrees are from the University of Pennsylvania, Adelphi University, Technical University, Berlin (1990) and the University of Nancy, France (1997). In 1992 the American Society for Aesthetics honoured Goodman with a seminar on his work on their fiftieth anniversary. Goodman’s work has been celebrated in Europe with various international colloquia during the last decade of the twentieth century, including: “Author’s Colloquium” (1991) at the Zentrum für interdisziplinäre Forschung, Bielefeld University, Germany (Bieri and Scholz 1993); “Colloquium on Representation” (1991) at Rome University/Tuscia University, Viterbo, Italy; “Nelson Goodman et les Langages de l’Art” (1992) at the National Museum of Modern Art, Georges Pompidou Centre, Paris; “Manière de Faire les Mondes” (1997) at the University of Nancy, Pont à Mousson, France; and “Weisen der Welterzeugung” (1998) at Heidelberg University, Germany (Fischer and Schmidt 2000). Goodman died on 25 November 1998 in Needham, Massachusetts, at the age of 92, after a stroke, and was buried in a family plot in Everett, Masschusetts. His wife had preceded him in death in 1996. In a memorial note, Hilary Putnam, Goodman’s colleague at Harvard, considers him to be “one of the two or three greatest analytic philosophers of the post-World War II period” (Harvard University Gazette 1998). Goodman’s work comprises eight books and numerous articles and smaller works. The content of these will be our topic for the remaining chapters.
11
Nelson Goodman
The historical background Before we come to Goodman’s own views, however, we first have to set the stage by providing some of the historical background that Goodman developed his ideas in. Some ideas are easier to grasp when one knows what they contrast with, and some peculiarities are easier to assess when one learns in what climate they were developed.
The arch-enemy: Henri Bergson What was the contrast to Goodman’s philosophy? Let us begin with Goodman’s declared “arch-enemy”, the philosopher Henri Bergson, and his followers, the Bergsonians. Bergson (1859–1941) is today not widely known, especially among analytically minded philosophers in Anglophone countries. Although Bergson had a recent revival due to the work of Gilles Deleuze, this was limited to postmodernist circles. At the time that Goodman was a young student, however, Bergson was among the most famous and influential philosophers. Bergson’s fame was not restricted to Europe. When he first visited the United States in 1913, his appearance in New York was probably the cause of the first traffic jam in the history of Broadway.11 In 1928 Bergson was even awarded the Nobel Prize for Literature. With Bergson’s concern with phenomenology and epistemology in general (we discuss Goodman’s view on this matter in Chapter 5), there might be something like a common philosophical interest with Goodman. Bergson’s role in Goodman’s writings is, however, not as a representative of a specific philosophical position that is worth detailed investigation. Whatever Bergson had to say about evolution, perception, memory, religion or morality does not seem to show up in Goodman’s writings. Bergson and his followers are rather stereotypes of irrationalism (at the time euphemistically referred to as “mysticism”), of an anti-scientific attitude towards philosophy and of hostility towards formal methods. Indeed, this has some basis in Bergson’s writings. According to Bergson, all we sense are images. The representations we form of these images, be they perceptions or subtler representations arrived at via analysis and synthesis, are always diminutions of the images we started with. Therefore knowledge, like scientific knowledge, which represents the world in a certain way, cannot be absolute knowledge; it necessarily leaves something out. 12
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Whereas philosophers who arrived at similar views have shrugged and turned to the question of the relation representations have with respect to reality or the thing in itself, Bergson offered a further theory of how we eventually could arrive at absolute knowledge by sidestepping the limits of representations. This is done by way of “intuition”, which is for Bergson another form of experience with the help of which we are able to place ourselves in the position of (parts of) the things. By “entering into” the things we can gain absolute knowledge of them. This view seems to be the basis for Goodman’s arch-enemy construct. In a hypothetical dialogue in “The Way the World Is” (1960a), Goodman lets his opponent characterize his position with the following words: All our descriptions are a sorry travesty. Science, language, perception, philosophy – none of these can ever be utterly faithful to the world as it is. All make abstractions or conventionalizations of one kind or another, all filter the world through the mind, through concepts, through the senses, through language; and all these filtering media in some way distort the world. It is not just that each gives only a partial truth, but that each introduces distortions of its own. We never achieve even in part a really faithful portrayal of the way the world is. (PP: 25) For Goodman this view is totally mistaken. The wrong presupposition of Bergsonian thinking is to believe that there is only one way the world is, namely the reality behind our representations. But for Goodman, as we shall see in detail in Chapter 8, there are many ways the world is and every right version captures one of them: Since the mystic is concerned with the way the world is and finds that the way cannot be expressed, his ultimate response to the question of the way the world is must be, as he recognizes, silence. Since I am concerned rather with the ways the world is, my response must be to construct one or many descriptions. The answer to the question “What is the way the world is? What are the ways the world is?” is not a shush, but a chatter. (PP: 31) Similarly, the use of formal methods to improve clarity and precision is defended against Bergson, who holds “that the application of any precise concepts can only result in distorting and in effect killing actual experience” (PP: 47). Whereas the possibility of error is granted by Goodman (formal methods can be more or less suited for a certain topic), formal methods are employed with a hope, the hope that we might be able to achieve something clearer or better founded 13
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than the “tenuous generalizations that have nourished philosophical controversy for centuries” (ibid.).
The inexplicably hostile ally: the Brits Surprising as it may be, another contrast to Goodman’s philosophy is to be found within analytic philosophy. As Michael Dummett, who was nineteen years younger than Goodman, reported from his own experience in his youth, analytic philosophy was for a long time divided into two camps: the ideal-language tradition, which goes back to the work of Gottlob Frege and whose main promoter was Carnap; and the ordinary-language tradition, which is usually traced back to the work of the later Wittgenstein and was promoted by Gilbert Ryle and associated with the philosophers of the University of Oxford. Dummett, who was Ryle’s student at Oxford, explains in his “Can Analytical Philosophy be Systematic, and Ought it to Be?” (1977) that at that time the main opposition to Ryle’s conception of analytic philosophy was not Heidegger or some other continental philosopher, but Carnap. Goodman, as we shall see in the next section, stood in Carnap’s tradition and hence in opposition to the British ordinary-language philosophy. One of the main differences between both types of analytic philosophy was their attitude towards systematicity in philosophy. As is well known, the later Wittgenstein abjured systematicity in philosophy completely (see his Philosophical Investigations (1953)). As Goodman interpreted him, Wittgenstein would regard philosophical problems as diseases spread via natural language. The philosopher is accordingly a therapist who in single cases of confusion comes to help with a cure that is specific to the case at hand. The way Goodman understands this ambulance model of philosophy allows philosophers to stop doing philosophy whenever they please. Since they are not interested in constructing a systematic theory, to stop philosophizing will not prevent them from reaching a final goal. Their aims are all temporary: to help the poor souls who find themselves trapped in a puzzle of natural language.12 Goodman rejected this view. First of all, philosophical puzzles do not arise for the man on the street who just tries to make a living. Philosophical puzzles arise for philosophers and they arise only because the philosopher has set up standards of understanding that might or might not be met by a literal understanding of natural language. Hence: 14
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the philosopher’s puzzlement about language is always a puzzlement about interpreting ordinary statements in a philosophical way. The puzzlement or confusion is a function not only of the language but of our standards or sense of philosophical acceptability. Wittgenstein triumphantly exclaims that his conception of philosophy allows him to stop doing philosophy whenever he pleases. But he can stop doing philosophy, or at least stop needing to do philosophy, only when all philosophical puzzlement and confusion are resolved. (PP: 43–4) Thus philosophers cannot stop philosophizing as they please; they can stop philosophizing only if either all philosophical confusions are resolved by a reinterpretation of ordinary language that conforms to the standards of philosophical acceptability or if they relax their requirements enough to take language as it is. Philosophers are not therapists of ordinary people. They are the ones having the problem of understanding and will not be able to stop doing philosophy before such understanding is achieved. A second criticism that Goodman raises against the British style of analytic philosophy is that it is ill motivated by the belief that antifoundationalism implies anti-systematicity: [T]he rejection of absolutistic justifications for system-building does not of itself constitute justification for the extremely asystematic character of typical current British analysis. Unwillingness to accept any postulates of geometry as absolute or self-evident truths hardly diminishes the importance of the systematic development of geometries. Unwillingness to take any elements as metaphysical or epistemological ultimates does not make pointless all systematic constructions in philosophy. There are virtues in knowing where we began, where we have gone, and where we are going, even if we fully acknowledge that we might as well have begun somewhere else. (1958a/PP: 44) Whereas Goodman was opposed to the anti-systematic attitude of the British philosophers of verbal analysis, he was rather surprised by their hostility towards the ideal-language tradition. After all, he thought, both ways of doing analytic philosophy were complementary: Verbal analysis is a necessary preliminary and accompaniment to systematic construction, and deals with the same sphere of problems. For example, the verbal analyst may well concern himself 15
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with explaining the vague locution we use when we say that several things are ‘all alike’; and he may well examine the difference between saying that a color is at a given place at a given time and saying that a color is at a given place and at a given time. The constructionalist dealing with qualities and particulars will likewise have to be clear on these points. The analyst, treating these as separate problems, may well miss the intriguing relationship between the two, while a systematic treatment shows them to be cases of a single logical problem. But verbal analysis and logical construction are complementary rather than incompatible. The constructionalist recognizes the anti-intellectualist as an arch enemy, but looks upon the verbal analyst as a valued and respected, if inexplicably hostile, ally. (1956a/PP: 17) In a sense, the end of philosophy for Goodman is further away than for the “verbal analyst”. While the (stereotypical) “verbal analyst” stops in his philosophical endeavour after the analysis, for Goodman this is only the first part of the enterprise; a systematic construction (for instance like the ones we present in the rest of this book) has to follow. Here lies a second major difference between Goodman’s understanding of the aim of philosophy, and that of Wittgenstein or the ordinary-language philosopher. For the later Wittgenstein there are no real philosophical problems, merely “puzzles about language”. What seems to be a philosophical problem inevitably must turn out to be a misunderstanding of what our words mean, or result from a misuse of those words. Philosophy, therefore, cannot be revisionary. The (correct) use of the words in natural language is the standard that needs to be respected; it cannot be that a philosopher uncovers that this use is not in good order. Goodman, on the other hand, is in for surprises. In the course of doing philosophy, so-called “common sense” (what Goodman calls “the repository of ancient error”) and the pre-systematic use of words can, and in interesting cases will, be declared defunct.13 Philosophy leads to revisions, and discovers errors in, for example, ordinary-language categorizations. Goodman’s philosophy is critical in that sense14 in a way that Wittgenstein or ordinary-language philosophy is not. For Goodman there are real philosophical problems that can and need to be solved, not just verbal confusion and language puzzles. The divide between these two traditions became very narrow during the twentieth century. We shall say a few words about the contemporary scene in Chapter 9. But now, after having reviewed contrasts to Goodman’s philosophy, we should turn to his roots and more friendly allies. 16
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Allies I: Carnap and logical empiricism As we have already said, Goodman clearly belongs in the tradition of analytic philosophy that is usually labelled ‘ideal-language philosophy’. The beginning of that tradition is marked by the year 1879, the year that Gottlob Frege, a German professor of mathematics at the University of Jena, published his first major work, the Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens [Concept Script: A Formal Language of Pure Thought Modelled upon that of Arithmetic] ([1879] in Frege 1967). In this book Frege developed what we now call predicate logic. Of course, philosophers had done research on logical matters at least since Aristotle. Frege, however, was the first to develop a comprehensive formal system: a whole ideal language. In this formal language large parts of natural language could be reformulated in a precise way. Moreover, it was also possible to reformulate a sufficiently promising part of mathematics, such that the idea that mathematics is nothing but logic (so-called logicism) gained for the first time a degree of plausibility. This was a very powerful new tool, not only for foundational problems in mathematics, but, as became clear very soon through the works of Bertrand Russell, Whitehead and Wittgenstein, also for all other areas of philosophy. Frege was not a very prominent figure during his lifetime. What he achieved was appreciated only much later. However, among the few students in his auditorium in Jena in the 1910s, when Frege was giving his lectures on the Begriffsschrift, was Carnap, a young student from Wuppertal-Ronsdorf (a small town in the west of Germany) who was to become one of the most influential philosophers of the twentieth century.15 Carnap was not only well equipped as a student of Frege, he also came under the influence of Russell’s work on logic and was among the first philosophers to use the symbolic language developed in Russell and Whitehead’s Principia Mathematica (Whitehead & Russell 1910–13) for the clarification of scientific discourse. Russell’s programmatic words in Our Knowledge of the External World (Russell [1914] 1969) set the task for the whole of Carnap’s work: [T]he study of logic becomes the central study in philosophy: it gives the method of research in philosophy, just as mathematics gives the method in physics. … All this supposed knowledge in the traditional systems must be swept away, and a new beginning must be made. … To the large and still growing body of men engaged in the pursuit of science, 17
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… the new method, successful already in such time-honored problems as number, infinity, continuity, space and time, should make an appeal which the older methods have wholly failed to make. … The one and only condition, I believe, which is necessary in order to secure for philosophy in the near future an achievement surpassing all that has hitherto been accomplished by philosophers, is the creation of a school of men with scientific training and philosophical interests, unhampered by the traditions of the past, and not misled by the literary methods of those who copy the ancients in all except their merits. (Russell [1914] 1969: 243–6; quoted in Carnap 1963: 13) In Our Knowledge of the External World, Russell not only suggested logic as the primary methodological tool of philosophy, but also declared the logical constitution of assumed entities as its primary topic. Borrowing Whitehead’s method of extensive abstraction (which we shall come to shortly), Russell sketched how philosophically dubious entities such as abstract objects (e.g. single time points and properties) could be constituted logically from less problematic entities (such as events and sets of mutually similar concrete objects, respectively). Russell’s declared motivation for this was a version of Ockham’s razor (see Chapter 4): Entities are not to be multiplied without necessity. In other words, in dealing with any subject-matter, find out what entities are undeniably involved, and state everything in terms of these entities. Very often the resulting statement is more complicated and difficult than one which, like common sense and most philosophy, assumes philosophical entities whose existence there is no good reason to believe in. (Russell [1914] 1969: 112) The project of logical constitution sketched here started a tradition that lead directly to Goodman’s chief work, the constructional system of The Structure of Appearance. In 1924 Carnap made contact with the Viennese philosopher Moritz Schlick, who later was the nominal leader of what became famous as the “Vienna Circle”,16 a heterogeneous group of scientifically minded philosophers who met in Vienna to discuss new achievements in logic and the philosophy of science. Carnap moved to Vienna in 1926. His famous book The Logical Structure of the World (the Aufbau, [1928] 1961) (which we shall discuss in some detail in Chapter 5) served for a while as the frame theory of the Vienna Circle. In the Aufbau, Carnap 18
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tried to provide in detail a constitutional system of all subject matter: a very ambitious implementation of Russell’s programme. In 1935, due to the increasing influence of fascism in central Europe, Carnap emigrated to the United States. Carnap was already acquainted with Quine at Harvard and Charles Morris in Chicago and quickly took up a permanent position at the University of Chicago that he held from 1936 to 1952 (then moving to the University of California, Los Angeles). A number of his fellow philosophers from the Vienna Circle also emigrated to the United States. Slowly they began to modernize American philosophy with the help of Quine and other pragmatists, and built up a strong network of analytic philosophers. From the early 1950s it is fair to say that this group ruled American philosophy, with Carnap as the leading figure. The kind of philosophy represented by that branch of early analytic philosophy can best be characterized with reference to its motifs, basic assumptions and drawn consequences. One basic motivation was to replace Kantian transcendental philosophy, which seemed to be clearly refuted by the recent developments of logic and natural science. On the logical side, Kant’s main argument to assume synthetic a priori truths had been the alleged nature of mathematics. Mathematical statements such as ‘7 + 5 = 12’ did not seem to be logically true, if judged by Aristotelian syllogistic. So, Kant concluded, as these a priori truths are not logical truths, and did not appear to him to be analytic in any other way either, mathematics had to be synthetic.17 Modern logic made it possible to analyse some mathematical truths as truths of logic18 and thereby undermined Kant’s philosophy of mathematics. At the same time, the second major argument for the idea of synthetic a priori truths, the intuitiveness and “obvious” empirical adequacy of Euclidean geometry, was destroyed by Einstein’s theory of relativity: Kant’s eternal a priori truths turned out to be a posteriori falsehoods. This disaster called for a new epistemology, an epistemology that would recognize the new advances in logic as well as the new developments in physics. A second motivation sprang from discontentment with the standard theory dynamics in philosophy. Traditionally, one absolute system had always merely been replaced by another incommensurable absolute system. Philosophical progress seemed impossible if this process was continued. Philosophy should rather be done in a way analogous to science. The perception about science was that big projects were subdivided into special problems and in a division of labour each part 19
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of the whole of the scientific community could contribute to the big project by solving small specialized problems.19 The two basic assumptions of the early analytic philosophers concerned the foundation of human knowledge and the meaningfulness of expressions. Concerning the foundation of human knowledge, the logical empiricists believed that knowledge could only be achieved through experience. But if that is so, all classical metaphysical research programmes were pointless. Sentences that could not be tested by experience were cognitively and theoretically empty. Metaphysical claims, like the claim of the metaphysical realists that reality is mind independent as well as the claim of the idealists, that it is not, are both of this kind. As Carnap pointed out in Pseudoproblems in Philosophy ([1928] 1961), two scientists might well have diverging opinions about this question of metaphysics, but they would clearly agree on all empirical questions, for example, on whether or not there is a mountain in a certain place in Africa. Classical philosophical problems were thus deemed to be pseudoproblems that philosophy should get rid of. Sentences that did not belong to logic or mathematics but nevertheless lacked empirical content were all considered meaningless. The consequences that follow from these basic assumptions are threefold. First, traditional philosophy appears to be a vain endeavour and we should clear all areas of human thinking of its influences. Secondly, after all philosophical problems are revealed as being mere pseudoproblems, the function of philosophy is the syntactic, semantic and pragmatic analysis of (scientific) discourse: “Philosophy is the syntax of scientific language”.20 Thirdly, philosophy should bring all sciences together into a unity of science. If scientific expressions are only meaningful if based in experience, and hence reducible to statements about observations or classes thereof, all scientific discourses should prove to be intertranslatable and expressible in a common elementary language. In contrast to the ordinary-language philosophers, the logical empiricists did not think that ordinary language would be basically in good order and that simply a better understanding of it would reveal the dissolutions to our philosophical (pseudo)problems. On the contrary, the positivists believed ordinary language to be inexact and misleading and were engaged in constructing a better substitute. This made necessary a systematic reconstruction of discourse in an artificial ideal language: the language of formal logic. As we shall see in detail, Goodman’s philosophy did in some respects differ from logical empiricism so characterized. However, logical 20
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empiricism defined the problems and the background Goodman was working in.
The roots at Harvard Goodman’s philosophical training was already over when logical empiricism washed over America. As we have said, by 1935 Goodman was already considered by Quine to be an expert on Carnap’s Aufbau. Where did Goodman receive this early training? Of course, when Goodman was studying philosophy at Harvard, the university was associated with logic because of Whitehead, Sheffer, C. I. Lewis, Charles Sanders Peirce and Josiah Royce. Although – as Quine said in retrospect – at that time “really the action was in Europe” (Quine 1985: 83), Harvard’s younger generation was soon familiar with the work by Carnap, Kurt Gödel, Jacques Herbrand, Alfred Tarski and others. Cooley introduced Quine to Carnap’s Aufbau around 1932 (ibid.: 86), the year in which the Vienna Circle member Herbert Feigl took up a postdoctoral grant at Harvard. After Quine returned from his Sheldon Fellowship in Europe, he began to lecture on European logical positivism in Harvard as early as winter 1934. Also interested in logic was Leonard, who, with Goodman, started the project to construct a calculus of individuals, which later led to The Structure of Appearance (see Chapter 5). Both were members of Quine’s informal seminar on Carnap’s logical syntax. In 1935 Leonard and Goodman told Quine about their project. Quine was immediately interested and supported Goodman’s studies. That night, Quine writes in his autobiography (ibid.: 122), they discussed matters until four in the morning. Thus Goodman was clearly supported by the younger faculty at Harvard, who were all very soon familiar with the work that was done in Vienna, Prague, Warsaw and Berlin. But Goodman also received support and inspiration from his teacher and supervisor C. I. Lewis, the epistemologist and logician, and probably also from Whitehead. Let us first have a look at Whitehead’s influence. Born in 1861, Whitehead was already 63 years old when he was hired by Harvard as a professor of philosophy and came to the US. Until then he had been teaching mathematics for 40 years at Cambridge and London. As a mathematician,21 Whitehead was well known for his work on universal algebra and geometry. However, the mathematician Whitehead is certainly best recognized for Principia Mathematica, the foundation of modern logic, which he wrote with Russell 21
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and which was published in three volumes between 1910 and 1913. Principia Mathematica was the major tool and topic for Goodman’s generation of formal philosophers. As we have said, Carnap had already noticed that the formalism of modern logic greatly helped to clarify philosophical issues and Goodman was to follow him in this. But Principia Mathematica also served as a source for interesting new problems for Goodman’s generation of graduate students at Harvard. The subtitle of Quine’s PhD thesis The Logic of Sequences ([1932] 1990) was “A Generalization of Principia Mathematica”. Leonard’s thesis Singular Terms (1930) (for details see Chapter 5), was also intended and motivated as a further elaboration of Principia Mathematica. Clearly, Goodman was directly and indirectly influenced by this milestone of formal philosophy. When Whitehead then started to lecture at Harvard, he had his debut as a philosopher. Whitehead the philosopher – to the surprise (and shock)22 of the Harvard philosophy department – turned out to be deeply engaged in a sort of speculative metaphysics that was very unfashionable if considered in contrast to the awakening modern analytic philosophy. Nevertheless, even aspects of Whitehead’s philosophy might well have influenced Goodman. In particular, four themes from Whitehead can also be found in Goodman’s approach to philosophy: (i) the interest in a construction of a mereological theory; (ii) the distrust in natural (“ordinary”) language and the programme of reconceptualization as a means of solving philosophical problems; (iii) a form of ontological pluralism or anti-foundationalism; and (iv) an interest in other forms of symbolization and representation than merely science and language. The first of these four themes, the interest in mereology, was closely related to Whitehead the mathematician. The missing fourth volume of Principia Mathematica was to include Whitehead’s treatise on geometry (see Simons 1987: 81; Ridder 2001); instead, part of the material entered in the form of Whitehead’s mereology into his An Enquiry Concerning the Principles of Natural Knowledge (Whitehead 1919) and his Process and Reality (Whitehead [1929] 1978).23 Whitehead’s motivation to develop a mereology was the construction of geometrical entities such as lines and points from non-geometrical objects of knowledge and perception. This motivation and the resulting theory originated independent of and before the (better known) mereology of the Polish logician Stanisław Leśniewski.24 Whitehead’s mereology remained only an informal sketch of a theory that could serve as a basis for his notion of “extensive abstraction” (see 22
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Ridder 2001), a method by which geometrical entities are constructed as an abstraction from complex and concrete entities. Whitehead’s definition of geometrical points as “abstractive classes” of overlapping events later served as a prime example in Goodman’s writings for an explication or definition in his sense (we return to this later). As we said above, it also inspired Russell’s and Carnap’s projects of logical constitution. Leonard’s system in Singular Terms (1930) was a first somewhat rigorous formal outline and further development of Whitehead’s more or less sketchy ideas, even if (see Chapter 5) he applied it to domains other than geometry.25 Although Whitehead’s mereology was (if reconstructed formally) logically distinguishable from the theory of the Polish logicians Leśniewski and Tarski (see Sinsi 1966), in the hands of Leonard and Goodman it was turned into a theory formally equivalent to the Polish system (see Ridder 2001). Reflecting for a moment on Whitehead’s construction of geometrical points will lead us to the second commonality between Goodman’s and Whitehead’s thought. As is probably evident to the reader, and as is pointed out by Goodman many times, our common notion of a point (if there is any such common notion) is not that of an “abstractive class” of certain volumes or events. But allegiance to ordinary usage or ordinary language is not a criterion of adequacy in Whitehead’s conception of philosophy just as it is not in Goodman’s. As Whitehead emphasizes in Process and Reality ([1929] 1978), ordinary language is neither stable nor clear enough to allow for interesting philosophical insights on the basis of meaning analyses. Often a philosophical problem can be solved by reconceptualizing the whole problematic area rather than by analysing the ordinary usage of a term. Whitehead’s idea of reconceptions in philosophy is strikingly similar to Goodman’s conception of it. Whitehead’s project to construct points from volumes is not driven by the idea that points “really are” abstraction classes of volumes, but by the idea that volumes are entities of our acquaintance, in terms of which we might better understand what points are. If a better understanding can be achieved in this way, major revisions in our conceptual system are in order (see Hampe 1998). Whitehead, however, did not see the solution to all philosophical problems in a mere logical reconstruction of the traditional terminology. Instead he suggested major terminological revisions in all areas of philosophical discourse. Whitehead’s programme to revise philosophical terminology had a successor in Goodman and Elgin’s Reconceptions in Philosophy and other Arts and Sciences (1988), in 23
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which they plead for the replacement of some of the most central philosophical notions (as we shall see later). When Whitehead constructs points as abstractions from volumes and takes processes as basic in his ontology, he does not thereby claim that volumes are any more real than points or that everything but processes are mere fictional entities. On the contrary, Whitehead claims that points are just as real as the volumes they are abstracted from. This ontological tolerance (or whatever you want to call it) will reoccur in Leonard’s and Goodman’s writings (see Chapter 5) and constitutes another important feature that Goodman’s and Whitehead’s philosophies share in common. Finally, Whitehead’s later work promotes the idea that art, religion and the different sciences all use different “languages”, differing systems of symbolization and representation, dedicated to different perspectives on the world. Clearly, this is a topic that also appears in Goodman’s work, whereas it is less clear that Goodman was under the direct influence of Whitehead’s views on the matter (see Hampe 1998: 182–3). The second significant influence on Goodman from the older faculty of Harvard was C. I. Lewis, the supervisor of Goodman’s PhD thesis. Lewis is nowadays best recognized as a grandfather of modern modal logic. His interesting pragmatist epistemology, which combined influences from the German (or Austrian) “positivists” with the pragmatism of Peirce, William James and John Dewey, is often overlooked. It was this aspect of Lewis’s philosophy, however, that influenced Goodman. In his famous “The Pragmatic Element in Knowledge”, Lewis summarizes his pragmatist epistemology as follows: In short, if human knowledge at its best, in the application of mathematics and in the well-developed sciences, is typical of knowledge in general, then the picture we must frame of it is this: that there is in it an element of conceptual interpretation, theoretically always separable from any application to experience and capable of being studied in abstraction. When so isolated, concepts are like Platonic ideas, purely logical entities constituted by the pattern of their systematic relations. There is another element, the sensuous or given, likewise always separable by abstraction, though we should find it pure only in a mind which did not think but only felt. This given element, or stream of sensation, is what sets the problem of interpretation, when we approach it with our interests of action. The function of thought is to mediate between 24
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such interests and the given. Knowledge arises when we can frame the data of sense in a set of concepts which serves as guides for action, just as knowledge of space arises when we can fit a geometrical interpretation upon our direct perception of the spatial. The given experience does not produce the concepts in our minds. If it did, knowledge would be pure feeling, and thought would be superfluous. Nor do the concepts evoke the experience which fits them, or limit it to their pattern. Rather the growth of knowledge is a process of trial and error, in which we frame the content of the given now in one set of concepts, now in another, and are governed in our final decision by our relative success – by the degree to which our most vital needs and interests are satisfied. ([1926] 1970: 253–4) The first part of these two components of knowledge, the conceptual system that interprets what is given in experience, constituted the realm of the a priori. Nevertheless, this conceptual system is neither preconfigured in the mind, nor dictated by experience. As Lewis became aware in his study of different systems of logic (e.g. in his “Alternative Systems of Logic” (Lewis [1932] 1970)), which conceptual or logical system we choose is a matter of what we are interested in. His influential Mind and the World-Order (1929) argues that knowledge is in a crucial way relative to pragmatic considerations. We make truths in so far as our conceptual systems interpret what is given in experience, using conceptual schemes that are of our making. There is no objective scheme; our knowledge of the world represents it in a way that serves us best at a certain point in time: [T]he truths of experience must always be relative to our chosen conceptual system in terms of which they are expressed; and that amongst such conceptual systems there may be choice in application. Such choice will be determined, consciously or unconsciously on pragmatic grounds. New facts may cause a shifting of such grounds. When this happens, nothing literally becomes false, and nothing becomes true which was not always true. An old intellectual instrument has been given up. Old concepts lapse and new ones take their place. (Lewis [1926] 1970: 257) That truths are relative to conceptual systems, and that the choice of conceptual systems is a pragmatic affair is also an integral part of Goodman’s philosophy. He would, however, drop one important ingredient of Lewis’s epistemology: the indubitable given. 25
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As Lewis argues in “Logical Positivism and Pragmatism” ([1941] 1970) the main difference between the empiricism of the pragmatists and the empiricism of the logical positivists (especially the Carnap of Philosophy and Logical Syntax (1935)) is that the latter were ready to analyse empirical knowledge fully in the so-called formal mode, as more or less coherent systems of accepted sentences, some of which are “protocols”, some sentences of mathematics and logic, some generalizations and so on. The content of such knowledge would be explicated only in terms of deductive consequences and logical relations, but not in terms of the experiences connected with certain terms and statements. In particular, the formal mode would not distinguish between statements such as ‘This object looks red’ and ‘This object is red’. Instead, logical positivism would (according to Lewis’s interpretation of it) recognize both statements as one and the same “observation-sentence”. For Lewis, this sort of empiricism was not worth its name. After all, the experiential element did not seem to show up at all in this kind of formal analysis. Lewis claims that a proper empiricism must treat sentences of the form ‘This looks red’ as special, indubitable statements. We might err when classifying things as being red, but we cannot err when it comes to recognizing things as looking red. This is “the given” in experience, the phenomenal states we find ourselves in when making experiences. Without such an indubitable element, Lewis feared that our epistemology would necessarily collapse into a coherence theory of truth: [E]ither there must be some ground in experience, some factuality it directly affords, which plays an indispensable part in the validation of empirical beliefs, or what determines empirical truth is merely some logical relationship of a candidate-belief with other beliefs which have been accepted. And in the latter case any reason, apart from factualities afforded by experience, why these antecedent beliefs have been accepted remains obscure. Even passing that difficulty, this second alternative would seem to be merely a revival of the coherence theory of truth, whose defects have long been patent. (Lewis [1952] 1997: 112–13) Thus, besides the “chicken and egg” problem of why we should ever actually come to accept any system, we would not know how to choose between the many equally coherent systems that are all logically possible. As we shall discuss in much more detail in the following chapters, Goodman was ready to bite that bullet when throwing away the indubitable given. Lewis, the major advocate of pragmatism, 26
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commented on this move by Goodman that his “proposal is, I fear, a little more pragmatic than I dare to be” (ibid.: 118).26
Summary All this constituted the philosophical background against which Goodman was developing his philosophy. In the following chapters we shall see in more detail what Goodman made of these influences. Those that we have highlighted in this chapter were based for the most part on obvious personal relations rather than references provided by Goodman. When reading Goodman, one of the things to notice is that there are only relatively few footnotes devoted to the historical origins of a certain problem or some idea to its solution. This should not be interpreted as a sign of ignorance on his side. Goodman was interested not in the merely historical or exegetical questions of who had said what when, but in the systematic questions of philosophy. Occasionally we shall refer back to the historical background presented here. In Chapter 2, however, we shall jump right into the systematic way of dealing with philosophical problems, with Goodman’s infamous “new riddle of induction”.
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Chapter 2
If this were an emerald it would be grue: problems and riddles of induction That the sun will rise every morning, that bread nourishes, that ravens are black and that matches will light when struck under favourable conditions are all truths about the world that we believe. Clearly, they are very helpful for us. Those just mentioned all have in common that they express regularities that hold in the world. They tell us that a certain state of affairs is always followed by a certain other state of affairs, or that certain things always have certain features. Regularities, expressed by general statements such as ‘all Fs are Gs’, are very valuable things to know when it comes to planning your day, driving a car, or just trying to survive for a while. Without knowledge of regularities, everything would always come as a complete surprise: be unexpected. It is easy to imagine how likely it would be that we all unintentionally killed ourselves within a couple of days without the capacity to have beliefs of regularities (possibly all by the same method, being unable to learn from the failure of others), given that our nosiness can overrule the guidance of our natural instincts. Since regularities play such a big role for us, we developed (by some long process of cultural evolution) the sciences to find as many of them as there are, using methods that (we hope) put our beliefs in regularities on a firm basis. After all, believing a general statement that is in fact false – for example that fly agarics nourish or that if one jumps from a very high building one will safely and smoothly land on one’s feet – might be just as damaging as believing none of them. The methods science uses to find out about regularities are observation, prediction and experiment. By using these methods we try to find true general statements (that do express regularities) and separate them from the false ones. Although we seem to be doing 28
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pretty well at this, it is almost a mystery why we do so well. How can observation, prediction and experiment lead to justified beliefs in general statements?
The Humean riddle of induction In his Treatise of Human Nature ([1739–40] 2000) and his Enquiry Concerning Human Understanding ([1748] 1999) David Hume attacked all rational bases for belief in any necessary connection that was not a truth of mathematics or logic. The justification for any belief in the necessary connection of causes and effects and therewith the belief in regularities inferred from past observations were also subject to Hume’s devastating attack. Hume started his investigation into the foundations of scientific knowledge by distinguishing two types of reasoning: reasoning concerning relations of ideas and reasoning concerning matters of fact and existence. All reasoning falls into one, and only one, of these categories. The first type seems largely unproblematic. Mathematics and logic are the sciences in which the relations of ideas are investigated. Both sciences use deductive arguments to arrive at their conclusions, forms of arguments that are necessarily truth preserving. If the premises of a valid deductive argument are true, so is the conclusion. But not all scientific reasoning is of this kind. If we, for example, infer that the sun will rise tomorrow from the observations that it did so every morning in the past, we make an inference from the observed (the rising of the sun in the past) to the unobserved (the rising of the sun tomorrow). This reasoning concerns matters of fact and existence. In such cases the conclusion (that the sun will rise tomorrow) goes beyond the content of the premise (the report of what has been observed in the past). As we said at the start of this chapter, the general statements that express real regularities are of immense importance for us, and it is their generality that enables them to play this role. These statements do not only talk about events that have happened at some specific day at some specific place, but they talk about what happens at all times at all places. The laws of physics, for example, state generalities that not only apply to the observed events that happened in the laboratory and led to the formulation and confirmation of these laws, but also to events far away from our galaxy in future times. This way we are able to use knowledge that we gained from past observations. 29
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Hume asked what the foundation of our inferences from the observed to the unobserved is, and came to the conclusion that such reasoning is based upon relations of cause and effect. We believe that certain states of affairs will regularly be followed by certain other states of affairs because we think that there is a causal connection between them. Lightning is followed by the sound of thunder, because the former causes the latter. Footprints in the sand indicate that some person recently walked here, because the former is a causal effect of the latter and so on. But if our apparent knowledge of regularities and our inferences from the observed to the unobserved are based on knowledge of cause–effect relations, how is this knowledge established? The first possibility that Hume considered was that our apparent knowledge of a cause–effect relation is a priori. Can we deduce from a cause what its effect is? A person having no prior experience with fire or snow can obviously not deduce that the former will feel hot and the latter cold. The same holds for the other direction from effect to cause: by just knowing (de re1) of some “effect” by knowing that a certain phenomenon occurred, pretty much anything might have caused it, as far as I can tell a priori. Causal relations are not deduced: knowledge of them must be based upon experience. But if we know about causal relations from experience, causality must be something observable, such that we can observe a “cause”, an “effect” and somehow the causal connection between them. But Hume argued that we cannot locate this third item anywhere. Every time we observe what we later extrapolate into general statements, we only observe temporal priority of what we then call the “cause”, spatiotemporal proximity of “cause” and “effect” and constant conjunction: if we repeat an experiment many times we will find the same “effects” following the same “causes”. But what we do not observe is some sort of causal relation or causal power that our extrapolation is based on. It is perfectly conceivable that next time the “effect” will not follow the “cause”; nothing in the observation that the “effect” followed the “cause” up to now guarantees that the “effect” will do so in the future. For example, having observed two events in spatiotemporal proximity only once, we cannot tell whether there is a causal connection between the two. Although we feel inclined to assume that there is a causal connection if we observe many times that events of the one kind are followed by events of the other kind, it might nonetheless only be coincidence that one event closely followed the other. Moreover, if the causal connection between the two was itself observable, we would 30
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not need repeated observations; instead we would be able to observe the causal connection in the first instance. But if we cannot deduce “effects” from “causes” nor “causes” from “effects” and cannot observe causal connections, what else could be the basis for our judgements about causal relations? Hume’s answer was that it is all just a matter of custom or habit. We observe some event e1 and see it followed by some other event e2. On another occasion we see some event e3 followed by some event e4. Events e1 and e3 are events that we group into a certain category, say ‘events of type C ’. Events e2 and e4 are classified as “events of type E ”. Relative to our classification, events of type E often follow events of type C, which is why after a while when we notice an event of type C we begin to expect an event of type E following it. That this is so is just a brute fact of human psychology, but completely without any logical necessity involved. Hume’s challenge, or the Humean riddle of induction, was to uncover the following problem. We wanted to know what justification we have for inferring unobserved events from observed ones, or on what basis we are justified in extrapolating generalities. Hume’s observation was that we base our justification on assumed relations of cause and effect. But what is our justification for assuming these? The answer is that we just psychologically anticipate that the future will be like the past, that nature is uniform. But that anticipation cannot be founded in anything else. If you want to base the conviction in the uniformity of nature on past experiences (“nature has always behaved in a uniform way, therefore it will continue to be uniform in the future”) you merely presuppose what you are attempting to establish, namely that nature is so uniform that it will continue to be uniform. If we need a justification why we should trust observed past uniformities at all, the fact that we have observed in the past the uniformity that trusting such observations was successful cannot suffice. It would obviously be circular (or would lead to infinite regress) to argue in that way. So there is no empirical justification forthcoming for the uniformity thesis. On the other hand, there is also no a priori justification to be expected; it is absolutely conceivable that nature is not uniform. Clearly, we do not expect it to be non-uniform, but we can also imagine non-uniformity without noticing any contradiction. What seemed to be the most central method of science, induction from observation, turns out to be unjustifiable. There is no reason why we should have any confidence in scientific predictions; for all we know, any scientific prediction might fail and, indeed, we cannot even 31
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say that scientific predictions are probable. There is – after Hume – no rational basis for placing more confidence in the predictions of science than in wild guesses.
Reactions to Hume’s problem Of course, philosophers of science could not just shrug off Hume’s conclusion and turn to other matters. Scientific predictions are more trustworthy than wild guesses or the predictions of fortune-tellers. But why is that so? We shall sketch two attempts to escape the old riddle in order to see how both approaches will be equally ineffective in giving a solution to Goodman’s new riddle (see below) and to present Goodman’s own solution of the Humean problem in the light of their failure. One family of solutions tries to save induction. One way to do this is by an ordinary-language dissolution of the problem (A. J. Ayer (1956) and Peter Strawson (1952) tried this), in which one argues that basing beliefs on inductive evidence is what it means to be rational, such that the problem of why it is rational to do so can no longer arise. Induction is a basic principle of rationality and there are no more fundamental principles we could turn to in order to justify it; that is what it means to be a basic principle. Another approach from the same family (going back to Hans Reichenbach; see Reichenbach 1951: 245) is to vindicate (in contrast to validate, i.e. proving it from more fundamental principles) induction by a pragmatic argument. In all possible circumstances we could be in, nature will either be uniform or not.
We use induction We do not use induction
Nature is uniform
Nature is not uniform
Success
Failure
Success or failure
Failure
If nature is not uniform we are unable to find regularities by induction, but we will do no better using any other method. In those possible circumstances in which nature shows uniformity, we will find it by the inductive method in the long run. Hence, it is overall better to use the inductive method if it is unknown whether or not nature is uniform. After all, if (in the bottom-right box) there was a better method (with more predictive success than induction), this, again, would be a regularity that the inductivist could find in the long run 32
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and exploit (using the alternative method found via induction from observed successes – sometimes called meta-induction – in the long run the meta-inductivist could then approximate the predictive success of the others). Therefore, whatever nature is like and whatever alternatives to induction there are, in the long run the inductivist is either better off than a non-inductivist or at least as well off as a non-inductivist. Neither of the accounts in that family is very promising. The first strategy is undermined by the second. If it makes sense to ask whether it will in most cases serve our purposes to reason by induction, the flight to the fact that induction is a basic principle is of no help (Hume’s problem would reappear in terms of vindication). Clearly, ‘Is it reasonable to be reasonable?’ sounds like a silly question. But we can distinguish two senses of ‘reasonable’ corresponding to two senses of ‘justification’ if we draw a distinction between validation and vindication. One sense of asking whether something is reasonable, the one corresponding to vindication, is to ask whether it is a good means for achieving a desired goal. We shall call this sense ‘reasonable1’. The other sense of ‘reasonable’, the one corresponding to validation, is a matter of adopting generally accepted basic principles of rationality. This sense we shall call ‘reasonable2’. Now we can ask, ‘Is it reasonable1 to be reasonable2?’ or, in other words, ‘Does using the accepted rules of inductive inference serve our goal of predicting correctly as often as possible?’ Clearly this is just a reformulation of the original Humean problem, not a step further (see Earman & Salmon 1999). The second strategy, however, seems doomed to failure. Worlds are conceivable that are non-uniform, but controlled by an evil omniscient demon who only informs his believers about the next events he has planned to happen in that world. Because the demon hates inductivists, he takes care to inform a particular believer only if the inductivist would not follow this believer’s predictions (because of the bad track record the believer had when the inductivist followed him). It seems possible that in such a world it would (in terms of predictive success) be overall better to be a believer than to be an inductivist. A second family of solutions accepts Hume’s argument and the conclusion that induction is not justifiable. However, in this family this is not seen as a devastating problem, for science never used induction as a method. But when induction does not occur in scientific methodology it is no longer in need of justification. Popperian deductivism (named after Karl Popper, who championed this approach) 33
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is one example of this strategy. Popper and his followers claimed that science does not need justification of the belief in regularities by induction. Science proceeds instead by inventing bold explanatory hypotheses about the world and testing them against observations. Doing this does not involve induction (only the deduction of testable consequences from the hypothesis). If the accepted empirical results are not in accordance with the prediction deduced with the help of the hypothesis under scrutiny, the hypothesis would be accepted as falsified (again, deductively, by a sort of modus tollens). This would not lend positive support to any single hypothesis, but would help us decide which of the alternative hypotheses we presently have at our disposal is the one we should continue to work with. Hypotheses are, in Popper’s view, not confirmed by past observations, but corroborated by having “survived” many rigorous tests. Whether that “solution” is promising is dubitable. If that approach really wants to do without any inductive element, the question will be what relevance a high degree of corroboration should have for working with this hypothesis in the future. Without reassurance that high corroboration indicates something about the future success of the hypothesis, there is a need for an explanation of why it should be of enough relevance for the scientists to care about it. Moreover, it seems that inductive as well as deductive methods are indeed used in the sciences; then, however, it is just not true that the sciences proceed only deductively.
Goodman’s answer to the Humean riddle Goodman approaches his own answer to Hume’s problem of induction by first investigating what kind of justification actually is called for when we ask for a justification of our inductive inferences. The problem cannot be to explain how we know that certain predictions will turn out to be true. That is something that we simply do not know in advance. Similarly the problem cannot be to tell true predictions from false ones in advance. If this were possible, we would have found a method of clairvoyance. Nor can the problem be to tell which prediction is more probable, for even this will either be something we cannot know in advance, namely if ‘being more probable’ expresses a relation between the prediction and certain future events, or something that seems totally irrelevant for matters of justification, namely if ‘being more probable’ has nothing to do with future events. 34
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Following his strategy of trying to change the question to another perspective if a problem seems hopeless, Goodman, leaving induction aside for the moment, first asks: what justifies deduction? Well, instances of deductive inferences as in (1) All ravens are black. (2) Paul is a raven. (3) Paul is black. are justified by showing that they are inferences in accordance with accepted rules of inference. If an inference is in accordance with accepted rules of inference, the inference is valid. That does not imply that its conclusion is true. Inference (3) might well be false: Paul may be white. The mere validity of the inference does not guarantee the truth of the conclusion. To check whether a deductive inference is justified does not involve checking the truth of any fact that is involved in the inference. All we check is whether the inference was in accordance with the accepted rules. How is that done? To show that the inference of (3) from (1) and (2) is in accordance with the rules, we would first reconstruct the argument in a deductive logical calculus and then check whether the inference above is valid in it. Indeed it can be represented in predicate logic:2 (1) (2) (3) (4)
∀x (Raven(x) ⊃ Black(x)) Raven(paul) Raven(paul) ⊃ Black(paul) Black(paul)
assumption assumption from (1), universal instantiation from (2) and (3), modus ponens
This inference is in accordance with the inference rules of predicate logic. Why is predicate logic of importance here, and not just some set of inference rules? It must, of course, be a system with valid rules, and the rules of predicate logic are valid. Why are they valid? Goodman’s answer to that question struck many as odd. According to Goodman the rules of classical predicate logic, or perhaps some alternative deductive system, are valid because they are more or less in accordance with what we accept as a valid deductive inference. On the one hand, we have certain intuitions about which deductive inferences are valid and on the other hand we have rules of inference. When we are confronted with an intuitively valid inference, we check whether it accords to the rules we have already accepted. If it does not we might reject the inference or the argument based on it as invalid. If, however, our intuition that the purported inference is valid 35
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is stronger than our confidence that the rules are correct, we might also consider amending the rules. This soon leads to a complicated process. We have to take into account that the rules must remain coherent and not too complicated to apply. In logic, for example, we want the rules to be topic neutral, that is, applicable to inferences (as far as possible) independent of the specific subject matter and so on. On the other hand, we also want to extract as much information from premises as possible, so we do not want to risk being too cautious in accepting rules. In this process we make adjustments on both sides, slowly bringing our judgements concerning validity in a reflective equilibrium3 with the rules for valid inferences until we finally get a stable system of accepted rules: This looks flagrantly circular. I have said that deductive inferences are justified by their conformity to valid general rules, and that general rules are justified by their conformity to valid inferences. But this circle is a virtuous one. The point is that rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification for either. (FFF: 64/PP: 374) People who found that odd were quick to point out that the deductive inference rules are not just “intuitively” valid or in accordance with our intuitive judgements of validity.4 First, normal folk “intuitively” judge inferences to be valid that are not valid at all; this seems to be completely at odds with Goodman’s proposal. Does this not show, as, for example Stephen Stich and Richard Nisbett (Stich & Nisbett 1997)5 claim, that the actual “intuitive” judgements of normal folk have nothing to do with validity? They contend that the validity of inferences is an objective affair that we investigate in logic and of which we might have a false or insufficient reconstruction, for example in Aristotelian syllogistic as viewed from the standard of modern predicate logic. This might then be in need of revision, despite it not being a reconstruction of what we – as reasoners – believe about validity (we shall call such a position ‘logical realism’). Stich, for example, argues: In each of these cases … it is very likely that, for some people at least, the principles that capture their inferential practices would [be in reflective equilibrium for them]. If this is right, it 36
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indicates there is something very wrong with the Goodmanian analysis of justification. For on that analysis, to be justified is to [be in reflective equilibrium]. But few of us are prepared to say that if the gambler’s fallacy [which is the fallacy to infer that, for example, in a game of craps the likelihood of rolling a seven with a pair of dice increases each time a non-seven is rolled] is in reflective equilibrium for a person, then his inferences that accord with that principle are justified. (Stich 1998: 100) This objection does not appear to cut any ice, however. It seems to miss the point, since a reflective equilibrium of intuitive judgements and rules is not something that is achieved quickly by one person alone concerning one rule and one pattern of inference. We have to take into account a whole range of inferences intuitively judged to be deductively valid and a whole system of inference rules to represent that. This might well be a complicated affair. As can be seen in the logical inference above, we needed two rules to represent the inference that originally consisted of only three lines (not four). Thus, the “normal folk” inference, as in the unregimented argument, is represented in formal logic, but not necessarily with anything that resembles the original argument. To come up with a somewhat satisfying system of deductive validity took 2,500 years, counted from the first attempts to do so. This indicates that it is not that easy to find a consistent set of rules that is in accordance with previously accepted valid rules, intuitive judgements and so on. That normal folk make many mistakes (by our elaborated standards of validity) and do not come up with a system themselves that equals our standards does not come as a surprise. A second argument against Goodman’s position, championed by John Earman and Wesley C. Salmon, starts from the observation that there does not appear to be any reference to intuition when we establish that a certain system comprises only valid inference rules. In the case of predicate logic, for example, the deductive validity of the inference rules, the so-called soundness of the proof theory, is not checked by taking polls in the supermarket. It is checked by a soundness proof, that is, a proof that establishes that every rule that is allowed in predicate logic can never take us from a true premise to a false conclusion (Earman & Salmon 1999: 62). Earman and Salmon suggest abstracting away from the system of rules and sentences we have, the so-called “deductive system”, and looking at the inference rules from a metalevel. What a sentence means – if we follow the argument by Earman and Salmon – is considered to 37
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be independent of what syntactic proof rules apply to that sentence. If it is possible to show that any sentence that is inferred by syntactic rules of the deductive system will always be logically true if inferred from no premises, or true if inferred from true premises, the deductive system is apparently justified: it always leads from truth to truth.6 Such soundness proofs are metatheoretical proofs, since they do not prove the validity of the deductive system within the deductive system, but on a metalevel. If that is still circular (e.g. because the metatheory is deductive), this circularity is at least not as blatant. We are not proving the validity of the system of rules within the very same system, but show that the rules – if applied correctly – always lead from truth to truth. Earman and Salmon write: Goodman’s claim about deductive logic is difficult to defend. We reject, as fallacious, the form of affirming the consequent because it is easy to provide a general proof that it is not necessarily truthpreserving. The rejection is not the result of a delicate adjustment between particular arguments and general rules; it is based upon a demonstration that the form lacks one of the main features demanded of deductive rules. Other argument forms, such as modus ponens and modus tollens, are accepted because we can demonstrate generally that they are necessarily truth preserving. (Earman & Salmon 1999: 62) It is true that we typically check the adequacy of a deductive system by giving a “general” soundness proof. Soundness proofs establish that there is a certain relation between two formal systems. On the one hand there is the deductive system, which tells you from what kind of lines in a proof you are allowed to proceed to what other kinds of lines in a proof. On the other hand there is the model-theoretic semantics, which interprets the formal symbols in the language and all complex expressions build from them. If the deductive system allows you to go from a line P to a line C, the semantics must be such that it never assigns truth (or whatever corresponds to that notion) to the line P when assigning falsity (or whatever corresponds to that notion) to the line C. Soundness proofs establish nothing else; their results are relative to a deductive system and to a semantics. Clearly, this does not tell us anything about any sort of objective or general validity of rules of inference. The next question would be why we think that the model theory that accords with the deductive system is adequate. The question of whether the model theory is adequate, however, is in part a question of what we “intuitively” 38
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think is the right semantics for certain logical constants (e.g. the conditional), which, in turn, is a question of what role they play in intuitively acceptable inferences.7 Soundness proofs thus do not help us out of the aforementioned regress if we do not possess any independent reason to think that the model theory is adequate, but no such reason is presented by Earman and Salmon; nor does one appear to be forthcoming elsewhere.8 Goodman saw that problem quite clearly9 and offered the best solution he could: a reflective equilibrium of validity judgements and accepted rules. It is important to realize that there always might be more than one reflective equilibrium to which that process leads,10 which is why we nowadays have more than only one accepted system of deductive inference rules (and needless to say all of them have their soundness proofs). This shows us that the explication of valid deductive inference is still an open topic in philosophy. This is why there can be no such thing as “the true logic”, according to Goodman’s conception. A system of deductive rules might be pragmatically better than an alternative system, but there simply is no set of objectively valid rules. If what we argued above is true, namely, that any justification of deductive rules must at some point or other be founded on a reflective equilibrium between our intuitions and accepted rules, every logician who subscribes to some sort of logical realism (the view that there is only one true logic) is obviously in trouble. Logical realists, unlike Goodman, have the burden of proving why the specific reflective equilibrium arrived at is justified, if (a) for every initial set of intuitions and antecedently accepted rules more than one equilibrium is possible, and (b) the specific initial set of intuitions started with is different for subjects with other cultural or socioeconomic backgrounds (as Stich and Nisbett would presumably continue to argue). How Goodman thought about Hume’s problem becomes clear. Hume’s solution, namely that induction is just a matter of custom or habit might be incomplete, but it is basically correct. [The point concerning the justification of deduction] applies equally well to induction. An inductive inference, too, is justified by conformity to general rules. And a general rule by conformity to accepted inductive inferences. Predictions are justified if they conform to valid canons of induction; and the canons are valid if they accurately codify accepted inductive practice. (PP: 375/FFF: 64)
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The remaining task of solving the induction problem is then to explicate the pretheoretic notion of valid inductive inference by defining rules of inference that can be brought into a reflective equilibrium with intuitive judgements of inductive validity. This can be done in a variety of ways; integrating intuitive judgements as well as general considerations might lead to several alternative solutions.11 This project is undertaken in the various attempts to explicate the notion of confirmation and to construct systems of inductive logic.
The new riddle of induction The comfort we can take in the fact that the Humean challenge just disappeared will not last long. We shall now encounter Goodman’s own challenge to induction: the so-called “new riddle of induction”. Goodman first formulated his new riddle of induction in a brief paper of 1946 titled “A Query on Confirmation”. The paper was directed at the theories of confirmation and induction proposed by Carnap (1945a,b) and Carl Gustaf Hempel (1943, 1945). Hempel and Carnap both reacted to the riddle quite quickly (Carnap in print in 1947), but it seems fair to say that this first publication of what later became the new riddle of induction seemed to be a non-starter; at first very few people took notice of it. Since its second publication in Fact, Fiction, and Forecast nine years later, however, Goodman’s riddle of induction became one of the most discussed philosophical problems of the twentieth century and is still discussed today. In 1994 Douglas Stalker catalogued 300 learned discussions of it and the literature is still growing. A widespread explanation of the fact that it took a while for the riddle to attract the attention of other philosophers is that the earlier paper had three shortcomings: (i) it looked as if it was only highlighting a technical problem in Carnap’s and Hempel’s theories of confirmation, which were themselves pretty technical theories, and at that time there were not yet many philosophers around who were interested, let alone well trained, in formal logic and formal philosophy of science; (ii) the earlier paper did not discuss the astonishing symmetry between projectible and non-projectible predicates (i.e. the fact that whether a predicate is “positional” depends on which set of predicates you start with – we shall come to the notions of positionality and projectibility later), which might have led to the impression that there is an easy solution to the problem; (iii) nowadays you 40
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need a catchy terminology to get your point across – Quine’s fame is intimately connected with ‘gavagai’, Goodman’s certainly with ‘grue’ – but in the earlier paper it was not ‘grue’ that was used to make the point, but only a clumsy description concerning marbles drawn from an urn being red up to some day. (Some philosophers think that (iii) is doing most of the explanatory work here.) What is ‘grue’? What is the new riddle of induction? Consider the following two (true) statements: (B1) This piece of copper conducts electricity. (B2) This man in the room is a third son. B1 is a confirmation instance of the following regularity statement: (L1) All pieces of copper conduct electricity. But does B2 confirm anything like L2? (L2) All men in this room are third sons. Obviously it does not. But what makes the difference? Both regularity statements (L1 and L2) are built according to the exact same syntactical procedure from the evidence statements; they are generalizations of B1 and B2. Consider a reformulation in predicate logic to see this point: (B1*) (PieceOfCopper(a) ∧ ConductsElectricity(a)) (L1*) ∀x (PieceOfCopper(x) ⊃ ConductsElectricity(x)) (B2*) (ManInTheRoom(a) ∧ ThirdSon(a)) (L2*) ∀x (ManInTheRoom(x) ⊃ ThirdSon(x)) In both cases, the relation between the evidence statement and the regularity is syntactically the same. Therefore it does not seem to be for a syntactical reason that B1 confirms L1 but B2 fails to confirm L2. The reason is that statements like L1 are lawlike, whereas statements like L2 are not: L2 expresses only an accidentally true general statement. Lawlike statements in contrast to accidentally true general statements have two interesting features: they are confirmed by instances of them; and they support counterfactuals. Statement L1 supports the counterfactual claim that if this thing I have in my hand were a piece of copper, it would conduct electricity. Suppose, in contrast, that L2 is indeed true for all the men in this room. Still, L2 would not support that if that man on the street were here in the room, he would be a third son. To tell which statements are lawlike 41
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and which statements are not is therefore of high importance in the philosophy of science. A satisfying account of induction (or corroboration) as well as a satisfying account of explanation and prediction needs such a divide. Goodman, however, shows that this is extremely hard to get. Here comes the riddle. Suppose that you do research in gemmology. Your special interest lies in the colour properties of certain gemstones, in particular of emeralds. All the emeralds you have examined before a certain time t were green; your notebook is full of evidence statements of the form ‘Emerald no. xyz found at place yxz date yzx (yzx ≤ t) is green’. It seems that at t, this supports the hypothesis that all emeralds are green, L3. Now Goodman introduces the predicate ‘grue’. This predicate applies to all things examined before some time t just in case they are green but to other things (observed at or after t) just in case they are blue: (DEF1) x is grue =df x is examined before t and green ∨ x is not so examined and blue Until t it is obviously also the case that for each statement in your notebook there is a parallel statement asserting that the emerald no. xyz found at place yxz date yzx (yzx ≤ t) is grue! Each of these is analytically equivalent with a sentence in your original notebook.12 All of these grue-evidence statements taken together confirm the hypothesis that all emeralds are grue, L4, and they confirm this hypothesis to the exact same degree as the green-evidence statements confirmed the hypothesis that all emeralds are green. But if that is the case, then the following two predictions are also confirmed to the same degree: (P1) The next emerald examined after t will be green. (P2) The next emerald examined after t will be grue. However, to be a grue emerald examined after t is not to be a green emerald, an emerald examined after t is grue if, and only if (iff), it is blue. Hence we have two predictions. Both are confirmed to the same degree by the past evidence, but taken together they are nevertheless incompatible. This is the new riddle of induction. It is also obvious that we could potentially define infinitely many other predicates like ‘grue’ that would all lead to new similarly incompatible predictions (and we could do this for all kinds of things, not just emeralds). After Goodman, philosophers of science have cooked up quite a number of these. The immediate lesson should be that we cannot use all kinds of weird predicates to formulate hypotheses or to classify our evidence. 42
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Some predicates (which are the ones like ‘green’) can be used for this; other predicates such as ‘grue’ must be excluded if induction is supposed to make any sense. If there were absolutely no way of excluding such predicates anything could be predicted on the basis of the same evidence, using the appropriate grue-like predicate. That is already a very interesting result, since now we know that for valid inductive inferences it must matter what predicates we use. The problem this riddle poses is not that we lack a justification for accepting a general hypothesis as true on the basis of only positive instances and no counter-instances (which was Hume’s problem); it is to explain why some general statements (such as hypothesis L3) are confirmed by their instances, whereas others (such as L4) are not. Again, this is a matter of the lawlikeness of L3 in contrast to L4, but how are we supposed to tell the lawlike regularities from the illegitimate generalizations? A reply that immediately comes to mind is that the illegitimate generalization L4 involves a certain temporal restriction (whereas L2 was spatially restricted). That was also Carnap’s first reaction to the problem when he confronted it in the late 1940s (see Carnap [1947] 1997). The idea is that the predicates that cannot be used for induction are all analytically positional, that is, their definitions refer to individual constants (for places or times). A projectible predicate, that is, a predicate that can be used for induction, has no definition that would refer to such individual constants but is purely qualitative (e.g. because it is a basic predicate). The trouble with this reply is that it makes it essentially relative to a language whether or not a predicate is projectible, since it is relative to a language whether ‘grue’ is positional or ‘green’ qualitative. If we begin with a language containing the basic predicates ‘green’ and ‘blue’ (as in English), ‘grue’ and ‘bleen’ are positional, where ‘bleen’ is defined as follows: (DEF2 ) x is bleen =df x is examined before t and blue ∨ x is not so examined and green But if we start with a language that has ‘bleen’ and ‘grue’ as basic predicates, ‘green’ and ‘blue’ turn out to be positional: (DEF3 ) x is green =df x is examined before t and grue ∨ x is not so examined and bleen (DEF4 ) x is blue =df x is examined before t and bleen ∨ x is not so examined and grue The qualitative–positional distinction seems to depend solely on what 43
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language you start with. But then, both languages are completely symmetrical in all their semantic and syntactical properties.13 In other words, the positionality of predicates is not invariant with respect to linguistically equivalent transformations. But if that is the case then there is no semantic or syntactic criterion on the basis of which we could draw the line between projectible predicates and predicates that we cannot use for induction.14 This certainly was terrible news for logical positivists. However, we need to draw such a line. We cannot simply accept that the predicates we use in usual discourse in our language seem fine for induction and just go ahead: If our definition works for such hypotheses as are normally employed, isn’t that all we need? In a sense, yes; but only in the sense that we need no definition, no theory of induction and no philosophy of science. … The odd cases we have been considering are clinically pure cases that, though seldom encountered in practice, nevertheless display to best advantage the symptoms of a widespread and destructive malady. We have so far neither any answer nor any promising clue to an answer to the question what distinguishes lawlike or confirmable hypotheses from accidental or non-confirmable ones … It is this problem that I call the new riddle of induction. (PP: 386/FFF: 80–81) This time the problem is not a problem for inductivists only. Although Feyerabend (1968) and others have thought that Goodman’s riddle is no threat to (Popperian) deductivism, it certainly is. Everything that was said about confirmation could also be phrased in terms of corroboration and everything said about “positive instances” could also be phrased in terms of “negative instances” (see Foster [1969] 1997). It is also of no help to retreat to ostensive learnability. Many have thought that exactly those predicates should be projectible that are ostensively learnable. However, many predicates, such as ‘conducts electricity’, are not so learnable but clearly projectible, whereas gruelike predicates might well be ostensively learnable. Note that they need not have to involve an implicit reference to a certain date, but might make reference to modes or states of the observer (see Hullett & Schwartz [1967] 1997). Before we learn what Goodman’s own answer to his new riddle of induction is, we shall briefly follow the route by which Goodman came to the problem of induction in order to see what areas of epistemology, 44
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philosophy of language and philosophy of science are involved. This is very instructive, for it will become clear that the new riddle of induction is not merely a technical puzzle for certain kinds of formal theories of confirmation. Following Goodman’s footsteps also shows how Goodman approaches philosophical problems, and how he arrives at solutions to them.
Induction and projectibility: counterfactuals In Fact, Fiction, and Forecast, Goodman published two lectures in one book. The first lecture was presented to the New York Philosophical Circle on 11 May 1946. In this lecture he discusses the problem of counterfactual conditionals, which eventually leads him to the problem of lawlikeness and to the problem concerning which predicates are projectible (which he could not solve in 1946). The second part of the book contains the Special Lectures in Philosophy that Goodman gave at the University of London on 21, 26 and 28 May 1953. In this part he again departs from the problem of counterfactuals, discusses its connection with dispositions, gives an analysis of modality and then turns to the problem of induction and projectibility (and argues for his solution of the problem). How are these topics connected? The issue of counterfactuals seems to be a problem in the philosophy of language (or formal semantics), the problem of modality seems to be a problem of ontology, whereas the projectibility issue belongs to philosophy of science and epistemology. Let us begin with counterfactuals. Counterfactuals such as (E1) If this match had been struck it would have lit. seem to have weird truth-conditions. Typically their antecedent is actually false; the match has not been struck. Moreover, in this case the consequent is false too; the match has not lit. The normal truthconditions of a conditional do not apply here. The truth-function expressed by the material conditional is displayed in the following truth-table: p T T F F
q T F T F
p⊃q T F T T
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Hence, a material conditional with a false antecedent is always true, which would make (E2) If this match had been struck it would not have lit also true, but it clearly is not if (E1) is true. Goodman identifies two problems with counterfactuals. One is the problem regarding which implicit boundary conditions are stated when a counterfactual is stated. The second problem is which quality does the implicit regularity have that is stated when a counterfactual is stated. Boundary conditions specify the states of affairs the counterfactual is about. The explicit boundary conditions are that, in the states of affairs the counterfactual is about, there is a match and that it is struck. Some boundary conditions must also implicitly be stated when such a counterfactual is stated. Matches do not always light; they only do so if the match is dry, if there is enough oxygen in their vicinity and so on. Thus (E1) is only true if such boundary conditions were also the case; thus the implicit boundary conditions are necessary truthconditions of counterfactuals. The set of these boundary conditions, together with the sentence ‘This match is struck’ and the regularity that matches light when struck under favourable conditions, should then lead to the consequent of (E1) expressing that the match is lit. On the other hand, these boundary conditions do not include all that is the case about the match, since one of these things that are the case about the match is that the match is not struck. But then the union of all boundary conditions and the sentence ‘The match is struck’ would imply everything and would, again, also make (E2) true (ex falsum quodlibet sequitur; given an inconsistency any formula whatsoever can be derived15). Hence one problem with the truth-conditions of counterfactuals is that we need to know what the right set of boundary conditions is that are implicitly stated by a counterfactual and thus belong to its truth-conditions. For Goodman, this part of the problem is a dead end. There does not seem to be a way to single out the right boundary conditions without using a counterfactual, but that would render the analysis of counterfactuals viciously circular. The closest we get to an analysis of counterfactuals is that we need to find a set of boundary conditions B such that B together with the antecedent A and a law imply the consequent. But the restrictions on B are the trouble. (DEF5) A counterfactual with antecedent A and consequent C is true iff there is a set B of true sentences such that: 46
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(i) B is compatible with C and B is compatible with ¬C, (ii) The set that contains all the sentences in B and also the sentence A is consistent, and all sentences of that set are simultaneously assertable, (iii) the conjunction of all sentences of B with A, A*, is such that there is a law and (a) ‘A* ⊃ C’ is implied by that law, (b) there is no set B* compatible with C and compatible with ¬C such that B* together with A and a law would imply ¬C, (c) there is no law such that B or B* would be implied by ¬A and that law. Whether or not this analysis is confronted with further counterexamples is a side issue. The second half of condition (ii), the simultaneous assertability of the sentences of B together with A, is implicitly nothing but a further counterfactual: to check whether B together with A is simultaneously assertable is to check whether ‘If A were true, the conjunction of all sentences in B would be false’ is true, which in turn (by application of DEF5) would mean to check whether there is a set B**, which contains sentences that are simultaneously assertable with A and imply ¬B (by some law) and so on. The second problem with counterfactuals is the law that is needed to imply the consequent together with the appropriate B. General statements such as ‘All matches which are struck under favourable conditions light’ do support counterfactuals (e.g. ‘If this match had been struck under favourable conditions it would have lit’), whereas general statements as ‘All items in your fridge have gone off’ do not support counterfactuals (check ‘If this yoghurt were in your fridge it would have gone off’, unless you have a magical fridge that does not like you at all).
Dispositions Having convinced himself that the problem of counterfactuals does not seem to have an easy solution and therefore does not promise to be illuminating, Goodman turns to dispositions instead. Disposition statements are usually stated in indicative form; they talk about “inner states” of things rather than external boundary conditions but are nevertheless intimately connected with counterfactuals. In fact one reason to analyse counterfactuals was to find out what disposition statements say. But maybe this way of analysis went in the wrong direction. Counterfactuals seem very complicated; maybe they are more complicated 47
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than disposition statements and therefore make a bad analysans. Maybe the path to explication lies in the other direction. Goodman cannot accept that disposition predicates refer to properties; such an analysis would not help to clarify the issue at all, since talk of “properties” is even more obscure than talk of dispositions. We have disposition predicates and the objects they apply to, but where on earth are the properties of the latter? Properties are on the list of notions Goodman finds in need of explanation, so he could not take any comfort in an explanation that referred to them. As he says at the beginning of Fact, Fiction, and Forecast: [S]ome of the things that seem to me inacceptable [sic.] without explanation are powers or dispositions, counterfactual assertion, entities or experiences that are possible but not actual, neutrinos, angels, devils, and classes. … You may decry some of these scruples and protest that there are more things in heaven and earth than are dreamt of in my philosophy. I am concerned, rather, that there should not be more things dreamt of in my philosophy than there are in heaven or earth. (FFF: 33–4) The task must therefore be to analyse disposition predicates as expressions that apply to actual objects. However, a disposition predicate such as ‘inflammable’, which applies to the book you are now reading, seems to talk about a possible state of this book; the book does not burn, but under favourable circumstances it could. As is clear from the quote just given, talk about possible states is as unacceptable for Goodman as talk about properties, if this cannot be translated into talk about manifest predicates of concrete things. Goodman’s idea is to analyse disposition predicates as extensions of certain manifest predicates. Imagine a book that is actually burning. Here the predicate ‘burns’ is manifest. The book you are reading now, on the other hand, is in the extension of inflammable, because the predicate ‘burns’ is so connected with the predicate ‘inflammable’ that extending ‘burns’ by ‘inflammable’ also covers this book. The question is under which circumstances it is allowable to extend ‘burns’ in this way. This might in single cases be a question of which manifest predicates we take as good indicators of inflammability. If having chemical constitution X is taken to be a good indicator, then a partial definition of ‘inflammable’ is ‘burns or has chemical constitution X’. This way we are not talking about things that could happen to this book, but about manifest predicates true of this book. In the general case it is a question of which predicates are projectible. 48
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Possibilia Goodman’s analysis secures that disposition statements talk about actual things, not about possible objects. He extends this into an actualist analysis of possibilia. To see why that is an extremely attractive position, compare the following alternative. Say you have two books on your table, in particular two copies of Heidegger’s Sein und Zeit, which you received as Christmas presents from someone who does not know you well and someone who does not like you much. After reading some pages you decide to turn to more practical matters and set one of the copies on fire. Now, one copy burns, the other does not, but both copies are inflammable. Why is the copy that actually does not burn inflammable? One story philosophers might tell you to explain this is that counterfactual sentences do not directly talk about anything in our actual world, but about things and states of affairs in other mere possible worlds. What follows is the story that a so-called modal realist might tell you to “explain” the semantics of counterfactuals. There are as many worlds as there are possible ways this world could be, all concrete entities just like the world you live in, although causally unconnected with it.16 When we here in our world say that something is possible, we are really talking about what is the case in one of these worlds. These possible worlds are ordered. Some of them are closer to the actual world, not spatially (due to their spatiotemporal isolation from our world), but in the sense that they are more similar in many respects, whereas there are other possible worlds, very different from the actual world and so farther away. In some of the closer worlds there are counterparts of your copies of Sein und Zeit on your counterpart’s table; and, again, in some of them the counterpart of you has decided to burn the other copy of the book or both, or lightning has struck your counterpart’s desk, or your counterpart’s house burns down. Whatever happened there, the counterpart of the other copy burns. If it burns in all close worlds in which it is set alight under favourable conditions then this is why in your world this copy is inflammable although it is not actually burning. Now, if this kind of talk can be replaced by talking of manifest predicates that apply to the objects there on your table, we do not seem to overcrowd the universe of discourse with all these strange entities and might eventually arrive at an explanation that is worth its name. Modalities are brought back to earth in this way: the non-burning copy is inflammable only because one copy actually burns and because the other copy is actually of a certain chemical constitution. The 49
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question is whether by mere projection of manifest predicates we can produce as many possibilities as we want to use (for semantics, metaphysics and epistemology). Goodman thinks that the possibilities we need for a philosophy of science and epistemology are indeed analysable this way.17 The only remaining question to answer then is which predicates are projectible, and we will be able to tell which things have which dispositions. So we can at last turn to Goodman’s own solution to his riddle of induction.
Goodman’s solution: a theory of projectibility Of course, ‘projectible’ is itself a disposition predicate and we do not yet know generally how dispositions should be analysed. We know, however, that single disposition predicates can be (partially) analysed without presupposing a general solution for all disposition predicates. This is what we did with the disposition predicate ‘inflammable’ above; it applies to all things that burn and the things that have chemical constitution X (which we take as a good indicator for inflammability). If we can do the same thing with ‘projectible’ we could solve our problems concerning dispositions once and for all. The inflammability example showed us what we have to do if we want to analyse a single disposition predicate. The lesson we learnt there can now help us to solve the problem here. When we know when to project ‘inflammable’, we know what indicators tell apart for us the inflammable things from the not-inflammable ones. Obviously, if we knew when to project ‘projectible’, we would know which indicators tell apart for us the projectible predicates from the unprojectible ones. But this is just what we need to solve the disposition problem once and for all. When we know how to project ‘projectible’, we know when to project any given predicate. But this also will tell us when it is legitimate in general to project a “manifest” predicate to a disposition predicate. We have then reduced the old general problem of how to analyse disposition predicates to the singular problem of how to analyse the disposition predicate ‘projectible’. The project is then to define what distinction our mind is making when it distinguishes legitimate from illegitimate projections. Just as we did with ‘inflammable’ we shall now take some manifest predicate and extend it to cover all hypotheses with predicates that are projectible (for brevity’s sake we shall call a hypothesis with a projectible predicate a ‘projectible hypothesis’). The first predicate that comes to mind is ‘projected’. 50
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(DEF6) A hypothesis is projected iff (i) it is accepted after the positive test of some of its instances (predictions), (ii) not all of its instances are tested yet, and (iii) no instance falsified the hypothesis. Projected hypotheses are not necessarily all (and still) projectible. Whereas all burning things obviously are inflammable,18 not all projected hypotheses are projectible (some at earlier times projected hypotheses might now be known to be false or are now exhausted). To find the extension we want, we need to exclude all projected hypotheses that are not projectible and include all projectible hypotheses not yet projected. Let us start with the exclusions. We shall first exclude all hypotheses that are at the moment exhausted or violated by negative instances. But what about our hypothesis L4, ‘All emeralds are grue’? Hypothesis L4 is not yet exhausted, and nor is it falsified. However, we know that L4 is in conflict with L3, which says that all emeralds are green. We know that there is no syntactical (or semantical) difference between the two hypotheses that we could use to make a decision. There is, however, a historical difference that we can use to make a decision. ‘Green’ is much better entrenched in our language, which means that we projected much more hypotheses with that predicate or predicates with the same extension than we did with ‘grue’ (in fact, we never projected any hypothesis with ‘grue’ or with any predicate coextensional with it). Thus, a hypothesis is excluded from projection if it is in conflict with a better entrenched predicate; in that case the hypothesis is overridden. Given these ideas about exclusion and this terminology, we can define the rule by which we decide projectibility, unprojectibility and nonprojectibility: (DEF7) A hypothesis is projectible iff it is supported, unviolated and unexhausted, and all hypotheses conflicting with it are overridden. (DEF8) A hypothesis is unprojectible iff it is unsupported, exhausted, violated or overridden. (DEF9) A hypothesis is nonprojectible if it and a conflicting hypothesis are supported, unviolated, unexhausted and not overridden. The last definition takes care of the fact that we are confronted with two hypotheses that are in conflict and neither has a better entrenched predicate. Entrenchment can even be further refined to account for 51
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cases in which a predicate inherits the entrenchment of another that it is derivative from and so on. Of course, this makes projectibility essentially a matter of what language we use and used to describe and predict the behaviour of our world. Is that satisfying? You might think that whether or not a hypothesis is lawlike should depend not on such contingent matters as the way we use and used our language up to now, but on more fundamental things. Should it matter whether a predicate refers to a real property or whether a kind-term refers to a real substance? What we want is that the predicates of our hypotheses cut nature at its joints, but can we really be sure that the history of our language use will guarantee that? As Goodman puts it: Are we not trusting too blindly to a capricious Fate to see to it that just the right predicates get themselves comfortably entrenched? … In the case of new predicates … the legitimacy of any projection has to be decided on the basis of their relationship to older predicates; and whether the new ones will come to be frequently projected depends upon such decisions. But in the case of our main stock of well-worn predicates, I submit that the judgment of projectibility has derived from our habitual projection, rather than the habitual projection from the judgment of projectibility. The reason why only the right predicates happen so luckily to have become well entrenched is just that the well entrenched predicates have thereby become the right ones. (FFF: 98) Making predictions and having theories about lions, emeralds and green and blue things is of interest if we suppose that there are lions, emeralds and green and blue things. But this does not seem to play the tiniest role in this definition of projectibility. If we recall how Goodman defined his project, we find that such further demands are inadequate (if we agree to his definition of the project). Goodman’s task was to define ‘projectible’ in a way that conforms extensionally more or less with the rule we use to tell projectible hypotheses from unprojectible or non-projectible ones. For justifiedly finding fault with the result you need to present extensional differences between the defined rule and the actual practice to a degree that would make the definition given above unacceptable as a proper explication. We are not suggesting that this cannot be done. What we want to emphasize is that the mere fact that the definition sounds unfamiliar does not mean that it is inadequate (by Goodman’s own standards).
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Summary In this chapter we have tried to give a first impression of Goodman’s philosophy. We have chosen Goodman’s new riddle of induction for that, because we thought that the reader might already have encountered it in an epistemology or philosophy of science class. We hope to have shown three interesting things about Goodman’s philosophy that we want to follow up in subsequent chapters. The first is his technique to detect dead ends and to change the direction of explication. In Chapter 3, in which we shall say more about Goodman’s general conception of philosophy, we hope to make it somewhat clearer why he thinks that this might sometimes be a good idea. Secondly, and closely connected, is the whole issue of explication as the main project of philosophy. What exactly is an explication? How does it differ from other kinds of definitions? We have said that Goodman thinks that it is important that an explication is extensionally more or less in accordance with our practice. Why does he think so? This, again, will be a central topic of Chapter 3. Finally, his analysis of projectibility in terms of entrenchment sounds rather constructivist. After all, language is of our making and arbitrary, but is it equally up to us and arbitrary whether all emeralds are grue or all emeralds are green? Does Goodman really think that contingent facts about our practice to project certain predicates rather than others in the end determine which hypotheses are at all projectible? This is an issue that will be a topic not only in Chapter 3 but also throughout the rest of the book. In this chapter we have tried to present Goodman’s views on induction, justification of inference rules, counterfactuals, dispositions, modality and projectibility. To keep things at a comprehensible level, we did not follow all details and all aspects of Goodman’s thoughts on these matters and, moreover, have not said much (next to nothing) about other people’s views on the topics involved. In Chapter 9 we shall make good this omission with respect to the views held by others. With respect to further aspects of Goodman’s thought on the matter, some things will be supplemented in the chapters to come, for other things you might want to read Fact, Fiction, and Forecast, and Problems and Projects.
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Chapter 3
The big picture
In this chapter we sketch how Goodman conceives of the purpose, aim and method of philosophy. We also indicate the way in which his thoughts on seemingly unrelated matters, such as art and induction, are connected to form a coherent whole. Few philosophers of the twentieth century have been as influential as Goodman, particularly across such diverse fields as the philosophy of art and the philosophy of science. What we hope to show is that this is due not only to an idiosyncratic coincidence of interests, but also to Goodman’s account of philosophy. What gives unity to Goodman’s thought is his conception of philosophy as an activity directed at understanding and elucidation. For Goodman, such elucidation is achieved by way of definitions. One of the most remarkable aspects of Goodman’s theory of definitions is that, in contrast to the ordinary-language tradition, a definition does not need to be synonymous with (i.e. identical in meaning to) the expression defined. As we shall explain, this is partly due to Goodman’s conviction that no two distinct expressions of a language are identical in meaning. This provocative thesis is central to Goodman’s thought.
What is philosophy good for? Before turning to the questions of what – according to Goodman – philosophy is about and how it gets done, it might be instructive to see how Goodman conceived of its purpose and use. These days, philosophy is increasingly challenged to prove its worth to society. Not only philosophy, but all sciences are evaluated under that perspective. The 54
The big picture
more immediate and practical the expected benefit of a given pursuit, the more worthwhile it appears. Accordingly, sciences involved in fundamental research are in some trouble. Although a pharmaceutical research project might be able to promise the development of a very important new drug that will help many people after three years of research, scientists doing fundamental research can usually at best claim only indirect value for their expected outcomes. Quantum mechanics made lasers possible, which in turn led to the invention of CD-players. But CD-players were absolutely unforeseen by the forefathers of quantum mechanics, and it would have been ridiculous if Niels Bohr had written anything like “In fifty years we shall be able to develop new technology that will cause a revolution in the music business and sell like hell” into a proposal for a research grant. Philosophers are even worse off. Although they can justifiably claim that the computer and the whole idea of an artificial programming language goes back to philosophers and/or philosophically interested mathematicians, everybody knows that of the very many things that Heidegger (and most other philosophers) said, nothing eventually found its way into technology (which is, presumably, a very good thing) or into any other practical improvement. So what could reasonably be said in favour of philosophy? To questions about the purpose of such things as philosophy, art, fundamental science and so on, Goodman would (as so often) reply that the question is asked in the wrong way: it does not apply at all to philosophy and the like. Philosophy, art and science answer the question ‘Why do we do x?’, but their existence does not raise it. It is nonsense to ask what philosophy is good for. Everything else is good for philosophy. It does not need a purpose; it is the purpose of all other things we do. Many people who stumble over this remark find it either very arrogant or worse. It seems arrogant for it seems to downgrade the existence of all people who do not happen to work in philosophy or science departments. Is the fact that some philosopher is sitting in his office and reflects on his pet problem what gives meaning to all these poor fools who work hard to make a living for them and their families? Goodman did not think of philosophy, art or science as the privilege of the few people who later become philosophers, artists or scientists. Art and science education should basically be taught to everyone. That it could be taught and how such education could be systematically improved was the subject of Project Zero at Harvard. Project Zero emphasized the cognitive aspect of art and the like such that art became universally teachable (compared with the received 55
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view that art is some kind of entertainment) and systematically accessible (in contrast to the also received view that understanding art is the privilege of a gifted few). Serious study of education for the arts has also been stunted and side-tracked by the prevalent notion that the arts are instruments of entertainment. Some newspapers list plays, concerts, and exhibitions under “amusements”; and among a week’s amusements may be a Bach Mass, King Lear, and an exhibition of Goya’s Disasters of War. No real progress in attitudes toward education can be hoped for when Cezanne’s pictures are classed with cookouts, and arts programmes with playgrounds. On the other hand, we encounter almost as often the equally detrimental mistake of exalting the arts to a plane far above most human activities, accessible only to an elite. (BA: 5) Art, philosophy and the sciences enhance our understanding. They do not do this for some extrinsic purpose; understanding is rather a good in itself. This autonomy of science was independently motivated from another perspective. In his talk “Definition and Dogma” first delivered in 1951, five years after the Second World War, Goodman argues against the challenge that esoteric1 science would even undermine the strength of a society and its resistance to totalitarian propaganda: As the philosopher becomes more scientific in the sense that he becomes more an investigator of problems than an advocate of doctrines, he becomes more and more the object of complaints like those currently raised against the scientist. He is charged with wasting his time on trivial matters of intellectual curiosity rather than on problems of vital and pressing importance to human survival. He is charged with failing to attend to the important problem of establishing a scale of human values. And his skeptical spirit, his critical examination of even the fondest beliefs, and his exposure of the fallacies in even the most elementary and widely accepted opinion, are held to be responsible for undermining the faith that we need to protect us from the inroads of totalitarian doctrine. (PP: 52) Goodman’s reply to this challenge is twofold. First he argues that even if science would like to answer the great and grave problems confronting society, it could not possibly do so while the simplest and most familiar matters that fundamental science and philosophy deal with remain 56
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unsolved puzzles. “Isn’t this like trying to solve equations in higher algebra before we have the laws of arithmetic straight?” (PP: 53). Goodman’s second argument is directed against the more specific charge that the sceptical attitude of science undermines faith and thereby the strength of a society to resist the influence of evil-doers and fanatics; that, therefore, the esoteric research undertaken by science does not serve society. Goodman does not deny this; indeed, science and analytic philosophy do not establish a scale of values. They do not produce a counter-dogma or any sort of religion substitute that could serve as a basis for society. But that is not a problem. On the contrary, it is being devout to whatever dogma that makes individuals most susceptible to propaganda: But let us turn now to the charge that science and analytic philosophy undermine all our faiths and leave us prey to any onset of forceful propaganda. It seems to me that no idea could be more mistaken – that there could be no worse misunderstanding of the dynamics of belief. As a matter of fact, the most promising candidate for apostleship in a new creed is the passionate devotee of an old one, not the skeptic who subjects all proposals to critical scrutiny. There is nothing very surprising about the political fanatic who suddenly becomes a religious zealot. What leaves us open to new dogmas is the habit of uncritical acceptance of beliefs. (PP: 53) Science, with its sceptical attitude, provides just the right antidote to totalitarian or religious propaganda, whereas to present a counterreligion would be to undermine the purpose. To avoid getting drunk on bourbon by drinking copious amounts of gin is of little help, when what you really desire is to be sober. As Goodman says, “What one needs to stay sober is to learn how to distinguish between various offers and how to say ‘no’. This is also just what we need to protect ourselves from propaganda” (PP: 53). But even if a scientific attitude might be sufficient to resist propaganda, is it also sufficient as cement for society? Does it, in situations of conflict and danger, sufficiently motivate people to defend their society, maybe even risk their lives for it? Goodman thinks so and found encouragement in reports saying that most soldiers in the Second World War were not fighting for “shibboleths or slogans or grandiose ideals, they were not fighting for an abstract idea or for somebody’s system” what they were fighting for was “to get home and eat some blueberry pie”. 57
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Let no one delude us into thinking that our only choice is between dogma and dogma. As long as we are free to choose, let us choose definition rather than dogma – hypothesis rather than hysteria. It is time enough for hysteria when hope is lost; and time enough for dogma when it is forced upon us. (PP: 55) Having said what purpose philosophy has according to Goodman, we can now turn to its aim. We have already said that philosophy aims at understanding. What this means and how it is to be achieved will be our topic for the rest of the book.
The systematic background: kinds of definitions As we saw in Chapter 2, Goodman took the task of philosophy to be to provide definitions of certain kinds. Understanding – as the aim of philosophy – is hence achieved if problematic notions (such as, for example, ‘induction’) are given a rigorous definition in unproblematic terms. As we saw in Chapter 2, Goodman thinks the solution to the problem of induction is to provide definitions of inductive rules: “The problem of induction is not a problem of demonstration but a problem of defining the difference between valid and invalid predictions” (PP: 375/FFF: 65). If analytic philosophy is done in this way, we should try to find out what a definition is and when it is acceptable for the solution of a philosophical problem. First of all, there are different types of definitions, which all serve different purposes within philosophy. Moreover, each type has its own standards of adequacy. We shall briefly review them and discuss their differences. The types we shall discuss are nominal definitions, real definitions and explications. The classic distinction is between nominal definitions and real definitions. We shall first discuss nominal definitions, which are the ones that you frequently hear cannot be true or false: “everybody can define their terms as they like” and so on. Nominal definitions, indeed, are mere stipulations. They usually introduce new words into the language that serve as abbreviations for longer complex expressions of the language. Here is an example: (D1) The term ‘tiglon’ is an abbreviation (is synonymous with) ‘offspring of a male tiger and a female lion’. We shall call the new term, which is defined by the definition, the ‘definiendum’, and the terms of the language, by which the term is 58
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defined, the ‘definiens’. In the example just given, ‘tiglon’ is the definiendum and ‘offspring of a male tiger and a female lion’ the definiens. A nominal definition stipulates that definiens and definiendum should be used synonymously. A nominal definition thus gives meaning to a new term of the language; it assigns the definiendum the meaning of the definiens. Since these definitions assign meanings to terms via other terms, they are expressly about linguistic expressions. A new linguistic expression is introduced as an abbreviation for a longer one. Definition (D1) is not about tigers or lions; it is about the word ‘tiglon’ and the string of words ‘offspring of a male tiger and a female lion’ as well as all strings synonymous with it. Since these kinds of definitions are stipulations, they cannot be true or false. They, nevertheless, have to obey certain criteria of adequacy, such as: ● Eliminability
A nominal definition has to state the conditions under which the definiendum can be eliminated from every context in which it occurs. ● Conservativeness A nominal definition must not lead to new truths in the theory, that is, every proposition that is true according to the theory after the definition is introduced must have been so before. Without such adequacy criteria it would be possible to introduce contradictions into the language. As you can see from the criterion of eliminability, it is important that we can eliminate definienda from all contexts (i.e. complex sentences) in which they occur. To summarize, nominal definitions are about terms, they cannot be true or false but are correct or incorrect (with respect to the adequacy criteria) and they introduce new terms into the language. Now let us turn to real definitions. Traditionally, real definitions state the “essence” or the “nature” of things. It is not very clear what is meant by that. Consider the following example: (D2) x is a living organism iff (i) x is composed of a discrete amount of matter with a definite boundary, (ii) x continuously interchanges matter with its surroundings without manifest alteration of properties over short periods of time and (iii) x came into existence by some process of division or fractionation from one or two pre-existing objects of the same kind. 59
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The term ‘living organism’ is already a term of the language. If this real definition is about linguistic expressions, it does not introduce a new word, but talks about the meaning of an expression that was already part of the language. We shall call real definitions interpreted this way ‘meaning analyses’. A meaning analysis can be true or false. It is true iff the meaning of the definiendum is the same as the meaning of the definiens (to be more precise, a meaning analysis is true for a language S iff the term d1 of S stating the definiendum is synonymous in S with the term d2 of S stating the definiens). Definition (D2) does not have to be about the linguistic expressions involved, however; it might well be about living organisms. In that case it tells us not what the meaning of ‘living organism’ is in English, but what living organisms are. We shall call these definitions ‘empirical analyses’. An empirical analysis can also be true or false. It is true iff the phenomenon referred to by the definiendum always, with nomological necessity, coincides with the phenomenon referred to by the definiens. To summarize, meaning analyses are about terms that are already in use in a language. They can be true or false and their truth-value depends on whether or not they state synonymies in a language. Empirical analyses are about the referents of terms, objects in the world. They also can be true or false but their truth-value depends on the obtaining of nomological supervenience relations between the referents of definiendum and definiens. Nominal definitions are of use in philosophy whenever new technical terms are introduced. Examples for such technical terms are ‘a priori’, ‘consequentialism’, ‘supervenience’, ‘nominal definition’ and the like. As we have seen, the logical empiricists thought that philosophy is merely concerned with the clarification of scientific language and not with the empirical analysis that scientific theories are about. This was assumed to be the job of the sciences. Therefore, empirical analyses are not within the scope of philosophy. What is in the scope of philosophy is the analysis of meaning. As we have learnt from the brief remarks on Carnap’s philosophy, however, logical empiricists did not think that a meaning analysis of natural language would in all cases lead to a sufficient clarification. Natural language is unstable. Some speakers might use terms synonymously that others would not use that way; the meaning of some terms might lack sharp boundaries; these terms might be vague; others are ambiguous and so on. Although meaning analysis is an important part of early analytic philosophy, it is not its end. The aim of ideal-language philosophy was 60
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to overcome the ambiguity and vagueness of natural language. This was done with the help of modern logic and by way of explications. An explication is a type of definition that is a hybrid of nominal definitions and meaning analyses. Since philosophy tries to clarify our way of speaking, it has to depart from the terms and expressions we already use in the language. These terms are assumed to be imprecise and that is why they lead to philosophical problems. If we want to clarify these terms, we have to substitute them with terms that are in the relevant respect clearer than the ones we have started with. The new terms, however, should cover the same subject matter as the old ones, of course. Otherwise philosophy would be too easy. Consider the following example. Say we have a philosophical problem stated in normal English to do with the notion of free will. The philosophical problem is how we can be free in our will (the way we assume we are) when at the same time we are subject to physical laws that, together with initial conditions that were in place long before our birth, absolutely determine what we will do and want (as we also assume we determine). A philosopher might think that it is because of the concept of “free will” that this puzzle arises, and that we should clarify English to get rid of the problem. Nothing seems easier than that. Just restrict English to the fragment that is about elementary algebra and you are done. The problem of free will can not reoccur in “clarified English” simply because there are no terms in clarified English with which to state the problem. There is no such term as ‘free will’ to begin with. Therefore we want the problematic expression of ordinary or prescientific language, the explicandum, to be approximated by the meaning of the substitute, the explicatum. That they will differ to some degree in their meaning is, of course, intended. After all, the explicandum had a meaning that was too vague or ambiguous for the purposes of science or analytic philosophy. To be as precise as possible when it comes to formulate the datum for an explication, the explicandum, a trick must be used. Since the explicandum is vague or ambiguous, it cannot be directly used as a datum. Instead the scientist or philosopher chooses sentences of ordinary, pre-systematic discourse in which the explicandum is used in a meaning that the scientist wishes to preserve. These sentences then serve as additional adequacy criteria for the explication. The explicatum must be such that it is interchangeable salva veritate for the explicandum in all these sentences (i.e. if the explicandum is replaced by the explicatum in these sentences, the sentences do not change 61
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their truth-values). Other requirements for an adequate explication are exactness, fruitfulness and simplicity. The first guarantees that the explicatum is introduced into a well-connected system of scientific discourse. The fruitfulness criterion is satisfied if the new concept is useful for the formulation of many interesting universal statements. Finally, an explicatum should be as simple as possible, as measured by the form of its definition and measured by the forms of the laws connecting it with other concepts. (We shall say more about simplicity in Chapter 5.) When Goodman speaks of definitions as the method by which philosophy arrives at rational reconstructions of ‘induction’ or ‘pictorial representation’ and so on, he has explications in mind. As we have seen, explications presuppose a certain familiarity with the explicandum, the term as used in ordinary or pretheoretic discourse. This familiarity can be achieved by the method of conceptual analysis, that is, a meaning analysis of the concepts involved. In this respect Goodman acknowledges the accomplishments of British ordinary-language philosophy. Conceptual analysis of ordinary-language concepts can clarify the explicandum to a degree that makes it possible to judge the similarity of explicandum and explicatum. Conceptual analysis, however, is only half way towards a satisfying philosophical solution. The next steps involve a creative act: the clever stipulation of a substitute concept that fits nicely into a satisfying system of definitions. But when are such definitions satisfying?
Systems of definitions Recall Goodman’s solution to the problem of induction from Chapter 2. He intended his system of definitions concerning projectibility (DEF6–DEF9) to be (more or less) coextensional with our pretheoretic notion of projectibility. What does that mean? The grue paradox taught us a certain lesson, namely that a mere syntactic definition of the rules of induction would also justify considering a hypothesis such as: (L4) All emeralds are grue to be well supported by the empirical evidence, for only green emeralds were observed up to t. This causes a problem in the definition of induction: it seems that all kinds of incompatible predictions could be made on the same evidence (if they predict incompatible states 62
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after t). A theory of justified inference, however, should not be that permissive. Only some predictions should be justified on the basis of certain evidence, not virtually everything. We know what has to go: L4 is not justified by the evidence we have. We would not regard it as well justified intuitively. This is an aspect of our pretheoretic notion of induction that has not yet been captured by the syntactic definition of induction. This is why Goodman wants to supplant it with a notion of projectibility. The explicandum now is ‘projectible’. Intuitively L4 is not projectible, whereas L3 clearly is. But is it possible to find a good definition of ‘projectible’? When is a definition a good one? Well, it is good if it can tell L4 apart from L3. We have seen that positionality could not serve as a satisfying explicatum, for it was dependent on which language we start with. If we started with a language having ‘grue’ and ‘bleen’ as basic predicates, positionality would count L4 again as projectible and L3 as non-projectible. Instead Goodman offers a definition based on the notion of entrenchment. Entrenchment could be used to define when a hypothesis is overridden and could thus serve as a partial explication of projectibility. Entrenchment is not language dependent in the way positionality is. If we started with just the ‘grue and bleen’ language, but project predicates that are coextensional with the predicates that are in fact entrenched, we would project a hypothesis that is coextensional with L3, but not with L4. So far, so good. The important point is that this explication is almost coextensional with our pretheoretic concept of projectibility; each concept applies to almost all the cases that the other one also applies to. This is why the definition is deemed satisfying (at least by Goodman). Coextensionality does not imply sameness of meaning. An explication in Goodman’s sense does not aim at finding a definition that agrees in all actual and logically possible cases with the pretheoretic concept. ‘Organism with a heart’ and ‘organism with kidneys’ are coextensional predicates; every organism with a heart also has kidneys and vice versa. However, the two expressions are not synonymous. Hence, coextensionality does not imply synonymy. There might even be cases in which a definition does not have to be coextensional. Clearly, when it comes to explications coextensionality might already be too strong a criterion. If the pretheoretic usage is muddled, our explicata should be less muddled. That implies that the explicatum and the explicandum will not agree in all cases. Borderline cases of the explicandum might be clear cases of the explicatum, or they might also fall out of its extension, if that seems more fruitful. 63
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Zoologists explicated the term ‘fish’ as it is used in ordinary language but the explicatum does not include whales or dolphins. The reason was that the zoologists found out that animals living in water have nowhere near as many properties in common as the animals that live in water, are cold-blooded vertebrates and have gills throughout life. It seemed more fruitful to restrict the extension of ‘fish’ in the latter way. As we shall see in the following section, even approximated coextensionality might be too strong a requirement for a system of definitions. This is the case if the structure of something is of more interest to us than its specific realization. In these cases it is enough if the system of definitions preserves the important relations between the explicatum structure and the structure of the explicandum, that is, that they are structured in the same way in the relevant aspects.
The reconception of philosophy As we have said, explications replace problematic concepts in order to lead to better theories. In our example above, the meaning of ‘fish’ was replaced by a new zoological meaning, which included fewer animals than the ordinary-language concept did. Sometimes explications might also shift the whole extension over the domain of individuals. In such cases the new concept might have some new instances that the ordinary-language concept did not apply to, and at the same time might cease to apply to others. If such decisions promise to lead to theoretical advances, nothing is wrong with that. Goodman’s reconception of philosophy by way of explication allows for even more radical shifts, as we shall see in the following chapters. We shall, however, partially outline the main idea here. Goodman tried to solve philosophical problems by explication; that is, by reconceptualizing the problematic terms. Whenever Goodman encounters a philosophical problem that seems to be at a dead end, judged by the history of failed attempts to solve it, he tries to tackle it by taking some other perspective on the matter. We have already seen examples for this when discussing the problem of induction; there did not seem to be a forthcoming general solution for the general problem of disposition predicates until Goodman recognized that definitions for singular disposition predicates are sometimes nevertheless available and that a partial solution for the disposition predicate ‘projectible’ will yield a general solution after all. Thus shifting the perspective might 64
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sometimes lead to new observations and new insights and might be a promising strategy if we seem constantly to be banging our heads against the same wall. To see how far this reconceptualization might take us, consider the concepts of truth, certainty and knowledge, which are clearly key concepts of philosophy. All three prove to be problematic at best. Truth is problematic if conceived as correspondence of discourse with reality. There does not seem to be a world independent of discourse, and, anyway, correspondence of a description with something undescribed seems problematic to grasp. (There will be more on this in Chapter 8.) Certainty is an even less clear notion. If ‘certainty’ means trust or faith, then it is independent of truth, but merely depends on a psychological relation to a given proposition. If it means incontestability then it is trivially satisfied by all true sentences and even by some false ones whose falsehood cannot be demonstrated. Finally, knowledge seems to be related to truth and certainty and therefore inherits their problems. If, however, truth is not built on certainty, but on likeliness or high probability, we get into further trouble. Assume that you believe, justified on stochastic considerations, that the first card in a well-shuffled deck of cards is not the ace of hearts. If that is true, did you know it was true? These notions prove to be very problematic when it comes to being captured by satisfying explications. They are, obviously, mutually related. Again Goodman pleads for a replacement of these concepts, but this time a much more radical replacement. Instead of explicating the notions with others that are almost coextensional, Goodman pleads (in a paper jointly written with Elgin (RP: ch. X )) for their replacement with notions that only preserve the interrelatedness in a certain way, but have an otherwise wholly different extension. As a replacement of ‘truth’, Goodman proposes ‘rightness of symbolic function’. (We shall discuss Goodman’s theory of symbols in detail in Chapter 6.) This notion is much broader: whereas ‘truth’ applies only to linguistic statements, ‘rightness’ also applies to all ways a symbol might work, be it in denotation, depiction, exemplification or expression. ‘Rightness’ sometimes just replaces ‘truth’ when it comes to statements, but sometimes a statement might be “true” (e.g. ‘Snow is white’) but just not “right” (e.g. if ‘Snow is white’ is put forward as an answer to the question ‘What density does granite have?’). Hence, ‘rightness’ is clearly not coextensional with ‘truth’. However, ‘rightness’ might be easier to characterize, since it involves not the explication of the relation between world and Reality, but the degree of fit of 65
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a symbol into a discourse and the way it is effective in it. Moreover, rightness seems to have a relation to adoption and understanding similar to the relation truth has to certainty and knowledge. It is thus proposed to replace ‘certainty’ by ‘adoption’. ‘Adoption’ is as broad as ‘rightness’: we can “adopt” habits, strategies, terminologies and styles as well as statements. Again this notion is clearly not coextensional with ‘certainty’. However, adoption is clearly connected with entrenchment. Entrenchment is nothing but continued adoption. This way adoption contributes to rightness, since the entrenched predicates are the “right” predicates in a given discourse to represent the world. As a replacement of ‘knowledge’, Goodman proposes ‘understanding’. Again this notion is sufficiently broad to cover more than just statements or only those entities that are truth-apt; one can “understand” (or not) questions and orders, for instance, but it does not make much sense to say that one knows a question (it must not be confused with elliptical uses of this phrase, which are short for ‘knowing the answer to that question’ or ‘knowing that someone asked that question’, ‘knowing that the quiz master has that question on his list’, ‘knowing that this question will turn up in the exam’, etc.). Thus ‘understanding’ fits with ‘rightness’ and ‘adoption’. Understanding might take the position of knowledge, since it seems to be a reasonable candidate for what our cognitive endeavours aim at. If cognition involves more than truth-evaluable entities, but also symbols that are only classified by correctness, as Goodman thinks, knowledge would be far too restricted as the overarching aim of philosophy and other arts and sciences.
Meaning, synonymy, analyticity Goodman’s insistence that meaning analyses impose much too strong criteria on good definitions, “sameness of meaning” in particular, can also be explained from another angle. As we have said, one of the consequences that the logical positivists drew from their basic assumptions was that philosophy, being concerned with the “syntax of scientific language”, was dealing with statements clearly different in kind from the statements the other sciences were concerned with. Whereas the empirical sciences were associated with synthetic statements, philosophy was associated with analytic statements: statement that are true in virtue of their meaning alone. The truths of 66
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logic and logical analysis were considered to be analytic truths, just as the statements in which conceptual analyses are expressed were. The analytic–synthetic distinction seemed to be clear enough to the logical positivists. One of the major turning points in philosophy during the twentieth century, however, was when Morton White, Quine and Goodman suddenly declared their discontent with the distinction. On 25 May 1947, White, who was at that time Goodman’s colleague at the University of Pennsylvania (and soon to become Quine’s colleague at Harvard), wrote a letter to Quine asking for advice on a paper in which he tried to deal with a solution to C. H. Langford’s paradox of analysis proposed by Alonzo Church. Langford had raised the problem for G. E. Moore’s conception of analysis, but it applies to the notions of analysis in this chapter as well:2 Let us call what is to be analyzed the analysandum, and let us call that which does the analyzing the analysans. The analysis then states an appropriate relation of equivalence between the analysandum and the analysans. And the paradox of analysis is to the effect that, if the verbal expression representing the analysandum has the same meaning as the verbal expression representing the analysans, the analysis states a bare identity and is trivial; but if the two verbal expressions do not have the same meaning, the analysis is incorrect. (Langford 1942: 323) The way Langford formulates the problem, and the way White discusses it, shows that they are concerned with a paradox of reference analysis, applying to real analyses. The paradox arises easily, however, for meaning analyses as introduced in this chapter. As we noted above, the truth requirement for a meaning analysis says that a meaning analysis is true iff the term d1, stating the definiendum, is synonymous with the term d2, stating the definiens. This requirement seems to lead to paradox, however: meaning analyses are doomed to be either trivial or false. The argument that leads to this paradox goes as follows: Consider the following analyses: (D3) ‘Bachelor’ is synonymous with ‘unmarried man’. (D4) ‘Bachelor’ is synonymous with ‘bachelor’. Clearly, (D3) states that two different expressions are synonymous, whereas (D4) just says that one and the same expression is 67
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synonymous with itself. We regard statements like (D4) to be trivial and uninformative. Hence, (P1) (D4) is trivial. The question of whether (D3) is also trivial could be understood to be a question of whether (D3) has the same meaning as (D4) (if triviality of a statement is understood as a matter of the meaning of this statement). Thus: (P2) All statements that are synonymous with (have the same meaning as) a trivial statement, are themselves trivial. If we turn to (D3) again, the following seems to be presupposed for (D3) and (D4): (P3) Either (D3) is synonymous with (D4) or it is not. If we think that (D3) and (D4) have the same meaning and therefore are synonymous, it seems we must, given (P2) and (P1), also accept that (D3) will then be trivial: (P4) If (D3) and (D4) are synonymous, (D3) is trivial. That is already the first horn of the dilemma caused by Langford’s paradox of analysis. To get to the second horn, we need a principle of compositionality3 for meaning and a relatively unproblematic observation concerning (D3) and (D4). First, the principle of compositionality: (P5) Compositionality: The meaning of a complex expression is solely a function of the meaning of its subexpressions and the way they are combined syntactically. If (D3) is supposed to be non-trivial, it thus must not be synonymous with (D4). In other words, there has to be a difference in meaning between (D3) and (D4). Compositionality tells us that two expressions cannot differ in meaning if both are of the same syntactical structure and if the subexpressions of both have the same meaning. Statements (D3) and (D4) are, however, of the same syntactical structure: (P6) The syntactical structure of (D3) and (D4) is the same. Moreover, (D3) and (D4) have most of their syntactical parts in common. The only difference seems to be the syntactical part ‘unmarried man’ instead of ‘bachelor’. 68
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(P7) The only subexpressions that make a difference between (D3) and (D4) are ‘unmarried man’ and ‘bachelor’.4 Compositionality, however, assures us that: (P8) If (D3) is not synonymous with (D4), then there is a meaning difference between ‘bachelor’ and ‘unmarried man’. We know already that: (P9) If two expressions differ in their meaning, they are not synonymous. We also have said that: (P10) Meaning analyses are true iff the term d1 stating the definiendum is synonymous with the term d2 stating the definiens. But that leads us straight to the second horn of Langford’s dilemma: (P11) If (D3) is not synonymous with (D4), (D3) is not correct. Therefore, meaning analyses are either trivial or incorrect. There are a number of ways to avoid this problem. The ways discussed by White had to do with the fineness of grain of the meaning analysis. Clearly, one of the problematic premises is (P2). Maybe it is possible to make a difference between, say, ‘sameness of meaning1’, which is a necessary and sufficient condition for the adequacy of meaning analyses (and applies to (D4)), and ‘sameness of meaning2’, which is a sufficient condition for two terms to be trivial if one of them is. To make such differences, some philosophers of language postulated abstract objects, intensions, such that a difference in intensions of sorts could explain the difference between ‘sameness of meaning1’ and ‘sameness of meaning2’. To solve the problem for real analyses one could postulate Fregean senses (as one kind of intension), but in order to solve the problem for meaning analyses we would need something even more finely grained. The details of these accounts do not matter too much for us here. The important point is only that certain abstract objects were postulated to explicate the notion of synonymy. White sent his discontentment with the proposed solutions to Quine (White’s original paper appeared in print in 1948 under the title “On the Church–Frege Solution of the Paradox of Analysis”) and then sent Quine’s answer to Goodman. In 1947 the three discussed the matter by letter,5 until White was eventually chosen to write a 69
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survey of their discussion, which appeared in print in 1950 under the title “The Analytic and the Synthetic: An Untenable Dualism”. Quine presented his view on the matter in an address to the American Philosophical Association, which was published in 1951 as his famous “Two Dogmas of Empiricism” (Quine 1951c). At that time the described postulation of new abstract objects in order to explicate a certain notion of synonymy seemed an unacceptable move for someone with nominalist6 leanings such as Quine and a purist such as White. For Quine, an explication of ‘synonymy’ or ‘analyticity’ and the like should rather be given in behaviouristic terms. The explication should tell us in what way ‘analyticity’ and ‘synonymy’ make a difference in speaker behaviour. To learn that the difference lies in postulated abstract objects did not seem to explicate the notions in any promising way. Goodman’s original discontentment with the whole situation was even more serious. In a letter to White and Quine he claimed that not only did he find the explications of ‘synonymy’ and ‘analyticity’ so far provided to be problematic, but he did not even understand what these terms were supposed to mean pretheoretically: When I say I don’t understand the meaning of ‘analytic’ I mean that very literally. I mean that I don’t even know how to apply the terms. I do not accept the analogy with the problem of defining, say, confirmation. I don’t understand what confirmation is, or let us say projectibility, in the sense that I can’t frame any adequate definition; but give me any predicate and (usually) I can tell you whether it is projectible or not. I understand the term in extension. But ‘analytic’ I don’t even understand this far; give me a sentence and I can’t tell you whether it is analytic because I haven’t even implicit criteria. … I can’t look for a definition when I don’t know what it is I am defining. (Goodman in a letter to Quine and White, 2 July 1947, in White 1999: 347) The official result of their discussion was that any sharp analytic–synthetic distinction is untenable and should just be abandoned: I think that the problem is clear, and that all considerations point to the need for dropping the myth of a sharp distinction between essential and accidental predication (to use the language of the older Aristotelians) as well as its contemporary formulation – the sharp distinction between analytic and synthetic. (White 1950: 330) 70
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Goodman’s view on the matter had already appeared in print in 1949 under the title “On Likeness of Meaning”. Goodman here proposes a purely extensional analysis of meaning, the upshot of which is that no two different expressions in a language are synonymous. Goodman first compares an intensional theory of meaning with an extensional one. The main difference between the two is epistemic in nature: there is no comprehensible way by which we can know whether two expressions have the same intension, but there is a relatively unproblematic way to find out whether two terms have the same extension. This is so because of the assumed nature of intensions. Here are some well-known examples and their respective problems: (i) Two terms/expressions have the same intension iff they stand for the same real essence or same Platonic idea. This proposal is confronted with the epistemological problem simply because we have no idea how to tell what Platonic idea a term stands for. We clearly need something more practical. (ii) Two terms/expressions have the same intension iff they stand for the same mental idea or image. Now we have dragged the problem from Platonic heaven down to human psychology. However, this proposal is still confronted with two problems. First, it does not seem to be very clear what we can and what we cannot imagine. Secondly, many terms (e.g. ‘supersonic’) do not seem to have mental images associated with them. That should lead to a different construction that is more liberal than imaginability: (iii) Two terms/expressions have the same intension iff we cannot conceive of something (or some states of affairs) that satisfies one but not the other. Many would have the objection to this analysis that we can conceive pretty much everything, leaving us with no criterion at all.7 In any case, the only limitation that seems to be imposed on our conceptual powers is possibility. But if only those conceptions that correspond to some real possibility should count, the criterion becomes possibility rather than conceivability: (iv) Two terms/expressions have the same intension iff there is nothing possible that satisfies one but not the other. Here the question is whether we talk of something that actually satisfies one but not the other, or something that possibly satisfies one 71
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but not the other. If we take the former, this proposal is purely extensional: if I know that two predicates are satisfied by the same actual objects this already excludes the possibility that they are not satisfied by them. If, however, also merely possible objects should matter, rather than only actual objects, we are confronted with the problem of how to tell in any non-circular way what is possible. Conceivability was already ruled out in reaction to proposal (iii). An alternative could be found in consistency; such that, for example, two predicates differ in meaning if ‘is a P or a Q but not both’ can be shown to be consistent. However, this does not help if P and Q are different predicates and the logic at our disposal does not include meaning postulates. In that case, for every couple of predicates P and Q this expression is consistent. In a logic with meaning postulates the problem is not solvable in general if the language is sufficiently rich (see Cohnitz 2005a) and, anyway, where do we know the meaning postulates from? This was the original question; we are back where we started. An extensional theory for sameness of meaning is not plagued by these or similar arguments. The claim that: (v) Two terms/expressions have the same meaning iff they have the same extension. has the advantage that, as Goodman argues, we can “decide by induction, conjecture, or other means that two predicates have the same extension without knowing exactly all the things they apply to” (PP: 225). But an extensional theory is not thereby free of problems. Consider, for example, the expression ‘unicorn’ and ‘centaur’, which have the same extension (namely the null-extension) but differ in meaning. Hence, whereas sameness of extension is a necessary condition for sameness of meaning, sameness of extension does not seem to be sufficient for sameness of meaning. Goodman proposes an extensional fix to this problem that gives necessary and sufficient conditions for sameness of meaning. He observes that although ‘unicorn’ and ‘centaur’ have the same extension, simply because of the trivial fact that they denote nothing, ‘centaur-picture’ and ‘unicorn-picture’ do have different extensions. Clearly, not all centaur-pictures are unicorn-pictures and vice versa. Thus the flight to compounds makes an extensional criterion possible: “[I]f we call the extension of a predicate by itself its primary extension, and the extension of its compounds as secondary intension, the thesis is as follows: Two terms have the same meaning iff they have the same primary and 72
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secondary extensions” (PP: 227). The primary extensions of ‘unicorn’ and ‘centaur’ are the same (the null-extension), but their secondary extensions do differ: the compounds ‘unicorn-picture’ and ‘centaurpicture’ differ in extension. (We shall discuss this proposal in detail in Chapter 6.) If we allow all kinds of compounds equally, we arrive immediately at the result that by our new criterion no two different expressions have the same meaning. Take the expressions ‘bachelor’ and ‘unmarried man’: ‘is a bachelor but not an unmarried man’ is a bachelor description that is not an unmarried-man description. Hence, by our criterion, the secondary extensions of ‘bachelor’ and ‘unmarried man’ differ because the primary intensions of at least one of their compounds do. Since the same trick can be pulled with any two expressions, Goodman is left with the result that no two different expressions are synonymous, but he is ready to bite this bullet. P-descriptions that are not Q-descriptions are easy to construct for any P and Q (provided these are different terms) and these constructions might well be relatively uninteresting. If only such uninteresting constructs are available to make a difference in secondary extension, P and Q, despite being not strictly synonymous, might be more synonymous than a pair of predicates for which we are able to find interesting compounds (as in the case of ‘centaur’ and ‘unicorn’). This turns sameness of meaning of different terms into likeness of meaning, and synonymy and analyticity into a matter of degree.8 This conclusion is, however, in full accordance with the conclusion that was drawn by White as the result of the exchange between White, Quine and Goodman: I am not arguing that a criterion of analyticity and synonymy can never be given. I argue that none has been given and, more positively, that a suitable criterion is likely to make the distinction a matter of degree. If this is tenable, then a dualism which has been shared by both scholastics and empiricists will have been challenged successfully. Analytic philosophy will no longer be sharply separated from science, and an unbridgeable chasm will no longer divide those who see meanings or essences and those who collect facts. Another revolt against dualism will have succeeded. (White 1950: 330)
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Summary In this chapter we have introduced Goodman’s general idea of the purpose, aim and method of philosophy. For the purpose, Goodman has a negative answer: philosophy is just its own purpose; there is nothing reasonable that philosophy is good for, however, there does not need to be – which is what he would say about the arts and science too. All that matters is that our understanding is promoted by these activities, as this is, in itself, valuable. We then turned to Goodman’s conception of aim and method of philosophy. Philosophy aims at understanding and clarification and it does so by way of explication. We introduced the notion of an explication, and in what respect explications differ from other kinds of definition. Finally we have introduced a vital aspect of Goodman’s philosophy: the rejection of the analytic–synthetic distinction and his purely extensional analysis of meaning.
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Chapter 4
Particulars and parts
In Chapter 3 we saw that one consequence of taking philosophy to be directed at understanding and elucidation is that a philosophical explication cannot be given in terms of unintelligible entities. That was the reason why Goodman did not accept an analysis of meaning in terms of intensions. Intensions are not the only philosophical constructions he repudiates, however. Goodman is, among other things, most famous for another radical doctrine: his nominalism. In the twentieth century the debate between realism and nominalism was an almost foolproof source of heated discussion and verbose polemic (and sometimes rather entertaining rhetoric), and it still is today. The conflict is over ontology. The nominalist denies the existence of certain objects, while the realist affirms their existence. There are different ways in which one can be a nominalist depending on, for example, what kinds of things it is that one does not believe to exist. We shall distinguish these below. Often the nominalist denies the existence of abstract objects (such as numbers, shapes or groups) or universals (such as redness, courage or density). Doing so has a deep impact on disciplines such as philosophy of science and philosophy of mathematics, but also in all areas where metaphysical considerations play a role. We shall also see that there is a specific twist to Goodman’s nominalism. The debate has been rekindled (if it ever really died out) in the past twenty years or so, which makes Goodman’s contribution to the field of particular interest. Goodman stands on the side of the nominalists, and has defended his view by compelling arguments and by way of example, namely, by producing rigorous and fruitful philosophical theories that are acceptable to the nominalist. He has produced some remarkable results in this field, which we shall deal with below. 75
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In this chapter we are mainly concerned with a precise definition of Goodman’s nominalism, and with distinguishing it from related notions. We also introduce the calculus of individuals, Goodman’s mereological system. Once we have equipped ourselves with the necessary techniques, we show, in Chapter 5, how Goodman puts these to use in A Study of Qualities and The Structure of Appearance.
Nominalisms One of the most controversial features of Goodman’s philosophy is probably his nominalism. It is advisable, though, to pay close attention to characterizing Goodman’s position exactly. A range of different views is routinely subsumed under the label ‘nominalism’, and it is important to be clear about which of these sundry positions Goodman actually holds. In A Study of Qualities, Goodman traces nominalistic thoughts back to Plato’s Sophist (SQ: 22–4). The first important and more or less systematic discussion, though, seems to have occurred in the Middle Ages. The participant in that discussion who is most prominent today is William of Ockham (c.1285–c.1349), who rejected the existence of universals. Universals such as redness or courage are taken to be entities that exist over and above the (particular) things that are red, or (particular) persons that are courageous. The existence of universals is asserted by the medieval realists, and is also fairly common among contemporary philosophers. Ockham insists that the postulation of such entities makes no sense, and that only particulars exist. Today, Ockham is probably best remembered for the principle of ontological parsimony named after him, Ockham’s razor, which is often stated as: “entities are not to be multiplied beyond necessity”. In a very intuitive sense, this principle seems to be acceptable to every philosopher. Why would anyone want to assume the existence of more things than one has to in order to explain everything there is to be explained? (This, at least, is the most common understanding of the necessity mentioned in Ockham’s razor.) One can often read that Ockham’s motivation for his nominalism can be found in his acceptance of this principle, despite the fact that it does not occur in this form in any of his writings. At least some current Ockham scholars, however, disagree with this claim that Ockham’s nominalism is grounded in his razor.1 This historical debate is not going to concern us here. 76
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We can, in any case, note two positions that are commonly called ‘nominalism’: (N1) Universals do not exist. Everything is particular. (N2) The more parsimonious ontology is to be preferred (all other things being equal). It is easy to see how (N1) is more controversial than (N2), and indeed we already said that probably every philosopher could agree on (N2). It should also be clear, however, that neither follows from the other. That means that everyone is free, in principle, to adopt one view and reject the other, or adopt both, or reject both. We say that (N1) and (N2) are independent of each other. One does not run into a contradiction merely by adopting any one of the possible combinations of these views (as one would if one held that it was true that cats exist, agreed that cats are mammals, but denied that mammals exist). (N1)-nominalism is sometimes rejected by philosophers who seek to explain certain things by appealing to universals. David Armstrong, for example, holds that one needs universals in one’s ontology to give an account of the laws of nature (see e.g. Armstrong 1997: 223–30). If he is right, then it is necessary in order to give an account of these laws to assume the existence of universals in the sense of Ockham’s razor as stated above, and the parsimony constraint of (N2) would not be violated. There is something else that one can believe that is often called nominalism. It is connected in one way or another with physicalism: the view that everything in the world is physical, made out of the matter that physics talks about, and governed by the laws of nature (the physical laws). What a nominalist in this sense denies is the existence of abstract objects: (N3) Abstract objects do not exist. Typical examples of abstract objects include numbers, shapes, directions and lengths, but also sets, groups and maybe football teams (which are not to be confused with their players). Goodman’s favourite abstract objects are qualia; we return to them in Chapter 5. What exactly an abstract object is supposed to be is up for debate. No definition has been found yet that is generally accepted.2 The rough and ready idea, though, will suffice for our purpose here. Abstract objects are contrasted with concrete objects, such as tables, chairs, you and me; or perhaps electrons, quarks or strings. The claim that abstract 77
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entities exist not only seems to contradict physicalism, but might also give rise to an epistemic worry. As a physicalist especially, one might have a causal theory of knowledge that says, roughly, that we gain our knowledge of things by standing somewhere in a chain of the right sort of causal connections to these things. To pick a simple example, we know that there is an apple in front of us because light bounces off it and into our eyes, that there causes some biochemical reaction that transmits this information to our brains. You, the reader, now have knowledge that at the time of writing this chapter there was an apple in front of us, because this caused us to type it into the computer, which we saved as an electronic file, a copy of which was used somewhere in the process of printing the very book that you hold in your hand now and read by receiving the light that bounces off the pages of this book and into your eyes and so on. If the causal theory of knowledge is right, though, abstract objects are more than dubious: we could never have knowledge of them, since we can never get into causal contact with them,3 simply because that is exactly what it means to be abstract (or, at least, that very often features in attempts to define ‘abstract’). There is certainly a lot of room for manoeuvre here. (N3)-nominalism is not the same as physicalism (although (N3)-nominalists are typically physicalists), and physicalism certainly comes in different varieties as well. (Unfortunately, there is no space here to go into that.) Moreover, neither physicalism nor the rejection of abstract objects is wedded to the causal theory of knowledge. There are many rival theories of knowledge out there that can be adopted. As a reason to reject the causal theory of knowledge, one might point to something that many philosophers believe, namely, that we can have a priori knowledge, that is, roughly, knowledge that is not based on our experience of the world. Knowledge of the laws of logic, or mathematical knowledge, is often held to be of that sort. To know that ‘2 + 2 = 4’ is true, we do not have to investigate the world; reason alone tells us this, independently of any experience. One can also argue that physicalism is not at all incoherent with the postulation of abstract objects. To reject abstract objects without being a physicalist might be trickier, but ghosts or Cartesian egos may provide examples of things that are supposed to be non-abstract but also non-physical. A tempting thought might be that particulars are always concrete objects, and that if universals are supposed to be, as we said, something over and above these, they have to be abstract. None of this is the case, however. First of all, some philosophers, most notably 78
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Frege, believe numbers to be objects, that is, particulars. It seems very obvious, however, that numbers are not concrete, physical objects; we cannot find them in the world like sticks and stones.4 Therefore, they must be abstract, and hence abstract particulars. Goodman also recognizes things that he takes to be abstract particulars: for example. spacetimes and mereological sums of these (dealt with in detail in Chapter 5.) So one can believe in abstract particulars but reject universals. Nor need universals be abstract. They might be construed this way, and often are, but Armstrong, to give a famous example, holds that universals are physical, despite being something over and above the particulars that instantiate them (see Armstrong 1978b, 1989). Statements (N2) and (N3), again, are logically independent of each other, for pretty much the same reasons as given for (N1) and (N2). And (N1) and (N3) are also independent of each other. We already mentioned that universals need not be considered as abstract. If that is an option, then one could hold (N3) while believing in universals and hence rejecting (N1). Can one also reject universals and embrace abstracta? Yes, one can. We have already brought mathematics into our discussion here as an example. We have now singled out three doctrines, each of which is frequently labelled ‘nominalism’, and each of which is independent of the other two. These are by no means all the different kinds of nominalism that one can distinguish. Armstrong presents (and discusses) a greater variety of nominalisms, in part by distinguishing more finely between views that we lump together here (Armstrong 1978a: chs 2–5). The coarser categorization is sufficient for our purpose, though. Which one of these is Goodman’s nominalism? The surprising answer is: none of them. But it is a common misunderstanding, partially caused by Goodman himself, that he held (N3). We shall investigate how this misunderstanding came about, before we go on to see what Goodman’s nominalism is. (We shall say a little bit more about the historical development of Goodman’s nominalism in Chapter 5.)
The 1947 nominalism of Goodman and Quine We do not believe in abstract entities. No one supposes that abstract entities – classes, relations, properties, etc. – exist in space-time; but we mean more than this. We renounce them altogether. … Any system that countenances abstract entities we deem unsatisfactory as a final philosophy. (PP: 173) 79
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Thus starts the paper, jointly written by Goodman and Quine in 1947, called “Steps Toward a Constructive Nominalism”. Given this rather strong statement it might seem excusable that one should get the idea that Goodman and Quine held (N3), at least at this point. On the very same page, however, the first page of the article, they retract. Abstract universals, for example, phenomenal qualities, are admitted as the basic building blocks of the world, just as they admit physical objects or events. And, indeed, Goodman already had used qualia in his construction in his PhD thesis A Study of Qualities and would go on to use them in his later The Structure of Appearance, which appeared three years after the 1947 joint paper with Quine. (We return to this in Chapter 5). The target of “Steps Toward a Constructive Nominalism” is mathematics. Goodman and Quine show how some notions that were generally believed to be mathematical through and through, with no hope for an account that does not appeal to abstract, mathematical objects, can be recast in a nominalistically acceptable way. (Here and for the rest of this section, ‘nominalistic’ is meant in the sense of (N3) unless stated otherwise.) The paper is still, with very few competitors for the title, one of the most remarkable efforts in that direction, if not the most remarkable one. It can be divided into two parts. In the first part, Goodman and Quine show how some statements that seem to be about abstract mathematical entities can be paraphrased and formalized in such a way that any mention of abstracta disappears. In the second part, they successfully undertake what is still, in spite of their demonstration (which has apparently been largely forgotten by the philosophical community), often believed to be unachievable: the construction of the syntax for a (formal) language by nominalistically acceptable means, and a likewise acceptable definition of ‘theorem’ and ‘proof ’. A full exposition of the material of the paper would go too far here, and some of the constructions are technically rather complicated; this is especially true of the second part. We want to give a few examples, however, of how this “nominalization” works. First, it has to be noted that neither Quine, who is famous for this,5 nor Goodman believes that predicates refer to abstract entities or universals that predicates such as ‘is red’ stand for. Thus ‘a is red’ requires no more than that a exists, and that it is red. No universal property redness is required that a instantiates and that ‘is red’ refers to; ‘a is red’ merely requires that ‘is red’ is true of a. (In that sense, Goodman and Quine here also advocate (N1).) 80
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One of the main targets in the paper is classes. Classes, or sets as they are more commonly called today, are collections of objects, which are called their members. Sets are also reified, that is, they are objects themselves. They are abstract particulars. We shall say more about classes below, since Goodman has another axe to grind here. Consider the statement: (1) Class A has three members. Class A could, for example, be the class of planets in our solar system that are closer to the Sun than Mars. (There are indeed three: Mercury, Venus and Earth.) On the face of it, sentence (1) talks about a class, and maybe even about numbers (‘three’). Goodman and Quine suggest rephrasing the statement as: (1′) There are distinct objects, x, y and z, such that anything is A iff it is identical to x or y or z. Recast in the formalism of predicate logic, the statement looks like this: (1′′) ∃x∃y∃z(x ≠ y ∧ y ≠ z ∧ x ≠ z ∧ ∀w(Aw ≡ (w = x ∨ w = y ∨ w = z))) Now ‘A’ in (1′) and (1′′) is a predicate that is true of all and only the things that non-nominalists, or ‘platonists’ as they are commonly called,6 would take to be members of the class A. In our example it would be the predicate: ‘is a planet in our solar system that is closer to the Sun than to Mars’, which is true of exactly three things (Mercury, Venus and Earth). More generally, since classes can contain all sorts of random things that might not fit under such a neat description like the one for A, but might be sundry things such as Buckingham Palace, the Moon and the present First Minister of Scotland, any specification of the class will do as a predicate, even if it is a mere list of things. In the latter case, for instance, it would be ‘being either Buckingham Palace, the Moon or the present First Minister of Scotland’. In a similar fashion, statements about the relations between classes can also be “nominalized”. A class A is said to be a subclass of a class B, if all members of A are also members of B. That leaves it open whether A and B have exactly the same members. In that case, A and B would be identical. Identity between classes is defined extensionally: A and B are the same class iff they have exactly the same members. If A is a subclass of B, but the two are not identical, we say that A is a proper subclass of B. The class of all mammals, for example, is a proper subclass of the class of all animals. But this statement can 81
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straightforwardly be rephrased in a way acceptable to the nominalist: ‘All mammals are animals, and there are animals that are not mammals’. It is probably obvious now how even some statements that on the surface explicitly claim the existence of a class can be rephrased so as to be palatable to the nominalist. Take for example: (2) There is a class that class A is a proper subclass of. To rephrase (2), we just generalize the insight from the mammals example above: (2′) There is something that is not A. (2′′) ∃x ¬ Ax Since any objects whatsoever, taken together, form a class, the only thing (2) requires is that there is one further thing that is not a member of A. A class containing that thing and everything that is a member of A will be a class that A is a proper subclass of. That there is such a thing that the predicate A does not apply to is exactly what (2′) and (2′′) express. Goodman and Quine present more nominalistically acceptable rephrases of platonistic statements, and of much more complicated ones. Among these are ‘There are more human cells than humans’ and ‘There are exactly one third as many Canadians as Mexicans’. Rephrasing these sentences requires a bit more technical apparatus than mere predicate logic. Since this will only be introduced in the following section, we leave it at that here, trusting that the impression one gets from the examples we give is sufficient to see what Goodman and Quine are up to in this paper. What more is needed is commonly called ‘mereology’: the theory of parts and wholes. Rather than coming back to the examples given in the paper, we shall give some of Goodman’s constructions of The Structure of Appearance as examples of how the mereological apparatus can be put to use. It is not all that important to cover all the examples Goodman and Quine give here. There is no general way, no standard recipe for translating platonistic statements into nominalistically acceptable language; at least there was none known to Goodman and Quine, and there still is none known today.7 The enterprise of their paper was not to recover all of the platonists’ talk; it seems likely that this is impossible, at least with the resources that they allow. (Other resources might be available to the nominalist; see for example our discussion in § “Logic and mereology”, p. 218.) Their aim is to save what is salvageable. Talk about classes is deemed unacceptable in “Steps Toward a Constructive Nominalism”, so Goodman and Quine give some examples of how to 82
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do without it. The hope is that this will suffice to do everything one wants – and needs – to do. One of those things is to construct a syntax and a proof theory for a formal language, since these are necessary tools for the nominalist as well as the platonist. The platonist uses classes to construct a syntax and to give a proof theory for a formal language. This is familiar from every introductory book of mathematical logic. But this is not available to the nominalist. If nominalists cannot even account for these tools which they need to use, nominalism must be bankrupt. The refutation of this criticism is one of the reasons why Goodman and Quine undertake the project of a nominalistically acceptable construction of syntax and proof theory. There is a second reason, however. If abstract objects, and classes in particular, are basically unintelligible, how is it then that mathematicians can work with them, and agree, or reasonably disagree, about what they are doing? How can mathematics examinations be assessed and mistakes in them penalized? For Goodman and Quine, the: answer is that such intelligibility as mathematics possesses derives from the syntactical or metamathematical rules governing those marks. Accordingly we shall try to develop a syntax language that will treat mathematical expressions as concrete objects – as actual strings of physical marks. (PP: 182) The mathematical language they take as an example, the language of set theory, is treated as mere “strings of marks without meaning”, so the issue created by the fact that Goodman and Quine find the language unintelligible does not arise; no meaning of the marks has to be assumed. The wide agreement among mathematicians concerning mathematical methods and proofs derives, according to Goodman and Quine in 1947, from the possibility of dealing with them in such a schematic, uninterpreted way. Again we are not going into detail here too much, but merely describe the first few steps of the constructions. We shall stop at the point where mereological resources come into play because we have not yet introduced them. The steps we take will suffice to give a good idea of the flavour of the project. Commonly, the vocabulary of a language would be described as a class of signs (e.g. letters), the formulae would be the class of strings of such signs that are put together according to the formation rules for the language. This is not only unacceptable to the nominalist because of the use of classes, but also because letters and other signs, thus construed, are abstract objects as well. One common, platonistic 83
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manner of speaking is to say that letters are abstract types that have tokens as their instances. The two ns in ‘instance’, for example – yes, the very marks in front of you now, the black ink on this page of this very book – are two tokens of the type n. The tokens are therefore concrete physical objects: marks on paper, in this case. Without resorting to the type–token story, Goodman and Quine build up the whole syntax for the formal language they consider by just talking about such concrete marks, or inscriptions, as they call them. They do so without appealing to types, classes or other abstract objects. The concrete marks are distinguished by their falling under different predicates. A particular v-inscription, for instance, can be distinguished from a ⊃-inscription, because the predicate ‘is a v-shaped inscription’ is true of the v-inscription, but false of the ⊃-inscription.8 Such predicates are innocuous from the nominalist point of view, as we have already seen above. The vs are the variables in the system. One variable, of course, will not be enough, and there is no telling how many are going to be needed. Platonistic syntax often uses the natural numbers (1, 2, 3, …) to index the variables (‘v1’, ‘v2’, ‘v3’, …), but these are not available to the nominalist. Instead, the accent, ‘′’, is used to generate distinct variables, ‘v’, ‘v′’, ‘v′′’, ‘v′′′’, … . An aside is needed at this point. Since inscriptions are physical marks, the number of variables will be constrained by the size of the actual physical universe, which is very big, yet finite as current science tells us. For any actual mathematical practice this seems to be good enough, but full-blooded platonists will balk at these finitist limitations, which they do not have; they have infinitely many numbers, sets, and other abstract objects in their toolkit. In their 1947 paper, Goodman and Quine declare: We decline to assume that there are infinitely many objects. … If in fact the concrete world is finite, acceptance of any theory that presupposes infinity would require us to assume that in addition to the concrete objects, finite in number, there are also abstract entities. (PP: 174) This sounds, as if they want to suggest that nominalism and finitism have to go hand in hand, but in fact neither follows from the other. In his 1957 publication “A World of Individuals” Goodman states this explicitly. Nominalism is not incompatible with the rejection of finitism, it is “at most incongruous … The nominalist is unlikely to be a non-finitist only in much the way a bricklayer is unlikely to be a ballet dancer” (PP: 166).9 84
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Let us return to the construction of the nominalistically acceptable syntax. The device used to chain the signs of the language together is called ‘concatenation’. To say that signs are concatenated basically means that they stand next to each other. In the construction, ‘C’ is used to abbreviate concatenation. ‘Cxyz ’ says that x is an inscription that consists of y followed by z. For example, ‘v′’ is the concatenation of ‘v’ and ‘′’. On the basis of this, longer concatenations can be defined. Next, the syntactic rules of the language are provided. First, the basic pieces of vocabulary are called ‘characters’ (i.e. all inscriptions that fall under the predicates describing the shapes of the inscriptions, ‘is a v-shaped inscription’, for example), and a predicate ‘Char’ is introduced that is true of all and only the characters. Next follows the definition of an inscription. Something is an inscription iff either ‘Char’ is true of it, or it is the concatenation of two inscriptions. Meticulously, the whole syntax is built up like this, using only resources acceptable to the nominalist. Goodman and Quine define what a variable is (either a ‘v’, or a concatenation of a ‘v’ and a string of accents, where a string of accents is either ‘′’ or a concatenation of a string of accents with ‘′’), what a quantifier is (the concatenation of a left parenthesis and a variable and a right parenthesis), and so on, step by tedious step, until they can say what a formula is, namely, an inscription in which the signs are put together in the right way. Formulae are basically the well-formed sentences of a formal language. In predicate logic, for example, our (2′′) is a formula, but ‘x ( ⊃∀ ¬ F ’ is not, although of course the latter is still an inscription, that is, a concatenation of a series of characters. To cut the rest of the story short, a theorem (i.e. a statement that is provable in a formal system) is defined as a formula for which there is a proof, and a proof is a series of inscriptions, which are lines of the proof, such that each line is a formula that is an axiom of the system, or a direct consequence of the lines that precede it, according to the (syntactic) inference rules of the system. Shortly after the joint paper Quine abandoned the “no classes” stance. In his 1975 paper “On the Individuation of Attributes” he says that he came to “grudgingly admit” classes into his ontology (Quine 1981: 100). Quine came to believe that classes were indispensable after all, despite all the efforts he and Goodman had made, and Goodman continued to make throughout his career. But this is not the only difference between Goodman and Quine. Even though the nominalist tendencies of both converged in the 1947 rebellion against classes, the motivation for each of them was different. We shall see in Chapter 5 85
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that Goodman admits qualia, which he takes to be abstract entities, as a basis for his construction in A Study of Qualities, and continued to do so in The Structure of Appearance. Quine, on the other hand, had already proposed a series of class theories, for example in his “New Foundations for Mathematical Logic” in 1937.10 So it might seem that this joint paper was more of a flirtation with strict nominalism for Quine, a mere experiment to see how far one could get, although this might not do justice to the situation. In Of Mind and Other Matters, Goodman retrospectively reviews the situation like this: From the beginning, our formulations of the basic principles of nominalism differed. For Quine, nominalism could countenance nothing abstract but only concrete physical objects. For me, nominalism could countenance no classes, but only individuals. This difference, noted in the second paragraph of our joint paper “Steps Toward a Constructive Nominalism”, in no way affected our interest in or the value of the constructions undertaken in that paper. … Since “Steps”, Quine has somewhat reluctantly adopted the platonist’s luxuriant apparatus, while I inch along in stubborn austerity. Actually, the difference is not that marked; for Quine, given the chance, would gladly trade any platonistic construction for a nominalistic one, and I sometimes make use of platonistic constructions as a temporary expedients awaiting eventual nominalization. (MM: 50–51) We shall return to the question of why Quine stepped away from nominalism below. Here, however, we have finally arrived at a formulation of Goodman’s nominalism. He says, “Nominalism for me consists specifically in the refusal to recognize classes” (PP: 156). (N4) No classes are allowed in constructing a system of the world.11
Goodman’s nominalism Goodman also rejects many things that the typical (N1)- or (N3)nominalist rejects. Properties, for example, are often taken to be universals, and Goodman sees no room for them in a final philosophy. He mainly dislikes properties because they are intensional,12 though, and 86
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not merely because they are universals. Goodman is also generally suspicious of universals, but he does not consider this to constitue his nominalism, which only refuses to recognize classes. For Goodman, universals should generally be shaved off by Ockham’s razor. He does not consider it necessary to assume anything over and above individuals. The classes that Goodman rejects according to (N4) are sometimes taken to be universals (by Quine, for example), but probably more often they are taken to be particulars. They are, however, also quite often taken to be abstract objects. An (N3)-nominalist who believes this will, like Goodman, reject them. Goodman does not hold (N3), though; he accepts qualia as abstract universals (see Chapter 5). He is also wary of the distinction between abstract and concrete. He finds it “vague and capricious” (PP: 156).13 Without a proper definition of ‘abstract’ one would not even know what to reject. It is easy to see that this variety of nominalism is of a different quality from what we have encountered so far as (N1)–(N3). When Goodman wrote about nominalism in A Study of Qualities, he meant something like (N3), as we shall see in Chapter 5. For Goodman, from The Structure of Appearance on, ‘nominalistic’ is a predicate that applies to systems; roughly speaking, it is true of systems that do not incorporate classes or something similar to them. Put in precise terms, it is a matter of the system’s generating relation (Goodman 1958a). A system is nominalistic iff it does not generate more than one entity from exactly the same atoms. The atoms of the system are those entities from which other entities are generated and which themselves do no have any proper parts (see § “Mereology”, p. 92, for a precise characterization of ‘proper part’). A nominalist in the sense of (N4) might well accept abstract individuals as a basis for his system (in fact, Goodman does in The Structure of Appearance). What he rejects is the “undue multiplication of entities” (PP: 163). (Strictly speaking, this is not quite the same as (N4), even though Goodman seems to take it to be. We return to this later, and for now follow Goodman’s way of presenting the issue.) Goodman finds the generating relation of the theory of classes (or set theory) offensive in this way. As we mentioned above, classes contain individuals, are identified by what objects they contain, and are themselves entities. The class containing the individuals a and b is denoted {a, b}. Since {a, b} is an object itself again, we can stick it in another class, say, together with a again: {a, {a, b}}. This latter class has two members: a and {a, b}, just as {a, b} has two members, a and b. Since the members of the two classes are different, the classes are 87
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different as well, although they are generated from the same individuals. This is what Goodman objects to. Such a multiplication of entities he finds unintelligible, and hence, as he and Quine write, “unsatisfactory as a final philosophy” (PP: 173). What is acceptable to Goodman is the generating relation of the theory of parts and wholes, called ‘mereology’. If we have the two atoms a and b again, there is only one further thing that is generated from those, namely the whole that has as parts a and b.14 Further adding a to it does not make any sense: it is already a part of it. Imagine that the world contains only a banana b, which is composed of two atoms: its interior i and its skin s. Neither i nor s is taken to have any smaller parts that it is made up from, since we presuppose here that they are atoms. ‘Atom’ here is obviously not to be understood in the sense that modern physics ascribes to it, as having protons and neutrons as a nucleus with electrons whizzing around it. ‘Atom’ in our context means nothing more and nothing less than ‘thing that is not composed’ or ‘thing that does not have any proper parts’. (We shall cover mereology in more detail in § “Mereology”, p. 92.) So, if we consider s and i together, this is b. But there is no sense in adding s again to b; it is part of b already. If we form a class of s and i, though, {s, i}, this is different from the class {{s, i}, s}. Even if we wanted to identify {s, i} with b, {s, i} would still be different from {s, b}. If b is identical with {s, i}, then just exchanging the names in ‘{{s, i}, s}’ does not make any difference. And we can go on like this: {{s, i}, s} is different from {{{s, i}, s}, s}, and both are different from {{{{s, i}, s}, s}, s}, and so on. Out of the two atoms we started with, class theory generates infinitely many entities in this way. To be more precise, the atoms are not needed at all to pull off this “trick”. We already talked about the empty class being an entity as well. We can denote it with ‘{ }’ or ‘∅’; the latter is the common sign for it. Now, given what we already know, we can form the class that contains the empty class, ‘{∅}’, which is different from the empty class: It has a member (namely the empty class), but the empty class has no members. Then we can put this class into yet another class, either alone, ‘{{∅}}’, or together with the empty class, ‘{{∅}, ∅}’, and continue like this indefinitely. Voilá – we have generated infinitely many entities out of nothing! With only mereological composition, however, the number of entities that are generated from a given number of atoms is comparatively moderate. From three atoms, for example, exactly seven individuals are generated: the three atoms individually, each pair of them taken together, 88
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and all three of them together. More generally, starting out with any number n of atoms, one ends up with 2n – 1 individuals.15 Finitely many atoms, therefore, only ever give rise to finitely many individuals. Goodman’s worry about what sense it makes to inflate one’s ontology in the way the theory of classes does is what nurtures his nominalism; he finds it incomprehensible. This does not mean, of course, that he does not understand the theory of classes from a technical point of view (after all, he used it in A Study of Qualities); it does not make any sense to him from a philosophical perspective. If philosophy is meant to make sense of, for example, science (see Chapter 3), and clarify and explain things, and classes are unintelligible, then classes must not be used in the philosophical enterprise. Is this nominalism though? Classical nominalism seems to be something that is much better characterized as (N1) or (N3), but (N4) seems to be something different altogether. As one probably already expects, given Goodman’s approach to philosophy that we got to know in Chapter 3, he is not too worried about this. He defines precisely what he means by his nominalism. He takes his nominalism to be motivated by the classical worry about the “undue multiplication of entities”, that is, something like Ockham’s razor, and therefore by a position that motivated our (N2). He also takes his nominalism to be a reasonable formulation of this traditional view, and remarks, “I willingly submit this claim to Father Bocheński16 for adjunction. If he rules against me, he deprives me of nothing but a label that incites opposition” (PP: 163). Goodman’s motivation might have something to do with (N2), but (N4) does not follow from it, of course. Quine gives up his nominalism because he takes classes to be required for science, that is, his rejects (N4), but he surely holds (N2), as probably every sensible philosopher does. Quine steps away from (N4) because he takes mathematics to be indispensable for science (Quine 1960: §55).17 Roughly, his thought is that modern science is the best theory of the physical world we currently have, but it makes heavy use of mathematics and it cannot do without it. Putnam, who is on Quine’s side, states that: quantification over mathematical entities is indispensable for science, both formal and physical; therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. This type of argument stems, of course, from Quine, who has for years stressed both the indispensability of quantification over mathematical entities and the intellectual dishonesty of denying the existence of what one daily presupposes. (Putnam 1979b: 347) 89
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The theory of classes, or set theory, comes into play since it is strong enough to represent virtually any part of mathematics within it, and many mathematicians (at least whose who care about these questions) and some philosophers of mathematics in the twentieth century as well as today, would take it to be the foundation for mathematics. In the more recent debate, Quine’s and Putnam’s claim that mathematics is indispensable to science has been challenged by the next generation of nominalists. Hartry Field, for example, in 1980 published a book called Science without Numbers. In true Goodmanian spirit, he provides a construction that covers the whole of Newtonian gravitational theory without any use of numbers or classes. Admittedly, to achieve this he had to modify Goodman’s system, which we do not have space to discuss here. He still, however, sticks to (N4).18 Field’s book, Goodman and Quine’s “Steps Toward a Constructive Nominalism” and Goodman’s The Structure of Appearance have much in common. All are astounding achievements in constructing systems on a very slender basis and in particular obeying (N4), and all three went far beyond what was believed to be achievable with nominalistically acceptable means. Also, all these constructions provoked massive uproar among the platonistically minded majority of the philosophical community. Gideon Rosen and John Burgess, for instance, launched an attack on nominalism after Field published his book. One among the many points that they raised concerned the awkward, unnatural and cumbersome appearance of Field’s system, which is unsuitable for scientific practice, and will only hinder scientific research and progress (Burgess 1983: 98; Burgess & Rosen 1997). Having merely seen the very first steps of Goodman and Quine’s construction, one might be able to guess where they are coming from. Field replies that what seems awkward and unnatural largely depends on what one is used to; for someone who was only used to nominalistic techniques, mathematical theories must seem highly awkward and unnatural. He also illustrated his point as follows: As I once heard Hilary Putnam remark, you need to introduce an awful lot of definitions and an awful lot of background theory before you can formulate the laws of electromagnetism on a Tshirt. Imagine what they’d look like formulated in set theoretic terms, using ‘∈’ as the only mathematical primitive! (Field 1990: 210) Goodman, responding to the same kind of worry, reminds us that he does not want to force scientists to change what they are doing. 90
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The scientist may use platonistic class constructions, complex numbers, divination by inspection of entrails, or any claptrappery that he thinks may help him to get the results he wants. But what he produces then becomes raw material for the philosopher, whose task is to make sense of all this: to clarify, simplify, explain, interpret in understandable terms. (PP: 168) So, since Goodman takes classes to be incomprehensible and to make no sense from a philosophical point of view, the use of classes stands in the way of this task, and cannot be admitted. In this light, it seems unfair to charge Goodman with “intellectual dishonesty”. Quite the opposite seems to be the case; intellectual honesty in his unwillingness to make use of something in his philosophy that he finds incomprehensible drives Goodman to “inch along in stubborn austerity” (MM: 51). Another criticism that is often put forward against nominalism is how little can be achieved using only the limited resources that the nominalists admits. Goodman’s system, of course, is much weaker than full-blown platonistic mathematics, so, in a sense, nominalists restricting themselves to these means will never be able to use something that equals the luxurious resources of the platonist. But there is no telling how far the nominalist can go. Until Field’s advances, Quine’s contention that science is impossible without mathematics seemed obviously true. Now, there is at least a strong doubt.19 Goodman suggests that more nominalistically acceptable techniques might be found, and it might well be that all the physics that the platonist can do today will one day be available to the nominalist as well. At the very least, there is no way of showing that it is impossible. On the flipside, the platonist has no guarantee either, that all of future physics can be done with the mathematics available today (e.g. PP: 167; MM: 51).20 One thing especially puzzles Goodman concerning the platonistic criticism of the nominalist’s efforts: every method used by the nominalist is acceptable by the platonist’s light; everything the nominalist does, the platonists do as well, or at least they could do it. The progress is slower (which might partly be because far fewer people are working within a nominalistic framework), but when “the nominalist and the platonist say au revoir, only the nominalist can be counted on to comply with the familiar parting admonition they may exchange: ‘Don’t do anything I wouldn’t do’” (PP: 171). The advantage of a nominalistic system is, as Goodman points out in the original preface to The Structure of Appearance, that any nominalistic system 91
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can straightforwardly be turned into a platonistic one without any problems. The reverse, though, is not the case.21 On purely methodological grounds, he takes nominalistic systems therefore to be preferable to platonistic ones.
Mereology Around 1930, together with Henry Leonard, Goodman developed the system called the ‘calculus of individuals’. Leonard used some of their results in his PhD thesis, Singular Terms (1930), which was probably also influenced by Whitehead’s views on this matter, Whitehead being Leonard’s supervisor.22 In 1936 Leonard and Goodman read a paper presenting the system before the Association of Symbolic Logic, and it was published in 1940 (Elgin 1997a). The calculus of individuals is a mereological system. In slightly altered (but equivalent) form, Goodman later used it for his construction in A Study of Qualities and The Structure of Appearance. The calculus of individuals was originally developed by Leonard and Goodman in order to solve some technical problems dealt with in Leonard’s Singular Terms and Goodman’s A Study of Qualities. It was meant as a supplement to the calculus of classes, rather than as a replacement of it.23 The calculus only later becomes important for Goodman in his nominalist programme and his rejection of classes. It turns out that the calculus of individuals actually suffices to carry out Goodman’s construction in The Structure of Appearance; the calculus of classes is not needed. The constructions using the calculus of individuals also satisfy Goodman’s demands for an acceptable explication, as presented in Chapter 3, whereas the “unintelligible” classes do not. In this chapter we shall discuss Goodman’s later nominalist attitude towards the calculus of individuals. We shall return to the technical advantages of the calculus for the constructions of A Study of Qualities and The Structure of Appearance in Chapter 5. Leonard’s and Goodman’s system was not entirely new, however. Quine, who learnt of Leonard and Goodman’s project in 1935 noticed an independent predecessor (Quine 1985: 122). The Polish logician Stanisław Leśniewski (1886–1939) developed the first formal mereological systems, and published his first results in 1916. Later Tarski, who was Leśniewski’s student, presented mereological systems as well, which were based on modern predicate logic rather than on Leśniewski’s term logic.24 92
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Leśniewski’s system struck Leonard and Goodman as “rather inaccessible”, lacking many definitions that they wanted to make use of, and “set forth in the language of an unfamiliar doctrine” (Elgin 1997a: 130). However, all these systems – Leśniewski’s, Tarski’s, Leonard and Goodman’s, and Goodman’s later system – are equivalent. They can be translated into each other, and the same sentences are theorems according to them in the respective translations.25 Leonard and Goodman remarked on this, without proof, in their 1940 publication. We shall present the basics of Goodman’s calculus of individuals from The Structure of Appearance. Above, where we described the construction of “Steps Toward a Constructive Nominalism”, we noted the enormous generosity of Goodman and Quine concerning predicates; basically, anything of the right grammatical category that applies to individuals will do. In The Structure of Appearance, Goodman is yet more explicit about this. A nominalistic language may even contain “platonistic-sounding” predicates, such as ‘belongs to some class satisfying the function F ’. The nominalist does not acknowledge classes and functions by allowing for such a predicate. The predicate is a string of words that cannot be broken down into its components, since the words of the predicate are not separable units of the language. The only restriction on predicates is that they have to be predicates of individuals. The choice of predicates “will be governed not by demands of nominalism, but by such general considerations as clarity and economy” (SA: 27). For his version of the calculus of individuals, Goodman uses a very economical choice (i.e. one made according to simplicity considerations) of predicates indeed: he has only one primitive predicate. An expression is said to be primitive in a system iff it is not defined in that system. This primitive (two-place) predicate of his system is ‘overlaps’. (In the Leonard–Goodman version of the calculus, incidentally, the system was built on the notion of discreteness, which will be defined in the The Structure of Appearance calculus later on the basis of overlapping.) Goodman uses the symbol ‘o’ for ‘overlaps’ in the formalism. He informally glosses what the predicate is intended to mean as: “Two individuals overlap if they have some common content, whether or not either is wholly contained in the other” (SA: 34). The first thing that can be said more formally about overlapping is that in all and only those cases where two individuals x and y overlap, there is an individual z such that whatever overlaps with z also overlaps with x and y. x o y ≡ ∃z∀w(w o z ⊃ (w o x ∧ w o y))
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It is easiest to imagine this with a spatial example. If two regions in space overlap, then there is a region that is wholly contained in both of them; namely in that region where the overlap occurs. Whatever overlaps with that region, has to overlap the two original ones as well (you can try to draw a two-dimensional picture of this). It is easy to see that this still holds when one of the two regions is wholly contained in the other one (like Scotland in the United Kingdom), or even when the regions are identical. With the help of ‘overlaps’, ‘is discrete from’ can easily be defined as well. Two individuals are discrete iff they do not overlap. (Had we started with ‘is discrete from’, we could have just run the definition in the other direction.) x ∫ y =df ¬ x o y We can also define what a part is, which is vital, of course, since we want to end up with a mereology, that is, a theory of parts and wholes. So, x is a part of y iff everything that overlaps with x also overlaps with y. x < y =df ∀z(z o x ⊃ z o y) This does not yet rule out the identity of the individuals. In other words, on this definition of ‘is part of’, everything is a part of itself (‘∀x (x < x)’). It might be useful for some purposes, though, to have a notion of ‘is part of’ available, where if x is a part of y then they are not identical. This can easily be defined from ‘<’, by saying that x is a proper part of y iff x is a part of y, but y is not a part of x. x << y =df x < y ∧ ¬ y < x We shall see in Chapter 5 how important the predicate ‘is part of’ is for Goodman, and how he puts it to use. We have already come across this predicate in this chapter: the banana b, we talked about above, has three parts, namely its skin s, its interior i and b itself, but only s and i are proper parts of b. Goodman does not take the identity, ‘=’, of individuals as primitive, as is usually done in first-order predicate logic. He defines it in terms of overlap as well: x and y are identical iff they overlap with exactly the same individuals. x = y =df ∀z(z o x ≡ z o y) It is important not to confuse ‘=’, the symbol for identity in the system, with the metatheoretical ‘=df’. The latter merely indicates that 94
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the expression on the left-hand side is an abbreviation of the expression on the right-hand side. (We discussed definitions in detail in Chapter 3.) Very important for Goodman’s project are so-called ‘mereological sums’ (‘sums’, for the sake of brevity). Our banana b, for instance, is the sum of s and i. Generally, the “sum of two individuals is that individual which exactly and completely exhausts both” (SA: 36). That means that all the parts of x and y are parts of their sum, which is pretty much what one would expect. We cannot say, however, that the sum of x and y has only those individuals as parts that are either parts of x or y. This might seem strange, at first, but the reason for it is straightforward. Consider seven individuals, a, b, c, d, e, f and g. Say, c is the sum of a and b, f is the sum of d and e, and g is the sum of c and f. Now, clearly, a is a part of g, since it is a part of c, and d is a part of g, since it is a part of f; since c and f make up g, everything that is part of either c or f is part of g. Here is the problem, however: the sum of a and d is part of g as well, since a and d are, but this sum is a part of neither c nor f. Think of the sum of two countries, say, England and Scotland. Edinburgh is part of Scotland, and London is part of England. Each of the cities is a part of the sum of England and Scotland, but the sum of both cities is neither part of England (since Edinburgh is not part of England), nor of Scotland (since London is not part of Scotland). We can, however, define the sum of two individuals as that individual that overlaps exactly those that overlap at least one of the two to get the desired result. (You can also play that through with Scotland and England, if you like.) x + y =df ı z[∀w(w o z ≡ (w o x ∨ w o y))] (The operator ‘ı’ abbreviates a definite description. Read ‘ız’ as ‘the z, that is such that’, meaning that there is one, and only one, such thing.) It follows from this definition that every two individuals have a sum, and that this sum is unique. The latter reflects what was introduced above in an informal way. The generating relation of the calculus of individuals is mereological summation: all individuals that are not atoms of the system are sums of individuals, and ultimately composed of their atoms.26 The system is nominalistic in the way defined by Goodman, since it is not possible to “generate” two distinct entities out of the same atoms. This follows from the sum of two individuals being unique. So, here we have encountered Goodman’s formal and precise way to cash out this demand. 95
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∀x∀y∃z∀v (x + y = v ≡ z = v) Reflecting on mereological summation, one might come up with an apparently odd feature: Absolutely any two individuals have a sum, which is an individual itself again. This way, we get the individual that is the sum of the Moon and Buckingham Palace, for example; and the individual that is the sum of that and the present First Minister of Scotland; and your left big toe, if you wish (and, in fact, even if you do not). The principle that any individuals whatsoever have a sum is often called unrestricted composition today. Its getting a name is a good indication that rival views to it exist. Criticism has been raised that having all these sums around is blowing up the ontology too much. Or one might find it disturbing that these sums with widely dispersed parts, which are individuals according to Goodman, have seemingly nothing to do with our ordinary conception of an object. By now we know Goodman’s attitude towards these sorts of objection well enough to expect that he is left unmoved by such criticism. ‘Individual’ is a technical term in Goodman’s system, and as such he can define it as he pleases. The mistake is to try to equate this technical term with some everyday language concept. Goodmanian individuals go far beyond what are ordinarily called ‘things’ or ‘objects’. Those ordinary-language predicates probably vaguely apply to medium-sized dry goods: chairs, umbrellas, pins, houses, cars and the like. Mereological sums of individuals, on the other hand, can be widely scattered across the universe without any intuitively unifying feature. Every ordinary object seems to be a Goodmanian individual, or at least capable of being one, given the right basis of the system. The converse, however, is not the case; not every Goodmanian individual is an ordinary object. It is important to keep in mind that mereological sums are not “extra” entities in any sense. They are nothing over and above their parts. The sum of Mars and Edinburgh Castle, for example, is not a new and strange thing. There is nothing particularly strange about Mars, nor about Edinburgh Castle. If we are okay with these two things the mereological sum of them should not bother us; it just is those two, taken as one. If you have an apple, you also have the lower and the upper half of it. You do not, however, have in addition to these two halves the whole apple. You just have one apple, not the two halves and a whole one, which suspiciously sounds as though you have two in total.27 Goodman’s generosity regarding mereological sums mirrors his attitude towards predicates, which we have already encountered: let 96
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us have them all! To rule out some sums from the start might leave us with a notion that is not wide enough to cover all the cases we need to cover. It might restrict our resources too far. More restricted notions can always be defined later, but only if the wide notion is available. Think of the definition of ‘proper part’ on the basis of ‘part’; the reverse definition is not generally available. As a reply to Quine, who brings up similar issues (Quine 1951b: 559), Goodman additionally mentions that this complaint, as put forward by a platonist, backfires anyway. However our imagination is burdened by mereological sums, class formation must fare even worse. Whatever individuals can be summed by mereological means can just as well be put together in a class according to class theory. And, as we have seen above, class theory goes even further. Criticism of unrestricted mereological summation does not, however, have to come from platonistically minded philosophers. Peter Simons (1987: 1 and throughout), for example, is wary of being too generous with mereological sums, too, while he certainly cannot be accused of being a platonist. There are, however, attempts being made to recover something that more closely resembles the ordinary notion of an object, or at least a philosophically informed one (since the vagaries of pre-systematic natural language make it difficult to figure out what the “ordinary notion” of an object might be). One idea is to introduce a second primitive two-place predicate ‘inner part’ into the language. With its help, and some clever definitions, those sums can be singled out that have a common border, that is, those that are not scattered.28 Moreover, since Goodman wrote about this, non-extensional mereologies have been thought up. These systems do not have the uniqueness of the mereological sum as a feature. Two distinct entities, say, c1 and c2, where c1 ≠ c2, can be composed from the same atoms. Here it becomes clear, how, strictly speaking, (N4) comes apart from Goodman’s spelling out of his nominalism in terms of the generating relation and his sameness-of-content criterion. The generating relation in a non-extensional mereology violates the content criterion, but does not make use of classes (at least not on the face of it; maybe non-extensional mereology is set theory in sheep’s clothing). Such a system would be unacceptable to Goodman too. Goodman’s framework recognizes only systems that have his own construal of mereological summation or class formation, or both, as generating relations.29 (David Lewis (1991: 38–41) complained about this fact; his criticism is discussed in § “Logic and mereology”, p. 218.) All three cases Goodman 97
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considers (classical mereology, set theory and the mixed case) are extensional, and, as he stresses in Ways of Worldmaking, extensionality is the only thing that he really holds as sacrosanct (we return to that in Chapter 8). Let us briefly return to the topic of this section before we end the chapter. Goodman proceeds from the point where we left the calculus of individuals above to define more notions on the basis of ‘overlaps’. He then uses those defined predicates in his construction of The Structure of Appearance that we introduce in Chapter 5. We shall not develop the full system here, since this would take up too much space. The first steps we took should suffice, though, to give a good impression of the rigorous and precise construction Goodman develops.
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Now that we have introduced some of the formal machinery that Goodman developed to approach philosophical problems, we are almost ready to understand his chief work. A Study of Qualities, which was first published in revised form as The Structure of Appearance, is certainly the most difficult piece Goodman ever wrote. It is full of technical subtleties and philosophically relevant observations. To understand its significance, however, we first have to look back at the philosophical context in which it was developed. We have emphasized in the previous chapters that Goodman’s work is best understood as situated within a certain branch of analytic philosophy, departing from Frege’s conception of ideal-language philosophy. Goodman’s 1941 dissertation A Study of Qualities is in large part a thorough analysis and further elaboration of the work of Carnap, his most famous predecessor in this tradition. Therefore we shall first characterize Carnap’s project in the Aufbau ([1928] 1961). Although Goodman’s work is usually classified as being an anti-foundationalist version of Carnap’s project,1 Carnap and Goodman in fact agreed on many more issues than is usually recognized. In fact, the main characteristics2 of Carnap’s philosophy of the 1930s also characterize Goodman’s philosophy: ● the methodological outlook of constructionalism; ● an anti-foundationalist epistemology; ● the emphasis on multiple systems and starting-points adequate
to their respective purposes (i.e. methodological and ontological pluralism); ● the view that what are often taken as “ultimate” metaphysical questions are pointless except when relativized to a system (i.e. metaphysical and ontological relativism). 99
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As we indicated in Chapter 4, Goodman was well acquainted with Carnap’s work of that time. As early as 1935 he was attending Quine’s lecture on Carnap’s The Logical Syntax of Language ([1934] 1937). Even if it were not necessary for the historical explanation of Goodman’s work, in order to assess Goodman’s achievements we have first to see what Carnap had already accomplished.3
The Aufbau In 1903 Russell and Whitehead joined forces to work on a project that had been in the air since Frege’s Begriffsschrift (1879), and was extended, but not yet carried to completion, in Frege’s The Foundations of Arithmetic ([1884] 1950) and The Basic Laws of Arithmetic ([1893–1903] forthcoming). The project was called ‘logicism’, and its ultimate aim was the reduction of mathematics to logic. Frege’s early attempt to achieve that goal was defeated by Russell’s paradox in 1902.4 In Frege’s logic it was possible to define a class5 by quantifying over a totality of classes that included the class being defined. This made it possible to define, for example, the class of all classes. The class of all teacups does not have itself as a member; it has teacups, but not classes as members. However, the class of all non-teacups has as members all things that are not teacups. Classes are not teacups, and so the class of all non-teacups is not a teacup. Therefore, for the class of all non-teacups to contain everything that is not a teacup, it has to contain itself. Equally, the class of all classes is itself a class and thus contains itself. However, this also made it possible to define what has come to be called the “Russell class”. This class, R, contains all classes that do not contain themselves. Now, what about R? Does it contain itself? If it does contain itself, it should not belong to the class of classes that do not contain themselves. So, by definition, it should not contain itself. But if it does not contain itself it is a class that does not contain itself and should therefore be contained in itself by definition. So the definability of the Russell class leads to a contradiction. The theory of types that Russell developed in his “Mathematical Logic as Based on the Theory of Types” (1908), on which the system of Principia Mathematica is built, was designed to solve this problem. All classes in this theory belong to a certain type, and these types are ordered hierarchically. It is only possible for a class to have elements 100
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that are of a type lower than that of the class itself. Given such a hierarchy of types, the definition of a class could not range over all classes including itself. Avoiding Russell’s paradox gave logicism a certain structure. Given that when defining a class in Russell’s system we can always only appeal to the elements of a lower level, the reconstruction of mathematics gives rise to a hierarchy. In addition, Whitehead had started to provide a method of logical construction, the so-called “method of extensive abstraction”, by which philosophically dubious entities (such as properties or geometrical points6) could be abstracted from unproblematic concrete entities, thereby providing a method appropriate to reductive analyses. In Our Knowledge of the External World, Russell, taking the case of points, explains the problem: The space of geometry and physics consists of an infinite number of points, but no one has ever seen or touched a point. If there are points in sensible space, they must be an inference. It is not easy to see any way in which, as independent entities, they could be validly inferred from the data; thus here again, we shall have, if possible, to find some logical construction, some complex assemblage of immediately given objects, which will have the geometrical properties required of points. … Exactly how this is to be done I do not yet know, but it seems fairly certain that it can be done. ([1914] 1969: 119) The reason for Russell’s optimism “that it can be done” was Whitehead’s apparent success in abstracting points from classes of physical volumes. Although this does not provide a complete reduction of points to sense data, it comes quite close. The next question is whether the objects of physics could be constructed from experiences. The physical “objects” construed from sense data need not be given an independent ontological status, and thus such a construction of physical objects might properly be viewed as a reduction to sense data. Russell enthusiastically advertised this idea in Our Knowledge of the External World: [Whitehead’s method of abstraction] clears away incredible accumulations of metaphysical lumber …. When a group of objects have that kind of similarity which we are inclined to attribute to possession of a common quality, the [method of extensive abstraction] shows that membership of the group will serve all purposes of the supposed common quality, and that therefore, unless some 101
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common quality is known, the group or class of similar objects may be used to replace the common quality, which need not be assumed to exist. (Ibid.: 51) Russell then sketched how concrete physical objects might be constructed from phenomenal experiences, how instants of time might be abstracted from overlapping events and so on. Carnap’s Aufbau is in part the adoption of this programme for the purposes of epistemology, and is traditionally, although not quite correctly, considered a work of reductive empiricism.7 According to the principles of empiricism, sensory experience is the only source of knowledge and consequently all our knowledge is reducible to the given, the sensory experiences. The traditional interpretation reads the Aufbau as providing exactly such a reduction, in accordance with Russell’s doctrine that “[t]he supreme maxim in scientific philosophizing is this: Wherever possible, logical constructions are to be substituted for inferred entities” (Russell [1914] 1986: 11). This reading was prominently promoted by Quine, which might well be the reason for the similarities in later interpretations of the Aufbau. To interpret Carnap’s work in this way is not completely unreasonable, as the above quote of Russell’s was chosen by Carnap as the epigraph for the book. In addition, Carnap refers to Russell frequently at the start of the Aufbau, he adopts Whitehead’s method of extensive abstraction, and he draws connections between his work and Russell and Whitehead’s logicist reduction of mathematics.8 However, in recent years it has been emphasized by many scholars that the important new aspect of Carnap’s Aufbau was really its use of modern logic and the theory of relations. For Carnap, a constitutional system that is straightforwardly built on elementary experiences (we define ‘constitutional system’ properly a bit further below) was not the principle aim of the work; his aim was rather to show in general how logic and mathematics can be used for such a construction. Carnap’s presupposition was that scientific statements are really statements about structure; otherwise science could not be objective. Carnap thought that all reference to the material or concrete was, after all, subjective. To see this, note that our experience when making a scientific observation is private. We cannot compare the experience we have during the observation with the experience had by another scientist. Each person’s experience is unique and subjective. What we can do, however, is agree (or disagree) on structural relations between such experiences. Imagine carrying out a chemical experiment during which a liquid suddenly turns a certain colour. The 102
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qualitative phenomenal state you are in when experiencing this colour is, first of all, something private and ineffable. You cannot communicate to others exactly what it is like to experience the exact colour you experience. What you can communicate, however, is whether this colour is the same as that colour (pointing to a specific colour on a colour chart) or whether it is brighter or darker; you can talk about relations between such experiences and thus talk about structural aspects in an objective way. For science it is therefore possible and necessary to talk only about structure (Aufbau: §16). But if all scientific statements are really all about structure, contrary to our prima facie understanding, then they all must be translatable without loss into statements that obviously are only about structure. How is such a transformation achieved? Carnap draws an analogy to a railway map. The stations on a railway map are usually labelled with names. This is unnecessary, however. It would be more than sufficient to identify the stations via their structural role on the map. Instead of ‘In der Krim’9 (at the centre of Figure 5.1), the structural description might identify this junction as ‘2-line T-junction which is one junction away from a 4-line T-junction and two 1-line junctions’. If this definition does not suffice to identify the point in question we can add more information about that junction’s structural relationships. It seems that we can identify any point by its structural relations, as long as there is enough information provided by the map. If this part of the map does not suffice to
Figure 5.1 Partial map of the public transport system of Ronsdorf (Wuppertal, Germany).10
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tell two points apart, we could turn to the larger map of all Ronsdorf, or all Wuppertal, or the whole region. If we adopt this programme, all scientific statements are assumed to be translatable into structural descriptions. If a difference cannot be captured in this way, that is, if a difference cannot be translated into a structural difference (given all the information that science can offer), this difference is not objective. The translatability thesis by Carnap thus works like a demarcation criterion. Only those statements that are translatable into structural statements are considered scientific statements. A constitutional system in Carnap’s sense is a stage-by-stage ordering of objects such that the objects at a certain stage are constituted by the objects of a lower stage. Due to the transitivity of the constitution relation, all objects of the system are constituted from the objects of the first stage or level, the so-called “basis” of the system. As an example of such a constitutional system, Carnap considers the system of arithmetic concepts. In this system, all kinds of numbers – rational, real and so on – are constituted from the natural numbers, as pairs of natural numbers, equivalence classes of such pairs of natural numbers, and so on. This way all statements about the objects of arithmetic can be reformulated into statements about the basic objects: the natural numbers. This example also shows that a constitutional system need not mimic the actual process of knowledge acquisition. Few people have real numbers psychologically represented as Dedekind cuts (the name of one such construction of the real numbers). A constitutional system is a rational reconstruction of our intuitive constitution of the world. It operates with fictitious assumptions and idealizations, which need not have counterparts in actual processes. One such fiction is “the given”. That Carnap did not naively consider it an unproblematic basis of knowledge becomes clear from the fact that he also offered other possible bases (see Mormann 2000: 89–90). Such idealizations are not true or false, but are – in Goodman’s sense – more or less “right”, that is, more or less pragmatically justified. They have to be idealized to keep the constitutional definitions as clear as possible; if they serve this purpose they are “right”. Thus, there are two general points about constitutional systems that we should keep in mind: ● Constitutional systems are rational reconstructions. That is,
they are undertaken after science is already done, so to speak, but do not try to build up a system of scientific knowledge independent of science.11 104
From Vienna Station to Boston Terminus ● Constitutional systems are rational reconstructions. They do
not aim to match the actual genesis of our knowledge. A constitutional system operates with idealizations and simplifications and is not affected by criticism that merely highlights that “really” the acquisition of knowledge proceeds differently.12 After these general remarks, we now turn to examine the details of Carnap’s Aufbau.
The basis in the Aufbau The first problem in giving such a constitutional system is to select its basic constituents. Although this selection is a matter of convention, it is not arbitrary. The limits of choice were – according to Carnap – set by positivism and transcendental idealism. Positivism claimed that the sole material of knowledge is the experiential given, whereas idealism emphasized correctly that we need a system of order and basic relations to get the system of knowledge off the ground.13 As we have already indicated, the problem of choosing a basis for a constitutional system involves two sub-problems. The first is finding the basic objects and the second is finding the relations that can hold between these objects in order to build up from those basic objects. In set-theoretic terms, the basis chosen must be a structured set, a relational system. Carnap favours for his constitutional system a system that is built in (loose)14 accordance with the actual process of knowledge acquisition. This is why his stages of constituted objects, the different levels of the system, are ordered with respect to their epistemic primacy. That means that concepts such as ‘red’ and ‘hard’ appear on a lower level than concepts such as ‘energy potential’ or ‘conducts electricity’. Carnap chooses as his main example a constitutional system that has a solipsistic base. Since this base is the only one he considers in detail, later interpreters have taken the Aufbau to concern only that system.15 It seems clear, however, that Carnap’s system is not phenomenalistic in the traditional sense as so many authors have claimed.16 Phenomenalism, as for example in the writings of Ernst Mach (as in his [1922] 1991), starts from sense data, treating “phenomena” as basic. In Carnap’s sense such phenomena are not epistemically primary. Sense data are abstractions from unstructured elementary experiences and occur in a later stage of the constitutional system. Carnap’s basis (following the Gestalt-psychologists 105
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of his time) comprises elementary experiences (“erlebs”, as Goodman later called them, abbreviating the German “Elementarerlebnisse”), which are time slices of the total stream of experiences of the constituting subject. These erlebs are primitives within the system. In addition, Carnap needs a basic relation among these primitives. Carnap’s choice of a basic relation, ‘recollection of similarity’, Rs, is also motivated by Gestalt-psychological considerations and the intention to keep the constitutional system as simple as possible (see Mormann 2000: 94; 2003). Rs is characterized as follows: elementary experiences x and y of some individual stand in the relation Rs iff x and y are elementary experiences that are judged as partially similar by the individual on the basis of a comparison of the recollection of x with y, that is, they are almost identical with respect to some experiential part. The relation of part-identity, Pi, is defined on Rs. Pi is reflexive and symmetric, but not transitive (we will use Pi in our examples below (for convenience’s sake); Carnap does not use Pi for his actual constructions). Although all the systems that Carnap considers in the Aufbau have such a simple similarity relation as their basic relation, other basic relations are conceivable (Aufbau: §104), and later Carnap thought that a system with more than just one basic relation would be more capable (Stadler 1997: 298; Carnap in Schilpp 1963: 947). After the basis is chosen, the problem becomes constructing all other objects from this basis alone. Of course, the problem is that in the system the basic elements are primitive, that is, they do not have any properties to which we could appeal for the constitution of the next stage. The most important achievement of the Aufbau was to have demonstrated in detail how enough information can be distilled from a set of property-lacking, atomic elements to start the process of constitution for objects of higher order. Carnap achieved this by the method of quasi-analysis, to which we now turn.
Carnap’s quasi-analysis Carnap probably derived his method of quasi-analysis from Whitehead’s method of extensive abstraction, which the latter had used for the constitution of geometric objects (briefly discussed in Chapter 3), having learnt about it from Russell’s presentation.17 For Carnap the method of quasi-analysis is the method for the constitution of scientific objects in general. Whereas Whitehead was concerned with abstract 106
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objects only, Carnap adopted the method of constitution for all nonbasic entities. “Quasi”-objects are in no way less real than other objects. An object is a quasi-object iff it is constituted via quasi-analysis from the basic elements. ‘Quasi’ thus denotes a logical status. In Carnap’s terms, all “real objects are quasi-objects” (Aufbau: §52). (Again, this is a statement that is rather alien to any classical form of empiricism, but should sound familiar given what was said about Whitehead’s ontological pluralism in § “The historical background”, p. 12.) To see how this programme is meant to function, we start with an example of proper analysis. As we have said, the primitive objects are erlebs: elementary experiences. Such erlebs are time slices of the whole stream of experience of the constituting individual. Our constituting individual is Paula. Paula has only very limited visual experiences (and only visual experiences, to keep the example simple). In particular, her visual field consists of simple “coloured” areas; these are her erlebs. However, Paula has no colour concepts to begin with; all she has are erlebs and the recollection of similarity relation, Rs. We assume that Paula has only a crudely working visual system and that the erlebs she has collected after an exciting afternoon among black, white and grey coloured objects are the following:
Let us use A to F to name the six different erlebs, represented by the boxes above, We know that for Paula these erlebs are all primitive, that is, erlebs are, at this point, merely different wholes. Paula has no concept of colour that she could use to classify them, nor does she even notice that the erlebs have any properties. What is given to her instead is a relational ordering of the erlebs. For simplicity, we shall use the relation of part identity, Pi. Two erlebs are related by Pi if they have some quality in common.18 If we order Paula’s erlebs in this way, we obtain the following set of ordered pairs: {
, , , , , , , , , , , , , , 107
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, , , <E, A>, <E, E>, <E, F>, , , , , , } This is all the information Paula has. She knows which erlebs are distinct (indicated by the different letters) and how they are related according to Pi. This relation between her erlebs could also be represented as a graph, thereby keeping the analogy to Carnap’s railway map. Such a graph for Paula’s erlebs would look like this:
Here we have represented each pair of Paula’s distinct Pi related erlebs as directly connected by a straight line (and those not Pi related are unconnected).19 Given these part identities, she can now single out those classes of erlebs that are all pairwise Pi related and for which there is no erleb outside the class that is Pi related with each erleb in the class. This will give Paula the following classes: {A, B, C, F}, {A, E, F}, {C, D, F} But these are just the classes of (partially) black, white and grey erlebs. Hence, although Paula had no information about the colour of the erlebs and no notion of their parts and so on, but only an extensional ordering by Rs to begin with, she was able to retrieve the complete colour information. The “parts” the erlebs have in common are “quasi-parts” because the erlebs were originally given as primitives. However, we have now ordered them as if they had parts and as if they had properties. The quasi-properties “white”, “grey” and “black” are now our second-order objects. This is the first step in constituting the world from nothing but similarity ordered primitives. Given these second-order objects, it is now conceivable how Paula could proceed. She could again order them with a similarity relation of second order and thereby constitute third-order objects. Carnap provides such a constitution only for the very first steps of a constitutional system, constituting the quasi-properties and relations of 108
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quasi-properties. He then claims that all scientific objects and properties are retrievable that way. A presupposition of Carnap’s constitution idea is that such quasianalytically constituted properties and relations are fully determined by their extension. All intensional differences are deemed scientifically irrelevant by the Carnap of the Aufbau. But note that intuitively distinct and scientifically respectable properties such as ‘is an organism with kidneys’ and ‘is an organism with a heart’ could have the same extension, and could have these even nomically so. We shall later return to study this observation in some detail.
The upper levels The overall plan of the Aufbau is to constitute the world in three phases: ● Lower levels: autopsychological objects (phenomenal qualities) ● Middle levels: physical objects and their properties ● Upper levels: psychological objects (other minds) and cultural
objects A detailed constitution is only provided for the first steps of the lower levels; all other constitutions are merely sketched. At the lower levels, we have seen that Carnap started with the erlebs of one individual. The quasi-parts of these erlebs are then interpreted as qualities. After that, a similarity relation between qualities can be defined: two qualities Q and Q ′ are similar iff every erleb of Q is similar to every erleb of Q ′ and vice versa. This way we can obtain the different senses. Two qualities Q and Q ′ belong to the same sense class iff there is a chain of similarities (a chain of pairwise similar qualities) such that the first element of the chain is Q and the last Q ′. Every colour can, by gradual changes, be transformed into every other colour, but a colour cannot by gradual changes be turned into a sound. Sounds, however, are quasi-parts of erlebs just as colours are. Now, within such a sense-class we can structure the qualities. For example, we can characterize the sense “sight” as a five-dimensional space: every colour is defined by the three dimensions of the colour solid, namely, hue, saturation, and brightness and the two (spatial) dimensions of the visual field. Accordingly, we can constitute all autopsychological objects, all perceptions of the constituting individual. The constitution of the 109
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autopsychological objects is the constitution of an individual, multidimensional state space in which for every point of spacetime there is a vector that describes the experience of the constituting individual at that point (Richardson 1998; Mormann 2000). Of course, this multidimensional space is an entirely subjective entity. It constitutes the solipsistic world of one single individual. How can all these multidimensional spaces, one for each individual, be brought together to make possible one intersubjective, common physical world? For this step Carnap introduces a new method of constitution, which is prima facie alien to the idea of quasi-analysis. He postulates a mapping between the solipsistic space and the objective physical world, expressed by statements of the form ‘Quality q is at spacetime point (x, y, z, t)’. As Quine ([1951c] 1961: 40) and others have emphasized, this is incompatible with the project to build up the world only from sense data (or erlebs, for that matter) with the help of logical and mathematical constructions. Such a mere mapping of qualities to points of spacetime cannot belong to a quasi-analytic constitution.20 However, as we have indicated repeatedly, it is not completely clear that Carnap was really attempting to realize Russell’s programme as sketched in Our Knowledge of the External World.21 The constitution of the third phase is only sketched by Carnap. The world is not only objective in the sense that it is independent of our subjective world (this much is achieved by the second phase), but it is objective in the sense that it is intersubjective: a world that many individuals can participate in. Carnap tried to represent this intersubjectivity by constituting the world of the other minds within the solipsistic world. Paula, for example, has her autopsychological world represented by her five-dimensional state space. This she maps onto the four-dimensional physical space and thereby constitutes the physical world. Now the autopsychological world of her friend Peter is the five-dimensional state space of Peter, and Peter constitutes the physical world by mapping it onto physical space as well. However, the intersubjective world of Peter and Paula is a construction within the worlds of Peter and Paula. Paula constitutes Peter’s world within her world and vice versa. If in Paula’s system ‘Quasi-object a has quasi-property Q’ is a truth, and ‘Quasi-object a* has quasi-property Q*’ is a truth of Peter’s system, there is an intersubjective mapping between a and a* and Q and Q* such that the conjunction of these sentences is intersubjectively true for Peter and Paula.22 The Aufbau is a very important work. It marks Carnap’s transition from neo-Kantianism to logical empiricism (Cirera 1994; Coffa 1991). 110
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We have already noted several problems with it which make it hard to assess whether Carnap succeeded in what he was trying to do. So far we have presented it from a modern perspective, reading Carnap in a more neo-Kantian way than his immediate contemporaries might have done. We shall have to see whether Goodman would agree with our reading. But before we turn to Goodman’s interpretation and the continuation of Carnap’s programme, we first have to emphasize a few more themes from Carnap that might well have influenced Goodman’s thesis.
Themes from Carnap Three important themes from Carnap that shaped Goodman’s philosophy should be emphasized in the light of what we have discussed thus far. We have seen that Carnap is rather tolerant when it comes to the question: which is the right basis for the Aufbau? Although there are some constraints on what can or should be used as a basis, the decision to choose erlebs does not seem an entirely principled one. This kind of relativity concerns the basic elements of scientific knowledge. What we consider as “the given” is more or less unimportant. It is in any case only a fiction that we use, an idealization; how good it is to use one basis rather than another is a question of how clear our constitutive definitions will turn out to be. Beyond this tolerance with respect to the basic elements of the constitutional system, Carnap later began to stress tolerance with respect to the logics involved in the rational reconstruction. If you consider logical and mathematical truths as uninformative, as the logical positivists did, or as nonampliative (which means that deductive consequences can never transcend the content of the premises), it should not matter which logic you use in the rational reconstruction. Since choosing a certain conventional system will not add any truth nor require any truth to be revised, it simply does not affect the rational reconstruction.23 Again, which logic is used is a matter of taste and functionality. This was expressed in Carnap’s famous principle of tolerance: Principle of Tolerance: It is not our business to set up prohibitions, but to arrive at conventions. … In logic, there are no morals. Everyone is at liberty to build up his own logic, i.e. his own form of language, as he wishes. All that is required of him is that, if he 111
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wishes to discuss it, he must state his methods clearly, and give syntactical rules instead of philosophical arguments. (Carnap 1937: 51–2) Finally, all questions of ontology are relative to the framework you adopt. Ontological questions are meaningless if asked without qualification. They must be relativized to a specific framework and, within that framework, such questions are trivial. For example, the question whether there are numbers is meaningless, whereas the question whether there are numbers in arithmetic is meaningful, but trivial: of course there are. This implies a certain tolerance towards the basic elements of reality. In his later paper “Empiricism, Semantics, and Ontology”, Carnap expressed it thus: The acceptance or rejection of abstract linguistic forms, just as the acceptance or rejection of any other linguistic forms in any branch of science, will finally be decided by their efficiency as instruments, the ratio of the results achieved to the amount and complexity of the efforts required. To decree dogmatic prohibitions of certain linguistic forms instead of testing them by their success or failure in practical use, is worse than futile; it is positively harmful because it may obstruct scientific progress. The history of science shows examples of such prohibitions based on prejudices deriving from religious, mythological, metaphysical, or other irrational sources, which slowed up the developments for shorter or longer periods of time. Let us learn from the lessons of history. Let us grant to those who work in any special field of investigation the freedom to use any form of expression which seems useful to them; the work in the field will sooner or later lead to the elimination of those forms which have no useful function. Let us be cautious in making assertions and critical in examining them, but tolerant in permitting linguistic forms. ([1950] 1956: 221, original emphasis) As we shall see, this tolerance of Carnap’s is even broader than Goodman’s. Whereas Goodman renounces platonistic methods of construction, Carnap argues (in the paper just quoted) that platonistic methods (in particular the postulation of such abstract entities as classes or meanings) do not carry problematic ontological commitments that could speak against their usability. What should also be stressed is Carnap’s early conventionalism with respect to the empirical basis. As we have seen, Carnap did not 112
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think that the phenomenal basis is an unproblematic starting-point for knowledge. The protocol sentence debate (with Neurath and Popper) further convinced him that there is nothing like the “pure” and innocent given on which our knowledge could be based.24 A protocol sentence (an observation report that can stand in logical relation to scientific theories) is, in all cases, already theory laden; thus there is no pure given with which the scientific theories could be compared, and that would, in the end, serve to justify their acceptance. Carnap was convinced that we accept protocol sentences by decree and luckily manage to agree on most of them. If one day we failed to agree on all or even many of our observational reports, science would become impossible. Unfortunately, there is nothing principled in the way of such disaster: It would be conceivable that each person could make his protocol sentences agree with those of others only with great difficulty or not at all … luckily, in fact we find ourselves in a position to bind together our protocols with those of a hundred other people in a common elaboration. If someone appears who, on the basis of his protocols, builds a science that is not consistent with the one constructed by our hundred people, then we vote him down; we say of him (depending on the circumstance) that he is colorblind, or a poor observer, or a dreamer, or a liar, or a madman. If one found that against our hundred there is another one hundred with a common science that cannot be unified with ours, then we couldn’t vote them down. In case further research would not lead to agreement we should accept the fact that different groups possess unalterably diverse scientific systems. Luckily, this is not the case. (Carnap translated in Coffa 1977: 217) Clearly, Carnap’s position of this period is hardly compatible with the standard picture of phenomenalistic fundamentalism.25 But let us now leave Carnap and Vienna and turn to Goodman and Boston.
Goodman’s construction A Study of Qualities and its descendant The Structure of Appearance both follow Carnap’s programme in many respects. Just as Carnap did in the Aufbau, Goodman tries to build a constitutional system (he calls it a ‘constructional system’), given a certain primitive basis and 113
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an ordering on that basis. The two main differences, however, are that Goodman only tries to construct a first level, and thus the problems of intersubjectivity and the reconstruction of other minds do not arise. In part this is because of the second major deviation: Goodman’s basic elements differ from Carnap’s. As the title of A Study of Qualities suggests, Goodman builds his system on “qualia”: phenomenal qualities. This leads in turn to other differences; qualia do not come temporally ordered, as erlebs, being time slices, do. Therefore, time has to be constructed as well (which was not necessary in Carnap’s system). But let us go through Goodman’s work step by step. In doing so, we shall not always follow the structures of The Structure of Appearance and A Study of Qualities. The two books are organized in different ways and each contains material not contained in the other. We shall emphasize the differences when they are important.
Extensional isomorphism Goodman begins his analysis in The Structure of Appearance with metatheoretical considerations. We shall assume familiarity with the various notions of definition and explication discussed in Chapter 3. As we have said, a constructional system is a system of definitions such that, given a basis, all other concepts of science can be constructed from this basis. In Carnap’s system, the definitions were accurate if the definiens turned out to be coextensive with the definiendum. For Goodman this is too strong a criterion for the accuracy of a definition. Goodman argues that the definiens of an accurate definition need have neither the same intension nor even the same extension as the definiendum; thus, for example, in a constructional system, points in space may be defined equally well as certain classes of straight lines or as certain infinite convergent sets of concentric spheres; but these alternative definientia are neither cointensive (synonymous) nor coextensive with each other. A set of sets of straight lines is just not the same set of objects as a set of infinite convergent sets of concentric spheres. Hence, their accuracy notwithstanding, the respective definitions are not coextensive with, let alone synonymous with, the definiendum. Accuracy of constructional definitions amounts to no more than a certain homomorphism of the definiens with the definiendum. This means that the concepts of the constructional system must provide a structural model for the explicanda in the sense that for every connection between entities that is describable in terms of 114
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the explicanda, there must obtain a matching connection, stateable in terms of the respective explicata or definientia, among the counterparts that the entities in question have within the system. In this way the two different definitions of ‘point’ serve their purpose equally well. The objects in the sets generated – although being very different in kind – stand in just the right relations to one another within the sets to serve as an explicatum for ‘point’ as geometry demands.26 This criterion of adequacy is well in accordance with the project Russell had in mind when he started the serious work on constitutional systems in Our Knowledge of the External World: It is customary to think of points as simple and infinitely small, but geometry in no way demands that we should think of them this way. All that is necessary for geometry is that they should have mutual relations possessing certain enumerated abstract properties, and it may be that an assemblage of data of sensation will serve this purpose. (Russell [1914] 1969: 119) This rather pragmatic criterion of adequacy for philosophical analyses serves Goodman well for a number of reasons. One is that Goodman did not believe there was any such thing as identity in meaning of two different expressions (see Chapter 3). Thus, if synonymy was made the criterion of adequacy, no analysis could ever satisfy it. But even if we put that consideration aside, enquiry into the meaning of an expression, such as ‘point’, would require considering not only what points actually are, but also what points could possibly be. As is familiar from all areas of philosophy, conceptual analysis (as the analysis of the meaning of a term) is carried out by way of thought experimentation. We ask ourselves whether it is conceivable that certain counterfactual events occur and apply our concepts to these events in order to learn how they behave. For Goodman this just did not seem a clear enough method on which to base a scientific philosophy: “It is fortunate that nothing more [than extensional isomorphy] is in question; for the notion of ‘possible cases’, of cases that do not exist but might have existed, is far from clear” (SA: 4). Goodman’s scepticism concerning possible cases and thought experiments in conceptual analysis is nowadays echoed by many “naturalistically” minded philosophers, who also advocate more pragmatic criteria of adequacy for philosophical analyses (see Kornblith 2002; Bishop & Trout 2005).27 At the time Goodman wrote A Study of Qualities and The Structure of Appearance, this view was not very fashionable. Goodman defended Carnap’s criterion of extensional identity and even went a step further 115
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(see also his 1963c). In requiring mere extensional isomorphy, A Study of Qualities and The Structure of Appearance already differ from the Aufbau in an important respect. We now turn to some even more significant differences.
Goodman’s criticism of the Aufbau Goodman’s A Study of Qualities and The Structure of Appearance are famous as detailed studies of Carnap’s Aufbau. In Chapter V of The Structure of Appearance Goodman summarizes the main steps of Carnap’s construction and gives detailed critical commentaries. His two most serious attacks on Carnap’s construction are, however, two problems that have to do with Carnap’s idea of quasi-analysis. We have introduced this method earlier in this chapter with an example of proper analysis. In that case there was a series of erlebs of a certain kind as experienced by Paula, which had real parts, namely different colours. The task was to retrieve the real parts from only limited information, the information stored in the Rs relation. In the example that we discussed above, this seemed largely unproblematic. We were able to retrieve all colour information from the Rs relation alone. The rule we used was simply this: single out those classes of erlebs that are all pairwise Pi related and for which there is no erleb outside the class that is Pi related with each erleb in the class. But now consider a case in which the following unfavourable circumstances obtain:
This time, Paula starts with six slightly different erlebs. Obviously the extension of the Pi relation would be this: {, , , , , , , , , , , , , , , , , , , 116
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<E, A>, <E, B>, <E, C>, <E, E>, <E, E> , , , , , } Or as a graph:
But now, applying our rule to categorize the erlebs into the right colour classes would give us all colour classes except the class {A, E, F}, the colour class for ‘white’. Why is that so? Well, in the circumstances described, white only appears in constant companionship with the colour black. So B cannot be excluded from the class {A, E, F}, for B is part identical to each member of the class. This problem is called ‘companionship difficulty’. Carnap had noticed this problem, but thought that it should not occur provided the number of erlebs is sufficiently high.28 It is, however, far from obvious that this really is the case. It is perfectly conceivable, for example, that a certain shade of blue always co-occurs with another shade of blue. But then those two colours will not be quasi-analysable into two colours by Carnap’s method.29 Consider also the following situation:
This time, Paula has another six slightly different erlebs. Ordered by part similarity, we obtain the following list: {, , , , , , , , , , , , , , , , <E, A>, <E, E>, <E, F>, , , , , } 117
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Or again as a graph:
Given this list and our rule, {A, C, F} should be a colour class. All elements are pairwise Pi related and no other erleb outside the class is pairwise Pi related with all elements of it. But what colour is common to A, C and F? Well, obviously none at all. This is called ‘the difficulty of imperfect community’. Again, it seems that Carnap has no clear way out of this problem. Both problems reoccur at various levels in Carnap’s analysis, and Carnap seems unable to offer a non-circular solution to this problem. Goodman took this to be devastating to Carnap’s entire project.30
The basis of The Structure of Appearance and the basic relations We said above that Goodman chooses a basis other than that adopted by Carnap. In Goodman’s new terminology (the terminology of The Structure of Appearance), Carnap’s system is “particularistic”; its basis is a basis of concrete entities, erlebs. Qualitative aspects of these erlebs are quasi-analysed. A certain time slice of my stream of experience might be the experience of a red spot, if red is a quasipart of this erleb (if this erleb is quasi-analysed into the class of red things). This relation is turned around in Goodman’s construction. As atomic individuals, Goodman takes not concrete phenomenal things or events, but what he calls “qualia”. A quale is a qualitative characteristic of phenomenal experience such as, say, a certain shade of purple occurring in the presentation of a certain piece of cloth in a particular light. Note that qualia are distinct from properties as characteristic of physical objects. The qualia Goodman chooses as atoms include colours, times, visual-field places, and various non-visual qualia, which he does not specify in detail. Thus, moments of phenomenal time as well as phenomenal places are conceived here as repeatable universals. A place 118
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can be at, or “together with”, several times, several colours and so forth. The totality of individuals in Goodman’s system consists simply of all the sums that can be formed with any of the atomic individuals, or qualia. Goodman conceives the total stream of experience to which his system is to be applied as containing only a finite number of qualia; consequently, the number of all individuals countenanced in his system is finite as well. As Goodman points out, his choice of qualia as atomic individuals makes his system phenomenalistic rather than physicalistic, and realistic rather than particularistic. In a physicalistic system, the individuals are concrete physical objects or properties of such; in a particularistic system, the individuals are concrete entities rather than abstract ones (see also the end of this chapter for an overview of the terminology used here). In view of the realistic character of his system, Goodman’s first main problem is that of concretion, that is, that of constructing unrepeatable concrete individuals from qualities. In the visual realm, a concretum is a colour-spot moment, which may be construed as the sum of a colour, a visual-field place and a time, which stand in a peculiar relation of togetherness. Goodman adopts this relation as a primitive and then shows how, by means of it, it is possible to define the concept of the concrete individual as well as the various relations of qualification in which qualia and certain sums of qualia stand to the fully or partially concrete individuals that exhibit them. After this is done, Goodman faces his second major constructional objective. He has to order the qualia into different categories. The problem is to construct for each of the categories (colour, time, place and so forth) a map that assigns a unique position to each quale in the category, and that represents the relative likeness of qualia by nearness in position. The solution to the problem requires in each case the specification of a set of terms by means of which the order at hand can be described, and then the selection of primitives suitable to define them. He thereby shows how, subsequently, predicates referring to size and shape of phenomenal concreta may be introduced, and he suggests briefly some approaches to the definition of the different categories of qualia by reference to their structural characteristics. Since Goodman does not deal with time slices of experiences, which come already with a temporal order, but has phenomenal time among the basic qualia, he has to reconstruct temporal order as well as any other ordering of qualia. This is done in the final chapter of The Structure of Appearance, “On Time and Eternity”, which deals with the ordinal 119
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aspects of phenomenal time, the linguistic devices used to express temporal relations and some connections between phenomenal and physical time. As we have already observed, Goodman is only concerned with the first level of a constructional system. As Goodman himself points out, it is not obvious how one should proceed to construct the upper levels (SA: 274–5). One of the main problems at that point certainly is the reconstruction of disposition terms and the problem of distinguishing laws from accidental generalizations, which is needed for the physical level.31 We have seen already in Chapter 2 that these problems lead Goodman to a radically new analysis of disposition terms and counterfactual sentences.
The given and constructionalism At the beginning of this chapter we noted already that The Structure of Appearance is often considered to be an anti-foundationalist version of Carnap’s Aufbau. Elgin, for example, writes: Traditionally, phenomenalism maintains that all a posteriori knowledge derives from what is given in experience. If so, the goal of a phenomenalist construction is to provide the derivation. That is what Carnap attempts in the Aufbau. Goodman changes the subject. He believes the myth of the given cannot survive the repudiation of the scheme/content distinction. He denies that, independent of any prior systematization, some things are and other things are not really primitive. (2001: 681) At the beginning of this chapter we tried to show that Carnap was not a foundationalist in the Aufbau nor during the period immediately following that work. Thus we should not interpret the Aufbau the way that is suggested above by Elgin. Goodman does not seem to have endorsed such a foundationalist interpretation of the Aufbau himself. Neither in A Study of Qualities, nor in The Structure of Appearance is Carnap accused of foundationalism. In fact, Goodman correctly says: Carnap has made it clear that what we take as ground elements is a matter of choice. They are not dignified as the atomic units from which others must be built; they simply constitute one possible starting point. … In choosing erlebs, Carnap is plainly seeking to approximate as closely as possible what he regards as the 120
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original epistemological state … Yet whether it does so or not is no test of the system. A construction is avowedly not an “epistemological description” but a “rational reconstruction” … of the knowing process. Indeed not even that much need be claimed, for the sole criterion for any construction, according to Carnap, is whether all propositions containing the original term can be translated into logically equivalent propositions containing only logical constants and the proposed expression. Hence … argument concerning whether the elements selected are really primitive in knowledge is extraneous to the major purpose of the system. (SQ: 96–8) Hence Goodman himself did not consider his constructionalism as an epistemological alternative to Carnap’s. In so far as epistemology does play a role in The Structure of Appearance or A Study of Qualities, this seems to be directed against C. I. Lewis’ philosophy, as we saw in Chapter 1. Lewis held the view that empiricism must presuppose the incorrigibility and indubitability of what is given in experience. I might need to revise my belief that I saw a plane crossing the sky when I learn that what I mistook for a plane was Superman. Nothing, however, can make me revise my belief that there was a blue and a red spot in the centre of my visual field that then led to the (false) belief that there was a plane. A Study of Qualities, on the other hand, begins with the argument that even the simplest judgements of this sort might be revised in the light of new evidence. My judgement that I had a blue spot in the middle of my visual field yesterday when I looked at a ripe apple under normal conditions might be revised when I now judge that I have a red spot in my visual field, looking at the same object under the same conditions and knowing that it could not have changed its colour. However, if such revisions can be made in retrospect, nothing of the “given” is indubitable or incorrigible. Judgements about qualia, in this sense, are decrees. Which ones we accept is a matter of the overall coherence of our system of beliefs and our other qualia judgements (see also Goodman 1952c; Lewis [1952] 1997).
Goodman’s use of the calculus of individuals In Chapter 4 we said quite a bit about Goodman’s “nominalism” as well as his mereological system. We can now show that originally Goodman’s 121
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main reason for endorsing such a mereological construction was to avoid the problems for constructional systems mentioned above. Carnap’s constructional system, like that of Russell and Whitehead, included in its logical apparatus the formation of classes, classes of classes, and so forth, of whatever entities function as individuals. The various non-primitive terms are defined by using constructions of classes. In The Structure of Appearance, as we said, the use of the class concept is eschewed as “platonistic”, and Goodman adheres instead to a version of nominalism that rejects classes. However, the road towards this nominalism is not as straight as it might seem at first.
Singular terms As indicated in Chapter 1, Goodman collaborated closely as an undergraduate student with Leonard, who was at that time a student – and later PhD student – at Harvard. Leonard’s PhD thesis discusses issues related to Whitehead and Russell’s Principia Mathematica. In the preface to Singular Terms (1930), Leonard thanks his supervisor Whitehead and “Mr. H. N. Goodman”, with whom he “discussed together nearly every point developed in this thesis”. Leonard summarizes the topic of his thesis as follows: The calculus of classes achieved success through its disregard of the traditional abstract terms. The object of this thesis is to show that this disregard was justified, because abstract terms are singular and not general, that on the other hand, symbolic logic should and can provide a treatment of these terms in a calculus of singular terms and that with this development, it is possible to see that symbolic logic has not thrown over intension, but only its traditional association with abstract terms. (1930: 1) It seems likely that Leonard’s thesis was the initial motivation for Goodman to start the project carried out in A Study of Qualities, presumably long before he had even heard of Carnap’s project (see Chapter 1). To see this, let us first consider what at that time was understood to be an abstract term. In traditional logic “abstract and universal terms” were names of attributes (properties, such as redness) and relations. They were taken to be different from concrete general terms (such as ‘red thing’) on metaphysical grounds. Leonard’s conviction that logic should not settle metaphysical disputes in one way or other led him to favour a treatment of names of attributes as 122
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names of additional individuals. Principia Mathematica, being primarily interested in the reconstruction of mathematics could not provide the means for doing this: Ideally our symbolic logic should offer us a calculus which analyses immediately the structure of the propositions that employ abstract terms. And until it does that, our symbolic logic is incomplete. … The object of the present paper is to seek a solution to this problem. In general, our solution consists in holding that the calculus of classes is the calculus of general terms, that abstract terms are rightfully excluded from the type called “general”, but that they belong to the type called “singular.” Thus, instead of omitting them entirely, we add a new chapter to symbolic logic, and it is this addition which characterizes our whole position. (Ibid.: 7–8) In other words, Leonard did not intend to replace any part of the calculus of classes, but to add new resources to it, to deal with problems the original calculus was not designed for. After an interpretation of various foundational issues in Principia Mathematica (which are of no concern here), Leonard introduces the main ideas of his calculus of singular terms, which turns out to be a mereological system. In this system, variables range over individuals that can be summed together and can form new units. Applications considered in Leonard’s examples are volumes and qualities. The calculus deals with, among others, the part-of and crossing relations. (All of these were notions already familiar from the informal sketches in Whitehead’s writings.) In Part V of his dissertation, Leonard discusses different possible interpretations of his calculus. His interesting result is that the calculus whose variables should be interpreted as ranging over parts of the world can serve just as well for a realistic conception of the world as for a nominalistic conception. In a realistic conception qualities would be treated as basic units and all concrete objects or other units defined as complexes built up out of these. Leonard also considers realistic systems built on phenomenal qualia rather than objective qualities. All units are equally real, but in order to introduce system in our view of the world, we must take certain ones as basic and describe others in terms of these. In the suggestions which we have just outlined, we have taken quality units as basic, where 123
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under “quality units” we include units of space and time. In terms of these, we describe units of other types. On this view quality units are real parts of our world, the basic units in a world view. (Ibid.: 238) Nominalistic conceptions, on the other hand, would take concrete particulars as basic and construct qualia or qualities out of these. What you start with turns out to be completely arbitrary. Eventually, Leonard comes to his own principle of tolerance, claiming that for different purposes (“everyday activity”, “science”, “art”) different systems might be adequate and that none of them can claim to be more real than any other. Logic is considered to be the study of what is common to all “unitations”, but is neither concerned with developing a new unitation (or world version) nor with singling out one such unitation as privileged. This thought would become one of the main themes in Goodman’s philosophy.
The platonism and realism of A Study of Qualities Goodman’s dissertation project might in its first conception have been started as a further elaboration of Leonard’s dissertation. Just as in Singular Terms, A Study of Qualities does not replace the calculus of classes in the construction, but adds a mereological system to it. In A Study of Qualities nominalism is not an issue at all. Here Carnap’s system is described as “nominalistic”, in virtue of Carnap’s having started with erlebs, which are taken to be concrete particulars. The system of A Study of Qualities, on the other hand, is described as “realistic” because its basis comprises phenomenal qualia. The method of construction in both systems, however, is platonistic, for Goodman and Carnap both make use of the calculus of classes (although Goodman makes less use of it). The calculus of classes is completely abandoned in The Structure of Appearance and replaced by a mereological system. Now Goodman considers his system to be “nominalistic”, this time with respect to the method of construction, and Carnap’s system to be “platonistic”. The old division, based on the choice of different bases, is now expressed as the difference between “particularism” (Carnap) and “realism” (Goodman). (Both systems are, however, phenomenalistic rather than physicalistic. See also the end of this chapter for an overview of the relevant terminology). 124
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Nominalism in this new sense rejects the use of any language containing names or variables for classes; it countenances merely the truth-functional connectives, names and variables for individuals, quantifiers to bind the latter, and one- and many-place predicates that apply to the individuals of the system. In Goodman’s construction some of the tasks of the calculus of classes are accomplished by the calculus of individuals. The central concepts of this theory are relations among individuals, particularly the relations of overlap, discreteness and parthood; and certain functions such as the sum and the product of individuals. All these concepts have analogues in the theory of classes and exhibit many formal similarities to them. As explained in Chapter 4, the main difference is this: whereas any class of classes of individuals is distinct from the class of all individuals involved, the sum of any sum of individuals is identical to the sum of all the individuals involved (this much was already pointed out by Leonard in his Singular Terms (1930)). In this manner, the calculus of individuals vouchsafes the identity of any two entities with the same “content”, and, therefore, precludes the possibility of forming, from some finite initial set of individuals, an endless array of distinct abstract entities. The latter point is relevant in The Structure of Appearance, because the method of construction guarantees that the system of The Structure of Appearance will be more economical by Goodman’s calculus of simplicity than any alternative construction in terms of classes. Let us briefly examine this feature.
Simplicity A major metaphilosophical result of Goodman’s The Structure of Appearance, which is not similarly elaborated in A Study of Qualities, is Goodman’s theory of simplicity. In The Structure of Appearance this discussion follows the second chapter of Part One, in which the calculus of individuals is introduced. Goodman’s theory of simplicity has a direct bearing on many systematic decisions made in The Structure of Appearance. In a number of subsequent papers, Goodman further developed his theory of simplicity, not only in relation to constructionalist programmes, but also as a contribution to a general problem in philosophy of science: what does it mean for a scientific theory to be simpler than some empirically indistinguishable rival theory? For Goodman, science and simplicity are intimately connected. Without science there is no simplicity and without simplicity there is 125
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no science. Realistic-minded philosophers often object that the world might actually be complex and, consequently, that the methodological principle of choosing the simpler of two competing theories is epistemically ill-founded (it rests on the problematic assumption that the world itself is simple, which we cannot know in advance, i.e. independent of knowing which theory truly describes the world). This objection is – according to Goodman – off the mark. The world itself is neither simple nor complex, just as it is neither in English nor in German. The world is only simple if described in a simple system: The world, indeed, is as simple as any true system, but it is also as complex as any true system. And it is as grammatical, as ungrammatical, as coherent, as incoherent, as any true system. These descriptions apply to the world only obliquely, through applying to discourse about the world. We need not shun syntax or coherence or simplicity for fear the world is ungrammatical or incoherent or complex. (PP: 337) Simplicity, however, is as important as any aim of science, maybe even more important than truth.32 Science is – first of all – systematization, and systematization is a process aiming at simplicity. Truth alone could be achieved quite cheaply by merely collecting logically unconnected statements of fact, for example, or by stating trivialities. Seeking simplicity makes us search for lawlike relationships between different events, reduce theories to more fundamental laws and so on. Without the quest for simplicity, there would be no science. Notoriously, it proves extremely difficult to define or explicate what simplicity is and how it can be measured. Goodman has tried to find an explication of formal or structural simplicity (in contrast to semantic or psychological simplicity) that applies to a basis of a system of terms (in contrast to a system of statements). Given such an explication, we could then assess, for example, the simplicity of constructional systems such as Carnap’s, and compare it to alternative constructions, such as Goodman’s. One of the first ideas that comes to mind when we want to define the simplicity of a system’s extralogical basis in order to compare it with an alternative system, is that one basis is simpler than an alternative basis if the former contains some but not all of the terms contained in the other, and no additional terms. This criterion, however, would only allow us to compare systems in which the set of terms of the one system is a proper subset of the set of terms of the other system, but 126
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does not help in comparing systems that contain mutually differing terms, that is, when each contains terms not contained in the other. Given that we are dealing with systems of definitions, we might try to explicate simplicity via definability: a basis A is simpler than a basis B if A is definable from B but not B from A, and that two bases are equally simple if they are interdefinable. But in a constructional system, all terms are defined from the basic terms, and can be defined from the set of all terms. Hence, by this criterion the set of all terms is at least as simple as any narrower basis: a highly unwelcome result. Goodman tries a different approach based on two further observations. Note, first of all, that the system with fewer basic terms is not necessarily the simpler system, since the number of basic terms can be trivially reduced. Compare a system A that comprises the following set of basic terms: {ConductsElectricity(x); IsDenserThan(x,y)} This basis with a one-place predicate applying to certain materials and a two-place predicate relating certain materials contains obviously more basic terms than the basis B: {ConductsElectricityOrIsDenserThan(x,y,z)} In basis B we have only a single three-place predicate. It applies to objects x, y, z iff x conducts electricity or y is denser than z. However, our two other predicates are easily retrievable by definition in B: ConductsElectricity(x) =df ∀y∀z(ConductsElectricityOrIsDenser Than(x, y, z)) IsDenserThan(x, y) =df ∀z(ConductsElectricityOrIsDenserThan (z, x, y)) Clearly, B should not be considered simpler than A. If it were, maximum simplicity could always be achieved in this way by reducing all terms to one. We should also note that a simple count of the total number of predicate places would not help either. Say we assign complexity value 2 to a two-place predicate and 3 to a three-place predicate. Although that would give us the correct results in the case of A and B above, predicates with more predicate places cannot always be split into more predicates with fewer predicate places the way more predicates can be reduced to fewer with more places. Consider, for example, the predicate ‘IsParentOf(x, y)’. This predicate cannot be split into ‘IsAParent(x)’ and 127
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‘HasAParent(x)’ in such a way that ‘IsParentOf(x, y)’ can be retrieved (Prince Charles is a parent and John Cleese has a parent, but that does not make Prince Charles John Cleese’s parent). Instead, Goodman observes that a basis A is not simpler than a basis B if every basis of the same kind as B can always be replaced by a basis of the same kind as A. ‘Same kind’ here refers to the structural kinds of bases, determined by: (a) the number of predicates (b) the number of places in each (c) the reflexivity, irreflexivity, symmetry, transitivity, and selfcompleteness properties of the predicates We have discussed (a) and (b) already. In (c) we have a list of properties of two-place predicates. Consider a two-place predicate F(x, y). This predicate is reflexive provided ∀xF(x, x) (everything stands in that relation to itself), irreflexive provided ∀x ¬ F(x, x) (nothing stands in that relation to itself), symmetric provided ∀x∀y(F(x, y) ⊃ (F( y, x)) (the relation holds both ways for any two things to which the relation applies), transitive provided ∀x∀y∀z((F(x, y) ∧ F(y, z)) ⊃ F(x, z)) (everything that stands in that relation to something, that stands in that relation to something too, also stands in that relation to the latter), and self-complete (a strengthened version of transitivity) provided ∀x∀y∀z∀v((F(x, y) ∧ (F(z, v)) ⊃ F(x, v)) (any two things that stand in that relation to something stand in that relation to each other). Predicates with more than two places may exhibit analogues of these properties for a pair of their argument places. Now Goodman defines a calculus of simplicity as follows: one-place predicates receive the complexity value 1; the complexity value of many-place predicates is a function of their number of argument places depending on which of the properties mentioned under (c) are exhibited by the predicate. The function itself is rather complicated, but luckily the details need not concern us here.33 The complexity value of a basis, then, is the sum of the complexity values of the extralogical predicates it contains. Thereby, Goodman achieves a calculus for measurement and comparison of the simplicity of bases. Goodman’s subsequent work on simplicity has also led to two interesting negative results. One is that the treatment we have just given the simplicity of terms cannot be easily applied to the set of unproven extralogical statements of a system, as there is a simple procedure by which every extralogical postulate of that system can be completely eliminated. 128
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Consider, for example, a system that contains the primitive twoplace predicate ‘intersects’. Now, statements about ‘intersects’ enter into a system by way of extralogical postulates. It is, for example, an extralogical fact that ‘intersects’ is symmetrical, that is, that everything intersects whatever intersects it. Normally, we would now postulate symmetry for ‘intersects’ by such an extralogical postulate, thereby increasing the number of extralogical statements. However, we could just as well do the following. Instead of ‘intersects’, we add the primitive two-place predicate ‘cuts’ to our system with no extralogical postulate. So far the basis remains as simple as that containing ‘intersects’. But instead of postulating symmetry for ‘cuts’, we simply define ‘intersects’ now with the help of ‘cuts’: Intersects(x,y) =df Cuts(x, y) ∨ Cuts(y, x) Given this definition, we can prove that ‘intersects’ is symmetric.34 As Quine and Goodman have shown in “Elimination of Extralogical Postulates” (1940b), this trick can be used for all other postulates, and for properties more interesting than just symmetry (provided that the system is consistent and the logic is not particularly weak). Goodman could not remedy this problem. Of course, the number of definitions cannot replace the number of postulates as a measure of simplicity. First, having many definitions indicates that a system has a slender basis; hence it should rather be counted as simpler. Secondly, definitions are mere abbreviations and can always be dropped without essential sacrifice of deductive yield. A second important observation made by Goodman is that Popper’s idea, namely, that simplicity is identical with, and can thus be measured by, the degree of falsifiability, is hopeless. Popper conjectured that falsifiability increases with the strength of a hypothesis, thus to choose the stronger hypothesis should always result in choosing the simpler. Consider a botanist who examined many and widely distributed maple trees and found them all to be deciduous. Assume that the evidence leaves us with the following hypotheses: (1) All maples, except perhaps those in Eagleville, are deciduous. (2) All maples are deciduous. (3) All maples, whatsoever, and all sassafras trees in Eagleville, are deciduous. Hypothesis (2) is both, stronger and simpler than (1). Cases like these (where comparative falsifiability coincides with comparative 129
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simplicity) suggest that degree of falsifiability (which, as we said, is higher for stronger statements) is a measure of simplicity. However, although (3) is stronger than (2), and thus has a higher degree of falsifiability, (2) is nevertheless simpler than (3), and would certainly be preferred to it. We shall return to Goodman’s discussion of simplicity in Chapter 9. For now it is of interest to note that Goodman did produce a measure by which we are able to assess the simplicity of alternative constructional systems. All nominalistic scruples aside, it could be shown that a system in which the calculus of individuals completely replaces the calculus of classes is simpler by this measure. Towards the end of this chapter we shall be able to justify this claim. Since the simplicity considerations only enter with The Structure of Appearance and were not elaborated in A Study of Qualities, it is fair to assume that simplicity was not the only reason Goodman used a calculus of individuals in his construction. As we shall see, it probably was not even his primary concern.
A mereological fix for the difficulty of imperfect community Although Goodman briefly speculated about the greater economy of a nominalistic system in A Study of Qualities (SQ: 292–3), the main impact of the calculus of individuals seems to be the fact that it allowed him to circumvent the difficulty of imperfect community in the Aufbau. As described above, Carnap’s method of quasi-analysis may yield a quality class in which the members of that class do not share a common quality. As Goodman and Leonard showed in their “The Calculus of Individuals and Its Uses” (1940a), this problem does not arise if the resources of the calculus of individuals are used to construct qualities as quality wholes. Although the difficulty of imperfect community can be formally treated in this way for particularistic as well as realistic systems, the companionship difficulty, that is, the problem that some distinct qualities might be grouped in the same quality class simply because they always occur together, could not be solved by Goodman for particularistic systems.35 But let us go through Goodman’s solution to the difficulty of imperfect community step by step.
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Solving Carnap’s problem As we have said, Goodman favoured a mereological construction that does not include standard classes or set theory because, without them, a system is more comprehensible. This makes good sense in light of what we have said about Goodman’s conception of explication and the role of constructional systems in philosophy. It seems that in A Study of Qualities, Goodman was not yet aware that the calculus of individuals would suffice to renounce classes altogether. Goodman uses the calculus of individuals here as an addendum to the calculus of classes, just as Leonard did in Singular Terms. The early use of the calculus of individuals, therefore, appears to be motivated less by nominalistic intentions, but rather, as we have argued, by the belief that a constructional system can be more easily designed if qualities can be treated as individuals and thus be summed mereologically. We have introduced the problem of concretion, which Goodman faces in his construction. Since his system starts with qualia as the primitive entities from which everything else is to be constructed, he needs to find a way to get from qualia, which are abstract universals, to concrete particulars, such as a concrete experience in some sense realm at a certain time (Goodman calls this a ‘concretum’). This is just the reverse of Carnap’s problem. Since Carnap started with concrete time slices of experiences, he faced the problem of abstraction: he had to abstract qualities from concrete experiences. We have also explained briefly that Goodman chooses as his basic relation some sort of togetherness relation: We need, then, a primitive relation that will enable us to differentiate systematically between those classes of qualia that form concreta and those that do not. … The basic concreting relation is a symmetric relation of togetherness among qualia. Such a relation obtains, for example, between a color and a time or place at which the color occurs; likewise between a place and a time at which the place is presented. In general, it obtains between any two atomic qualia belonging to some one concretum. (SA: 144) It might seem problematically circular to explain the togetherness relation that is supposed to ground the construction of concreta from atomic qualia as the relation that obtains between any two qualia that belong to some one concretum. But the basic relation is only externally explained this way. Togetherness is not defined in the system as such 131
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a relation, because it is not defined at all in the system; it is basic, or primitive. Everything within the system, however, is defined only in terms of the primitives (the togetherness relation and qualia). This worked in the same way in Carnap’s Aufbau; there we wanted to construct qualities from concrete time slices of experiences, which were ordered by a relation such as ‘is-similar-in-quality-at-this-place-to’. Again, this was not circular because the primitive relation was only explained this way outside the system (and then given extensionally as a set of ordered pairs within the system). To make the construction of the togetherness relation as clear as possible, we shall introduce some vocabulary: ● Atoms of the system. In Carnap’s Aufbau we have basic objects
and a basic relation in which those objects stand. We have used ‘atom’ and ‘individual’ interchangeably to refer to those basic objects. However, the calculus of individuals will allow us also to treat sums of atoms as a further type of individual (thus choosing certain atoms does not yet fix the basic units of the system, the individuals). The atoms of Goodman’s construction comprise a certain set of qualia, qualitative aspects of experiences, such as single phenomenal colours, sounds, degrees of warmth, moments in time, visual locations and so on. Note that not all qualitative aspects of experiences are recognized as atoms in the system. For example, Goodman accepts colours as qualia, but not their hues. Just as in Carnap’s system, ‘being atomic’ does not mean ‘being pretheoretically indivisible’. It just means that it is taken in the system as indivisible, or, only further divisible by quasi-analysis. ● Categories of qualia. Qualia come in categories. A specific shade of red is a quale; it belongs to the category ‘colour’. Other categories are ‘place’ and ‘time’. Explaining the togetherness relation, we can say that no two qualia of one category are together, no place is at a place, no colour occurs with another colour. Togetherness is therefore an irreflexive relation. ● Sense realms. A quale, such as a time, might belong to more than one sense realm. Every quale, however, belongs to some sense realm, such as the visual realm. In order to further explain the togetherness relation, we can say that two qualia that occur together always belong to the same sense realm; qualia of different realms never occur together. (The time at which a sound is and the time at which a simultaneous colour spot is are not together, and neither are the sound and the colour spot.) 132
From Vienna Station to Boston Terminus ● Complexes and bicomplexes of qualia. Complexes are entities
that are contained within concreta. Degenerate complexes are all the single qualia, maximal complexes are concreta, and all other complexes fall somewhere in between. Two qualia that never occur together in a concretum do not form a complex. A bicomplex is a class of two qualia which are together. As the last sentence suggests, we shall tentatively treat qualia as atoms and at the same time as the individuals of the system. Thus our togetherness relation, Wh, is a relation between atomic qualia. Two qualia that stand in this relation form a bicomplex. It seems that we could simply proceed to the complexes by adding to a bicomplex a quale that occurs together with both qualia of the bicomplex and so on until there is no quale outside the complex that occurs together with every quale of that complex. But now you should hear an alarm bell ringing: the difficulty of imperfect community rears its ugly head. Note what happens if we turn from bicomplexes to tricomplexes. The notion of the togetherness of more than two qualia has just been explained as meaning that each quale is related by togetherness to each of the others, but clearly a tricomplex that satisfies this condition need not belong to any concretum. Consider the following qualia: a colour c, a place d and a time f, such that: Wh(c, d ) ∧ Wh(c, f ) ∧ Wh(d, f ) Although c is at d and at f, and d is at f, it need not be the case that they belong to some one concretum; c could well occur at place d at some other time than f, and c may occur at time f at some other place than d. Let us clarify this with the help of an example. We shall take Paula’s slightly enhanced visual realm that has two places, l (‘left’) and r (‘right’), Paula can discern two colours, g (‘grey’) and w (‘white’) and two phenomenal times t1 and t2. Consider the following concreta:
t1
t2
Here, g is at l, r is at t1 and l is at t1, and they all form a concretum: the grey “spot” at time t1 in the left half of Paula’s visual field. So the following truly describes a concretum: 133
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Wh(g, l ) ∧ Wh(g, t1) ∧ Wh(l, t1) But the same also applies to the following case:
t1
t2
But now, obviously, no true concretum is described. This time there is no grey spot in the left half of Paula’s visual field at time t1. The problem is this: when we say that a colour is at a place and a time, we intend to say that the colour is at a certain place-time. Place-times, however, do not belong to our set of atoms. A place-time can then only be construed as a place at a time, which seems not to be sufficient. Of course, this problem might lead us to choose other atoms for the system. We could simply add entities such as place-times and colour spots. This move would, however, be very ad hoc, and not very parsimonious. Moreover it would make the method of construction inapplicable to other sense realms. But instead of changing the atoms, we can do better and choose other individuals. Wh was a relation that obtained merely between qualia, taking the atoms of the system as the individuals of the relation. But instead of using a relation that obtains between all distinct atomic parts of a concretum we could try to use a relation that obtains between all discrete parts of a concretum. This new relation, W, could allow us to say the same things as Wh, and could be defined in such a way as to be symmetric, irreflexive and nontransitive. Just as with Wh, two individuals forming a W-pair would belong to different categories of some one-sense realm. To represent such a relation Goodman appeals to the calculus of individuals. With it he is able to construe individuals as sums of atoms and deal with all the relationships of overlapping, parthood and so on that we introduced in Chapter 4, and that may obtain between individuals so construed. In The Structure of Appearance the calculus of individuals is then accepted as a replacement of the calculus of classes: ‘o’ replaces ‘∈’, and ‘W ’ replaces ‘Wh’. Now, a bicomplex is to be construed as the sum, and not as the class, of two qualia that are together. This way we get a space-time as the sum of a space and a time. Tricomplexes are now bicomplexes 134
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formed by the sum of two individuals that occur together taken with a third individual occurring with that sum. Hence, if c is a colour and k is a place-time c is at, ‘W(c, k)’ expresses that relationship. If k is the sum of place d and time f, the relationship between all three could also be expressed now by ‘W(c, d + f )’. When we now define a complex as an individual such that every two discrete parts of it bear the relation W to each other, no individual will be a complex unless every sum of one or more of the qualia it contains occurs together with the sum of the rest. This new togetherness relation is now a proper “all-togetherness” relation. Using it, we can avoid the difficulty of imperfect community. In the example given above, ‘W(g, l + t1)’ is true of the first example, since green occurs at the sum of the place quale ‘left’ and the time quale t1. On the other hand, it is false for the second example: green does not occur together with the individual l + t1. Given the new definition of complex, a concretum can now be defined as any complex that bears the relation W to no individual (concreta are no proper parts of any complex). In this way, Goodman solves the difficulty of imperfect community for his own construction in terms of the togetherness of qualia. Carnap’s problem in the Aufbau, the problem of abstraction, could also be solved along these lines (at least in part). In the Aufbau, the atoms were erlebs and the basic relation was some sort of similarity relation between the atoms. This primitive relation could simply be broadened by adopting the calculus of individuals, allowing the similarity relation to obtain also between erlebs and sums of erlebs. A quality is no longer conceived as a class of erlebs that stand in the similarity relation, but a whole that consists of erlebs. We could conceive of a quality stretch as the sum of one or more erlebs that have a quality in common. Quality stretches would thus correspond to complexes in the realistic system. Our new primitive similarity relation, let us call it L, will obtain between every two discrete parts of a quality whole. A quality stretch will then be defined as an individual any two of whose discrete parts form an L-pair. In close parallel to the realistic system we could now define a quality whole as a quality stretch that is not a proper part of any other quality stretch. Whether you then want to identify qualities with quality wholes (in the mereological sense) or rather define them as classes of all the erlebs that are parts of a quality whole is more or less a matter of taste (the latter would force you, however, to reintroduce classes). At any rate, this solution would avoid the difficulty of imperfect community for a particularistic system. 135
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It would not thereby solve the companionship difficulty for particularistic systems, though. How is it solved in a realistic system? As we said above, the difficulty appears because two distinct qualities can always occur together in all erlebs, making it impossible for them to be distinguished (we ended up with too few qualities). The difficulty would appear in a realistic system if any concretum were composed entirely of qualities contained in some other concretum (we would then end up with too few concreta). But no two concreta have exactly the same qualities, nor could one concretum have fewer qualities than some other concretum of the same sense realm (and be thereby composed of qualities properly included in some other concretum). The reason for the latter is that the number of qualities in a concretum is the number of quale categories in that sense realm. If we set the issue of nominalism aside for the moment and recall Goodman’s simplicity considerations, we can compare the mereological construction to an alternative solution. Instead of using the calculus of individuals, we could also use set theory (the calculus of classes) and avoid the difficulty of imperfect community by using an alternative primitive relation Wt that obtains between each two separate subclasses of a concretum. We could then define a complex as any class of which every two separate subclasses form a Wt-pair. In a way, that would violate the idea of a constitutional system to a certain degree. The primitive relation would no longer involve the atoms of the system in any obvious way, but only classes thereof. Even in the platonistic construction of A Study of Qualities, Goodman was able to avoid this. (Note that one could not argue in the same way against W, since taking sums of atoms is quite different from taking classes of them. But we wanted to set that aside.) Thus, if we forget our nominalistic scruples for a moment, we can compare a system such as that of A Study of Qualities, involving the calculus of classes and the calculus of individuals (if the latter is constituted by ‘o’ and ‘W ’) with a system that does not involve mereology and is built up using ‘Wt’. By Goodman’s simplicity measure (sketched above), both symmetric (two-place) predicates ‘o’ and ‘W’ have a complexity value of 2, and thus the basis has a complexity value of 4. The complexity value of Wt, a two-place disjoint symmetric predicate of classes of individuals, depends on the maximum number of qualia contained in any complex in the field of Wt.36 If we take the last Paula example given above, in which a concretum has not more than three atoms (a place, a time and a colour) and thus complexes in the field of Wt have at most two qualia, the complexity value for any basis 136
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involving Wt would be at least 5 (compared with a complexity value of 4 for ‘o’ and ‘W ’).37 Therefore, even nominalistic scruples aside, there seem to be good reasons to favour a mereological construction over this set-theoretic alternative (if one accepts Goodman’s measure for simplicity).
Goodman’s realism In a way Goodman was a nominalist and a realist, coherently and simultaneously. For a while he was a platonist, but he was never a physicalist. Let us bring some structure to this confusing terminology.
Nominalism versus platonism This dichotomy applies to the method of construction. As explained above, Goodman’s “nominalism” is a position that accepts only individuals as entities but renounces classes and other non-individuals. The position that also accepts non-individuals he calls “platonism”. A nominalist can remain a nominalist even if he accepts qualia, which are abstract individuals. Goodman’s The Structure of Appearance is nominalistic in this sense. A Study of Qualities was not nominalistic in this sense, and neither was Carnap’s Aufbau.
Mereology versus set theory (calculus of individuals versus calculus of classes) This dichotomy also applies to a method of construction. Mereological constructions are acceptable to nominalists whereas set theoretic constructions are not. A platonist, however, can make use of both methods without ceasing to be a platonist. In A Study of Qualities mereology is used for the definition of complexes and concreta; A Study of Qualities is platonistic, however, as the calculus of classes is also used.
Realism versus particularism This dichotomy applies to the atoms of a system. Particularists accept only concrete entities as individuals. A particularist might also accept other entities as non-individuals (if he is a platonist), but he could not accept, for example, qualia as individuals. A particularist could, however, accept concrete physical things just as well as concrete moments of experience. Goodman is a realist in A Study of Qualities and The Structure of Appearance. Hence, he accepts abstract entities such as qualia as individuals throughout. Carnap, on the other hand, 137
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concentrated on a particularistic system in the Aufbau, and builds on concrete moments of experience. When Leonard in Singular Terms (1930) and Goodman in A Study of Qualities are speaking of the “nominalism–realism debate”, they mean the debate between “particularism” and “realism” in the sense defined here (which is how Goodman defines it in The Structure of Appearance (SA: 104–6)).
Physicalism versus phenomenalism A physicalist accepts only physical entities (e.g. electrons or fields) as individuals; a phenomenalist accepts only phenomenal entities, such as qualia or erlebs (SA: 99–104). Goodman is a phenomenalist in A Study of Qualities and The Structure of Appearance, and so is Carnap in the Aufbau, at least for the system to which he devotes most of the discussion.38
Monism (physicalism) versus pluralism Sometimes Goodman uses “physicalism” to refer to the position of philosophers (such as Quine) who think that only one basis is acceptable, namely, the physical one. One would do better to talk simply of ‘monism’ and leave it optional that such a position is also physicalistic as defined above. In this respect, Goodman’s A Study of Qualities and The Structure of Appearance are pluralistic, because he does not claim that any basis would be more primitive or more basic and thus preferred to any other. We have argued that the same is true for Carnap’s Aufbau.
Summary In this chapter we discussed the respect in which Goodman’s dissertation A Study of Qualities and his The Structure of Appearance are continuations of Carnap’s Aufbau. We introduced what a constructional system is and considered which criteria of adequacy could be used to evaluate those systems. This interest in constructional systems would remain central to Goodman’s later philosophy; his theory of symbols, for instance, can be seen as a straightforward continuation of that topic. Also, very many of the side issues dealt with in A Study of Qualities and The Structure of Appearance reappear in Goodman’s later philosophy. The ‘grue’-problem as a problem of what predicates to use for projection and the related problem of how to analyse disposition 138
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predicates, as well as the question of how to explicate simplicity, tense, aboutness and so on, are all problems that have their roots in Goodman’s dissertation. Alas, his most important work is also his most complicated, which is why it is so often ignored. Other writings by Goodman are seemingly more accessible and have thus attracted a wider readership. However, we do not think that the significance of Goodman’s “easier” pieces can be adequately assessed without relating them to the problems and projects of A Study of Qualities and The Structure of Appearance. In recent years, interest in constitutional systems as discussed in Carnap’s Aufbau and Goodman’s A Study of Qualities and The Structure of Appearance is on the rise again. Scholars working on similarity relations, time, topology, modern forms of nominalism and mathematical models for the cognitive sciences cope with the problems posed by Goodman’s analysis and extend the formal techniques he invented or combine them with new mathematical tools.39 This demonstrates that A Study of Qualities and The Structure of Appearance are not only of interest to historians of philosophy. These milestones of analytic philosophy are still a fruitful source of insight and inspiration in a number of systematic disciplines.
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Chapter 6
Follow the sign
Signs and symbols play an important role in our lives. We use them to extract and convey information, to deceive and to reveal. Some symbols are considered natural. Smoke, for example, is said to signal fire. Some symbols are clearly conventional, such as the string of words you are now paying attention to. Some are obviously part of a whole system, such as, for instance, a system of traffic signs. Others seem to stand alone, like calling a friend and letting the phone ring only once to let her know you are on your way without wasting the money for a call. One of philosophers’ abiding interests has been how we manage to represent the world with language. But just as there are more ways to do things with words than represent the world, there are also more ways to do that than with words. Goodman’s wider agenda concerning the philosophy of language can, again, be seen as a progressive shift. This time, however, in asking for a theory of language, the question is not asked in the wrong way, but it is rather too narrow. Language, Goodman contends, is merely one of many kinds of symbolic system. Although it is undoubtedly an important one, a full understanding of its working requires a general theory of symbols that encompasses and categorizes all sundry ways of symbolization, including languages, notations, pictures, diagrams and so on. Goodman provides an approach to a theory of symbols in Languages of Art that can in part be seen as a development of his theory of meaning that we introduced in Chapter 3. He also shows in Languages of Art how the application of the apparatus he develops offers solutions to various problems in the philosophy of art (see Chapter 7 below for a treatment of this). Goodman’s theory of symbols is not only of impact in the area of art, however. Any human intellectual effort makes use of 140
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symbol systems; this is common to science, art and philosophy, which are the three areas Goodman is principally interested in.1 Sometimes it is only language that is used, and, of course, the importance of language has always been acknowledged by analytic philosophers. Pictures and diagrams, however, also play an important role in, for example, the sciences. So Goodman sees his theory of symbols as providing “means for analyzing and for comparing and contrasting in significant ways the varied systems of symbolization used in art, science, and life in general” (LA: 157). In this chapter, we shall first present Goodman’s discussion of the ways symbols refer, and then proceed to his categorization of the various symbol systems. In the course of this which symbol systems count as languages will also be defined. As in previous chapters, we shall not be able to go far beyond the basics of Goodman’s incredibly detailed theory, due to lack of space. We refer the reader to Languages of Art for the fuller picture.
Ways of referring Goodman starts his investigation into the topic of reference by asking what criteria something has to fulfil in order to count as a representation of something else. He quickly dismisses the suggestions that A represents B iff A appreciably resembles B; or that A represents B to the extent that A resembles B. Resemblance, unlike representation, is reflexive and symmetric. Nothing resembles a given object to the degree that it resembles itself, but only rarely do objects represent themselves. (The notion of an object here is broadly construed to include not only ordinary things such as tables, chairs and people but also events, sea battles, for example.) While a portrait of Queen Elizabeth II resembles Elizabeth II to the same extent that she resembles it, Elizabeth II does not represent the portrait even though, of course, it represents her. The quick and dirty fix that it has to be a picture that does the representing does not cut any ice either. First, there is a danger of circularity if ‘picture’ were to be construed as ‘representation’. Even if that can be avoided, however, we run into the problem that the portrait of Elizabeth II resembles any other picture more than it resembles Elizabeth II herself. Most paintings are alike in that they are paint on canvas (or wood), but human beings are living creatures of flesh and blood, and nothing like paint on canvas. Despite that fact, our portrait represents Elizabeth II, and only her, 141
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and not any other picture. Another ad hoc adjustment that requires that what is represented must not be a picture, will not do either: for of course there are representations of pictures. Goodman takes it to be a “plain fact” that: a picture, to represent an object, has to be a symbol for it, stand for it, refer to it; and that no degree of resemblance is sufficient to establish the requisite relation of reference. Nor is resemblance necessary for reference; almost anything may stand for anything else. (LA: 5) He finds this so obvious that he does not even consider the possibility of a more sophisticated fix for the approach (at least not at this point; we return to this in Chapter 7). Maybe one could specify further in which respects a portrait has to resemble the portrayed person, and thereby establish a connection after all. The difficulties in coming up with a list of criteria that work for all representations, not merely for portraits, are apparent, however, and not only because of the case of representations of representations. What if we exclude these problematic cases? Can we then come up with something that works? Here are some examples that suggest that it does not work even if we restrict out attention to portraits. Some cubist portraits resemble the person portrayed as much as they resemble other people they do not represent (i.e. hardly at all). And the woman depicted in Jacques-Louis David’s drawing Marie Antoinette on the Way to the Guillotine could be anyone if judged from the appearance of the figure in the picture alone. Indeed, some interpreters take this to be exactly the point of the work. Yet the cubist portraits are representations of specific people, and David’s drawing portrays Marie Antoinette, and nobody else. To add another couple of examples: Leonardo da Vinci drew himself as an old man when he was in his twenties, and it is quite possible that the picture resembles some actual old man more than it resembles Leonardo. Elizabeth Vigée-Lebrun portrayed herself resembling Rubens’s actual wife. This list could be continued. The core of representation, Goodman suggests, is reference, or more precisely denotation, and denotation is independent of resemblance. We shall see in what follows that Goodman also identifies other ways in which a symbol can refer. In Chapter 7 we shall return to the question whether resemblance at least is either necessary or sufficient to distinguish those representations that are pictorial denotations, or depictions, from other varieties of denotation. As it will turn out, it is not. 142
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Denotation is the relation that holds between, for example, a predicate and what it applies to. If representing is a way of denoting, representations or pictures function much like predicates in this respect. While all the examples introduced so far have been representations of unique objects, pictures can, like predicates, denote several individuals. The picture of a tiger in an encyclopedia, for example, does not denote a particular tiger but stands for tigers in general. It might best be taken to denote the class2 of all tigers. But there are also pictures that do not have a denotation at all. What does a picture of a unicorn represent, for example? Or a centaur-picture? Pictures of unicorns and pictures of centaurs do not denote anything at all, and so represent the same, namely, nothing. But this does not force us to lump centaur-pictures and unicorn-pictures together. A picture of a unicorn is certainly not a picture of a centaur, nor a picture of a centaur a picture of a unicorn. We should recall Goodman’s treatment of the likeness of meaning of predicates encountered in Chapter 3. The terms ‘unicorn’ and ‘centaur’ differ in meaning, even though they have the same (primary) extension, the null-extension, since their secondary extension differs: the compound expressions ‘unicorn-picture’ and ‘centaur-picture’ do not refer to the same class of things. What might cause confusion is that ‘is a picture of a unicorn’ seems to be an instance of the two-place predicate ‘is a picture of’ with the second argument place filled by ‘a unicorn’. Goodman contends that such expressions are ambiguous. The predicate ‘is a picture of a unicorn’ should really be considered a primitive one-place predicate rather than an instance of the two-place predicate ‘is a picture of’. The predicate cannot be broken up to make room for a second argument place.3 That something is a picture of a unicorn does not mean that there is something that it is a picture of (i.e. a unicorn). The one-place predicate merely groups some things together, namely all those of which ‘is a picture of a unicorn’ is true. If, on the other hand, something is a picture of Winston Churchill, there is something that it is a picture of (i.e. Churchill). To disambiguate for the technical discourse at hand, Goodman suggests that the one-place predicates, those that cannot be broken up, be written in the hyphenated form, as in ‘is a unicorn-picture’. The two-place predicates, in contrast, should be the only ones written the other way, such as ‘is a picture of a man’. When we use the latter, we imply that the picture denotes what it is a picture of, while nothing about denotation is implied when we use a predicate such as ‘centaur-picture’. 143
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But how can the unicorn-pictures be grouped together if there is nothing they denote?4 In much the same way as pieces of furniture are grouped together as tables and chairs. Furniture does not usually denote, and it does not have to in order for us to be able to correctly apply ‘chair’ to some items but not others. It is the same with unicorn-pictures and centaur-pictures. As we somehow learn to distinguish chairs from other pieces of furniture, we somehow learn to distinguish unicorn-pictures from other pictures. There is no general way of determining how this happens but some sort of story can presumably be told in each case. All Pegasus-pictures, for example, are winged-horse-pictures; and all unicorn-pictures are horse-witha-single-horn-on-the-forehead-pictures. Indeed, we can only learn from unicorn-pictures and unicorn descriptions what kinds of things qualify as unicorn-pictures or unicorn descriptions. (Unicorn descriptions, of course, do not denote unicorns either.) We learn to apply the predicate ‘unicorn-picture’ correctly to things in much the same way as we learn to apply ‘chair’ correctly to things. We can also observe that the two kinds of predicates previously confused can also come apart in cases where representation, or pictorial denotation, succeeds. A caricature of Churchill that depicts him as a bulldog represents Churchill, and hence represents a man. It is therefore a picture of a man, depicted as a bulldog, but it is not a man-picture. Rather, it is a dog-picture, although not a picture of a dog (at least not literally). It seems clear from this example that we cannot successfully apply ‘dog-picture’ to objects merely because we recognize those objects as pictures of dogs. Someone who believed that would also have to explain how it would be possible to identify unicorn-pictures. The reason cannot be that we recognize them as representing unicorns, since there are no such beasts. The temptation to lump together the predicates that Goodman disambiguates and explicates has to be resisted. Not all pictures represent something. A suprematist composition by Kasimir Malevich, for instance, does not. Still we can recognize it as a picture, and as a suprematist composition, in the same way that we recognize unicorn-pictures as pictures, and some pictures as unicorn-pictures; and chairs as furniture, and some furniture as chairs. Note that it does not matter that at some point in history people might have thought that unicorn-pictures were pictures of unicorns. Nor could this belief have helped people to apply ‘unicorn-picture’ correctly; such a belief is not even always present. Think of Douglas Adams’s Ravenous-Bugblatter-Beast-of-Traal descriptions and the pictures produced according 144
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to it. Certainly, nobody in their right mind believes such an animal to exist. Denotation is not the only way of referring. Another one is exemplification, which, despite being widely neglected, plays a major role in the realm of art (as we shall see in more detail in Chapter 7). Exemplification runs in the converse direction of denotation. If x exemplifies y, then y denotes x, but the converse is not always the case. Consider a tailor’s swatches of cloth. Such swatches are samples that exemplify certain properties of the cloth (such as colour, texture and pattern) but not others (such as size, absolute weight or absolute value) (LA: 53). A sample has to refer to the property it exemplifies; but that is not enough. While any symbol can denote anything whatsoever, a sample can only exemplify properties that it possesses or instantiates. The talk of properties here is of course unacceptable to Goodman (properties are intensional and no intensional notions are acceptable to him); he only speaks of properties in a somewhat loose way so as to avoid cumbersome formulations. Strictly speaking, exemplification is a relation that holds (or fails to hold, as it might be) between a sample and a predicate or some other (non-verbal) label. That an object possesses or instantiates a property F can be defined as ‘is F ’ applying to the object. Extensionality is secured with this definition: ‘a possesses redness iff “is red” applies to a’ remains true if ‘red’ is replaced by any coextensive predicate (LA: 51, n.4). To always take ‘exemplifies redness’ to be a sloppy way of saying ‘exemplifies “red”’, however, might be too strict. A red swatch, for instance, exemplifies ‘rouge’ and not ‘red’ to a Frenchman. Goodman suggests as an alternative that we construe ‘exemplifies redness’ as elliptical for ‘exemplifies some label coextensive with “red”’. This, however, might be too broad. Socrates, discussing philosophy in Athens, exemplifies ‘rational animal’ but not ‘featherless biped’ even though both predicates are coextensive. (Recall Goodman’s discussion of the likeness of meaning; two coextensive predicates need not have the same meaning, and this is the case whether or not they have null-extension.) Goodman is content, though, to settle with this and let the context decide which of the coextensive labels is exemplified. It is often difficult to tell what labels a thing exemplifies, partly because what labels a thing exemplifies can change with context. A tailor’s swatch can on occasion exemplify being a tailor’s swatch. Just imagine someone who is not a native speaker of English and does not know what a tailor’s swatch is. A good way of “telling” him would be to just show him one. Usually, however, a tailor’s swatch does not 145
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exemplify being a tailor’s swatch but, rather, some (although not all) properties of the cloth. Similarly, what a symbol denotes depends on context. Raising one’s index and middle finger and making a V-shape with them will be understood as standing for victory in some countries and for good luck in others, whereas in the UK it can be an insult. In § “Symbol systems” (p. 149) and § “Notations and non-notations” (p. 158) we shall come across many more examples of symbols whose reference depends on context and we shall investigate this phenomenon further. In sum, it is sometimes difficult to figure out what a given symbol refers to. Knowledge of the context is often needed. We also always need to know the conventions that govern what the symbols stand for. Some conventions are just so common that we forget that we need to know about them to understand the symbols.5 Also for the case of exemplification, this kind of additional knowledge is required. Although a sample’s properties might be intrinsic to it, it is still a matter of context and convention which of its properties a given sample refers to. We should say a little more about labels before moving on. Whereas absolutely anything can be denoted, only labels can be exemplified. The most common labels are predicates; but labels need not be verbal. Exemplification does not depend on language in that way. Diagrams, gestures, pictures and so on can be labels too, and may be exemplified. However, not only can labels be exemplified, but they can also be denoted (as can anything). A label for Churchill, for example, is ‘man’; ‘word’, in turn, is a label for ‘man’; ‘word’ denotes ‘man’; and ‘man’ exemplifies ‘word’, just as Churchill exemplifies ‘man’. Note that ‘word’ both exemplifies and denotes itself. It should be mentioned that denotation and exemplification are not the only ways a symbol can refer to an object. Reference can go via a chain of denotations and exemplifications, and so can be indirect in that way (MM: 62–6). Someone might want to ask a friend sitting five metres away in the library for a pen, but be interrupted by a harsh hiss from the librarian, having said only “Could you give me a …”. Holding her own pen can convey the rest of the message: her pen exemplifies ‘pen’ which in turn denotes pens, that is, what she wants. But reference might instead involve neither denotation nor exemplification. Holding up a pencil and making a twisting gesture around its long axis can be asking someone for a pencil sharpener. The gesture might denote the event of sharpening a pencil; but the reference step from there to the pencil sharpener is neither denotation nor exemplification. Some symbols – signs – might refer by being caused by what they refer to (see note 5). 146
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With the cases of denotation and exemplification discussed so far we have only mentioned the literal use of symbols. But symbols can denote and exemplify metaphorically as well. This, again, will become very important in Chapter 7. How does metaphorical reference work? A picture of a rainy landscape painted all in grey, with a leafless weeping willow depicted in the middle, can be sad. This is literally false, of course. Only sentient beings can be sad, and pictures do not belong to those. It can be metaphorically true, though; but how does metaphorical truth differ from ordinary falsehood? Calling the grey picture ‘yellow’ is just as literally false as calling it ‘sad’. Calling it ‘happy’, on the other hand, is both literally and metaphorically false. Whether a label is literally or metaphorically true depends to some extent on how accustomed to its application to certain objects we have become. Sometimes, if we pay a lot of attention, we can figure out that some labels are indeed metaphors that have faded due to extensive use. Let us draw your attention to the previous sentence for example: it probably contains five metaphors that are so commonly used that we normally take them to apply literally. Maybe they have become literally true even though they started out as metaphors. Another example is the talk of “large numbers”. We use ‘large’ as applying to numbers without being aware that numbers are not literally large. Whether it is a matter of degree if a predicate is metaphorical or literal, or whether there is a point (a conventional one, presumably) where a fading metaphor becomes a label that applies literally, need not concern us here. There are two important observations that can be made, though. One is that novelty is an important feature of a metaphor; relative novelty is crucial for a powerful metaphor (we return to that later). The other is that labels that apply metaphorically function in many respects in the same way as labels that apply literally. Both kinds of labels group objects together. Literally, pictures can be grouped as grey pictures, and metaphorically as sad pictures. Calling a picture sad is not significantly different qua an act of classification from calling it grey. We come to call certain pictures sad, certain people lions, certain bedrooms dumps, in more or less the same way as we come to call certain pictures red, certain people cowards and so on. Metaphor, it seems to Goodman: is a matter of teaching an old word new tricks – of applying an old label in a new way. But what is the difference between merely a familiar label to new things and applying it in a new way? Briefly, a metaphor is an affair between a predicate with a past and an object that yields while protesting. (LA: 69) 147
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The longer story is that metaphors are classification schemata that are transferred from one realm (e.g. human emotions) to another (e.g. paintings). Merely relabelling the old predicates of a realm is not going to thereby produce a good metaphor. A metaphor is powerful in so far as it groups things of that realm together that were not previously so grouped, and creates new relations between objects that were not previously recognized. The groupings and relations that the schema yields for things of the realm where it applies literally are transferred by the metaphorical application to a new realm. A metaphor is good if this transfer proves to be insightful and new classification and relations are made that are interesting in one way or another. What about metaphorical truth, though? It is sometimes suggested that applying a metaphor is elliptical for a simile. Saying that a picture is sad, then, would be elliptical for saying that it is like a sad person. Metaphorical truth would then correspond to the literal truth of the expanded statement. There are obvious difficulties here partly parallel to those discussed above concerning the resemblance between a picture and a person. In what respect does the picture have to be like a sad person? Expanding the above metaphor by saying that the picture is like a person in being sad will not help. The whole point of the exercise is that ‘sad’ does not apply literally to pictures. It seems to be extremely difficult to figure out what feature common to both a person and a picture might be responsible for the picture being sad. To come up with a general method to unpack all metaphorical statements, which the metaphor-as-simile approach seems to require, appears impossible. Nor could we just say that the sad picture must share some feature in common with a sad person. Anything is like anything in some respect, but some metaphors are false. Goodman recommends the opposite approach. In some cases, a successful metaphor likens sad pictures to sad people, by highlighting common features. Goodman here agrees with Max Black, who writes: “It would be more illuminating in some … cases to say that the metaphor creates the similarity than to say that it formulates some similarity antecedently existing” (1962: 37). In a sense, the sad picture only becomes like a sad person after the metaphor is successfully applied. For Goodman, the “[s]tandards of truth are much the same whether the schema used is transferred or not” (LA: 79). Metaphorical application of a term is fallible and subject to correction, just like literal application. He does not consider the question why a given object possesses a certain property to be a very good one, irrespective of whether the object possesses the property literally or metaphorically: 148
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The question why predicates apply as they do metaphorically is much the same as the question why they apply as they do literally. And if we do not have a good answer in either case, perhaps that is because there is no real question. At any rate, the general explanation why things have the properties, literally or metaphorically, that they do have – why things are the way they are – is a task I am content to leave to the cosmologist. (LA: 78) To conclude, note that the truth of a metaphor does not yet make the metaphor effective. A good metaphor finds a balance between fit and novelty, aptness and surprise, obviousness and oddity: “A good metaphor satisfies while it startles” (LA: 79). Whether a denotation or exemplification is literal or metaphorical makes no difference for the reference relation. Pictures that exemplify the label ‘sad’ metaphorically possess metaphorical sadness and are denoted metaphorically by ‘sad’. The converse is not generally true, a bedroom that is metaphorically denoted by ‘dump’ (Mum says, “What a dump!” on entering the bedroom of her youngest child) need not act as a sample of metaphorical dumphood and thus need not metaphorically exemplify the label ‘dump’.
Symbol systems In the previous section we said that what a symbol refers to is not generally determined by some sort of resemblance between it and its referent. The physical marks (sounds, colours, inscriptions, pictures, etc.) might also stand for very different things on different occasions. To give some examples, the string of letters ‘chat’ refers to a certain kind of conversation in English but to cats in French; a coffee mug sliding across a table can symbolize a quarterback running across an American football field, or nothing at all (Elgin 1991); and ‘OO’ can be letters of the alphabet or Little Orphan Annie’s eyes (BA: 11). This is one of the reasons why Goodman emphasizes that a physical mark is only a symbol with respect to a certain system. English is such a symbol system and French is another, with ‘chat’ standing for different things in the two different systems. ‘OO’ in written English is not recognized as standing for anything, but in a drawing it can be Little Orphan Annie’s eyes, whereas in Germany and other countries, when found written on a door it usually indicates that the room behind the door is a toilet. Just as there is nothing internal to the 149
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symbol that determines what it stands for, there is nothing internal to it that determines what kind of symbol it is: whether it is a letter of the alphabet or a picture, for example. This is instead determined by the symbol system to which the symbol belongs. We return to this after we have the categorization of symbol systems in place. Goodman develops the framework for his taxonomy of symbolic systems by defining syntactic and semantic conditions – five in total – that a symbolic system has to satisfy in order to be a notation. The reason for this is not that notations are the most important symbol systems. It is rather that the requirements on a notation, namely, the fulfilment of all five conditions, are the strictest ones. Once we are clear on these, we shall see how other common kinds of symbol systems (such as language or depiction) can be characterized by “failing” to satisfy certain conditions. These “failures”, of course, are not necessarily a bad thing, but rather characteristics of the respective kind of system. Many of the systems that are important for art, for example, “fail” in this sense, and they have to do so in order to fulfil their purpose. We shall also see how important such non-notational systems can be for science. Before Goodman can come up with the criteria for a notation he first has to determine what a notation is supposed to achieve. The conditions he presents will then ensure that this purpose can be fulfilled by any symbolic system that conforms to the conditions. A notation can thus be defined as a symbol system that does indeed conform to these conditions. The primary function of a notation is to uniquely identify what it is a notation of. Traditionally, such systems have been strived for in order to notate sounds, such as scores for music or written language for spoken language. Goodman discusses both examples. Written English, he observes, has a double function. First, the string of letters ‘cat’, for instance, denotes the sound we make when we pronounce them. But it also stands for cats. Goodman distinguished these two systems and it turns out that not even the system in which the sounds of spoken English are denoted qualifies as a notation. It will be easy to see why once we have Goodman’s theory of notation in place. We will, however, concentrate on the example of a musical score here and not return to the written English/spoken English case.6 Uniqueness of a notation is the requirement that it must be possible to determine from the score whether a given performance of a piece of music complies with it; and for every piece of music, if a score can be written for it, there is exactly one that notates it. Goodman contends that all and only performances of a specific piece of music that comply with its score are performances of it.7 In Goodman’s words: 150
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“Not only must a score uniquely determine the class of performances belonging to the work [of music], but the score (as a class of copies or inscriptions that so define the work) must be uniquely determined, given a performance and a notational system” (LA: 129–30).
Syntactic conditions Goodman first deals with the syntactic conditions a symbol system has to fulfil to count as a notation. Goodman calls the syntactic part of a symbol system a ‘symbol scheme’. It consists of characters and, usually, instructions for how to form new characters from them. Goodman here defines a character as classes of utterances or inscriptions or marks. Goodman takes inscriptions to include utterances,8 and marks to include inscriptions. An inscription is any mark that belongs to a character, whether that mark is visual, auditory or perceivable in some other way. In defining a character as a class of all inscriptions, Goodman apparently violates his nominalistic guidelines. As already mentioned in Chapter 4, though, he takes this to be a temporary measure, awaiting nominalization (see also MM: 51). In Languages of Art, Goodman expresses his awareness of this, and also his conviction that the prima facie problem is not serious. In the introduction he writes: “I have tried not to regrind old axes. For instance, if some of the following pages violate the principles of nominalism, that is only because it seems unnecessary for me to show, for present purposes, how a nominalistic version may be formulated” (LA: xiii ).9 And we have seen in Chapter 4, where we first introduced the term ‘character’, what a nominalistically acceptable version of syntax looks like.10 What Goodman does here can be recast in the way shown there without loss, except for easy legibility of the exposition (and this is probably only because most of us are not used to nominalistically “clean” talk, as we also already hinted in Chapter 4). Now that we have introduced this terminology, we are ready to specify the first condition. For a notation, the particular inscription that is used must not play any role; it is only important which character it belongs to. Exchanging an inscription for another one that belongs to the same character has no syntactical effect. Every inscription of each character in a notation must be character-indifferent. Character-indifference Two marks are character-indifferent iff each is an inscription (i.e. belongs to some character) and neither one belongs to any character that the other does not. 151
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This condition also guarantees that no mark belongs to more than one character. Suppose that an inscription x belongs to two characters, C1 and C2. By character-indifference, any inscription that belongs to C1 has to belong also to C2 since x belongs to both; for the same reason every inscription that belongs to C2 has to belong also to C1. But since characters are defined as classes of inscriptions, and because classes are extensional, C1 and C2 are the same class. They are therefore not two different characters after all, but the same. Thus, the characters in a notational scheme are disjoint: no inscription belongs to more than one character. Written English, to take an example, is character-indifferent (although it is not a notation, as we shall see later). If you take a pencil, write down ‘bat’ in the margin of this page and then take an eraser and rub out the ‘a’, replacing it with a new inscription of an ‘a’, you still have the word ‘bat’. This is still the case if you write ‘a’ and get ‘bat’. Exchanging one letter for another one that belongs to the same character (in this case the character ‘a’), has no effect on which word is spelled. This is the case even if the shape of the letter changes, for example in the way we did it here by using a different font. Inscriptions of all sorts of different styles belong to the character ‘a’: ‘a’, ‘a’, ‘A’, ‘A’, and so forth. Which one is used makes no difference syntactically. Character-indifference, though, does not prevent us from making mistakes. We might mistake a given ‘a’ for a ‘d ’ or an ‘o’. In typefaces used for printing, of course, care is taken that this is ruled out. In handwriting, however, we have all encountered the problem. Usually, it is possible to figure out from the context which character is instantiated. If we find an inscription that we think could be either a ‘d’ or an ‘a’ and then it is revealed that to the left of it we find the inscription ‘What is it like to be a b’ and to the right of it the inscription ‘t?’, we will be able to determine that the inscription is actually an ‘a’. This will be the case even if a perceptually indistinguishable mark occurs in place of ‘_’ in another inscription that reads ‘Ways of Worl_making’.11 For a notational scheme it is a necessary condition, however, that it is possible, at least in principle, to determine which character a given inscription belongs to. To see the difference between that and merely practical difficulties with distinguishing characters, consider the following symbol scheme: straight lines of arbitrary length are recognized as belonging to different characters if they differ in length by however small a fraction of a millimetre. Goodman explains: Then no matter how precisely the length of any mark is measured, there will always be two (indeed, infinitely many) characters, 152
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corresponding to different rational numbers, such that the measurement will fail to determine that the mark does not belong to them. For a notational scheme, not only must sameness of spelling be preserved where error is avoided but error must be at least theoretically avoidable. (LA: 135) The crux here is that measurement is always precise to a certain degree, but lengths correspond to rational numbers (if not to real numbers) and these are densely ordered. We shall return to the concept of density shortly, and the example will become clearer then. The importance of the possibility of distinguishing characters should be clear, though, and this leads us to the second condition that symbol schemes have to obey to count as notational: characters in a notational scheme have to be finitely differentiated, or articulate. Finite differentiation/articulateness For every two characters K and K ′ and every mark m that does not actually belong to both, determination either that m does not belong to K or that m does not belong to K ′ is theoretically possible. Goodman leaves it open precisely what ‘theoretically possible’ means but whatever is ruled out logically will certainly be excluded. Before we come back to our example, note that finite differentiation is independent of whether or not the scheme recognizes infinitely many characters. There are infinitely many Arabic numerals (the symbols denoting the natural numbers), yet the symbol scheme is articulate. Any inscription of a numeral determinately belongs to a character. The following scheme with only two characters, however, is not articulate: all straight lines of less than a centimetre in length belong to the first character, all other straight lines to the second. Close to a centimetre it will become impossible to determine whether a given line belongs to the first or the second character. Call a scheme syntactically dense if it has infinitely many characters that are ordered such that between any two there is a third one. This does not yet exclude schemes with gaps, though. Think of a scheme all of whose characters correspond to all rational numbers less than 1 or not less than 2. The system is dense but obviously has a gap. Observe that when we add a character corresponding to 1, the system is not dense anymore. It is no longer the case that there is a third character between any two characters, for there is none between the characters (corresponding to) 1 and 2. (Before, no matter how close you got to 1, there was always another character between it and 2.) We can define a scheme to be dense throughout if no addition of a character will lead 153
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to the loss of density.12 A scheme that is dense throughout does not have any gaps. Note that although finite differentiation implies lack of density, this does not hold the other way around. The scheme we just presented, with a character for 1 inserted, is an example: it is not dense, but nor is it finitely differentiated. Coming back to the example of the symbol scheme that has as different characters straight lines that differ in length (no matter how small the difference might be), we can now see more clearly what the problem is. The characters are dense (and indeed dense throughout) but our only means for determining length is by measuring. Measuring, however, is only precise to a certain degree, while the lengths of the lines correspond to the rational numbers (if not the reals). If we measure that a given line is 1.4725 mm long, we can determine that the inscription does not belong to the character that corresponds to the rational number 1.4724, or to any number smaller than that; and nor does it belong to the character that corresponds to 1.4726, or to any rational number larger than that. Nevertheless, we cannot conclude that it belongs to the character that corresponds to 1.4725, since our measurement was not exact enough to determine whether the line might in fact be 1.47251 mm long. The character corresponding to 1.4725, however, is different from the one corresponding to 1.47251, so our measurement does not determine which character the line belongs to. Since between any two rational numbers there is a third one – that is, since the scheme is dense – the situation will be the same no matter how precisely we measure.13 With these considerations, involving the correspondence of lines to rational numbers, we seem to be sliding into semantic issues already. It is too easy to read the numerals for the rational numbers as denoting the lines. It is time, therefore, to introduce the semantics and define the semantic conditions for a notation. It is important to keep syntax and semantics apart, and seeing what a semantics looks like will help us to do so. Before we introduce the semantics, however, we shall take this opportunity for a little exercise. Consider the common scheme of Arabic fractional numerals, such as ‘½’, ‘⅝’ and so on. Is the scheme finitely differentiated?14
Compliance We get a symbol system if we assign a field of reference to a symbol scheme. Goodman is concerned with denotation here, rather than with exemplification or other kinds of reference (this is mainly for 154
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simplicity’s sake; we hint at how to generalize the account at the end of this section). And he uses phrases containing ‘compliance’ and its cognates as interchangeable with certain phrases containing the vocabulary we have introduced in connection with ‘denotation’: ‘complies with’ as interchangeable with ‘is denoted by’; ‘has … as a compliant’ as interchangeable with ‘denotes’; and ‘compliance-class’ as interchangeable with ‘extension’. Goodman writes that: “compliance is with an inscription. In a given system, many things may comply with a single inscription, and the class of these constitutes the compliance-class of the inscription under that system” (LA: 144). In English, for example, ‘horse’ has a compliance-class, and so has ‘eight-legged’. There are many inscriptions that do not have a compliance class, however. We shall not go into details here, but inscriptions that do not have compliance-classes include ‘ktnjc’, ‘square circle’ and ‘eight-legged horse’. Inscriptions that for whatever reason have no compliance-classes are called vacant. A character is vacant if all its inscriptions are vacant. Reasons for vacancy include explicit stipulation that a given character has no compliance-class, failure to assign a compliance-class, as well as there not being any such things specified as compliants. A mark can determinately be an inscription of a single character and still be ambiguous if it has different compliants in different contexts. A character is ambiguous if any of its inscriptions is ambiguous. All the usual examples of ambiguous English words – ‘bank’, for instance – apply here. But having only unambiguous inscriptions is not enough to guarantee that the character is also unambiguous. Natural examples for this are hard to find but it should nevertheless be clear how this is a theoretical possibility. Think of the word ‘bank’ in written English again, and assume that every past and future inscription of it is unambiguous. Some (but not all) inscriptions determinately have only river banks as compliants while only financial institutions comply to all remaining ones. The character is nonetheless ambiguous. A character is unambiguous iff all of its inscriptions have the same compliance-class.
Semantic criteria Now that we have introduced the basic notions of the semantics of symbolic systems (as rudimentary as those might be), we can state the three remaining conditions that a symbolic system has to fulfil to count as a notation. The first semantic condition for notations is that they must be unambiguous. To fulfil its purpose, the compliance 155
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relation of a notation must not vary, and hence the system must not include any ambiguous inscriptions. Also, all ambiguous characters, including those that have only unambiguous inscriptions, have to be banned. Notational systems have to be character-indifferent (the first syntactic condition). If ambiguous characters were allowed, the compliance relation could vary again, even if one unambiguous inscription is exchanged for another, as in the case where the two inscriptions have different compliance-classes. Unambiguousness A notation does not contain any ambiguous inscriptions or characters. The remaining two semantic conditions are parallel to the two syntactic ones (but they neither entail them, nor are entailed by them). The first is that in a notational system, the compliance-classes have to be disjoint, that is, it must not be the case that something belongs to two different compliance-classes. Remember that we placed on the wish list for a notation that it should be possible (now using the new terminology) to go from inscription to compliant and back without changing the identity of, for example, the work of music. If, however, something belonged to two different compliance-classes, such stepping back and forth might lead us from one to another. Consider a very simply symbol system. It has only two characters (for illustrative purposes borrowed from English): ‘green’ and ‘apple’. The complianceclass of ‘green’ includes exactly two things: one (green) apple a and one (green) car c; the compliance-class of ‘apple’ includes exactly two things, too: one red apple r and the green apple a. We can denote both a and r with ‘apple’, but we will not end up with a notation. Imagine that the instructions that go with this symbol system were to present a compliant when a piece of paper with an inscription of ‘apple’ or ‘green’ is shown, and to show a piece of paper with an inscription of either ‘apple’ or ‘green’ when one of their compliants is presented. It is easy to see that the system fails to be a notation. There is no guarantee that going back and forth between presenting an object and holding up a piece of paper will not take us from r, the red apple that complies with ‘apple’, to c, the green car that does not comply with ‘apple’. This, however, has to be ruled out for a notation. The parallel to a score denoting music is clear enough: step by step, tone by tone, one could go from Beethoven’s Fifth Symphony to The Eagles’s Hotel California. (We return to this in Chapter 7.) Less harmful, but still to be excluded since we want to be strict, is redundancy. A system is redundant iff there are two different 156
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characters that have the same compliance class; think of the notorious ‘renate’ (creature with kidneys) and ‘cordate’ (creature with a heart). That means that in such a system there will be an inscription that has a compliant that also complies with a second inscription that belongs to a different character than the first. So by going back and forth from inscription to compliant, we might end up with inscriptions of different characters, but at least the compliance-class will stay the same. In any case, this leads to the full statement of the second semantic condition. Goodman calls it the ‘disjointness requirement’, but it also bans redundancy (‘disjointness’ is a term of art, so Goodman is of course free to stipulate it in whatever way he likes). Disjointness No two characters of a notation have any compliant in common; not only must every two different compliance-classes in a notational system be disjoint but every two characters must have different compliance-classes. Even if we could exclude ambiguities from English (or any other natural language), disjointness would rule it out as a notation. Many English terms have intersecting compliance-classes; think of ‘mammal’, ‘animal’, ‘Englishman’ and ‘philosopher’. The final requirement for a notational system is: Semantic finite differentiation For every two characters K and K′ such that their compliance-classes are not identical, and for every object h that does not comply with both, determination either that h does not comply with K or that h does not comply with K′ must be theoretically possible. This condition closely mirrors the syntactic one of articulateness; and the considerations here are similar too. Consider a system that has as characters all fully reduced, positive Arabic fractional numerals less than 1 (i.e. classes of inscriptions thereof). Their compliance-classes are the corresponding fractions of a gram. The two syntactic and the first two semantic requirements are fulfilled; but – parallel to the case of straight lines in the syntactic case – any difference in weight, however tiny, means compliance with a different character. No matter how finely we weigh, there will always be characters for which it cannot be determined whether an object complies with them. This system is semantically dense, indeed semantically dense throughout. The definition of semantic density follows the lines of the syntactic notion. In summary, a symbol system is a notation if it fulfils these five requirements: (i) character-indifference; (ii) syntactic finite differentiation (or 157
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articulateness); (iii) unambiguousness; (iv) (semantic) disjointness; and (v) semantic finite differentiation. All five are mutually independent of one another in the sense introduced earlier. The semantic notions ‘ambiguity’, ‘disjointness’, ‘differentiation’, ‘redundancy’ and ‘density’ are defined for denotation only and not reference in general, as mentioned above. The generalization from ‘compliance’ to ‘reference’ and from ‘compliance-class’ to ‘reference-class’ is straightforward, though. Semantic differentiation in the general sense, for instance, can be defined like this: “For any two characters K and K′ and every element h not referred to by both, determination either that K does not refer to h or that K′ does not refer to h is theoretically possible” (LA: 234). This way, not only can denotational systems be classified in the theory, but so can systems that include exemplification or other ways of referring.
Notations and non-notations Now that we have defined what a notation is, we can go on to see how other symbol systems can be characterized as lacking one or more of the features of a notation. As should be clear from the previous section, natural languages, while satisfying the syntactic criteria, violate all three semantic ones. Nothing, though, keeps languages from being notational in principle. It is easy to imagine, for example, a computer programming language that is notational, even though actual such languages have some redundant characters. A pressure gauge might serve as an example of a dense symbol system. Suppose the gauge has an unmarked circular face and a single pointer that moves smoothly clockwise as the pressure increases, and back as it drops. Neither the syntactic, nor the semantic, requirement of finite differentiation is met. Each position of the pointer is a character in the system, but between each two there is a third one. The system is syntactically dense. Since the measured pressure is also dense, semantic finite differentiation fails too.15 We can alter this system, however, and use the gauge for a notation of the pressure. If we decorate the face in the way Goodman suggests, with fifty dots in equal distance around the face, the first step is made. The system is not yet notational, though. It is still to be determined how the gauge is to be read. If the characters are still the absolute positions of the pointer on the dial, nothing has changed: the system is still syntactically and semantically undifferentiated. But if the instructions to read the gauge are changed, we can indeed end up with a notation. Take 158
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each of the dots to be the centre of one of the fifty regions that correspond to the characters of the system. Whenever the pointer is in one of these regions, this counts as an inscription of the character. If the fifty regions are taken to be disjoint and separated by gaps, however tiny they might be, the symbol scheme fulfils the syntactic criteria for a notation. If, now, the compliance-classes of the characters are so determined that the ranges of pressure assigned to them are also disjoint and separated by gaps, the system is notational. One might be tempted to think that dense symbol systems and the instruments operating within them have no place in science or any other area where precision matters. If we cannot read off the exact pressure of the gauge, no matter how hard we try, surely such a gauge is next to useless where precise measurement matters. Yes and no. Instruments that operate in a dense system have the advantage of greater flexibility and sensitivity. In fact, they are (in principle) arbitrarily sensitive; we only need to have a closer and more precise look to get a more precise reading, in principle as precise as we like, even if we can never determine the reading exactly. There is no boundary of accurateness other than our ability to get finer and finer readings of the position of the gauge’s pointer in our example. Once it is determined how fine the discrimination of the readings has to be for a given purpose, the dense system can be replaced by a finitely differentiated one. It might be that instruments such as our non-graduated pressure gauge will only be used in the early stages of designing a new notational system and the instruments operating in it; it even might only be in use in order to figure out suitable units of measurement. That does not undermine the importance of dense systems, however. Pictures might fail on all five criteria. But since we shall say a good deal about the area in which pictures play the most important role – art – in Chapter 7, let us concentrate here on their close relatives: diagrams. Diagrams are often thought to belong to dense symbol systems, to be incapable of having the virtues of a notation, and thus to be unsuitable for science, mathematics or any other serious enterprise. The vital function of cardiograms alone spells doom for such a view, independently of what we have already said about instruments operating within dense symbol systems. Let us have a closer look at diagrams in the framework now available. Goodman suggests that the not uncommon belief that diagrams belong to a dense system results from their “somewhat pictorial look”; we think of them “as rather schematized pictures” (LA: 170–71). Some diagrams are indeed part of dense symbol systems but others are not. 159
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Some diagrams of carbohydrate molecules, for example, are notational. Others – road maps, for example – are mixed. Venn diagrams can be notational. It has been shown that they can even serve as a decision method for monadic predicate logic. Also, the use of diagrams in mathematical proof has recently received attention from philosophers of mathematics.16 These are still only examples, however striking. It hardly gets more seriously precise than formal logic and mathematics, however, and even here diagrams have their place. In a seismogram, typically, any point on the curve is the inscription of a character. Such a seismogram is syntactically and semantically dense. We can call diagrams that have these features graphic. A curve on a chart that shows the annual car production in the UK on the other hand can be notational, even if the points that stand for the number of cars produced each year are connected by lines to indicate the trend. If these lines are not taken to be characters of the system, the system can be notational. Figure 6.1 below is a diagram of the positions of figures on a chessboard. It is also a notation of their positions. The diagram is not a notation of the moves made in the game, of course. A series of diagrams placed in the right order, each showing the position of the figures after successive moves, however, might be such a notation. It is not even required that the single diagrams that are put into such a sequence are notations of the positions. Indeed, they could be pictorial representations of the board, although they do not even have to be that. The whole diagrams (pictures, or whatever else) are themselves the inscriptions that have the positions of the pieces on the board as compliance-classes. These do not need to have an internal structure that allows us to determine which position they denote. The only important considerations are that no two positions comply with the same diagram, that the diagrams can be distinguished, and so on: in short, that the five conditions for a notation are fulfilled. To take an easier example, consider a symbol system that has two characters both of which have only one inscription. The first one is a particular painting of a cat, the second one a particular cactus in its pot. A child uses these symbols to signal how much money she has in a box. If it is £5 or more she puts the picture of the cat to the right of the box; if it is less she puts the cactus there. It should be clear that all five conditions for a notation are fulfilled. The picture and the cactus are the inscriptions of the symbol scheme, and the amount of money in the box their compliance-classes. Although one of the symbols, the picture of the cat, seems to be a symbol that belongs to 160
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Figure 6.1 A chess diagram of the so-called “Grünfeld Defence”
a dense system, there is no contradiction. A given physical object can belong to different symbol systems. The very same object can be an inscription of a notation and a representation, that is, part of a dense pictorial system. How the symbol is classified depends on the system in which it figures, not on any internal features. What now if an artist, call him Casper Cohns, produced a painting that looked just like Figure 6.1 on a 4m2 canvas? As a painting and a work of art, it would (presumably) belong to a dense system. If, however, we read it as denoting the positions of the pieces on a chessboard just as we read Figure 6.1, it is nevertheless a notation of the characteristic position of the Grünfeld Defence. Goodman’s own example is that of a curve of a cardiogram that is indistinguishable from a Katsushika Hokusai drawing of Mount Fuji (LA: 229–31). We return to this in Chapter 7. Before we close this chapter, though, let us have a look at a “real-world” notation to see more clearly how a notation works. Here is a notational system for games of chess. Let the fields of the board be coded in the usual way, with small Roman letters ‘a’ to ‘h’ and the Arabic numerals ‘1’ to ‘8’ along the axes, so that each field is denoted by a pair of coordinates, with the letter stated first. In Figure 6.1, the white king is on e1, and the black queen on d8. Except for the pawns, we assign a capital Roman letter to every kind of piece (irrespective of the colour): ‘Q’ to queens, ‘K’ to kings, ‘B’ to bishops, ‘N’ to knights and ‘R’ to rooks. A move that White makes is noted down like 161
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this. If a pawn moves, the coordinate of the field it moves to is written down, for example, ‘e4’ (a popular opening move). If one of the other pieces moves, the letter denoting the kind of piece is put down, followed by the coordinate it moves to. For moves that Black makes, the notation is the same, only that two dots, ‘..’, are put down before the string of symbols, and a comma followed by a space, ‘, ’, behind it. That is almost all one needs for a notation of all chess games. (It will only be a notation for games that follow the standard rules, however. Showing why is left as an exercise.) Two additions, or adjustments, have to be made. First, we need a way of denoting castling: ‘O-O’ denotes castling on the king’s side and ‘O-O-O’ castling on the queen’s side. Secondly, there are situations where more than one pawn, rook or knight could move to the specified field. If, and only if, this is the case the coordinate that the piece is on before moving is written down immediately before the coordinates that it moves to. For example, if Black has one knight on f5 and the other on c6, and then moves the latter to d4, this would be denoted by ‘..Nc6d4, ’. Mark the end of a game by ‘1-0.’ if White wins, by ‘0-1.’ if Black wins, and by ‘.5-.5.’ for a draw or stalemate; if White made the last move, prefix this “end-of-game” mark with a comma followed by a space: ‘, ’. Games are always assumed to start with the standard set-up of the board and go according to the standard rules of chess. A notation of a game, then, is a string of symbols denoting the moves that are made in the order they are made, with the symbol for the outcome of the game at the end, if the game is played to the end.17 It should not be too hard to see that this notation is a notation in Goodman’s sense: it fulfils all criteria. To illustrate, here are a couple of chess notations: A very short game e4..e5, Qf3..Nc6, Bc4..Na5, Qf7, 1-0. Checkmate! The Grünfeld Defence d4..Nf6, c4..g6, Nc3..d5, At this stage we have reached the position in Figure 6.1. You can see that at every stage of the notation you know exactly what to do if you want to move the pieces on a board according to the notation. We could also have chosen a symbol system that provides linear notation of the position of the pieces on the board instead of the diagram in Figure 6.1. Here is an example how this might go: ‘00’ stands 162
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for an empty square; squares that are occupied by a piece are notated by ‘0’ or ‘1’ for a white or a black piece, respectively, followed by a ‘1’ for a pawn, ‘2’ for a bishop, ‘3’ for a knight, ‘4’ for a rook, ‘5’ for a queen and ‘6’ for a king. We start the notation on square a1, then move to the right until we reach a8, and then proceed to the next row up with b1 to b8, and so on. The position of Figure 6.1, then, comes out as: 04000205060203040101000001010101000003000000000000000 10100000000000000110000000000000000001311001111110011 1100111413121516120014 This, admittedly, is a bit difficult for us to parse, despite being notational, but it carries the same information as the diagram in Figure 6.1. It uniquely identifies, and is uniquely identified by, the setting of the board. It would be even less tractable for human beings if we put it into binary, but in that way, it becomes very easy to handle with a suitable computer program. This serves to illustrate two points: first, notationality of a symbol system does not entail easy legibility or that it would be easy for human beings to handle such a symbol system (LA: 154); and secondly, different symbol systems suit different purposes.
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Diagnosing art
In this chapter we outline Goodman’s philosophy of art, which can largely be found in his Languages of Art, with some additions made in Ways of Worldmaking and Of Mind and Other Matters. Goodman presents a symbol-theoretic approach to art. Artworks are (complex) symbols, and as such function cognitively. Elgin called this “Goodman’s Epistemic Turn” (1997a: ch. 3). Art, like science and philosophy, contributes to our understanding. Artworks present a world version (see Chapter 8), but in order to do so, they, in turn, must be understood: To understand a portrait, a partita, or a pas de deux, Goodman believes, is not to consider it beautiful, appreciate it, ascertain what its author intended by it, or have a so-called “aesthetic experience” of it. Rather, to understand it is to interpret it correctly – to recognize what it symbolizes and how it fits with or reacts against other world version and visions. Understanding works of art is not a matter of passive absorption, but of active intellectual engagement with symbols whose syntactic and semantic features are often elusive. No more than in science is correct interpretation in the arts assured. Thinking you understand a symbol does not make it so. (Elgin 1997a: 63–4; see also WW: 109–40) In philosophy of art as in the other philosophical areas, Goodman is far away from postmodern philosophers, who often tend to declare him one of their own. One has to get the interpretation of an artwork right. It is not the case that anything goes; indeed, most things do not. The understanding of a work of art is based, according to Goodman, on the way it functions as a symbol. Goodman takes his theory 164
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of symbols as a basis and builds his theory of art on it. In this chapter we show how this is done. (In this sense, this chapter presupposes the technical terminology of Chapter 6, especially in § “The sameness of songs”, p. 177.)
Innocent imitation In Chapter 6 we presented Goodman’s arguments against denotation being a matter of resemblance. Here we are picking up the discussion again. Anything can denote anything, as we noted before. Could it at least be the case, however, that pictures, that is, pictorial denotations, are distinguished from other varieties of denotation in that some kind of resemblance plays a role in what depicts what? In other words, is it essential to a portrait, for example, that it resembles the person it depicts, at least if it is supposed to be a faithful representation? Not surprisingly, Goodman does not think so. He goes through a series of ways of understanding and modifying the claim that a faithful or realistic picture has to “come as close as possible to copying the object just as it is” (LA: 6), and rejects them. First, think of an artist who wants to produce a portrait of a man. That man is a cloud of atoms, a complex of cells, a person and many other things as well: for example, a bachelor, a philosopher, a jazz drummer, a mountaineer and a friend. Which of these is the way the object is “just as it is”? Which of these aspects has to be copied to achieve a realistic picture? Surely, trying to include all of the above together with all other properties (whatever that might mean) would be a foolproof method of producing a picture that is very unrealistic. Thus representations have to pick out a certain aspect of what they represent. Maybe, then, to represent realistically is to represent the object the way it looks to the normal eye, under normal circumstances (regarding light, distance, angle, etc.), without the use of instruments, and without special interest or affection on part of the spectator, with no background knowledge and regardless of any interpretation. What we want, in other words, is the view of the innocent eye. The only problem with that is – and here Goodman sides with the art historian Ernst Gombrich (see e.g. Gombrich 1960, 1982)1 – that there is no such thing as an innocent eye: “The eye comes always ancient to its work, obsessed by its own past and by old and new insinuations of the ear, nose, tongue, fingers, heart, and brain” (LA: 7). Our vision is, like all perception, selective. In perceiving we classify, analyse and 165
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construct, guided by our present interests, needs and beliefs.2 Goodman takes the idea of the innocent eye to be akin with the myth of the given (we discussed Goodman’s lack of patience for the myth of the given in Chapter 5): The myth of the innocent eye and of the absolute given are unholy accomplices. Both derive from and foster the idea of knowing as a processing of raw material received from the senses, and of this raw material as being discoverable either through purification rites or by methodical disinterpretation. But reception and interpretation are not separable operations; they are thoroughly interdependent. The Kantian dictum echoes here: the innocent eye is blind and the virgin mind is empty. Moreover, what has been received and what has been done to it cannot be distinguished within the finished product. Content cannot be extracted by peeling off layers of comment. (LA: 8)3 An artist might of course try to see the things she paints with an innocent eye, and try to free the representation of traditional forms and prejudices. If she is successful, however, the result is likely to be much better described as a new look on things and a fresh insight, than as an innocent copy. The representation of an object is not merely copying it, since it would not be clear which aspect of an object has to be copied to make it a mere copy. A picture represents an object in a certain way, from a certain angle, in a certain light; it represents under an interpretation, and emphasizing some features of the object, neglecting others. But by providing representations, artists do not copy these interpretations or construals of the objects they depict, they achieve them. Maybe at least one aspect of the idea of the “innocent eye” can be salvaged from the wreckage. Gombrich and many other art historians and theoreticians wholeheartedly agree with Goodman’s rejection of the “innocent eye”, and have made the case before Goodman. Most of them, however, including Gombrich, want to make an exception concerning this relativity of vision and representation for the case of perspective. There is such a thing, the view goes, as the right perspective, and that is basically the one that was achieved in the Italian Renaissance. It is supposed to derive its special, non-negotiable status from the behaviour of light, written down in the physical laws of optics. The idea behind this is that, under the right circumstances, a picture will deliver to the eye a bundle of light that matches the one delivered by the represented object itself. This match is supposedly purely objective 166
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and mechanically measurable; and so the identity of the pattern of the light bundles coming from the picture and the actual object depicted must constitute a measure for a realistic representation. Goodman flags a number of problems with this view. First, the bundles of light hitting the eye from any given representation match bundles of light from any number of other objects as well as the one actually represented, if the conditions are adjusted in the right way. Think of a black box in a white room at a certain distance, to pick an easy example, and a slightly bigger box, slightly farther away in the same room. It can easily be arranged that the bundles of light coming from the room and the box are indistinguishable in both cases (maybe the lighting has to be changed, and maybe the room has to be bigger, depending on the set-up, but the idea is clear enough). Still, they are bundles of light from different objects. There are certainly more interesting examples, too. Also, in order to conform to the right viewing conditions one has to look from a certain distance and only with one eye (to prevent stereo vision, which might reveal the flatness of the representation), and that eye also has to be fixed in some way. Otherwise the bundles of light will not match. Even if we could be satisfied with the thought that such highly unnatural viewing conditions are supposed to reveal the most natural and realistic representations, there is a catch: human vision does not work properly if the eye is not moving (see Riggs et al. 1953). After a very short while of staring at the same spot, most of the visual field, and eventually all of it, blurs out. “The fixed eye is almost as blind as the innocent one”, as Goodman remarks (LA: 12–13). So, how are conditions that make normal vision impossible a measure for realistic representation? Maybe a slight movement of the eye can be allowed to prevent it from shutting down, but the problem of the abnormality of these viewing conditions remains. If we are allowed to create highly artificial conditions under which a painting creates the same appearance as the object it represents, why stop there? Special instruments (that might differ only in degree from a peep-hole with whose help we might achieve the fixed viewing conditions envisaged above), clever lighting, drugs (maybe to render the eye immobile, maybe for other purposes), lenses, smoke and mirrors, and whatever other stage-managing one might think of, will, if cunning enough, produce bundles of light from any arbitrary picture that will match the bundles from any object whatsoever. Furthermore, we have already mentioned that vision is not separable from the other senses and the beliefs and desires of the perceiver; 167
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it rather is “a dutiful member of a complex and capricious organism” (LA: 7). The viewing conditions for a cathedral are very different from the ones for a representation of it. In viewing either, we not only receive rays of light but all sorts of other information at the same time that in most cases will differ significantly from the context of the cathedral to the one of its representation. Under different circumstances the visual experience can differ vastly, irrespective of the identity of the pattern of the received bundle of light. All these considerations depend on granting that the perspective that we consider to be the right one actually does accord to the behaviour of light rays. This, however, is not even the case: By the pictorial rules, railroad tracks running outwards from the eye are drawn converging, but telephone poles (or the edges of a façade) running upwards from the eye are drawn parallel. By the “laws of geometry” the poles should also be drawn converging. But so drawn, they look as wrong as railroad tracks drawn parallel. Thus we have cameras with tilting backs and elevating lens-boards to “correct distortion” – that is, to make vertical parallels come out parallel in our photographs. (LA: 16) So, in order to please the Western eye and make the representation appear faithful to it, the “laws of geometry” have to be neglected. Figure 7.1 is in all relevant respects similar to a drawing that the artist Paul Klee included in his Pedagogical Sketch Book (Klee 1925). Goodman cites Klee as an ally with the painter’s remark that the drawing looks rather normal “if taken as representing a floor, but awry as representing a façade, even though in the two cases parallels in the object represented recede equally from the eye” (LA: 16, n.16). Façades of buildings are also typically represented with parallel lines for horizontal edges, take as an example almost any frontal picture of the Houses of Parliament. The Tuscan Renaissance artist Leonardo da Vinci already noted this problem in one of his sketch books in his studies of the perspective of column galleries (see Kemp 1989: 44–52; Pedretti 1963).4 Obviously, his insights did not catch on, and were not included in the cannon of painting in Western perspective. So, which is the “right” way to represent parallel edges of a building façade, and the like? In Figure 7.2, a represents the eye level of an observer, looking at the upper part of a façade b–c. At d–e we have a representation of that part of the building in the standard perspective and the right scale and proportions for that distance. The normal line of vision to the part of the façade is a–f, the normal line to the 168
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Figure 7.1 Floor or façade?
picture is a–g. As can easily be seen, the line a–g is perpendicular to the picture, and so vertical parallels in it will be projected by the bundle of light arriving at the eye as parallel. The line a–f, however, is at an acute angle to the actual façade, so the parallel vertical lines will be projected as converging upwards. In order to fix this mismatch between the light bundles, we have three options: (i) move the picture to h–i, (ii) tilt the picture and move it to j–k, and (iii) look at the picture where and how it is, but elevate ourselves to m in order to look at the façade. In the first two options, the scale of the picture will now be wrong, since we have had to move the picture closer to the eye to subtend the same angle. More importantly, however, we end up with very abnormal conditions again. We do not normally hang pictures far above eye level, or tilted in the way (ii) requires, and neither is our normal perception of the upper part of a building façade from a point corresponding to anywhere near m in Figure 7.2.
b f
m
façade
h
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Figure 7.2 An observer in front of a façade and a picture of it.
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Of course, even if the rules of perspective were revised to fit the laws of optics, and we at some stage got so used to them that the converging lines would no longer look odd to us, the general argument concerning the conventionality of perspective would still apply. “Briefly, the behavior of light sanctions neither our usual nor any other way of rendering space; and perspective provides no absolute or independent standard of fidelity” (LA: 19). That the standard perspective seems right to us, despite its failure to provide a faithful representation even by its own standards, witnesses that what looks right to us depends on what we are used to.5 It might be tempting to think that the problems here described have to do with the translation of a three-dimensional object into a plane (even though that should not make a difference to the light bundle hitting our eye). A sculptor who portrays a person, however, is faced with the same difficulties as the painter in picking out certain properties of the portrayee. “Duplicating the form of the head at a given instant is unlikely to yield a notably faithful representation. … To portray a person faithfully is to convey a person known and distilled from a variety of experience” (LA: 20). The French sculptor Auguste Rodin complained about the “unnaturalness” of the representations provided by photography, a technology that was relatively new in his days. Rodin considered photographs of walking people. They did not seem faithful representations for the act of walking to him; rather, the people in the pictures looked as if they were grotesquely holding one leg into the air, or as if they were jumping (Gsell [1912] 1984: 31–3). In his bronze Saint John the Baptist Preaching (1878), and especially in a torso derived from it, Walking Man (c.1900), he presents his own version of a representation of a walking person. Indeed, the sculptures give the impression of someone who is walking, or rather marching forcefully. Both feet, however, are represented as put down flat on the ground. This position never occurs in actual walking. When the back foot touches the ground with the entire sole, the foot in front is in the air, or at best the heel touches the ground, and when the front foot is flat on the ground, the back one is on its toes, or already lifted off the ground. To produce a credible representation of a walking person, Rodin created a sculpture that is not a “snap-shot”; it does not correspond to a position that a human body is ever naturally in, especially not while walking. One would probably have to strain one’s tendons in order to even stand the way Rodin’s Walking Man does. The sculptural representation of a walker in a “snap-shot” way, on the other hand, would seem as wrong as the photographs Rodin ridiculed. 170
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Any artist, whether she works in two or three dimensions, has to decide how she wants to represent the object under consideration. A mere copy is hardly possible, and trying to achieve one is likely to result in a work that is far from the desired outcome. A representation is particularly effective if the artist manages to provide a “fresh look” on the object, to depict a common thing in a new and insightful way. In this respect representations are much like verbal metaphors. Both are particularly successful if “the marking off of new elements or classes, or of familiar ones by labels of new kinds or by new combinations of old labels, may provide new insights” (LA: 33). A successful picture can make a genuine contribution to knowledge by providing surprising insights, not unlike the way new successful scientific theories can. Representations, like metaphors, are creative. They classify objects and make relations between them. Our perception of nature depends on the ways the arts and the sciences present it to us. Art and science, in that sense, create the world. (This will be the topic of Chapter 8.) Goodman illustrates this by quoting the artist Pablo Picasso: “To a complaint that his portrait of Gertrude Stein did not look like her, Picasso is said to have answered, ‘No matter; it will’” (LA: 33). Goodman got the Picasso quote slightly wrong here. What Stein actually reports Picasso as saying, however, strikes us as even more fitting: “Everybody says that she does not look like it but that does not make any difference, she will.” (Stein [1933] 1990: 12, emphasis added). What Goodman is aiming at in quoting Picasso’s quip is that art influences the way we perceive the world in the same way as the perception of the world version influences the creation and reception of art. That nature imitates art is too timid a dictum. Nature is a product of art and discourse. (LA: 33) That a picture looks like nature often means only that it looks the way nature is usually painted. (LA: 39) What is still open, however, is, as Goodman puts it, “the minor question what constitutes realism of representation” (LA: 34). He considers two more views that can commonly be found before he presents his own. The first is that deception is a measure of realism. The more the spectator is likely to be fooled into believing he sees the actual object, and not a representation of it, the more realistic is the picture. But most of the objections already put forward apply here as well. What is likely to deceive also depends on circumstances and what is actually observed. These circumstances, again, might involve all sorts 171
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of claptrappery, however, and what is observed depends on interest, beliefs, customs and habits. If we want to forbid smoke and mirrors in causing this deception, and only consider “normal” viewing conditions, we are no better off. The usual conditions for seeing a painting, framed and hanging exposed on a wall in a museum, art gallery or our living rooms, are also very unlikely to give rise to any sort of deception (and the remarks about “normal” viewing conditions mentioned above also still apply). Moreover, if ‘degree of deception’ is intended as something like ‘probability to take it for the object’ we are left with the awkward situation that, of course, the probability approaches 1 if we are confronted with the object itself; and as we said in Chapter 6, only rarely do objects represent themselves. The last alternative Goodman considers is that a picture is realistic to the degree that it conveys information about the represented object. In response, he asks us to consider the thought experiment of the following two pictures: the first one is painted in standard perspective and in ordinary colouring, that is, red is represented as red, blue as blue, and so on; the second reverses the perspective6 and every colour is replaced by its complementary colour, that is, we find green for red, blue for orange, and so on. Obviously, the second picture, interpreted appropriately, transports the same information about the represented object as the first. It is equally obvious that only the first one would count as a realistic picture in the normal understanding of ‘realistic’. One might argue that for the second picture one needs some sort of translation manual to decipher it, but Goodman contends that it is rather the case that we need such manuals for both representations. The difference is that in the first case we are so used to applying this manual that we do not notice that we are doing it. An analogy might spring to mind for those who are fluent in a second language, and still remember the process of first learning it. In the beginning, quite often one translates words and sentences that one hears (or wants to say) into (or from) one’s native tongue. After years of practice one reaches a certain state of familiarity with the language and this no longer happens. Understanding in the second language is much easier than translating it at this stage. Similar experiences can be had when one learns to read musical scores. Counting lines to figure out the note a certain symbol denotes will soon be replaced by the ready ability to play what one reads off the score, sometimes accompanied by the incapability of spontaneous naming of the note one reads. Whatever the symbol system is – language, score, depiction, or whatever you like – once we are sufficiently used to it, “reading” becomes automatic 172
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and effortless to the extent that we are no longer aware that we are interpreting.7 Precisely here, however, Goodman suggests, we have found what makes a realistic picture. We judge how realistic a picture is by how readily we can retrieve information from it about the object it represents. This, in turn, depends on how common the symbol system is in which it operates, how stereotypical the labels it uses have become. This is true of many systems, not just pictorial ones. If we consider linguistic examples we notice that this is not entirely unlike Goodman’s solution to his new riddle of induction (see Chapter 2): the predicates that seem “natural” to us are just those that are well entrenched in our language; and the pictures that look realistic are those that use familiar modes of representation. Native English speakers find it natural to group things together under the label ‘blue’, and are baffled when learning Italian and being asked to distinguish ‘azzurro’ (applying to a blue sky, but not the blue ocean) and ‘blu’ (including the colour of the blue ocean, but not the one of a blue sky), a distinction that is absolutely natural to a native speaker of Italian and that does not map onto the distinction between ‘light blue’ and ‘dark blue’ either. A present-day mathematician who is interested in the foundations of mathematics is likely to find it natural to think of numbers in terms of sets, whereas Leibniz and his contemporaries probably found it just as natural to think of them as geometrical magnitudes, line segments, for instance. Goodman writes: Realistic representation, in brief, depends not upon imitation or illusion or information but upon inculcation. Almost any picture may represent almost anything; that is, given picture and object there is usually a system of representation, a plan of correlation, under which the picture represents the object.8 How correct the picture is under that system depends upon how accurate is the information about the object that is obtained by reading the picture according to the system. But how literal or realistic the picture is depends upon how standard the system is. If representation is a matter of choice and correctness a matter of information, realism is a matter of habit. (LA: 38) Before we present how the different systems of representation work for the different forms of art, it seems apt to say something about another important way in which artworks refer.
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Expressing emotions? That it is important for artworks to express this or that is as commonly believed as that they are representations. As we have seen, Goodman construes representation quite differently from the way it is commonly understood; this is also the case for expression. Many different things are subsumed under the expression ‘expression’. We say that words and sentences express certain things – ideas, maybe – but also that persons express their feelings, or that someone has this-or-that facial expression. In the arts, expression is often connected with feelings or emotions. Some pictures express joy, some pieces of music sadness. Pictures are also sometimes said to express heat, or works of sculpture fragility. An important task in trying to understand what expression is in art is to bring order to this muddle. It might seem tempting to try a causal theory of expression. Surely, a facial expression of fear is caused by the fear of the person whose face it is. The interested expression many people can reliably put on their faces out of politeness while listening to the most boring things suggests that a causal theory of expression along these lines does not provide a general explanation; other examples are easy to find. Also, this proposal will not help us for art. Although the idea that a sad picture is sad because this is the way the artist felt when painting that picture is very romantic (and, indeed, we inherit it from the artists and art critics of Romanticism), it is also rarely true. Painting a picture takes a long time, and it is rather unlikely that a painter remains in a sad mood for days or weeks or even months. Goya’s series of etchings The Disasters of War expresses the terror and barbarism of war, but it is highly unlikely that he could have produced so many very skilful etchings while being terrified the whole time; it seems equally unlikely that he felt particularly barbaric during their production. The soldiers and generals in these pictures express brutality and arrogance, while the victims express fear and agony. Which of these sentiments did Goya feel? Or did he go through a rollercoaster ride of emotions etching one figure after the other? The interpretation, actually put forward, that Leonardo da Vinci wanted to express the joyful expectation of motherhood in his Mona Lisa is certainly wrong; it is not wrong, however, because he could not have had that feeling himself. Since we are interested in art, an actor might give us an insight. An actor on stage is usually not sad while she is expressing sadness, but perhaps the key is that her expression causes that emotion in us. 174
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Is the expression of sadness in a painting or by an actor successful to the extent that it makes the spectator sad? This seems to be slightly more plausible, but only slightly. The expression of sadness might cause sadness in the spectator, but it might also cause the feeling of sympathy; the expression of agony is more likely to create the feeling of pity than agony. This also does not account for the cases where something other than emotion is expressed. A sculpture expressing fragility does not make the spectator feel fragile. The idea that an artwork expresses the emotion it causes, or is caused by, goes hand in hand with the conception of art that was popular in Romanticism (as touched on above) that art is essentially expressing emotions. Although this idea might be important for art from that period, it does not appear to give a universally valid account of what is important about art. It does not explain Piet Mondrian’s paintings in a satisfactory manner, nor the Campanile of the cathedral in Pisa, nor Bach’s Goldberg Variations. “These confused notions of expression are entangled with the popular conviction that excitation of the emotions is a primary function of art” (LA: 48). What Goodman has in mind is primarily the “time-honored Tingle–Immersion theory”, which: tells us that the proper behavior on encountering a work of art is to strip ourselves of all vestments of knowledge and experience (since they might blunt the immediacy of our enjoyment), then submerge ourselves completely and gauge the aesthetic potency of the work by the intensity and duration of the resulting tingle. The theory is absurd on the face of it and useless for dealing with any of the important problems of aesthetics; but it has become part of the fabric of our common nonsense. (LA: 112)9 Goodman leaves it at that, but equipped with the knowledge of his pleading for the nonexistence of the innocent eye and the impossibility to perceive without interest and background knowledge (recall § “Innocent imitation”, p. 165) it is easy for us to see what he is aiming at. Expression, so Goodman holds, is as conventional as representation. As an example he cites Japanese art films, which were difficult for the Western audience to decipher when they first came over to Europe and North America. It was hard for the audiences back then to determine what emotions the actors where expressing, but it is less difficult for us now as we have become more used to these ways of expressing emotions. “Whether a face expressed agony or hatred or anxiety or determination or despair or desire was not always instantly 175
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evident; for even facial expressions are to some extent molded by custom and culture” (LA: 48). What seems to be a natural expression to us is only what we are used to, just as in the discussed cases of “natural representations” and “natural predicates”. The governing conventions are so deeply entrenched that we common folk do not notice it in everyday life. To witness that the professionals of the trade are well aware of the conventionality of expression, Goodman cites the choreographer and director Doris Humphrey: Along the way I have often been obliged to teach young men how to make love, and young girls how to be predatory or flirtatious or seductive, and I’ve had to advise everybody how to express anxiety, alarm and endless other emotional states. They may have felt these things, but the movements for them are complete strangers. (Humphrey 1959: 114; compare LA: 49) Goodman abandons the connection of human emotions with expression in the arts in favour of a definition that makes use of what he has already established in his theory of symbols. Goodman explicates expression as another way of referring, namely, as a mode of exemplification. In Chapter 6 we mentioned sad pictures. ‘Sad picture’ was explicated there as ‘picture that metaphorically exemplifies sadness’. Sad pictures, however, are those that express sadness. It is a small step from realizing this connection to defining ‘expression’ in terms of metaphorical exemplification. Merely identifying the two will do no good, though (see LA: 87). An important distinction would be lost in doing so. A play on Broadway can metaphorically, although not literally, exemplify being a bonanza; typically, it does not express its being a bonanza. We said in Chapter 6 that not all properties possessed by a symbol are exemplified by it. It is a matter of context and convention which properties are exemplified, since all and only those of its properties the symbol also refers to are exemplified by it, and reference is a matter of convention. The situation with expression is analogous: some, but not all, properties that are metaphorically possessed and exemplified are also expressed. Context and convention also determine here which of the symbol’s properties those are. We cannot therefore give a precise definition with necessary and sufficient conditions to delineate once and for all which kind of metaphorical exemplification expression is. We can give some necessary conditions for expression, however. If x expresses y, then x metaphorically exemplifies y.10 It follows from this that if x expresses y, then x possesses y, albeit metaphorically. 176
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One might note a slightly uncomfortable feature of this. Since the exemplification has to be metaphorical in order to count as expression, a sausage factory, for example, cannot express being a sausage factory, no matter how artful and with how much architectural ingenuity the building was designed and erected (compare LA: 89–91).11 Nothing is lost, however, if we follow Goodman. When the architect says that the building expresses being a sausage factory, Goodman says that it literally exemplifies this. To argue about what word is used seems out of place. The ordinary spectator and also the artist can still use ‘expression’ in the vague and shifting sense it has in ordinary language.12 Goodman’s partial explication of ‘expression’ turns it into a technical term that has the advantage of being more precise than the common language explicandum. With this, Goodman claims to have achieved a clarification of the concept of expression that “[s]ome writers, according to their temperament, have regarded … either as sacredly occult or as hopelessly obscure” (LA: 94).13
The sameness of songs Artworks are complex symbols, Goodman emphasizes, and as such they belong to symbol systems. In order to be able to understand the artwork, we have to understand its place in such systems, that is, understand the symbol-theoretic conventions that govern that respective art form. One consequence of the fact that art forms belong to different kinds of symbol systems is that there are also different identity conditions for different art forms. A discussion of those for some important examples of art forms is the topic of this section. 14
Forgeries Goodman’s discussion of identity criteria for works of different art forms takes him first to the issue of forgery. If we take painting as an example, we can distinguish between two types of fakes: copies of existing originals, and paintings for which no original exists by the artist whose work the painting is falsely declared to be. In the latter case, the forger will imitate the style, type of subject (where it applies) and so on, as closely as possible, typically in order to deceive. One reason why we dislike forgeries of both kinds is because we do not like to be deceived. For, if a forgery is produced without deception, 177
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that is, if a painting is clearly and openly labelled as a copy of an original or a painting “in the style of” so-and-so, we might even admire the skill of the forger – if it is well done – or at least, we usually do not feel offended. Goodman’s main interest lies in the question of whether there is a significant aesthetic difference between an original and a fake. Let us first turn to fakes that are copies of originals. We briefly mentioned in Chapter 1 that Goodman’s job as the director of an art gallery taught him to appreciate the importance of studying artworks while looking at the real thing, rather than, say, photographic reproductions. This is obvious when we are dealing with a bad reproduction, in which, for example, some of the details cannot be made out, or the colours are not represented faithfully. Black and white reproductions of Rothko paintings are utterly pointless, for instance, despite the fact that they can frequently be found. But is the same true of a “perfect” forgery? Imagine a copy of the Mona Lisa that we cannot tell apart from the original, even if both are put right next to each other. It appears that there could not be an aesthetic difference if there is no observable one. Goodman disagrees. First, he considers what tools are admissible in observing the work. Microscopes or X-rays might reveal differences that escape the “naked eye”, but how could the use of such devices be consistently ruled out? Using a stronger lamp to illuminate a painting is certainly admissible, using light that intensifies different areas of the spectrum most probably as well. Tiny shifts in the spectrum, however, will eventually take us from the visible light waves to ultraviolet light or X-rays. To forbid someone who, without wearing glasses, has problems distinguishing a painting from a hippopotamus to use his seeing aid seems “a little unfair” (LA: 100); but then a magnifying glass of the same strength might be considered admissible too. Goodman mentions, as examples, miniature illuminations and Assyrian cylinder seals that can hardly be distinguished from the crudest copies without using strong magnifying glasses (LA: 101). If these are admissible here, and taken to reveal aesthetically significant differences, why are they not admissible for larger paintings? Obviously, the discussion of the “normal viewing conditions” for a representation discussed above echoes here. We must also ask: who does the observing? A distinguished Leonardo scholar will be more likely to identify the forgery of the Mona Lisa than a cross-eyed wrestler. The claim surely cannot be that there is no aesthetic difference if there is somebody who cannot tell the difference. Goodman takes this to be the crucial point, and independent 178
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of the notorious question for the “right” viewing conditions. No one, not even the most reputed expert, can ever know that no one else is, or was, or ever will be, able to tell the difference between the original and the forgery merely by looking at it, merely because she cannot see it (LA: 101–2). This point can be illustrated by the case of Han van Meegeren’s forgeries of Vermeer paintings. Van Meegeren painted pictures “in the style” of Vermeer and sold them as Vermeers. For us today, the difference between original and forgeries is fairly easy to spot, and not just because we recognize the forgeries by what is represented. We notice, with a little experience in the appreciation of Flemish painting, significant aesthetic differences between authentic Vermeers and van Meegeren’s forgeries. At the time, however, leading experts in the field fell for the forgeries, and some even met van Meegeren’s eventual confession of the fraud with a stubborn disbelief (LA: 106, 110–11). The reason why we have no guarantee that a work that currently does not appear to be distinguishable from its forgery will never be so distinguishable is, according to Goodman, that painting belongs to a dense symbol system. Since the system lacks syntactic and semantic finite differentiation (see Chapter 6), the tiniest difference can be important, but the tiniest difference may easily escape us if we merely look at the work. Goodman therefore insists that in the case of a painting the history of production determines the identity of the artwork. The very painting that was created by a certain artist at a certain time is the only thing that qualifies as the artwork. No copy, no matter how good it appears, ever can. In other words, it is the physical object with its history that matters.15 The case is an entirely different one with music. It is certainly possible to attempt to pass on a piece of music that was not actually written by Sergey Prokofiev as his composition. “Copy” fakes are literally impossible, though, according to Goodman. Works of music are determined by their score. The score (at least one of the regimented kind we introduced in Chapter 6) is a notation of the work, and any performance of the score is a performance of the piece, and not a forgery of it. Any faithful score that is produced, however, is just a notation of the piece and not a forgery of it either. The original score that was written (if, indeed, there was one) certainly has some special value, much as a lock of Beethoven’s hair might have, but of course, just as a lock of Beethoven’s hair can be, that score can be faked. This faked score, however, would not be a forgery of the piece of music, but merely another notation of it. A first score is also special in the 179
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sense that it was the first inscription of the work. It and its history of production play no role in determining the identity of the work, however, other than being one of the notations of it. It certainly cannot be identified with the work. Burning the first score of a piece of music that was handwritten by Beethoven would certainly be a great loss, but it would not, however, destroy the piece of music that the score is a notation of. Music is very much unlike painting in that respect; if you burn the Mona Lisa, the work itself is gone. If neither performances nor scores can be copy fakes of a work of music, then nothing can. After all, what else is there? Does speaking of notations and performances of a piece of music not mean that there is something else that it is a notation of? Maybe an abstract object is the work.16 Goodman, of course, does not think so. Scores are symbols in the notation system. They have performances as their complianceclasses. There is nothing more to a work of music than the various physical objects that are notations of a correct performance, and the correct performance of physical sound waves, which accord to the notations. The performances are performances of the score, and the scores are notations of the performances; they together constitute the work. There is not in addition a third thing that they are performances and notations of.
Autographic and allographic art Goodman has thus drawn a principled distinction between painting and music that will apply to all art forms, although we still have to introduce a further refinement. But first let us introduce some terminology for what we have so far. Let us call a work of art autographic iff the distinction between original and forgery matters, and allographic otherwise. We can also call an art form autographic or allographic if a work that belongs to it is autographic or allographic, respectively. Painting is autographic, and music is allographic, as we saw above. Literature (be it novels or poetry) is also allographic. But how are we to classify etchings, for example? They have many instances, but still we want to speak of a significant distinction between original and forgery. Goodman introduces a second distinction to cover cases like this. Art forms such as painting or carved sculpture are one-stage, while music, etching and cast sculpture are two-stage. In the case of music, the composer writes the score – this is stage one – and this score then 180
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is performed – stage two. Everyone can (skills permitting) perform a piece of music or write down a notation of it. Neither counts as a forgery; it is allographic in both stages. Two-stage art forms need not be allographic, however. In etching, the first stage is the production of the plate; and in the second stage prints are taken from that plate. Both stages are autographic: a plate can be copy faked, and even the most precise copy of a print that is not taken from the original plate also has to count as a forgery. Is it the case, though, that all one-stage arts are autographic? Goodman takes literature to be an example of an allographic one-stage art. There are no copy forgeries of a poem or novel. Every inscription of it is an instance of the work. It is tempting to count recitations of poems or readings of novels as a second stage, analogous to performances of pieces of music. Goodman denies this, however. Most pieces of literature – think of War and Peace – are never read out loud, which suggests that the printed (or handwritten) version is the end product. If we wanted to count silent readings as a second stage of literature, Goodman argues, we would have to count “lookings at pictures” as a second stage too, and “the listenings to a performance” in the case of music would constitute a third stage (LA: 114). Let us now turn to selected specific arts.
Music Musical scores are the paradigm from which Goodman develops his theory of notation, so it comes as no surprise that scores end up being characters in notational systems within his framework. As we explained in Chapter 6, it is not only the case that a notational score uniquely determines which performances count as members of the complianceclass, but also that each performance uniquely determines its score. The shortcomings from the notational point of view of the actual standard notation include redundancy. The compliant with the characters for C sharp and D flat, for example, is the same in both cases, at least when played on a (well-tempered) piano. In a violin score, the two differ in theory, but the same tone seems to be accepted for both in practice (LA: 182). Redundancy, as we have seen in Chapter 6, is a venial sin. It might lead to different notations for the same compliance-class, but the compliance-class remains constant. A score is semantically finitely differentiated. Although any limit would do, tradition seems to have settled on five as the maximum number of flags that can be put on a quarter note (crotchet) to halve, quarter 181
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and so on its length. This determines a 1/128 note. The only thing that needs to be banned, however, is an infinite chain of shorter and shorter durations in order to guarantee finite differentiation. But common scores also include descriptive elements such as, for instance, the “figured bass”, which leaves the player a certain freedom to fill in notes “ad lib” (which is another non-notational element). The same goes for the indication of the tempo of a piece, such as ‘allegro’ or ‘adagio’. Although these two are pretty standard and can at least be pinned down to a more or less specific range of beats per minute, practice allows for all sorts of other terms, such as ‘allegro non troppo’, ‘minuetto con un poco di moto’, ‘moderato ed amabile’, ‘rondo alla Polacca’, and so on indefinitely. Semantic disjointness is lost, even if ambiguity could miraculously be avoided. A performance of John Cage’s Organ2/ASLSP started on 5 September 2001, in Halberstadt, Germany. The one-page score “specifies” that the piece be played “as slowly as possible”. The première in 1987 managed to stretch it to about 29 minutes, while the ongoing performance in Halberstadt is, more ambitiously, planned for 639 years. Is it not possible to play it even more slowly? Patience might be a limiting factor: the piece starts with a rest that, in Halberstadt, lasted for one and a half years.17 Cage was also one of the composers who designed alternative systems for writing music to rebel against the standard notation, which does not allow for enough freedom (other composers complained that it allowed too much, for some features of the performance are not prescribed by the score). Cage’s system provides for a rectangle in which various dots are inscribed that stand for single notes. Five straight lines, which stand for frequency, duration, timbre, amplitude and succession, run across the rectangle at varying angles. The sounds indicated by the dots are determined by the perpendicular distances of the respective dot to the five lines. Figure 7.3 looks roughly like one of Cage’s scores. Cage’s system is not notational. Smallest differences in the position of dots and lines make a difference in the note that is played, which violates finite differentiation. Two consequences of Goodman’s proposal for the identity of works of music are often found to be counter-intuitive. First, since the indication of the tempo does not belong to the notation, it is irrelevant for the identity of the work. This means that Cage’s Organ2/ASLSP performed in one second would still count as a performance of the work, as long as the notes are played according to the score. Beethoven’s Fifth Symphony could be performed in 5 minutes, or last 639 years, 182
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Figure 7.3 Roughly, an example of Cage’s system for writing music.
and provided all and only the right notes are played in the right order at the right relative duration it would still be a performance of the symphony. On the other hand – and this is the second point – playing just one false note would result in a performance that is not a performance of the work (LA: 186–7). We have already seen in § “Symbol systems” (p. 149) why Goodman forbids even the tiniest mistakes. The violation of the criterion of disjointness for a notation, that is, allowing just one mistake to be made in a performance would have, eventually, catastrophic consequences. Change just one note in Beethoven’s Fifth Symphony and write the notation for it, including that changed note. Then change another note in a performance, and write a notation of that again. Eventually, one would be able to arrive at any musical work whatsoever in this way. Since performances and scores determine each other, and together are identified with the musical artwork, we would end up with the result that each piece of music could be identified with every other one, for example, Beethoven’s Fifth Symphony with The Eagles’s Hotel California.18 This does not mean, however, that there is nothing more that can be said regarding such performances. A five-minute version of Beethoven’s Fifth Symphony can probably be judged to be a terrible performance of the work, although it is a performance. And even though, after Jenny has left a concert that promised a performance of Shostakovich’s Symphony No. 7, Leningrad, she, strictly speaking, has not heard a performance of the work if one of the violins played a single false note; she might still have heard an otherwise magnificent 183
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concert that was almost a performance of Leningrad, had it not been for the one mistake. It is also important to keep in mind that Goodman’s suggestions concerning the identity conditions of pieces of music are to be understood as explications. How well they fit the common notions is hence only one aspect – and not the most important one – that needs to be considered. Exactness of the stipulation and fruitfulness justify straying from the common, vague concepts. Even the bitterest critic should grant Goodman that his explication of the identity of a work of music led to a very precise and applicable criterion. Also, let us stress again that Goodman defines technical terms for a rigorous theory that is required for serious philosophical investigations. He has no desire to tell musicians or concert audiences what to call a performance. After discussing the requirement that not a single small mistake can be allowed, he writes: This is not to say that the exigencies that dictate our technical discourse need govern our everyday speech. I am no more recommending that in ordinary discourse we refuse to say that a pianist who misses a note has performed a Chopin Polonaise than that we refuse to call a whale a fish, the earth spherical, or a grayishpink human white. (LA: 187) The ordinary usage, however, as he stresses in another passage, “points the way of disaster for theory” (LA: 120, n.13).
Painting Painting belongs to a pictorial system, and hence lacks syntactic and semantic differentiation. The characters of the system have unit classes as compliants, that is, classes with only one member, the single painting. Would it be possible to devise a notational system for paintings? In one sense, the answer is a flat “yes”. In fact, it is very easy; here is a system that should be very similar to those systems that are typically used by museums and art galleries. Denote a painting by an ordered pair of numbers the first of which denotes the year the painting entered the collection, and the second of which is determined by the order in which the acquisitions were made in that year; ‘<2003,17>’, for example, stands for the 17th picture acquired in the year 2003. But unlike in the case of a musical score, it is impossible to systematically determine from the notation which picture is denoted 184
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here without having any further information. Also, the painting cannot be “performed” from ‘<2003,17>’. Even if the information could somehow be retrieved, any attempt to “repaint” the picture would result in a new work, and not one that complies with the old character. The flat answer misses the point. Asking for a notation for painting is asking whether it would be possible to free works of painting from the dependence on a particular artist who produced it, and the particular time and place it was produced. And here the answer must be “no”. Changes as drastic as this one would leave us with a new art form, one that has a notation, but that also lacks important characteristics of painting: its belonging to a dense symbol system (LA: 194–8; see also MM: 168–72).
Scripts, literature, and drama Scripts are characters in notational schemata but unlike scores they fail to meet the semantic requirements of a notation. ‘Script’, here, is not restricted to the works of a playwright or film writer. It includes all characters of natural languages and most scientific languages, novels, poems and also this book (excluding the figures). Even if ambiguity is banned from the language, semantic disjointness or differentiation is rarely achieved (LA: 199–200). All and only inscriptions of Anna Karenina, for example, (inscriptions still include utterances, although that might be more relevant for poems than for novels) are instances of the work. The identity of the work can be ensured from instance to instance because the scheme that is used is a notational one. The vocabulary consists of symbols that are syntactically disjoint and articulate. Translations of novels, however, do not belong to the class of inscriptions, and hence are not instances of the work (LA: 209). They depend in an important way on the original work, but, like variations in music, cannot be identified with them (compare RP: ch. IV). Any inscription of Anna Karenina, however, even if accidentally produced by a chimpanzee playing with a typewriter, or by an author intending to create an original work, counts as an inscription of Tolstoy’s work (LA: 199–201).19 In drama, as in music, the work is the compliance-class of the script containing its performance. The text of a play, however, is a composite of score and script. The dialogue is in a virtually notational system, with utterances as its compliants. This part of the text is a score; and 185
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performances compliant with it constitute the work. The stage directions, descriptions of scenery, etc., are scripts in a language that meets none of the semantic requirements of notationality; and a performance does not uniquely determine such a script or coextensive class of scripts. (LA: 211)
Dance Goodman is unusual among the philosophers of art in that he takes an interest in dance, which is not commonly the main focus of the debate. He takes it to be an important case since it is a form of visual art, like painting, but also temporal, like music. Painting does not have a notation, but music does. So, can there be a notation for dance? Notations are typically for auditory phenomena; music and spoken language were our major examples. That does not mean, of course, that there cannot be a notation of visual compliance-classes. Nevertheless, it seems that dance cannot have a notation: the movements of the dancer in three-dimensional space are highly complex and can involve subtle but important differences between movements. Something similar, however, is also true of music, yet a very rigorous notation was developed for it. While a notation can in principle be as precise as required, it is important to note that not all of the subtleties of dance have to be captured by the notation; this is again analogous to the case of music. The notation allows performances to be identified as belonging to a certain dance. More subtle features of a performance might have more to do with the quality of the performance, rather than with its identity, as is the case with tempo in music.20 Merely to insist, on the other hand, that a notation can be devised for absolutely everything, and hence also for dance, misses the point. A notation like the unhelpful one for painting that we mentioned above, is not what is looked for. A notation for dance must allow performances to be identified as belonging to the same work, and this categorization had better be close to the present common practice. It must also make it possible to identify two performances as being performances of the same dance without knowledge of the history of production. Notations like this one have indeed been suggested, for example by Rudolf Laban who worked in Vienna in the 1920s. His so-called Labanotation categorizes human motion and introduces a symbol system to note down these motions. Thus it provides an: 186
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impressive scheme of analysis and description, it refutes the common belief that continuous complex motion is too recalcitrant a subject-matter for notational articulation, and discredits the dogma that successful systematic description depends in general upon some inherent amenability – some native structural neatness – in what is described. Indeed, the development of Laban’s language offers us an elaborate and intriguing example of the process that has come to be called “concept formation”. (LA: 213–14)21 Goodman emphasizes that the creation and adoption of such a notation brings systematization with it, perhaps introduces more rigorous distinctions or puts things that were not previously recognized as belonging together with each other under a label. This is the “concept formation” Goodman mentions. Labanotation, for example, restricts itself to sixteen directions. Allowing for arbitrary angles on a “direction pin” (imagine a compass) for the direction of a movement would violate the notational requirement of both semantic and syntactic finite differentiation (see Chapter 6).
Symptoms of the aesthetic Given this manifold of different systems that are employed in the various forms of art – is there any hope of a definition? In Ways of Worldmaking, Goodman reminds us of one of his preferred strategies to tackle philosophical problems: the progressive shift, which we have encountered several times by now: “If attempts to answer the question ‘What is art?’ characteristically end in frustration and confusion, perhaps – as so often in philosophy – the question is the wrong one” (WW: 57). The crucial insight here is, says Goodman, that artworks are symbols and just as anything can symbolize anything, every object can, in principle, function as a work of art at certain times and under certain circumstances, and not at others. This is true of traditional, realistic painting as much as of concept art and ready-mades. The real question, therefore, is not ‘What objects are (permanently) works of art?’ but rather ‘When is an object a work of art?’; or, more snappily: ‘When is art?’ (WW: 66–7). A simple stone on the road, with no symbolic or artistic function at all, can become a work of art when put in a museum. On the road, the stone is usually not a symbol of any kind; in the museum it might exemplify various of its properties, 187
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its shape, colour or texture, but it can also refer to the struggle of the international proletariat against the bourgeoisie in some indirect way. Tracey Emin’s My Bed might cease (again) functioning as an artwork when carried out of the Saatchi Gallery in London, brought into a bedroom and slept in. Goodman contends that the repeated failure to characterize what distinguishes the aesthetic from the non-aesthetic in any way that comes even close to common usage might suggest that a different approach is called for. He suggests having a look at what the major features of the various symbol systems typically used by the arts are, rather than aiming at a crisp definition (LA: 252). One insightful example is that of the Hokusai drawing of Mount Fuji, whose white background and undulating line depicting the contours of the mountain just happen to look exactly like a given momentary cardiogram. The cardiogram, of course, is a (graphic) diagram (see Chapter 6) whereas the drawing of Mount Fuji is a work of art: a picture of the mountain it represents. That means, however, that both are symbols in dense systems, so where does the difference lie? The difference is not in the referent of the symbols; mountains certainly can be diagrammed, and there is nothing to stop us from creating a picture of heartbeats. The difference is syntactic. The relevant features of the diagram are narrowly restricted in comparison to the picture; the only ones that count are the ordinate and abscissa of every point on the centre of the line, and the rest play no role. It makes no difference whether the paper is pink or white or yellow; it does not matter what colour the line has, how thick or thin it is (within reason), and so on. All these could be of great importance for the picture, though. None of these features of the drawing can be ignored, neither the thickness or colour of the line, nor the quality or size of the paper. Both graphically diagrammatic and pictorial symbol schemes are not articulate, but many of the properties of a diagram can be ignored as contingent, whereas this is not the case for pictures. Goodman introduces the term ‘repleteness’ to distinguish between the two cases (LA: 229–30). Pictorial schemes are relatively replete. The opposite term, which applies to diagrams, is ‘attenuation’. There is no sharp boundary between the symbol schemata of diagrams and pictures, as there is none between dense and articulate ones. Repleteness is a matter of degree. Even some properties of paintings are usually irrelevant, such as weight or temperature (within reason, heating a painting up to 1,000ºC would most probably make a difference!), or being guarded by a 54-year-old person. There is also no upper limit for the relevant features in a diagram. 188
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Repleteness, Goodman states, is one symptom of the aesthetic. Two further symptoms are syntactic and semantic density. Syntactic density, as explained above, distinguishes linguistic from non-lingusitic schemes, and also pictures from scripts and scores. Semantic density is characteristic of representation and description. Goodman writes: All three features call for maximum sensitivity of discrimination. Syntactic and semantic density demand endless attention to determining character and referent, given any mark of the system; and relative syntactic repleteness in a syntactically dense system demands such effort at discrimination along, so to speak, more dimensions. (LA: 252–3) This also explains why, even though apparently only the cognitive function of an artwork matters to Goodman, it is so important to pay close attention to the physical symbol (the painting, sculpture, piece of music, play, etc.) itself, and not just look through it to what it obviously refers to, as we can with traffic lights or scientific texts. We must “attend constantly to the symbol itself as in seeing paintings or reading poetry” (MM: 69). Density and repleteness provide for a literally never-ending variety of possible new discoveries. As a fourth symptom Goodman identifies exemplification. In art, it is particularly often the case that what a symbol stands for is exemplified or expressed by it. Expression does not need to be mentioned separately, as Goodman defines it in terms of exemplification, but it is clear that it plays a significant role here. In Ways of Worldmaking, Goodman identifies a fifth symptom: “multiple and complex reference, where a symbol performs several integrated and interacting referential functions, some direct and some mediated through other symbols” (WW: 68). This does not mean ordinary ambiguity, as in the notorious ‘bank’. Examples for this are rather along the lines of the chains of reference we mentioned in Chapter 6. The relevant contrast is with science, where exactness and direct reference are strived for (see also MM: 61–6, 135–8). Thus, the five symptoms of the aesthetic are: ● ● ● ● ●
syntactic density semantic density relative repleteness exemplification multiple and complex reference.
Do these symptoms allow for a definition of ‘art’, or ‘the aesthetic’? They do not, but they come as close as it gets, according to Goodman. 189
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Failing to realize one or more of them does not disqualify anything as art, and showing all is no guarantee for arthood. Like symptoms of a disease they tend to be more often present than absent; but just as a patient can have symptoms of a disease without being ill, and be ill without showing the typical symptoms, something can be art without showing any of the symptoms of the aesthetic, while non-art can have them all. These symptoms, however, come fairly close to being disjunctively necessary and conjunctively sufficient. So close, that Goodman suggests it “might well call for some redrawing of the vague and vagrant borderlines of the aesthetic” (WW: 68–9; see also LA: 254).
Summary We have seen in this chapter how Goodman puts both elements of his theory of symbols to use in his philosophy of art. Artworks are characterized as complex symbols, and the insights about the ways in which symbols refer could be used to understand representation and expression. The theory of notation explains not only how different artworks function in different ways, which is important for their understanding, but also how some art forms can be forged whereas others are “unfakable”. Finally, we managed to cast some light on the question of “the aesthetic”. Although a strict definition does not seem to be available, Goodman managed to list five “symptoms of the aesthetic” that, although being neither necessary nor sufficient, at least tend to be present rather than absent. In the end, which of the many symbols are art depends on conventions. The presence of the symptoms of the aesthetic indicate that the symbol in question is likely to be an artwork, but the conventions we actually have seem to forbid a more rigorous real definition.
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In this chapter we shall present Goodman’s “irrealism”, according to which he rejects the notion of one single, neutral reality that underlies our true versions of what the world is like. Such a reality is neither sufficient nor necessary to explain matters of epistemology or to distinguish true from false versions. We explain how this view is a consequence of Goodman’s pluralism, constructionalism and anti-foundationalism, which we have encountered in the preceding chapters. It is also worth emphasizing that this obviously relativistic position does not collapse into an “anything goes”. “Irrealism” is not to be confused with “irrationalism”.
The plurality of versions Throughout the book we have emphasized that Goodman is a pluralist in many regards. Like Carnap he thinks that we can build up the world in many ways. What we take as primitive – as the foundation of our construction – is not settled once and for all. Depending on purposes and interests we can build up the world out of qualia, erlebs or physical objects. In this way, Goodman had already rejected absolutism in A Study of Qualities: Perhaps the conviction I should acknowledge most willingly is that absolutism must be rejected. But nothing is much emptier than a relativism that, without seeking to find any solution to a given problem, merely expresses a willingness to admit alternative solutions. Freedom has little value if we use it solely to declare that we have it. The recognition that theoretically there 191
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are many equally satisfactory systems is but the first step in the laborious task of realizing at least one of them. (SQ: v ) The standards for what counts as “satisfactory” are neither arbitrary nor easy to fulfil. When it comes to constructional systems we have seen how nominalism and simplicity considerations might delimit the possible strategies considerably, how unforeseen problems such as the companionship difficulty or the difficulty of imperfect community might occur on several levels of construction, and so on. That science is not based on some ultimate foundation was also obvious from Goodman’s new riddle of induction (see Chapter 2). The regularities we find and fail to find in nature are a result of the predicates we have chosen to formulate scientific hypothesis and to categorize scientific data. If we categorize by projecting ‘grue’, nature will, presumably, behave irregularly at t; if we project ‘green’, on the other hand, presumably it will not. We think that we capture the regularity by choosing ‘green’ for our projections, since we have projected ‘green’ often and efficiently in the past. There is no other principled reason, however, why ‘green’ is the better choice, according to Goodman. In Chapter 2 we discussed Goodman’s view on the justification of our standards for deductive and inductive reasoning. He argued that the same pragmatic considerations that constrain the object level of scientific categorization also apply to the meta-level of our normative standards of reasoning. Which deductive or inductive rules we use to make inferences on the basis of empirically acquired convictions is a result of balancing reasons, too. Pretheoretically, we judge some inferences as deductively or inductively valid, but pretheoretically many of us also are not very good rational reasoners. When we codify a logic, we do not codify the eternal rules of right inferences; rather, our codifications are the result of a process that reaches a reflective equilibrium of our pretheoretic judgements of validity on the one hand, and a coherent system of rules1 on the other hand (see Chapter 2). Goodman’s pluralism is not confined to the sciences, however. As we have seen, the symbol systems in the arts, for example, are also part of cognitive enterprises by which we hope to deepen our understanding. For these, of course, other standards for satisfactoriness are operating. Remember, for example, the discussion of “the right perspective” or the discussion of realism in the arts from the previous chapters. In his Ways of Worldmaking and Of Minds and Other Matters, Goodman fleshes out his pluralism in two further directions. On the one hand he attacks the monist; on the other hand he attacks the realist. Note that ‘realism’ here is used in a way different from how the 192
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term was introduced in Chapter 4. It does not label the position that is opposed to particularism and rejects the claim that only concrete individuals exist. Here, ‘realism’ means the claim that there is exactly one world, as will be discussed below. His rejection of realism leads Goodman to the claim that we – quite literally – have made the stars (compare MM: 41–2).2 Goodman’s attack on the monist is directed at philosophers like Quine and Carnap. Both held that every true and meaningful version of the world must somehow be translatable or reducible to a single version, in their case, the version of physics. Carnap defended this view, as we have seen already in Chapter 4, because he thought that only intertranslatability could guarantee the unity of science. Quine’s physicalism, probably better known today, justified his view of the correctness of only one single version by pointing out that “full coverage” – that is, a complete world version – is, as Putnam put it, “the business of physics and only of physics” (Putnam in McCormick 1996: 117). Goodman’s attack against the monist in this sense is well made. Reducibility is hard to get. Often it is only partial, and many areas of science (e.g. psychology) are so unlikely to be reducible to physics that the situation might seem hopeless. Against this argument Quine has defended a form of eliminativism according to which those parts of science using, for example, irreducible mentalistic vocabulary should be abandoned. But, Goodman replies, this physicalism is built on quicksand: If all right versions could somehow be reduced to one and only one, that one might with some semblance of plausibility be regarded as the only truth about the only world. But the evidence for such reducibility is negligible, and even the claim is nebulous since physics itself is fragmentary and unstable and consequences of reduction envisaged are vague. (WW: 5) In his discussion note to Ways of Worldmaking, Hempel supports Goodman’s argument emphatically: I would add that the physicalistic claim that the language of physics can serve as a unitary language of science is inherently obscure: The language of what physics is meant? Surely not that of, say, 18th century physics; for it contains terms like ‘caloric fluid’, whose use is governed by theoretical assumptions now thought false. Nor can the language of contemporary physics claim the role of unitary language, since it will no doubt undergo further 193
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changes, too. The thesis of physicalism would seem to require a language in which a true theory of all physical phenomena can be formulated. But it is quite unclear what is to be understood here by a physical phenomenon, especially in the context of a theory that has taken a determinedly linguistic turn. (Hempel 1980: 194–5) So far this argument is directed against a monistic reductionism. No one world version should be regarded as being the only truth. There are many true versions of the world, serving different purposes, answering to different interests. Clearly, not all versions are true versions. A version according to which fly agarics nourish is not a true version. But what does make the difference between true and false versions? The answer one might expect is that those versions are true versions that are in agreement with the way the world is. The true versions are true of the world; in the end, Reality decides which versions are true and which are false. One might also expect by now that this is not the answer given by Goodman.
Irrealism Goodman labels his own position ‘irrealism’. Irrealism is not the claim that everything or anything is “irreal”, but that the world (whatever it is) dissolves into versions and that ontology disappears. Goodman’s irrealism is certainly the most controversial aspect of his philosophy. Let us see what it means and why Goodman advocates it. In Goodman’s writings one can separate two lines of argument (Dudau 2002). First, he argues that there are conflicting statements that cannot be accommodated in a single world: some truths conflict (WW: 109–16; compare MM: 30–44). If that is the case, we need many worlds if any to accommodate the conflicting versions of the world and bring them in unison with the standard correspondence account of truth, that is, that the truth of a statement is its correspondence with a world. The second line of argument seems to be that we need no worlds at all if we need many. If we need a world for each version, why postulate the worlds over and above the versions? Let us first have a closer look at the first line of reasoning. The Earth stands still, revolves around the Sun, and runs many other courses as well at the same time. Yet nothing moves while at rest. As Goodman concedes, the natural response to this is that the sentences 194
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(S1) The Earth is at rest and (S2) The Earth moves should be understood as elliptical for (S1′) The Earth is at rest according to the geocentric system and respectively, (S2′) The Earth moves according to the heliocentric system. But, Goodman tells us, this is a wrong answer (WW: 112). Consider the following two historiographical sentences: ‘The kings of Sparta had two votes’ and ‘The kings of Sparta had only one vote’. The first sentence is part of a report by Herodotus, the second part of a report by Thucydides. There is, again, an inclination to understand these sentences as ellipses for ‘According to Herodotus, the kings of Sparta had two votes’, and ‘According to Thucydides, the kings of Sparta had only one vote’. But obviously these latter two sentences do not tell us anything about Sparta. They only tell us about what Herodotus and Thucydides said about Sparta. It is true that ‘According to Herodotus, the kings of Sparta had two votes’, even if they actually had no vote or had three votes. The same holds for the relativizations to the geocentric and the heliocentric systems: it is true that the Earth is at rest according to the geocentric system, but that still does not inform us about the world: Merely that a given version says something does not make what it says true; after all, some versions say the earth is flat or that it rests on the back of a tortoise. That the earth is at rest according to one system says nothing about how the earth behaves but only something about what these versions say. What must be added is that these versions are true. But then the contradiction reappears, and our escape is blocked. (MM: 30) Thus, if we assume that (S1) and (S2) are both true, we end up with a contradiction if we take them to be literally true of one and the same world. If we do not take them to be literally true, but to be elliptical and implicitly relativized, we end up with two truths that are not about any world. At least, they are not about the parts of the world we were interested in. They turn out to be truths about versions, but not truths about planets. The solution chosen by Goodman is to claim that they are about two different worlds. Both state a literal truth about a world, but just not 195
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about the same world. These worlds have to be sharply distinguished from the possible worlds we have talked about in Chapter 2 and which Goodman renounces. Possible worlds correspond to different ways the world could be and only one of them corresponds to (or is) the world as it is. Thus these possible worlds (except the one actual world) are not described by true but by false versions. The worlds considered by Goodman are not possible, but real worlds. They are not worlds answering to false versions; rather, all of them answer to true versions. All of Goodman’s worlds are actual.3 For Goodman, as we saw in Chapter 3, it does not make sense to talk of the correspondence of something described with something neutral. Worlds are not “given” in any uncategorized way. Of course, the way they are categorized or partitioned depends on versions. These versions, which are true versions of worlds, determine how these worlds are. In turn that means that true versions make the worlds that answer to them. It is not easy to get one’s mind around this, so let us go through it step by step. First we have to observe that it is important to keep versions and worlds distinct. A version can be in English and comprise words. Worlds are neither in English nor comprise words. However, for a version that is true of a world, the world has to answer to it in a way. A world that “corresponds” to (S1), for example, is a world with planets and spacetime that is so arranged that one of the planets, Earth, is at rest in it. But ‘planet’, ‘spacetime’, ‘at rest’ and so on are ways to categorize Reality that depend on the version. These predicates are the ones chosen (for good reasons, presumably) in this very version. There was no world that came ordered in correspondence with these predicates before this version was constructed. So, if Reality is categorized by versions, is there a reality after all, one reality that is simply categorized in different ways? Goodman does not commit himself at this point. He emphasizes: While I stress the multiplicity of right world-versions, I by no means insist that there are many worlds – or indeed any …. The monist can always contend that two versions need only be right to be accounted versions of the same world. The pluralist can always reply by asking what the world is like apart from all versions. … We do better to focus on versions rather than worlds. (WW: 96; also compare WW: 4; MM: 30–33) What Goodman insists on, however, is that “there are many worlds, if any” (MM: 127, see also MM: 31). 196
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We said above that there is also a line of reasoning in Goodman’s writings that toys with the idea that there are no worlds that the right versions answer to – or at the very least that such worlds are not necessary. The world versions suffice, and are really the only things that are directly accessible, anyway. The versions can for many purposes be treated as worlds (WW: 4). Accordingly, the “tolerant realist view” that a plurality of worlds can be versions of a unique underlying reality is also nothing but a useless addition. A reality underlying the worlds must be unstructured and neutral, and thus serves no purpose. Given what we have said about Goodman’s pluralism, this position makes sense. If there are many equally satisfactory versions of the world that are mutually incompatible, then there is not very much left that the “neutral reality” could be (see also Küng 1993). This reality would have no planets, no motion, no spacetime, no relations, no points, no structure at all. You can assume there is such a thing, Goodman seems to admit, but only because this reality is really not worth fighting for (or fighting against, for that matter). If we can tell true versions from false versions and explain why some are true versions and others false versions of worlds without assuming anything like an underlying reality, why assume it then? Parsimony considerations should make us refrain from postulating it. Still, did we make the stars? Of course, we made the word ‘star’, but did we make the celestial bodies the word applies to? How can we make anything that is so much older than we are (see Scheffler 1980)? Goodman’s answer is that we made it by making a true version in which the stars came into existence long before the version itself did (MM: 42).4
DIY: make your own world As should be clear by now, the view that worlds are “made” by answering to right versions does not collapse into irrationalism or a fancy form of cultural relativism favoured by postmodern thinkers. To make a true version is hard work. Not surprisingly, it is not any easier than making a true version is for a realist. How we make true versions is absolutely the same on both accounts; the difference is only with respect to what we do when we make true versions. The constraints on worldmaking are strict. We cannot just create things; predicates must be entrenched and thus there must be some close continuity with former versions. Simplicity will keep us from creating new things from 197
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scratch, coherence from making anything in conflict with beliefs with higher initial credibility, and so on. When new worlds are made, the only material that is available is the scrap of old worlds (WW: 97). New versions are constructed out of old ones. It is probably no coincidence that this bears a strong resemblance to Neurath’s metaphor, known as “Neurath’s ship”. Neurath likens the scientist who constructs new theories to a sailor who needs to repair and rebuild his ship at sea with no safe dock on land to carry out the work (Neurath 1932). The only thing the scientist can rely on are old theories that are found deficient, and observations that are already theory-laden. No safe, neutral and objective position is available from which this task can be carried out. Worldmakers are in the same position. They cannot start from scratch either. There is no secure, “given”, non-revisable starting-point available (MM: 40). (Recall the discussion of Goodman’s rejection of “the absolute given” and his insistence that everything is revisable in Chapter 5.) The resemblance between scientists and worldmakers is no accident: scientists are worldmakers. A world is made by making a world version. So the making of a world version is what has to be understood. The easiest way to wrap one’s brains around this is to think of world versions, initially, as constructional systems. Carnap’s Aufbau, as already mentioned, presents a world version, the systems in A Study of Qualities and The Structure of Appearance are world versions, and so are scientific theories. The heliocentric and geocentric worldviews are relatively primitive world versions, Einstein’s theory of general relativity is a more sophisticated one. World versions do not have to be constructed in a formal language, though; indeed, they do not need to be in a language, formal or informal, at all. The dense symbol systems used in the arts, such as in painting, for example, can be used in the process of worldmaking too. It is in this sense that philosophy, science and art are all epistemically significant; they all contribute to our understanding; they all help to create worlds. So making a world version is difficult. Acknowledging a great number of them does not make it easier. We cannot just make world versions as we like, either. Goodman writes: We make chairs, computers, books, and planes; and making any of these right takes skill, care, and hard work. A chair I make is likely to wobble; a book takes endless pain; I can’t make a computer at all; and no one has been able to make a plane that flies far on batteries. Making right world versions – or making worlds 198
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– is harder than making chairs or planes, and failure is common, largely because all we have available is scrap material recycled from old and stubborn worlds. (MM: 41–2) The hard work lies, for example, in creating a constructional system that overcomes the problems of its predecessors, is simple, uses well-entrenched predicates, or successfully replaces them with new ones (which is even harder, as we have seen), allows us to make useful predictions and so on. The scientist and the artist are faced with analogous problems. Also, world versions are not achieved by just welcoming them and lying back: mere acknowledgement of various worlds does not make one. “A broad mind is no substitute for hard work” (WW: 21). A cheap relativism that capitulates in face of the many options and declares that “anything goes” – the postmodern stance – is alien to Goodman: We have to start from premisses and principles; and there are no absolute and incontrovertible certainties available. But that does not mean that we must start from careless guesses. We follow our confidence and convictions, which are subject to strengthening or weakening or even reversal as we strive to build right versions or worlds on the basis of these. No starting points or ending points along the way are either absolute or arbitrary. None of this is peculiar to me. But I am repeatedly forced to insist that my relativism is equidistant from intransigent absolutism and unlimited license. (MM: 40) There is another pressing question, however. How can the author of Ways of Worldmaking be a nominalist? Is Goodman’s relativism, despite the constraints for rightness and the demand for rigour imposed upon it, not in tension with his nominalism? What stops us from making a world that contains sets? Never ceasing to surprise, Goodman’s answer is: nothing. It is fine. Go ahead. “[I]n this general discussion of worldmaking I do not impose nominalistic restrictions, for I want to allow for some difference in opinion as to what actual worlds there are” (WW: 95). Worldmaking considerations are independent of nominalism. When Goodman himself makes world-versions, as in The Structure of Appearance, he makes nominalistic worlds, as these are the only ones he finds acceptable. Platonistic world versions are not ruled out from the start; they are not disqualified as not even being in the right ballpark for being true world versions, or maybe even for being world versions at all. After all, Goodman takes Carnap’s world version of the Aufbau seriously in A Study of Qualities and The 199
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Structure of Appearance. If the mere presence of classes would prevent something from being a world version, there could not even be criticism and discussion. We saw already in § “Goodman’s nominalism” (p. 86) that the sciences are free to use all mathematics and as many classes as they like anyway. It is only philosophy, that has to make sense of all this, that underlies nominalistic restrictions according to Goodman (compare also WW: 21). Although Goodman does not insist on nominalism for worldmaking, he does insist on extensionalism (WW: 95, n.3). His detestation of intensionality, as we already hinted in previous chapters, runs deeper than his nominalism.
Truth and permanent acceptability That reality is a useless concept must in part be defended by showing that the difference between true and false versions can be explained without assuming an underlying reality. ‘Truth’, especially, has to be explicated without relying on any correspondence relation between versions and Reality. But what could truth be in an irrealistic conception? As we briefly explained in Chapter 3, Goodman rejects the explication of ‘truth’ as correspondence with facts. The argument he gives for doing so shows that he presupposes an epistemic conception of truth, for his reason for renouncing a correspondence theory is that reality is never given to us in an undescribed way and thus cannot be accessed independent of any description. Therefore, it cannot be compared with a version that is independent of any description either. Goodman seems to assume implicitly that an elucidation of the concept of truth should provide us with a strategy for testing truth-candidates (i.e. versions) (Künne 1993). Of course, epistemic definitions of truth in terms of acceptability or entitlement to belief are not unproblematic. Obviously, people in the past were entitled to accept all kinds of statements that are no longer credible; ‘The Earth is flat’ and ‘inflammable materials contain phlogiston’ are examples for this. That people were entitled to believe these statements does not make them true, not even for the period during which people were so entitled. The Earth did not change its shape in the meantime, nor did some ingredient of inflammable things suddenly disappear (Carnap [1939] 1949; Putnam 1981; Künne 1993). But Goodman offers a solution to this problem: 200
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Consider for a moment the notion of permanence – taken here to mean lasting forever after some given time. Although we can never establish permanence of an object or material, we can establish durability in varying degrees short of permanence. Likewise, although we can never establish total and permanent credibility, we can establish strength and durability of credibility in varying degrees short of that. Shall we then identify unattainable and permanent credibility with unattainable truth? To the ready protest that we might have total and permanent belief in a falsehood – that what is totally and permanently credible might not be true – perhaps the answer is that so long as the belief or credibility is indeed total and permanent, any divergence from the truth could never matter to us at all. The proposal seems to be that if there is any such divergence, so much the worse for truth: scrap it in favor of total and permanent credibility, which though equally unattainable, just as permanence is explicable in terms of durability. (WW: 123–4) It seems as if Goodman were ready to identify truth with permanent acceptability.5 In this case, permanent acceptability should be a necessary (N) and sufficient (S) condition for truth: (N) ∀x (x is true ⊃ x is permanently acceptable) (S) ∀x (x is permanently acceptable ⊃ x is true) As Wolfgang Künne (1993) has argued, neither (N) nor (S) is without problems. Consider the following example. Say that the first draft of this book contains a specific number of grammatical mistakes of a certain kind, K, but that no one bothers counting them. During the process of amending the manuscript, we get rid of most of them, always destroying the earlier versions of the manuscript. After a while no one is any longer able to find out how many grammatical mistakes of kind K were in the first draft. It seems that the following statement is true and credible: (i) ∃n (The first draft of this book contains n grammatical mistakes of kind K ∧ nothing ever confirms the belief that the first draft contains n grammatical mistakes of kind K) If (i) is to be true, however, some substitution instance of the open sentence after the existential quantifier has to be true too. So it could well be true that we made a certain grammatical mistake a hundred times. In this case the following could be true for all we know: 201
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(ii) The first draft contains 100 grammatical mistakes of kind K ∧ nothing ever confirms the belief that the first draft contains 100 grammatical mistakes of kind K. But although (ii) might well be true, nothing can ever confirm the belief that things really are as (ii) says they are. Statement (ii) is a conjunction of two statements. Let us denote the first statement by ‘A’ and the second by ‘B’. If there ever was any evidence that would confirm (A ∧ B), we could conclude that it also confirms A (according to the distribution rule, whatever confirms a conjunctive belief also confirms its conjuncts). But then this evidence would destroy the credibility of B, obviously. The truth conditions of (ii) are, so to speak, “recognition-transcendent” (Künne 1993: 115). And it follows that some true statements are never acceptable and therefore never permanently acceptable. This refutes (N). In his writings subsequent to Ways of Worldmaking, Goodman gives up (N) as well as his earlier claims implying it. In Of Mind and other Matters Goodman seems only to defend the sufficiency claim (S): “[U]ltimate acceptability – acceptability that is not subsequently lost … serves as a sufficient condition for truth …. I am not, despite some passages in WW that suggest the contrary, proposing to define truth as ultimate acceptability” (MM: 38 and n.8). In Of Mind and other Matters he further restricts it to “certain bounds” within which it is supposed to hold. Indeed (S) seems just as false as (N) was. We can easily imagine beings with inferior sense organs that nevertheless share with us the ability to construct empirical hypotheses. For such beings a theory could be permanently acceptable although plainly false (and recognizably so from our point of view). There seems no reason why the situation could not be the same for us, being also only equipped with finite powers. Goodman’s point might be that this is a difference that would not make a difference for us. We would never detect that truth was not indicated by permanent acceptability. Given that, truth is not supposed to be (partially) analysed by permanent acceptability, but rather replaced by it. This interpretation is also supported by Elgin’s reply to Künne’s arguments: Human involvement in the construction of truths and falsehoods does not guarantee the epistemic accessibility of truth. We might easily contrive categories whose instantiation we could never ascertain – for example, categories requiring absolute precision in measurement. But our involvement insures that epistemic accessibility 202
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is within our power to secure – provided we’re willing to pay the price. … Künne argues that if it requires identifying truth with permanent acceptability, the price is too high. For then we must reject seemingly valid inferences and hold that whatever our best evidence supports is true. Dummett is willing to accept such conclusions. After a brief flirtation, Goodman decided he was not. Goodman then proposed replacing truth with permanent acceptability. He suggested that the task philosophy expects truth to perform are better done by permanent acceptability. The prospect of unknowable truths and falsehoods is no longer ominous. For to demote truth is not to deny it. Evaluation of the feasibility of this proposal would require surveying the task in question to see whether permanently acceptable sentences prove more philosophically fruitful than (perhaps unknowable) truths. The answer is not obvious. (Elgin 1993b: 137) As we indicated briefly in Chapter 3, permanent acceptability is not the only replacement for truth. In Reconceptions in Philosophy, Goodman and Elgin argue for replacing truth with rightness, or, at least, marginalizing truth and emphasizing rightness. The driving force behind this replacement, however, is grounded not so much in the metaphysical requirements of constructionalism, but rather in Goodman’s conviction that many symbol systems play different cognitive roles and that truth only applies to the symbols of some of them (and often not to the important ones). (See also our discussion in Chapter 3.)
Summary In this chapter we have tied together some of the ideas that constitute Goodman’s constructionalism. This position is a consequence of his overall philosophy. Constructionalism in this sense is not akin to any form of postmodern irrationalism as defended by cultural relativists. Constructionalism is not the view that “anything goes”, nor the view that truth is simply a matter of point of view, nor that Westerners’ rationality is only one kind of rationality and that choosing between different kinds of rationality is arbitrary and so on. Such views are neither defended by Goodman, nor consequences of Goodman’s views. In fact, most of these are certainly incompatible with Goodman’s views. 203
Chapter 9
Never mind mind, essence is not essential, and matter does not matter In the preceding chapters our aim has been to introduce some of the main aspects of Nelson Goodman’s philosophy. We have occasionally mentioned criticisms of Goodman’s positions, when we thought that this was useful for a better understanding of his views. What we have tried to do is limit these critical remarks, however, so that they do not distract from the book’s main line of argument, namely that Goodman’s views on topics as diverse as induction and aesthetic expression are interrelated in interesting ways. Now that we are approaching the end of the book, a little more should be said regarding the critical evaluation of Goodman’s ideas, and we shall do so in sections devoted to specific branches of systematic philosophy: philosophy of science, metaphysics, logic and mereology. Inevitably, this is all rather eclectic. However, in the Further Reading we indicate books or papers in which more critical discussions of Goodman’s work can be found, concerning, too, the topics not treated in this chapter. None of the issues we raise in this chapter have been settled. They are all very much a matter of current philosophical debate in one way or other. We are not foolish enough to attempt to give a definitive answer to any of them, but rather hope that these open problems will spawn interest in further philosophical research and debate, be it in favour of, or against, Goodman’s positions.
Philosophy of science As we said in Chapter 2, Goodman’s new riddle of induction is one of the most debated topics in the philosophy of science and is still 204
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widely discussed today. We shall not attempt to give an overview of the growing literature in that field (which is, up to 1994, provided by Stalker (1994)), but will instead discuss a twist in the story that leads to new mind-boggling trouble.
Even more gruesome Recall the grue problem. We said that one of the main aspects of Goodman’s riddle is the fact that a fix in terms of positionality, namely, to favour the hypothesis that all emeralds are green over the hypothesis that all emeralds are grue on the basis that ‘grue’ is defined with reference to a certain time, whereas ‘green’ is not – cannot be used easily. If we started with a language having ‘grue’ and ‘bleen’ as basic predicates, ‘green’ and ‘blue’ would be positional and hence ‘all emeralds are grue’ should be favoured in this other language. It followed that a solution in terms of positionality would not solve the problem in a language-independent way. Now consider the following variation of the theme. Let us imagine a grue–bleen language as a real possibility, spoken by a community of what we shall call grue-speakers (we shall refer to members of our community, using ‘green’ and ‘blue’ for green and blue things as the green-speakers). In the grue-speaker society people learn ‘grue’ and ‘bleen’ to apply to objects, presumably in the exact same way we learn to apply ‘green’ and ‘blue’. They phrase their science using words such as ‘grue’ and ‘bleen’, and they mean by these words what we mean by ‘grue’ and ‘bleen’. However, they apply these predicates to those objects that we call ‘green’ and ‘blue’ and in theories in which we use ‘green’ and ‘blue’. Let us further assume that there is a tribe of grue-speakers who use the word ‘green’ in their language, having learnt it the way we did, but mean what we mean by ‘grue’: we shall call them green-sayers. They simply speak a dialect of the other grue-speakers. Their theories and observation sentences mean the same as the theories and observation sentences of the other grue-speakers, but they are expressed using different words. Just as we could translate ‘All emeralds are green’ into the German hypothesis ‘Alle Smaragde sind grün’, which means the same but is expressed in other words, we can translate from one grue-speaker community into the other. The green-sayers are nomads and, as it happens, they come to visit us. As one would imagine, we do not notice the fact that they 205
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are grue-speakers that speak a dialect, for it is still before t and they call everything ‘green’ that we call ‘green’. Consider for a moment the possibility that everyone (except yourself) in your vicinity actually is a green-sayer. Could you notice a difference? Do you know that the people in your actual language community are not green-sayers? How do you know that? You certainly cannot know it from the way people behave towards green objects, of course. They call them ‘green’; that is their word for these things. Nor does it help to ask them whether they think that green things will have the same colour as this green apple after t or whether it is going to be different, for they regard blue things after t to be of the same colour as present green things. Of course they think that it will have “the same colour” after t and “look the way it does now” and so on, simply because ‘colour’ and ‘looks the same way as’ are understood by green-sayers quite differently from how these expressions are understood by green-speakers. Gruesome, isn’t it? Let us go a step even further and consider the possibility that you yourself are a green-sayer. How could you exclude this possibility? Is there anything you could point to that excludes that by using ‘green’ you actually mean what the green-sayers mean? Here is an argument why you might not have anything to point to. Consider the following example from Kripke’s Wittgenstein on Rules and Private Language (1982).1 Since we are finite beings, we have used all expressions up to now only finitely often. Assume that during your lifetime until now, you have – incidentally – only added numbers that were less than 57. It was never necessary up to now to carry out additions with any greater number than that, for whatever reason. Your past behaviour, which is the results you came up with when you had to add two numbers (both of which were always less than 57), confirms the following hypothesis: (H1) By ‘plus’ you mean (and always meant) addition. Now let us define another operation that Kripke called quaddition. We shall symbolize with ⊕ (read ‘quus’):
( DEF1 ) x ⊕ y =def
⎧x + y ⎨ ⎩ 5
if x , y < 57 otherwise
As we know from Goodman’s riddle of induction, the following hypothesis is empirically equivalent to H1 since we assume for the sake of 206
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argument that you have never calculated a sum of numbers that were equal to or greater than 57: (H2) By ‘plus’ you mean (and always meant) quaddition. Of course, the two hypotheses lead to different predictions. If asked what the sum of 57 and 68 is, you will answer ‘125’, according to H1, but ‘5’ according to H2. But which of the two hypotheses is true? Your past behaviour is in accordance with both, as is everything you know about your past mental states, thus in your past there does not seem to be a fact that determines what you meant by ‘plus’. If you now answer ‘125’ when confronted with the problem, how do you know that the answer is in accordance with the rule you have followed in the past when solving addition problems? We assume your mental abilities to be idealized, that is, the problem does not arise because you forgot what you meant or what you did. You can remember everything there is to remember, but no fact of the past you can know of helps you to favour one hypothesis over the other. But if there is no such fact in the past, how can there be a fact in the present. Consider the following Kripke-type argument: (1) My epistemic situation with respect to my past behaviour and my former mental states and dispositions is idealized. (2) Whether I meant anything with an expression (e.g. addition and not quaddition by ‘plus’) is a fact about my behaviour and/or my former mental states, processes or dispositions. (3) If there is such a fact, I should know of it (given (1)). (4) I do not know of any such fact. (5) Therefore there is no such fact with respect to my former behaviour and/or former mental states, processes or dispositions. Thus, the upshot of this sceptical argument is that there is no fact of the matter what we mean by an expression. This is not a direct criticism of Goodman’s riddle, but it undermines Goodman’s solution to it. If we cannot tell whether we meant ‘green’ or ‘grue’ when saying (and projecting) ‘green’ in the past, we would lose any basis to discriminate between grue and green. Maybe ‘grue’ is better entrenched, because that is what we meant in the past when we said and projected ‘green’. Note that the problem is not that a different predicate, ‘grue’, might be entrenched instead of ‘green’. This would not constitute a problem for Goodman. A society that had ‘grue’, ‘bleen’ and so on as entrenched primitive predicates in their language would simply have 207
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a world version that differs from ours. According to ours, ‘grue’ is not projectible; according to theirs, ‘green’ is not (see e.g. WW: 11, 101). The problem Kripke is raising is that we do not understand what we are doing when we project predicates. In a sense, we do not know what the projections are that we are making. Kripke’s argument stands in the same relation to Goodman’s new riddle as Goodman’s riddle stood to Hume’s problem. Hume assumed that when we know that we can trust in uniformity, we would be justified to extrapolate from observed cases. Goodman’s new riddle shows that even knowing that nature was uniform would not help, for what is “uniform” depends on what predicates we use to project. Goodman, on his part, assumed that if we knew which predicates to favour, this problem would be surmountable. Kripke’s puzzle, however, suggests that the question of which predicates to favour presupposes that we know which predicates we are using, and that there might be no way of knowing this. Kripke’s sceptical argument did not remain unchallenged, of course.2 Should Kripke’s argument succeed, however, it is still advisable to keep in mind that Kripke’s riddle is not a riddle of induction specifically. It undermines Goodman’s solution to the new riddle of induction only in so far as it undermines every intellectual activity. If Kripke is right, we can never know whether we are right about what we think our words mean. So we would, quite literally, not know what we are talking about – or what Kripke is saying, for that matter.
As simple as that Goodman’s analysis of simplicity has also been criticized.3 One concern is that, being restricted to the simplicity of basic terms of a theory, Goodman’s simplicity measure does not tell us anything about the ontology presupposed by a theory. A theory of simplicity that was supposed to deal with the ontological commitments of a theory in this sense was proposed by Quine (Quine 1948). According to his theory of simplicity, a simpler theory quantifies over fewer sorts of entities. In other words, what a theory’s quantifiers range over is analysed, and then the kinds of entities so quantified over are counted. Quine argues that this constitutes the ontological commitment of a theory. In defence of Goodman’s theory it might be argued that the interconnectedness of basic terms as measured by Goodman’s criterion is a criterion of the systematicity of the theory and hence an indicator for the lawlikeness of the hypotheses formulated in this language. In 208
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other words, although Goodman’s theory does not measure ontological simplicity (as understood by Quine), it nevertheless measures a feature that is relevant for the comparison of alternative theories. Another problem for Goodman’s account is that often a problem of theory choice does arise within one and the same language. In this case, Goodman’s theory is of no help in choosing between competing hypotheses. However, given Goodman’s definability results, it is simply not clear that hypotheses formulated in the same language that appear to be different with respect to their simplicity really are different with respect to their simplicity and that investigating the latter might involve reformulating the hypotheses in a language with different basic terms (which would then allow for comparison à la Goodman).
Grue again A more interesting problem is Eli Hirsch’s division problem (see Hirsch 1993). The problem is why it seems reasonable for the words of our language to divide up the world in one way rather than another. Is there any rational basis for the fact that our language contains certain general words rather than others? Of course, other languages divide up the world in different ways than, for example, ordinary English does; think back to colour terms in English and Italian that were briefly mentioned in Chapter 6. Also, there might be languages (e.g. technical extensions of ordinary English) that describe the world in a more finely grained way. There might even be languages that divide up the world altogether differently. This seems largely unproblematic (think about the myth that the Inuit have many more words for ‘snow’ in their language than English has), unless we consider languages that divide up reality so significantly differently from our way of dividing it up, that we come to believe that there must be some normative constraints operating on our division practices, constraints that prove the significantly different practices to be irrational. What could such a significantly different language look like? Suppose that instead of starting with normal English and the predicates {Cat, House, Car}, we construct a language with only two predicates {Cathouse, Housecar}, which would be defined in English as follows: Cathouse(x) =def Cat(x) ∨ House(x) Housecar(x) =def House(x) ∨ Car(x) 209
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Although this language has only two basic predicates, it has the same expressive power, for in this language we could easily define our predicates: Cat(x) =def Cathouse(x) ∧ ¬ Housecar(x) House(x) =def Cathouse(x) ∧ Housecar(x) Car(x) =def Housecar(x) ∧ ¬ Cathouse(x) Thus the imaginary language has the same descriptive content that normal English has, but just classifies things in a very strange way. According to Hirsch, this way is so strange that we would intuitively regard it as irrational if we ever met a language community following such a practice. The question is, what are the normative constraints that are operating? Why do we think such a practice would be irrational? Hirsch states: In general, the division problem is to explain what good reasons there may be to favor ordinary languages over various imaginary strange languages, where a strange language is one that divides up reality in ways that strike us intuitively as absurd. [T]he intuitive idea, which the strange languages help to make vivid, is that there are definite limits on what can constitute a reasonable alternative to our ordinary division practices. The division problem is to understand what the nature of these limits might be. (Hirsch 1993: 6) Note that the problem is prima facie different from Goodman’s new riddle. Goodman’s riddle was a problem of projectibility. Why should we project ‘green’ rather than ‘grue’? Let us pretend that we (with the help of Goodman) found a satisfying solution to that problem. Let us assume that the reason we should project ‘green’ rather than ‘grue’ is that ‘green’ is much better entrenched than ‘grue’ is. So far, so good. But that does not help solve the division problem. A language community that has ‘grue’ and ‘bleen’ as basic predicates and lacks predicates such as ‘green’ and ‘blue’ should hence project ‘grue and examined before t or not so examined and bleen’ rather than ‘grue’, since ‘green’ is equivalent to ‘grue and examined before t or not so examined and bleen’. But that is already all that entrenchment tells us about the case. It does not tell us why it is irrational to divide up reality the way the ‘grue’-speaking community does. Now the question is whether Goodman has other resources on offer to deal with that new problem. At first sight it seems that the 210
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strange languages are somewhat intricate. It just does not seem very economical to project strange predicates, especially if entrenchment considerations force us to project disjunctions of these. Since economy is at issue, we might wonder whether Goodman’s simplicity calculus comes to our rescue. Alas, simplicity considerations do not deliver the desired result. Remember that every one-place predicate in the basic vocabulary of a language gets assigned the same value in Goodman’s calculus, namely ‘1’. Obviously, the theory with two one-place predicates is simpler – by Goodman’s measure4 – than a theory with three. But in our example above, in a language with ‘housecar’ and ‘cathouse’ we were able to reduce three predicates of ordinary English, namely ‘cat’, ‘house’ and ‘car’. On the basis of simplicity considerations alone, we should thus abandon our language and choose the language of cathouses and housecars (see Hirsch 1993). For many this seems a highly implausible result (Bremer 2005). At least, it is not the result we desired. It does not tell us, on pragmatic considerations alone, why it is more rational to divide up the world the way normal English does. Two possible remedies come to mind. One remedy could be a theory of natural kinds. If we had an independent clue what the natural kinds were we could choose a language that conforms to them and thereby surmount the problem. Clearly such a theory is far beyond what Goodman would accept. His relativism is incompatible with a theory of natural kinds.5 A second problem would be that two competing ontologies, both proposing certain, but differing, kinds as natural kinds, could not be compared by their simplicity. Choosing between competing naturalkind ontologies should thus proceed in a wholly different way. A somewhat more plausible fix would argue naturalistically that we are built in certain ways, which privileges certain predicates over others. Our cognitive make-up determines which predicates we prefer. (Basically, this is also a way towards a solution in the grue-puzzle case.) Presumably, Goodman would rather bite the bullet and accept that if such a society is actually coping, then the irrationality of the strange language community is merely apparent. The only reason why we think that other divisions are irrational is that we are so used to our own well-entrenched predicates. Note, that the fact that the division problem (if it is a problem) can apparently not be solved on the basis of entrenchment or simplicity considerations does not show that there is no other (maybe even purely syntactical) way to solve it that would be perfectly acceptable for a philosopher who shared Goodman’s standards. 211
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Metaphysics Goodman’s irrealism has also provoked a number of criticisms. As discussed in Chapter 8, Goodman tries to steer a middle course between realism and idealism. The intuition taken from realism is that true versions are true because they correctly describe the world. The idealist intuitions seem to be that (a) anything like a versionneutral unshaped reality is incomprehensible, and (b) there are true but incompatible versions. Goodman suggests that if we want to adhere to both, the idealistic intuition expressed in (b) and the realist intuition, we have to assume more than one world answering to the true versions. If we want to adhere to the idealist intuition (a), these worlds must, nevertheless, be version-dependent. We shall first discuss the latter point. Does accepting the fact that we are the ones who categorize the world into stars, cows and so on, commit us to the view that we made the stars and the cows? We shall then turn to the question how a plenitude of incompatible true versions might be reconciled with realism in other ways.
The argument from convention When pressed on the point whether we can really be said to have “made” the stars, Goodman replied with the example of the Big Dipper. The Big Dipper is a certain constellation6 of stars that we have picked out and labelled ‘Big Dipper’. The Big Dipper certainly was not a constellation of stars to be found by us; rather, by singling out one constellation of stars, we made the Big Dipper. Rather, we could have chosen any configuration of stars to give it a specific name and treat it as a constellation, “but saying that all configurations are constellations is in effect to say that none are” (MM: 36). But just as the Big Dipper (sometimes called the ‘Great Dipper’) is an artefact of our ordering, the stars are also “stars” simply because we have drawn certain boundaries around objects rather than others. In a fictitious dialogue (which we here quote in full), Goodman makes this point in response to Israel Scheffler’s criticism: “The Great Dipper was made by an adopted world version.” “No, it was made by Nature.” “Did Nature make it the Great Dipper?” “Well, no; it was made the Great Dipper by being picked out and so called by a version.” 212
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Figure 9.1 The Big Dipper. (Photo courtesy of Forrest J. Egan, www. digitalastro.com)
“What is the it that was made by Nature and was there to be picked out and named?” “A particular constellation.” “Was it made a constellation by nature?” “Well, no; it was made a constellation by a version that distinguished certain configurations of stars from others under the general term ‘constellations.’” “But did Nature make the stars?” “Certainly.” “Did it make them stars?” “Again, no; they were made stars by a version that distinguished certain conglomerations of particles, or objects in the sky, from others under the general term ‘star.’” “Did Nature make the —.” “This could go on and on; but your arguments seem at most to show that without versions stars, for example, do not exist qua stars, not that they do not exist at all.” “But do stars-not-qua-stars, stars-not-qua-moving and not-quafixed, move or not? Without a version, they are neither moving nor fixed. And whatever neither moves nor is fixed, is neither qua so-and-so nor qua not-so-and-so, comes to nothing.” (Goodman 1996b: 167) 213
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How could that argument be countered? Did we make the Big Dipper? Clearly, there is a sense in which we did. Indeed, we constructed a version in which that very group of stars is seen as exemplifying a dipper shape. In this sense, it was we who put the Big Dipper up into the sky. A realist would grant this but object immediately that there is a difference between the constellation that we named ‘Big Dipper’ and the stars that make up the constellation. Constellations are “artificial kinds”, categorizing certain stars into constellations on the basis of remote shape resemblances with wholly unrelated other objects, but this does not cut nature at its joints, so to speak. Stars, on the other hand, are “natural kinds”, they are not “made” by us in the way constellations are. Goodman would reply to this that our concept star has completely arbitrary boundaries. Is it not we who decide which objects are to be included into this category and which are to be excluded from it? But if that is so, in what sense is it then a “natural” kind? Goodman’s challenge is, in other words, to name some mind-independent stuff, something that we did not make. His strategy seems to work so well, because the very moment we name some purported mind-independent stuff, we must have lost the game. If we are able to name it, we have a category or a label for it and that will apply because of a conventional version ... and so on, and so on ... therefore we made it, after all. However, the argument from convention rests on a conflation. Some elements of our language, for example, proper names such as ‘Nelson Goodman’ or ‘Big Dipper’ are strongly conventional. The stars that constitute the Big Dipper do so because we introduced the convention that they do so. Someone who started to doubt that the constellation in the sky that we name ‘Big Dipper’ really is the Big Dipper would show that he is unable to use the name ‘Big Dipper’. But here is the difference: it is conceptually possible to express doubts about whether all celestial bodies constituting the Big Dipper are stars (one could imagine that we would get evidence for the hypothesis that one of them is a planet, or a far-away galaxy, or an alien spaceship observing us from that position for a quite a while now), but it is not in the same sense conceptually possible to doubt that the constellation we refer to as the Big Dipper really is the Big Dipper: One perfectly good answer to Goodman’s rhetorical question “Can you tell me something that we didn’t make?” is that we didn’t make Sirius a star. Not only didn’t we make Sirius a star in the sense in which a carpenter makes a table, we didn’t make it a star. Our ancestors and our contemporaries (including astrophysicists), 214
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Figure 9.2 The Big Dipper. (Photo courtesy of Forrest J. Egan; alterations by the authors.)
in shaping and creating our language, created the concept star, with its partly conventional boundaries, with its partly indeterminate boundaries, and so on. And that concept applies to Sirius. The fact that the concept star has conventional elements doesn’t mean that we make it the case that that concept applies to any particular thing, in the way in which we made it the case that the concept “Big Dipper” applies to a particular group of stars. (Putnam in McCormick 1996: 183) Goodman’s argument appears to obscure this difference. Whether or not the general name ‘star’, once introduced, applies to Sirius is not a matter of convention in the way it is a matter of convention what the proper name ‘Big Dipper’ applies to. We have to keep in mind that convention plays very different roles for the application of general names (such as ‘star’ or ‘cow’) and proper names (such as ‘Big Dipper’ or ‘Nelson Goodman’).
The argument from conflicting truths One of the phenomena that led to Goodman’s constructionalism was already the topic of The Structure of Appearance. There might be two incompatible but perfectly satisfactory versions of the world. We can 215
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regard points in spacetime as concrete particulars of which space consists or, alternatively, as mere limits, resulting from some sort of abstraction. Geometry and physics can be done from either point of view without problems. For different purposes one version is better than the other, so we would like to keep both for pragmatic reasons. The two versions cannot be both true of one and the same world, Goodman thinks. They are incompatible with each other. Accepting the sentences ‘points are mere limits’ and ‘points are not mere limits but parts of space’ leads to a logical contradiction. Goodman tries to solve the problem by suggesting that each true version applies to a world, but that they apply to two different worlds. There are, however, other ways to solve this problem. One way (suggested by Quine (1981: 21–2)) is to pick one of the conflicting versions at a time. When you do so you will regard the one you are using as true and the other as false. This form of schizophrenia might be a little less implausible than postulating more than one world and suggesting that we constantly travel from one world to the next when we choose another version to describe Reality. In the Quinean approach both are regarded as true of one and the same world but true at different times (and, presumably, for different persons). The objection from a Goodmanian perspective would be that our holding a version to be true does not make it true. (Frege, incidentally, is famous for having put this argument forward in various places.) If a version is right it does not matter whether we regard it as true at a time or not. So, if two right versions conflict, our using one or the other at certain times, but never both, does not matter. Also, for the realist, the neutral reality that underlies the versions or worlds cannot be dependent on what we believe at a time. Quine claims that “truth is immanent” and that “there is no higher” (Quine 1981: 21). Indeed, as the Goodmanian would reply, the metatheoretic point of view might better describe the relation between versions and their worlds in terms of the “rightness” of these versions, rather than their “truth”. But then, what Quine blames as a “confusion of truth with evidential support” on the side of the irrealist, namely, “to suppose that we can stand aloof and recognize all the alternative [versions] as true in their several ways [and] all the envisaged worlds as real” (ibid.) is not a confusion on the irrealist’s side, but rather a mere quibble over the right terminology. Another alternative (suggested by Putnam (1992)) highlights that for each true sentence of one version there is a corresponding true sentence of the other version and although this relation between the 216
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two versions is not identity of meaning (for something like this need not be preserved when we move a sentence from one version to compare it with a sentence of another version), it is a relation akin to that. We certainly cannot explicitly give the truth-conditions on which the translation relation between the two versions is based (for that would involve describing reality again with another version) but this should not lead us to the belief that the translation relation is not founded. It could, for example, be founded in the practices of scientists who are used to both versions and who know from their experience with both which sentence in one version corresponds to a sentence in the other. We should not draw the idealist inference that because reality cannot be described independently of our descriptions, there are only the descriptions.
Responses Do these arguments refute Goodman’s claims about worldmaking? Clearly, Goodman does not think so. As we discussed in Chapter 8, he insists that there are no worlds that are independent of right versions, and does not find the question whether right versions answer to worlds or whether they are worlds particularly interesting. We also quoted Goodman there as saying that making worlds is “hard work”. It might well be nigh impossible to make a world without stars, but one could argue that this does not yet show that they are not made. It might be impossible to make a plane that uses nitrogen as fuel, but that does not show that planes are found rather than made (compare MM: 41–2). What we create is not arbitrary, neither when we are making planes, nor when we are making worlds; that does not mean, however, that it is absolute, that is, that there is a unique right version, or a unique reality that all right versions have to answer to. The disagreement between Goodman and his critics is probably best characterized by asking what it is that determines the constraints on worldmaking. The realists’ answer is that it is the underlying reality. Goodman contends that this alleged underlying reality could not have any features that are interesting enough to do this job. Such a reality must be entirely unstructured to be able to underlie all conflicting versions or worlds. Rather, it is the entrenchment of certain predicates, stolidly hanging on to so-called “foundations”, old world versions, and the like, that constrains the making of a new world. “Worldmaking begins with one version, and ends with another” (WW: 97). 217
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In rejecting realism, Goodman is often taken to be an idealist. He denies this vehemently: “I am an anti-realist and an anti-idealist – hence an irrealist” (Goodman 1996c: 203). His irrealism is distinguished from idealism in more or less the same way that it is distinguished from realism. Realism and idealism, according to Goodman, disagree over what is admissible as the basic building blocks for a world version. Goodman’s irrealism is pluralistic in this respect and rejects the question: “According to my usage of these terms, ‘realism’ shuns all idealistic systems; ‘idealism’ shuns all realistic systems; ‘irrealism’ does not discriminate either way” (Goodman 1996b: 204). Concerning Putnam’s specific complaint that we presented above, Goodman would probably not agree with the premise that for each true sentence of one version there is a corresponding true sentence of the other version, whatever the relation between them might be. More importantly, however, Goodman replies that he does not claim that there are no worlds. He merely makes the conditional claim that there are many worlds if any.7
Logic and mereology In this section we are concerned with a criticism of Goodman’s views on set theory that at the same time could be construed as a development and an extension of Goodman’s work on mereology. We already mentioned in Chapter 4 that the calculus of individuals as developed by Leonard and Goodman is an important technical tool in metaphysical research today. David Lewis makes use of it, too, in various publications. One of these is his Parts of Classes (Lewis 1991),8 where he proposes that set theory and mereology are not as strictly separated from each other as Goodman might have thought.9 Lewis agrees with Goodman’s sameness-of-content criterion that no two different things are allowed to be generated out of the same atoms (we are ignoring gunk here). He holds, however, that class formation (or “the ancestral of membership”, as he calls it) is not a generating relation. He criticizes Goodman for just stipulating that it is: Given this stipulation, of course I cannot deny that the ancestral of membership is a generating relation; given the stipulation I deny instead that Goodman’s principle has any force. It says only that if a relation is either the proper part relation, or the ancestral of membership, or the logical sum of the two, then it must obey a certain condition which the proper part relation does obey and 218
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the ancestral of membership (or the sum of the two) does not. Why should anyone believe that, unless because he renounces classes already? (Lewis 1991: 40) The answer is, of course, that in rephrasing his talk in terms of the generating relation of a system, Goodman just restates the original point: that he finds classes incomprehensible. The cashing out of this by talking about generating relations is not best construed as a further reason to reject classes. The task of Goodman (1958a) is merely to define what a nominalistic system is (see § “Goodman’s nominalism”, p. 86). The paper contains nothing to suggest that additional arguments for the rejection of classes are being offered here. Incidentally, non-extensional generating relations – like the non-extensional proper part relation we mentioned in Chapter 4 – are not taken into account by Lewis either. These would provide a counter-example to the claim that the only generating relations are the ancestral of membership, the (extensional) proper part relation, and the logical sum of the two. Lewis continues, however, in the original spirit. He accepts Goodman’s criterion, but rejects that the ancestral of membership is a generating relation. How can he hold that? Lewis agrees with Goodman that “unmereological composition” is illegitimate, but prepares to argue that: “the generation of classes is not an unmereological sort of composition. In so far as it is unmereological, it isn’t composition; in so far as it is composition, it is mereological” (Lewis 1991: 40). Lewis shows that (given certain assumptions about the size of the universe – we return to that later) the whole of standard set theory can be captured by adding plural quantification and a singleton function to standard mereology.10 Lewis calls the system that results from adding plural quantification to standard mereology “megethology”. What is plural quantification? Basically, on the surface it looks like we are allowing quantification into predicate position, something that is usually called ‘second-order quantification’, which gives rise to second-order (predicate) logic, as opposed to first-order predicate logic, which allows quantification only into name position.11 It might seem natural to think of second-order quantification as quantification over properties or something similar. If we take (1) as an example, it would be read as something like (2): (1) ∃X Xa (2) There is a property that a has. 219
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It is standard today, however, to construe second-order quantifiers as ranging over classes of those things that the first-order quantifiers range over. Statement (1), then, may be understood in this way: (3) There is a class that a belongs to. Neither, of course, is acceptable to Goodman: properties are out because they are intensional, and classes are rejected by his nominalism. George Boolos, however, argues that one does not have to assume properties or sets to make sense of quantification into predicate position (see Boolos 1984, 1985). His idea is that instead of understanding second-order quantification as the same old quantification over new things (properties, classes, etc.), one could – or rather should – understand it as a new form of quantification over the same old things: as plural quantification. Plural quantifiers range over the same things that first-order quantifiers range over, the objects in the (first-order) domain, those things that the names of the language refer to. But they range over those things plurally, much like the English plural pronoun ‘they’ in comparison to ‘it’. So, if a first-order quantifier ‘∃x’ is to be read as ‘there is something that’, the plural quantifier ‘∃X ’ is read as ‘There are some things such that’; if one wants to read ‘Fx’ as ‘is F ’ or ‘is one of the Fs’ then ‘Xa’ becomes ‘a is one of them’. Our sentence (1) is then rendered in this way: (4)
There are some things such that a is one of them.
Things get a bit more complicated when the system of plural quantification is formulated in full detail, but the idea should be clear enough. Boolos and others who followed him argue that, understood in this way, quantification into predicate position does not commit us to any “new” entities at all. If this is right, plural quantification does not generate new entities either, to use the Goodmanian terminology. The generating relation of a system comprising plural quantification is not nominalistically objectionable on the grounds of its plural quantifiers. Boolos identifies (monadic) second-order quantification with plural quantification. For reasons that carry us beyond the scope of this book (and beyond the space available in it) Lewis does not like this identification (Lewis 1991: esp. 70–71). He likes plural quantification, however, and uses it to reconstruct set theory. Again, we are not able to go into detail here, but will merely give some hints on how Lewis’s construction works, explain what the basic idea behind it is, and keep the formalism out. Interested readers can find the details elsewhere.12 220
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First, Lewis defines fusion using plural quantification. A fusion of individuals is the mereological sum of them. So far we have only considered binary mereological sums: sums of two individuals. Since set theory will lead us into the realms of infinity, merely adding together two things at a time will not be enough; we would not get very far, in the grand scheme of things. Mereological fusion, plurally construed, gives us more power. However many things you specify (using a – possibly complex – predicate), the fusion of them is a thing as well (note the plural pronoun ‘them’). Now, how does that help us with classes? Lewis observes that there is a very intuitive way in which classes do have parts. These parts are not to be identified with their members, of course, since parthood is transitive and membership is not: a is a member of {a}, {a} is a member of {{a}}, but a is not a member of {{a}}. One can, however, understand the subclasses of a class as its parts. Being a subclass is transitive, and other nice features pop up as well. It turns out, for example, that classes can elegantly be defined as fusions of singletons, and little more needs to be said, other than what singletons are. Set theory identifies a singleton as a one-membered set (or class). The singleton of a, for instance, is {a}. If classes, however, are now defined on basis of the notion of a singleton, something else needs to be said here, and we return to that shortly. So fusions can not only be taken of individuals, but also of singletons. Any fusion of individuals is also an individual. The fusion of singletons is a class.13 Is this definition of classes as fusions of singletons sufficient, however? Observe first that singletons have to come out as classes if set theory is to be recaptured, and luckily they do. All singletons are classes since they are fusions of themselves; {a}, for example, is the fusion of {a}. It also fits neatly that we do not need to worry specifically about the other subclasses of a given class that are not singletons. They are taken care of naturally and in the right way by mereological fusion and the ‘part’ relation we got to know in chapter 4. Take, for example, the fusion of {a}, {b} and {c}; we get the class {a, b, c} (according to Lewis). Now, {a} is a subclass of this class, and a part of it, of course. And {a, b} is a subclass of {a, b, c}, too, so it should also be a part of it. And it is: {a, b} is the fusion of {a} and {b}, and since both singletons are parts of {a, b, c}, so is {a, b}. So far, so good. Now, being a member and being a subclass of a class are kept apart, as we want them to be: being a subclass of a class is defined as being a part of that class, while something is a member of a class iff its singleton is a part of that class. It is easy to see that a is a member of {a}, and also of {a, b, c}; a is not a part of 221
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either, though (we assume that a is not a class – if it were it could be part of it, of course; say, if it were the case that a = {b}). Classes that contain classes as their members also simply fall out from what we have established so far: we get the class {a, {b, c}} by taking the fusion of the singleton of a and the singleton of {b, c}, that is, the fusion of {a} and {{b, c}}. And {a, {b, c}} is different from {a, b, c}, as it should be, since it has different parts: {b} is a part (i.e. a subclass) of the latter, but not the former; and while {b, c} is a member of {a, {b, c}}, it is not a part of it – it is, however, a part of {a, b, c}. It takes some time to get used to thinking of subclasses as parts of classes, but it should be clear how Lewis reconstructs set theory in this way. The one crucial thing that is missing so far, though, is the empty class, or the null set, as Lewis prefers to call it for reasons that will become clear soon. The problem is, that no fusion of singletons will deliver it, since singletons are always singletons of something, so we cannot have a class that has less than one member. The empty class cannot be a singleton itself for the same reason; also quite intuitively, what would it be the singleton of? There is no such thing as a null individual.14 Something, though, is needed to play the role of the null set, if set theory is to be recaptured, and Lewis has no qualms just stipulating something in the universe to play that role. He divides what he calls “Reality” into two: individuals and classes (Lewis 1991: 19–21). Classes are fusions of singletons; individuals are fusions of individuals that might be atoms, but not singletons or other classes (following the definition of Chapter 4, singletons are atoms as well – they have no proper parts). No individual has a class as a part. Classes have members, individuals do not. So, if one of the individuals is stipulated to play the role of the null set, we can keep the claim that the null set does not have any members (since no individual does), even though we have to swallow the fact that the null set is not a class (since all classes have members). Any individual could do the job of the null set; Lewis plumps, arbitrarily, for the fusion of all individuals. This way Lewis gets a null set despite not having an empty class. Lewis now defines a set to be either the null set or a class that is not a proper class. Proper classes are classes that are just too big to be members of other classes themselves. Assuming that they can be without posing further restrictions leads into inconsistency. One famous example is the Russell class, which we have already encountered in Chapter 5. Lewis can define what it is for a collection to be too big to form a class that is not a proper class. We cannot go into details 222
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here, but let us tease you by simply stating (without explanation) that things get too big if they have the size of the universe. (Readers familiar with set theory and its history will recognize a similarity to a position labelled ‘limitation of size’.) Plural quantification plays a crucial role in formulating this restriction, too, but we cannot go into this either. Singletons can be formed from any individual and any set, but not from proper classes,15 since those, on pain of contradiction, cannot end up as members of classes. Although we omitted most of the details as well as the proof of the standard axioms of set theory in this framework,16 it should be clear now how mereology and set theory interact, and how all the set-theoretical concepts can be made clear in the, perhaps nominalistically acceptable, framework of megethology – all, except for singleton which, unfortunately, turns out to be the central notion. Lewis takes a sort of structuralist view on this: the singleton function does not have to be specified; the existence of a singleton function is sufficient. But here two problems occur. Does such a function exist? And what do we mean by function? The talk of the existence of a function might be seen as problematic, and perhaps it is. Lewis managed to convince himself that it is not. We cannot (as the normal mathematician often does) take functions to be special sets, since we do not have sets yet, but there might be a way out. Functions can be construed as special kinds of relations, and in an appendix to Parts of Classes (Lewis 1991), John Burgess, Allen Hazen and David Lewis show how quantification over relations can be simulated in megethology. In a first, more or less standard step, one can think of quantification over two-place relations as plural quantification over ordered pairs, and over triples, quartuples, …, n-tuples, for three-place, four-place, …, n-place relations. Pairs, and so on, are standardly defined as sets, though, and are hence not available yet; we only get them after we have the singleton function, which we are trying to get a handle on at the moment. Otherwise we could have defined a function as a special kind of set immediately. Burgess, Hazen and Lewis show that we can get substitutes for pairs, triples and so on, by using a clever coding trick (the details, again, have to be omitted here). This coding basically can be done using only megethology (i.e. mereology plus plural quantification), but it has to be assumed that there are infinitely many atoms. Further, it turns out that if we assume that the universe is large enough, such a singleton function can be proven to exist (Lewis 1993). How large? We are talking vast here. The more technical 223
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term used by set theorists is inaccessible, and that name alone might give a hint. Think of a set with three members. Now think of the set of the natural numbers (maybe you have to pretend for a while to be a platonist to do so). Now think of a set that stands to the set of the natural numbers as that one stands to the set with three members. You are probably not even close yet (unless you have done some advanced set theory). If we take the powerset of the natural numbers, that is, the set of all the subsets of it, we get a set that is of a higher infinite cardinality than the original one. The members of the two cannot be put into one-to-one correspondence as is possible for the natural numbers and the integers;17 that was proved by the father of set theory, Georg Cantor (1845–1918). The set of the real numbers, for example, is larger than the set of the natural numbers.18 If we apply the powerset operation over and over again, and also apply the union operation as often as we like – that is, throwing together everything that is in the sets we have so far to form a new set, so {a, b, c, d }, for example, is the union of {a, b} and {c, d } (this can be done with infinite sets as well) – we get sets of higher and higher cardinalities, larger and larger infinities. Inaccessible sets (note, that they are not proper classes yet!) are those that cannot be reached by proceeding in that way. Lewis requires Reality to contain inaccessibly many atoms (i.e. the set of atoms has to be of inaccessible size). Starting there, we will also get inaccessibly many singletons, and inaccessibly many sets. Incidentally, the existence of inaccessible sets is consistent with current standard set theory, but cannot be proved from the standard axioms. That is how large the universe has to be assumed to be, so that the singleton function is guaranteed to exist. Lewis takes himself to have pinned down exactly where the border to mathematics (in the form of set theory) is crossed: it is marked by the introduction of the singleton. The rest of the formal apparatus he uses (first-order mereology plus plural quantification) he considers innocuous: let us say nominalistically acceptable. Unfortunately, Goodman never made a statement in print about Lewis’s project of Parts of Classes. He remained unconvinced of Lewis’s arguments, however, despite acknowledging Lewis’s construction as an accomplishment.19 Plural quantification might just have been acceptable to him, although he remained suspicious of it, but he must have balked at extending mereological summation to classes, and at the singleton function in general. The singleton of a thing being different from the thing itself, even though nothing seems to have been added to it, is 224
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exactly the sort of undue multiplication of entities that Goodman complained about. But if such entities are not acceptable, one cannot form mereological sums of them, either. But now remember that Lewis does not take the singleton function to be generating or composing anything. As we said at the beginning of this section, Lewis, while accepting Goodman’s sameness-of-content criterion for generating relations, denies that the ancestral of membership is a generating relation. Class formation and membership are defined on the basis of the notion of a single function. Lewis also refuses to speak of the singleton function, but rather takes a structuralist view of it: any function that structurally plays the right role will do for him. And if Reality is big enough (i.e. if there are inaccessibly many atoms in it) such a function has to exist. Goodman’s finitist inclinations probably did not make him sympathetic to the Burgess–Hazen–Lewis result about relations in megethology, which assumes infinitely many atoms, and he was much less sympathetic to soothing the worries about the singleton function by proving that it must exist if the universe is inaccessibly large. This, though, suggests that perhaps he could have agreed with Lewis at least about the point where we enter the realm of mathematics. Lewis has reduced the mystery of classes to the mystery of the singleton function. He also took it that this mystery was removed, too, by the structuralist move and the proof of the existence of the function in a sufficiently large Reality. Inaccessible sets are standardly assumed by mathematicians who work in set theory today, so Lewis has no scruples to assume this for the size of Reality if it allows him to reconstruct set theory in megethology: “Will you tell the mathematicians to abjure their errors? Not me!” (Lewis 1993: 23)20 Lewis, however, even if we grant him the assumption that Reality contains inaccessibly many atoms, has failed to explain what singletons are. The singleton of a, on Lewis’s account, need not have anything to do with a at all. It is just some object that some not uniquely specified function (one or another of the singleton functions) maps to a. Buckingham Palace, for instance, could be the singleton of Edinburgh Castle, if Lewis is right. Further, since classes are mereological fusions of singletons there is no straightforward sense in which classes contain their members. Take the class of all mathematicians, for example. It is the fusion of the respective singletons of each mathematician. The singleton function, however, might map each mathematician onto a different molecule of a range of exquisite cheeses somewhere in the shop of a cheesemonger in the 225
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south of France. The class of all mathematicians thereby becomes the fusion of all these cheese molecules. It contains a lot of cheese, but no mathematicians, at least not in anything close to the normal sense of ‘contain’. Will you tell the mathematicians that? Not us! What Lewis gave us is a way of modelling our talk about sets in a way that on the face of it does not assume or rely on sets. This is an amazing achievement. It did not, however, remove the mystery of the singleton. Singleton a is something different from a by stipulation, but we are none the wiser concerning what it is. Also, classes do not contain their members in any recognizable sense of ‘contain’. Lewis himself, however, insists in many places that Cantor’s notion, that a class is a collection of many things into one, is essential to the concept of class (see e.g. Lewis 1991: 29–31). This “intuitive” containment relation between a class and its members is lost in Lewis’s account through the various non-generating moves he makes, such as the coding tricks for pairing and the structuralist moves concerning singleton functions. Goodman insists that removing this mystery of the notion of a class must consist in providing a solution to exactly the problems that Lewis leaves open: what is the distinction between an object and its singleton, and how can two different entities be generated out of the exact same atoms?
Epilogue In the preface to Problems and Projects, Goodman wrote: “The more problems the more projects; the more projects the more problems. Yet if there are more beginnings than endings in my work, I hope the reader may now and again have an intimation that not all problems of philosophy are immortal” (PP: xii ). We hope to have shown in this book that indeed some problems of philosophy can be solved, and that – the criticism reported in this chapter notwithstanding – Goodman has solved quite a number of them. He has also opened up many new ones, problems that were generally fruitful, often much more fruitful than anything considered problematic in certain branches of philosophy before Goodman. Elgin wrote in retrospect: Nelson Goodman’s philosophy combines judicious skepticism about received wisdom, uncompromising rigor, and seemingly unbridled creativity in reconfiguring philosophical problems, resources and objectives. The solutions he offers are not permanent resting 226
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places, but launch pads for further inquiry. The mark of a good answer, he thinks, is the question it raises. In 1946, Goodman said, “Descartes faced his world as a skeptic with a method – in other words, as a courageous, humble and hopeful man. Perhaps our glance back at him may remind us that there can be no security in traditions that failed us; that by patient and systematic use of our best faculties we may advance, but that there is no black market in truth; that the results of wishful and fearful thinking cannot survive encounter with conflicting facts; and – finally – that a belief that will not stand the strictest scrutiny of doubt and reason will not withstand the oratory of the next demagogue” [PP: 48]. The same might be said of Goodman himself. His work altered the contours of philosophy in the twentieth century. (Elgin 2000a: 16) There is not much to add. Instead of throwing more Goodmanpraise on you we end the book with food for thought: a snack, really. Goodman’s first publication actually was not “The Calculus of Individuals and its Uses” (with Leonard 1940a), as you might think, but a “daily brain-teaser” that was published in the Boston Post on the front page of the 8 June 1931 issue (reprinted in PP). The Truth-tellers and the Liars All the men of a certain country are either noble or hunters, and no one is both a noble and a hunter. The male inhabitants are nearly alike that it is difficult to tell them apart, but there is a difference: nobles never lie, and hunters never tell the truth. Three of the men meet one day and Ahmed, the first, says something. He says either, “I am a noble”, or “I am a hunter.” (We don’t know yet which he said.) Ali, the second man, heard what Ahmed said, and in reply to a query, answered, “Ahmed said, ‘I am a hunter’.” Then Ali went on to say, “Azab is a hunter.” Azab was the third man. He said, “Ahmed is a noble.” Now the problem is, which is each? How do you know?
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List of symbols
≡
material biconditional; read “if, and only if”
⊃
material conditional; read “if … then …”
¬
negation; read “not”
∧
conjunction; read “and”
∨
disjunction; read “or” (inclusive)
|
alternative denial (“Sheffer stroke”); read “not both of … and …”
∀
universal quantifier; read “all”
∃
existential quantifier; read “some” (there is at least one)
⇒
conditional in the metalanguage
x∈A
x is a member of A
s1 ⊆ s2
s1 is a subset of s2
∅ ≤, ≥
empty set less than or equal to, greater than or equal to ordered pair of a and b
=
identical, ‘equal to’ in mathematical contexts
≠
non-identical (disjoint), ‘not equal’ in mathematical contexts
xoy x∫y x
x overlaps with y x is discrete from y (x does not overlap with y) x is part of y x is proper part of y (mereological or arithemetical) sum of x and y the (unique) z, that is such that
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Glossary of technical terms
It is advisable also to consult the index for the terms defined here in order to find where they are mentioned or discussed in the main text. We often explain them there in more detail. The index, of course, also contains references to terms that do not occur here in the glossary. argument: (as in ‘argument places of predicates’): see PREDICATE. atom: atoms are the primitive elements that (together with certain ordering relations on the INDIVIDUALS built from those atoms) make up the basis of a CONSTRUCTIONAL SYSTEM. The atoms in The Structure of Appearance, for example, are QUALIA. axiom: postulated sentence or sentence schema (then also called ‘axiom schema’) of a deductive system (INFERENCE RULES) or THEORY. calculus of classes: a formal system that contains CLASSES (or SETS). Goodman rejects the calculus of classes in favour of the CALCULUS OF INDIVIDUALS (except in A Study of Qualities). At least in the beginning, he probably had Russell’s THEORY OF TYPES in mind (but see also SET THEORY). We discuss both calculi as well as Goodman’s views about and use of them extensively in Chapters 4 and 5. calculus of individuals: Leonard and Goodman’s mereological system (MEREOLOGY). It does not make use of classes or SETS, but acknowledges only INDIVIDUALS. See also CALCULUS OF CLASSES. class: often used interchangeably with ‘set’ (SET). Sometimes ‘class’ is taken to refer to the broader notion: all sets are classes, but there are so-called proper classes that are not sets. Proper classes cannot themselves be members (MEMBERSHIP) of classes, while sets can. They are often said to be “too big” to be members of classes (see § “Logic and mereology” p. 218). See also CALCULUS OF CLASSES and SET THEORY. coextensional: two expressions are coextensional iff they have the same EXTENSION. cointensional: two expressions are cointensional iff they have the same INTENSION. conclusion: a sentence in an argument that is claimed to follow from the presupposed sentences, the premises. conditional: see MATERIAL CONDITIONAL. constant, logical: typically, ‘and’, ‘or’, ‘if … then’, ‘not’, ‘all’ and ‘some’ are regarded as logical constants. Thus when sentences of ordinary English are translated into formal logic, these expressions get (cum grano salis) a constant meaning assigned
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Glossary of technical terms (TRUTH-FUNCTIONAL CONNECTIVES). These are not specific to the topic at hand. In contrast, the non-logical constants of a theory are the names and predicates that are specifically axiomatised. constitution system: see CONSTRUCTIONAL SYSTEM. constructional system: system of objects/concepts (of a certain domain) in which all objects/concepts (of that DOMAIN) are logically constructed from a proper SUBSET of these objects/concepts, the basis of the system. counterfactual: a sentence that claims how things would be if the world were different from how it in fact is. ‘If kangaroos had no tails, they would topple over’ is such a sentence. deduction, deductive system: INFERENCE RULES. definiendum: the expression/thing supposed to be defined; in a nominal the definiendum is the abbreviating term, see p. 58.
DEFINITION
definiens: the defining expression/set of properties; in a nominal DEFINITION the definiens is the complex term which is abbreviated by the DEFINIENDUM. definientia: plural of ‘DEFINIENS’. definition: what you typically find in a glossary. On pp. 58–61 we distinguish nominal definitions, which abbreviate complex expressions of an existing language by adding a new word to it and by stipulating meaning identity of the new word and the complex expression, from real definitions, which, in case of empirical analyses, state what all and only those members of a certain kind of entities have in common, and, in case of meaning analyses, state what a given expression of an existing language is synonymous (SYNONYMY) with in that language. Empirical analyses and meaning analyses can be true or false; nominal definitions, being stipulations, can only be more or less right. EXPLICATIONS are essentially nominal definitions. The only difference is that the EXPLICANDUM as an expression is already in use in the language; it is then given a new MEANING. de re/de dicto: two ways to pick out the referent of a certain representation. If, for example, Lex Luthor knows de re of Superman that he has superhuman powers, he also knows it de re of Clark Kent, since Superman is (identical with) Clark Kent. However, Lex Luthor might nevertheless fail to know de dicto that Clark Kent has superhuman powers from knowing de dicto that Superman has them, for Lex Luthor might not know that Superman and Clark Kent are identical. domain: contains the objects that a theory is about, for example INDIVIDUALS; usually taken to be a SET of those objects. The QUANTIFIERS in a THEORY are said to range over the things in the domain, and names in the theory refer to them. empty set: the (one and only) SET that has no members (MEMBERSHIP). It is usually denoted by ∅ or { }. See also SUBSET and SET THEORY. erleb: TIME SLICE of the stream of experience of a specific subject. explicandum: what is supposed to be explicated (EXPLICATION), see also p. 61. explicatum: the part of an 61.
EXPLICATION
that explicates the
EXPLICANDUM,
see also p.
explication: a clarification of an expression already in use in scientific or ordinary language. The explication regiments this use and thereby departs from the hitherto unclear or confused MEANING of the expression. See also p. 61 and DEFINITION. explicata: plural of ‘EXPLICATUM’.
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Nelson Goodman extension: what an expression refers to. The extension of a name is the person the name is of; the extension of a predicate is all the objects the predicate is true of (philosophers without nominalistic scruples would say that it is the SET of all these); the extension of a declarative sentence is usually regarded to be a truth-value, following Frege (Goodman, however, belongs to those philosophers who think that sentences do not have extensions). See also INTENSION. ideal language (philosophy): see ORDINARY LANGUAGE (philosophy). individuals: the objects ordered by the basic relation(s) of a CONSTRUCTIONAL SYSTEM. (E.g. ERLEBS (as in Carnap’s Aufbau), QUALIA (as in A Study of Qualities and The Structure of Appearance) or SUMS or SETS of those (as in A Study of Qualities and The Structure of Appearance). inference rules: rules that determine for a given language which inferences can be drawn from certain given (typically syntactically (SYNTAX) specified) sentences. Typically these rules hold between syntactically specified derivability claims (if a sentence of such and such syntactical form is derivable, a sentence of this and that syntactical form is also derivable). See, for example, MODUS PONENS. Inference rules, perhaps together with some AXIOMS, form what is called a deductive system for a language (see also MODEL THEORY). Sometimes the term ‘logic’ is (more or less loosely) used for such systems in which deductions in a THEORY are carried out. intension: refers, in contrast to EXTENSION, to the MEANING of an expression. That meaning and reference are to be distinguished is motivated by examples such as the following. Consider names like ‘Easter Bunny’ and ‘Santa Claus’. Both names (maybe you should make sure that you are sitting down before you continue reading) do not refer to anything. Thus both expressions, arguably, have the same extension, the null-extension. Nevertheless, they do not have the same meaning. If Paul believes that the Easter Bunny is the offspring of a rabbit and a hen, he does not thereby believe that Santa Claus is the offspring of a rabbit and a hen. But if ‘Easter Bunny’ and ‘Santa Claus’ were meaning identical, they should be replaceable in such contexts (at least according to a significant tradition in the philosophy of language). The intension of an expression is in any case a complicated affair. Goodman renounced intensions and tried to analyse the meaning of expression with the help of secondary extensions. See the end of Chapter 3 and Chapter 6 for this. irreflexivity: a property of relations; a relation is irreflexive iff none of the things that the relation applies to stands in that relation to itself. Formally: ∀x ¬ F(x, x). isomorphism: applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where ‘corresponding’ means that the two parts play similar roles in their respective structures. logic: see INFERENCE RULES. logical independence: two statements are logically independent iff the truth or falsity of either one of them entails neither the truth nor the falsity of the other. To illustrate, if p and q are logically independent, all of the following combinations are logically possible: p and q are both true; p is true and q is false, p is false and q is true, p and q are both false. material conditional: a truth-function (see also TRUTH-FUNCTIONAL CONNECTIVES) as specified on p. 45. Two symbols are common for it: ‘⊃’ and ‘→’ (read: “if … then”). See also MODUS PONENS and MODUS TOLLENS. meaning: here used as the INTENSION of a linguistic expression. membership: a
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SET
stands in the membership relation to the things it contains,
Glossary of technical terms usually symbolized ‘∈’. A set has those things as members that it contains. The set A = {Darren, Carrie, Brian, Lindsay} has Brian as one of its members, for example: Brian ∈ A. The members of a set are not to be confused with its SUBSETS. See also SET THEORY and SUM, MEREOLOGICAL. mereological system: see MEREOLOGY. mereology: the branch of logic (broadly construed) that deals with part–whole relationships. Although such logical structures have been studied by various authors of the tradition (e.g. Bolzano, Husserl, etc.) the name dates back to the system of Stanisław Leśniewski (1886–1939) who was interested in a theory which could replace SET THEORY as a nominalistically acceptable foundation for mathematics. See Chapter 4; see also CALCULUS OF INDIVIDUALS and SUM, MEREOLOGICAL. metatheory: a formal or informal system, in which properties of other, so-called object-theories, are proved. Typical metatheoretical proofs are soundness proofs that show that all inferences in the object-theory that accord to the INFERENCE RULES of the system the object-theory is formulated in correspond to the consequences of the MODEL THEORY. model theory: a set theoretic system that models the SEMANTICS of a (formal) language. Typically, a model is an assignment of (more or less arbitrary) objects to names, and SETS of those to PREDICATES. A sentence is defined to be true in a set-theoretic model (SET THEORY) iff the assignments in that model are such that the object that the predicate applies to is a member (MEMBERSHIP) of the set that is assigned to the predicate. A model-theoretic consequence relation is defined within the models, too. A sentence, the CONCLUSION, is a consequence of a set of sentences, if in every model in which all of the sentences in that set are true, the conclusion is true as well (according to the model-theoretic definition of ‘truth’). See also METATHEORY. modus ponens: valid inference (INFERENCE RULES) with typically two premises. In the standard regimentation, the first premise is a MATERIAL CONDITIONAL, ‘p ⊃ q’, the second premise is the antecedent of this conditional, ‘p’, and the CONCLUSION of the inference is the consequent of the conditional, ‘q’. Example: If it rains, we will stay at home. It rains. Therefore, we will stay at home. modus tollens: valid inference with typically two premises. In the standard regimentation, the first premise is a MATERIAL CONDITIONAL ‘p ⊃ q’, the second premise is the negation of the consequent of this conditional, ‘¬q’ and the conclusion of the inference is the negation of the antecedent of the conditional, ‘¬p’. If Peter is clever, he will take the logic class in the first year. It is not the case that Peter will take the logic class in the first year. Therefore it is not the case that Peter is clever. neo-Kantianism: a revived or modified type of philosophy along the lines laid down by Immanuel Kant in the eighteenth century. It played an important role in German philosophy, beginning in the 1860s. The neo-Kantian schools tended to emphasize scientific readings of Kant. nomic: other word for ‘lawlike’. Nomic relationships hold with necessity and thus support COUNTERFACTUALS. nominal definition: see DEFINITION. nomological supervenience: see SUPERVENIENCE, NOMOLOGICAL. ordinary language (philosophy): ‘Ordinary language’ as in ‘ordinary-language philosophy’ refers to a specific approach towards philosophical problems that is often traced back to the philosophy of the later Wittgenstein. Prominent figures in ordinary-language philosophy are Gilbert Ryle, John L. Austin and Peter Strawson. According to ordinary-language philosophy, philosophical problems are mere
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Nelson Goodman misunderstandings of ordinary language. If ordinary language is well understood, all philosophical problems disappear. Its contrast is ‘ideal-language philosophy’ that refers to a tradition that relies on the work of Gottlob Frege (1848–1925), but really dates back to Leibniz and Arnauld (or possibly even earlier). The view is that ordinary language is the real cause of philosophical problems and that their solution does not require a better understanding of ordinary language, but rather replacing it with a language freed of these problems. part: see SUM, MEREOLOGICAL. predicate: linguistic item that together with, for example, a name results in a sentence (e.g. ‘is red’ in ‘Sebastiano is red’). Predicates with more than one argument place, as, for example, ‘is the father of’, are called ‘n-place predicates’; n stands for the number of places the predicate has: ‘is the father of’, for example, is a two-place predicate, since it needs to fill two places with, for example, names in order to form a sentence (e.g. ‘Sebastiano is the father of Emma’). powerset: the powerset of a SET contains as members (MEMBERSHIP) all and only the SUBSETS of that set. The powerset of the set {Chiara, Patrick, Simon} is the set {{Chiara}, {Patrick}, {Simon}, {Chiara, Patrick}, {Patrick, Simon}, {Chiara, Simon}, {Chiara, Patrick, Simon}, ∅}. See also EMPTY SET and SET THEORY. premise: see CONCLUSION. quale/qualia: phenomenal qualities, such as a specific shade of red occurring in the presentation of a specific piece of cloth in a particular light. quantifiers: LOGICAL CONSTANTS of predicate logic that specify the extent to which a predicate holds over a range of things. The standard quantifiers are the universal quantifier, ‘∀’, for ‘all’, and the existential quantifier, ‘∃’, for ‘some’ (understood as ‘there is at least one’). real definition: see DEFINITION. reflexivity: a property of relations; a relation is reflexive iff all of the things that the relation applies to stands in that relation to itself. Formally: ∀xF(x, x). rules of inference: see INFERENCE RULES. semantics: the semantics of a language assigns reference and/or meaning to the complex and simple expressions of the language. set: a collection of objects that itself is treated like an object. The identity of a set is determined extensionally. A set A and a set B are identical iff they have exactly the same members (MEMBERSHIP). It does not matter how the sets are described: the set containing all and only organisms with a heart is identical to the set containing all and only organisms with kidneys; and the set of all vixens is identical to the set of all female foxes. Sets can also be members of sets, but set membership is not transitive. Let the set A = {Aidan, Andrews, Michael, Sune}, and let B = {A}, that is, B = {{Aidan, Andrews, Michael, Sune}}. B has exactly one member, namely the set A. It does not have Sune, or any other member of A as a member. See also CLASS, and SET THEORY. set theory: the theory of SETS was first introduced (informally) by Georg Cantor (1845– 1918). Many axiomatizations have been proposed during the twentieth century. The most commonly used set theory today is the axiomatization by Ernst Zermelo (1871–1953) and Abraham Fraenkel (1891–1965). Set theory accounts not only for sets with finitely many members, but also for infinite sets and different sizes of infinity. (We touch on this in § “Logic and mereology”, p. 218. Very many of the even more introductory textbooks to Zermelo–Fraenkel set theory can be recommended; one of them is Keith Devlin’s The Joy of Sets (New York: Springer, 1993).)
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Glossary of technical terms In pure set theory no so-called urelemente, that is, non-sets, have to be assumed, to “construct” sets of any size. We can just start with the EMPTY SET, ∅. If we take the POWERSET of the empty set, we get a set distinct from it, namely, {∅} (it is distinct, because it has one member, the empty set, while the empty set itself has none; see MEMBERSHIP). If we take the powerset of that set, we get a set with two members: {∅, {∅}}; and the powerset of that has three members: {∅, {∅}, {∅, {∅}}}. It is easy to see that this can be continued indefinitely. The UNION SET of all those infinitely many finite sets is the smallest infinite set. If we keep forming powersets and unions in this fashion, we reach larger and larger infinite sets. This convenient “richness” of set theory is the reason why today it serves as a framework and often also as a foundation of mathematics. See Chapter 4 for Goodman’s criticism of set theory; see also CALCULUS OF CLASSES, MEREOLOGY, and THEORY OF TYPES. subset: a subset of a given SET contains only members (MEMBERSHIP) of that set usually symbolized ‘⊆’. A = {Malcolm, Barbara} is a subset of B = {Malcolm, Barbara, Susan} (all of the members of A are also members of B; A ⊆ B), and every set is also a subset of itself. B is not a subset of A, since B has a member, namely, Susan, that is not a member of A. A proper subset of a set is a subset of it that is not identical with it. A is a proper subset of B, but no set is a proper subset of itself. The EMPTY SET is a subset of every set. See also SET THEORY. sum, mereological: an operation that applies to INDIVIDUALS. The sum of any individuals is an individual as well. These individuals are parts of their sum. As opposed to SET MEMBERSHIP, being a part is TRANSITIVE: The part of a part of an individual is a part of that individual. Let C be the sum of A and B, and let E be the sum of C and D. Then A is a part of E, since it is a part of C, which, in turn, is a part of E. Also, the mereological sum of A and C is just C itself, as nothing additional goes into the sum. A sum of individuals is sometimes said not to be anything over and above its parts. It is, in a sense, not an additional individual, and so does not allow the staggering multiplication of entities of SET THEORY. Out of n ATOMS exactly 2n – 1 individuals can be summed, no matter how often the sum operation is repeated. That means that if we start with finitely many atoms, there are only finitely many individuals summed from those atoms. See Chapter 4 (especially § “Mereology”, p. 92) and § “Logic and mereology” (p. 218); see also MEREOLOGY and CALCULUS OF INDIVIDUALS. supervenience, nomological: relation between different types of facts (e.g. the physical facts and the mental facts). One kind of fact α supervenes nomically on some other kind of fact β iff there can be no difference in the supervening facts α – with the necessity of a natural law – without a difference in the facts β. symmetry: a property of relations; a relation is symmetric iff the relation holds both ways for any two things to which the relation applies. Formally: ∀x∀y(F (x, y) ⊃ F (y, x)). syntax: the syntax of a language determines which expressions belong to a language. Usually the atomic (ATOM) expressions are listed together with instructions for how complex expressions can be formed from them. synonymy: identity in MEANING (or INTENSION); typically ‘bachelor’ and ‘unmarried man’ are regarded to be expressions identical in meaning. Expressions such as ‘organism with kidneys’ and ‘organism with a heart’ are, on the other hand, typically not regarded as identical in meaning, although both terms apply to the exact same entities. Such terms are said to be COEXTENSIONAL but not COINTENSIONAL. Goodman thought that no two distinct expressions are synonymous. He explicates synonymy with the help of secondary extensions. See Chapter 3 for his views on the matter. theory: a SET of sentences that contains all and only deductive (INFERENCE RULES) consequences of a given set of AXIOMS. (Lately, sometimes theories are characterized
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Nelson Goodman semantically, that is, as sets that contain all and only sentences that are semantic consequences of the axioms, MODEL THEORY.) In order to avoid the use of sets, a theory can be defined as those sentences that are consequences of the axioms. theory of types: a class theory introduced by Bertrand Russell (1908), and extensively developed in Whitehead and Russell’s Principia Mathematica. Until Zermelo– Fraenkel SET THEORY took over as the standard formal framework for mathematics, the theory of types of the Principia was predominant. Russell sought to avoid the paradox named after him (see p. 100) by the introduction of so-called type restrictions. Intuitively, the CLASSES are ordered hierarchically. Classes can only have other classes as members (MEMBERSHIP) if those are of a lower type. Especially, no class can hence contain itself. The circular construction of the Russell class that Russell held responsible for the paradox is thus banned. Such type restrictions are not present in set theory (while in most set theories a set cannot contain itself either). A very readable introduction to Russell’s theory of types is Irving Copi’s The Theory of Logical Types (London: Routledge, 1971). Today, there are also alternative theories of types, most famously the one developed by Per Martin-Löf (see his Intuitionistic Type Theory (Naples: Bibliopolis, 1984)). time slice: a “snapshot” of a course of events. Time slices are sometimes extended in time, thus a time slice of your stream of experiences might comprise all experiences you had during breakfast this morning. Here we will mostly consider time slices of a much shorter duration, real snapshots at a given instant of time. We will also mostly consider time slices of inner events (experiences) of a specific person rather than time slices of the history of the whole universe. transitivity: a property of relations; a relation is transitive iff for any A that stands in that relation to something B, while B also stands in that relation to something C, A also stands in that relation to C. Formally: ∀x∀y∀z((F (x, y) ∧ F (y, z)) ⊃ F (x, z)). truth-functional connectives: those logical CONSTANTS that apply to propositions. The typical ones are ‘∧’ or ‘&’ or ‘.’ for conjunction (‘and’), ‘∨’ for disjunction (‘or’), ‘⊃’ or ‘→’ for MATERIAL CONDITIONAL (‘if … then’), ‘≡’ or ‘↔’ for material biconditional (‘iff’), and ‘¬’ or ‘~’ for negation (‘not’). Less usual is ‘|’ for alternative denial, the so-called Sheffer stroke (‘not both of … and’). It has a remarkable property, however: it sufficed to define every other truth-function (see p. 247, n.8). According to the standard SEMANTICS, the truth-value of a complex sentence depends systematically on the truth-value of its compound expressions. For example, ‘p ∧ q’ is true iff both ‘p’ and ‘q’ are true, and false otherwise; ‘p | q’ is false iff both ‘p’ and ‘q’ are true, and true otherwise. See also MATERIAL CONDITIONAL. union set: the union set of a SET S of some sets is the set that contains as members (MEMBERSHIP) all and only the members of the sets in S. A = {Nikolaj, Philip, Robbie, Ross} is the union set of {A} and of {B, C }, where B = {Philip, Ross} and C = {Nikolaj, Robbie}. It is also the union set of {C, D}, where D = {Nikolaj, Philip, Ross} (and C as before) and of {B, C, D}, but neither of {B, D} nor {B, E}, where E = {Elizabeth, Lisa, Nikolaj, Robbie}, nor {A, F }, where F = {Philip, {Ross}}. See also SET THEORY.
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Further reading
Chapter 2. If this were an emerald it would be grue: problems and riddles of induction We have said already that there are numerous papers on Goodman’s new riddle of induction. For a start we suggest the very comprehensive collection by Douglas Stalker, Grue? The New Riddle of Induction (Chicago, IL: Open Court, 1994), which also includes a very helpful annotated bibliography. Another good starting-point is Volume 2 of Catherine Elgin’s The Philosophy of Nelson Goodman: Nelson Goodman’s New Riddle of Induction (New York: Garland, 1997).
Chapter 3. The big picture For Goodman’s views on philosophy see the first part of Problems and Projects (Indianapolis, IN: Bobbs-Merrill, 1972). Goodman’s conception of explication is discussed in more detail in Chapter 3, and also in G. Hellmann’s “Introduction”, in Goodman’s The Structure of Appearance, 3rd edn (Boston, MA: Reidel, 1977). Goodman’s philosophy of language and critical discussions of it are reprinted in Volume 4 of Elgin’s The Philosophy of Nelson Goodman: Nelson Goodman’s Theory of Symbols and its Application (New York: Garland, 1997). His theory of reference is further developed in Elgin’s With Reference to Reference (Indianapolis, IN: Hackett, 1983) and Rolf Eberle’s “Semantic Analysis without Reference to Abstract Entities”, The Monist 61 (1978), 363–83 and “Goodman on Likeness and Difference of Meaning”, Erkenntnis 12 (1978), 3–16; see also Of Mind and Other Matters (ch. III.3), for more discussion by Goodman and further references. The introductory chapter of Elgin’s Between the Absolute and the Arbitrary (Ithaca, NY: Cornell University Press, 1997) and “Denying a Dualism: Goodman’s Repudiation of the Analytic/Synthetic Distinction”, Midwest Studies in Philosophy 28 (2004), 226–38, deal with the rejection of the analytic–synthetic distinction in detail, and discusses Goodman’s approach in a wider framework.
Chapter 4. Particulars and parts We have mentioned a few literature recommendations concerning specific topics that spin off from Goodman’s nominalism and his advances in mereology in the notes to this chapter. More generally, Goodman’s own defence of his nominalism, “A World of
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Nelson Goodman Individuals” (PP: 155–72) is a very approachable read. The first volume of Elgin’s The Philosophy of Nelson Goodman: Nominalism, Constructivism, and Relativism (New York: Garland, 1997) contains papers on Goodman’s nominalism. M. Gosselin’s Nominalism and Contemporary Nominalism: Ontological and Epistemological Implications of the Work of W. V. O. Quine and of N. Goodman (Dordrecht: Kluwer, 1990) deals with Quine’s and Goodman’s nominalism. A very good introduction to the philosophy of mathematics that also covers the main contemporary positions is Stewart Shapiro’s Thinking about Mathematics (Oxford: Oxford University Press, 2000); its Chapter 9 deals with recent nominalist positions concerning mathematics. More advanced, and specifically on recent nominalism in the philosophy of mathematics is John Burgess and Gideon Rosen’s A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics (Oxford: Clarendon Press, 1997). As an introductory book to the philosophy of W. V. Quine we recommend Alex Orenstein’s W. V. Quine (Chesham: Acumen, 2002). Orenstein also touches on the issue of nominalism here. An excellent survey and comparison of a number of mereological systems, including the Leonard/ Goodman calculus, and Goodman’s system of The Structure of Appearance is unfortunately at present only available in German; it is Lothar Ridder’s Mereologie (Frankfurt: Klostermann, 2002). No less superb is Peter Simon’s Parts: A Study in Ontology (Oxford: Oxford University Press, 1987) which focuses on the formal and philosophical investigation of various kinds of mereologies of different strengths.
Chapter 5. From Vienna Station to Boston Terminus Again, some valuable material can be found in Elgin’s The Philosophy of Nelson Goodman: Nominalism, Constructivism, and Relativism (New York: Garland, 1997). Since little has been written on The Structure of Appearance or A Study of Qualities, we can only suggest G. Hellmann’s “Introduction”, in Goodman’s The Structure of Appearance, 3rd edn (Boston, MA: Reidel, 1977). For Carnap’s Aufbau and the early history of analytic philosophy we recommend A. Richardson’s Carnap’s Construction of the World: The Aufbau and the Emergence of Logical Empiricism (Cambridge: Cambridge University Press, 1998) and A. Coffa’s The Semantic Tradition from Kant to Carnap: To the Vienna Station (Cambridge: Cambridge University Press, 1991).
Chapter 6. Follow the sign In addition to Goodman’s Languages of Art and the fourth volume of Elgin’s The Philosophy of Nelson Goodman: Nelson Goodman’s Theory of Symbols and Its Applications (New York: Garland, 1997), we suggest Elgin’s With Reference to Reference (Indianapolis, IN: Hackett, 1983) and Israel Scheffler’s Symbolic Worlds: Art, Science, Language, Ritual (Cambridge: Cambridge University Press, 1997); both present thorough studies of the theory of symbols, partly building upon and developing further Goodman’s pioneering advances. Elgin’s Between the Absolute and the Arbitrary (Ithaca, NY: Cornell University Press, 1997) also contains some articles that tackle the topic from a variety of directions.
Chapter 7. Diagnosing art Languages of Art, of course, must be the starting point for an intense study of Goodman’s theory of art. Ways of Worldmaking, Of Mind and Other Matters, Problems and Projects and Reconceptions in Philosophy and other Arts and Sciences contain further material; some passages from Basic Abilities Required for Understanding and Creation in the Arts are reprinted in Of Mind and Other Matters. Volume 3 of Elgin’s The
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Further reading Philosophy of Nelson Goodman: Nelson Goodman’s Philosophy of Art (New York: Garland, 1997) is dedicated to Goodman’s philosophy of art. Elgin’s Between the Absolute and the Arbitrary (Ithaca, NY: Cornell University Press, 1997) and the festschrift in honour of Goodman’s sixty-fifth birthday, R. S. Rudner & I. Scheffler (eds), Logic & Art: Essays in Honor of Nelson Goodman (Indianapolis, IN: Bobbs-Merrill, 1972) also contain some interesting essays on the topic. An endless number of papers have been published in response to Goodman’s theory of art, as well as a good number of books. We cannot even start to list them here. Criticism of Goodman’s positions is also to be found in many books in the area that are not specifically on Goodman. Fruitful starting-points are: A. C. Danto, The Transfiguration of the Commonplace: A Philosophy of Art (Cambridge: MA: Harvard University Press, 1981), D. Davis, Art as Performance (Oxford: Blackwell, 2004), J. Levinson, Music, Art, and Metaphysics (Ithaca, NY: Cornell University Press, 1990) and K. L. Walton, Mimesis as Make-Believe: On the Foundations of the Representational Arts (Cambridge, MA: Harvard University Press, 1990). B. Gaut & D. Lopes, The Routledge Companion to Aesthetics (London: Routledge, 2001) is a very comprehensive collection of introductory essays into virtually all areas of philosophical aesthetics.
Chapter 8. Starmaking Some interesting papers on the topic of this chapter can be found in Volume 1 of Elgin’s The Philosophy of Nelson Goodman: Nominalism, Constructivism, and Relativism in the Work of Nelson Goodman (New York: Garland, 1997) and in Starmaking: Realism, Anti-Realism, and Irrealism (Cambridge, MA: MIT Press, 1996), edited by Peter J. McCormick. Israel Scheffler, Goodman’s student and colleague at Harvard, discussed the topics covered in this chapter on many occasions with Goodman. Goodman’s claim that we “make” the worlds in any objectual sense by making true versions is something Scheffler particularly balks at; he finds it completely unacceptable. A good overview of that controversy is provided by Scheffler in “My Quarrels with Nelson Goodman”, Philosophy and Phenomenological Research 62 (2001), 665–77. Elgin’s Between the Absolute and the Arbitrary (Ithaca, NY: Cornell University Press, 1997) contains a number of papers that address constructionalism, pluralism and irrealism in the context of various areas.
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Notes
Chapter 1. The worldmaker’s universe
1. Similar interpretations are even shared by some philosophers of science, who interpret Goodman’s solution to his riddle of induction (with disapproval) as a form of irrationalism. 2. Much of the material used in this section is based on O. R. Scholz, “In Memoriam Nelson Goodman: 7 August 1906–25 November 1998)”, in Symbole, Systeme, Welten: Studien zur Philosophie Nelson Goodmans, J. Steinbrenner, O. R. Scholz & G. Ernst (eds), 9–32 (Heidelberg: Synchron, 2005). We should like to express our gratitude to Professor Scholz for sending us a preprint of his paper. Unfortunately there is neither a detailed biography of Goodman nor anything like an autobiography, which is why all material on Goodman’s life has to be collected from obituaries, autobiographic remarks of his contemporaries and personal communication. 3. Phi Beta Kappa is an academic honours society committed to the promotion of scholarship and cultural interests among the students of American colleges. Undergraduate members, selected from a pool of candidates with the highest cumulative numerical grade point averages in their academic divisions, are elected on the basis of their scholarly achievement and breadth of intellectual interest. 4. “His most cherished discovery relating to his art endeavors was the artist Katharine Sturgis Goodman, his wife and companion of over fifty years. They met when she brought her watercolors of New England subjects for exhibition at his Boston gallery. Sturgis, ‘Cambridge spinster and heiress,’ and Goodman were both over forty when they married. Goodman continued with great devotion the advancement of her career throughout their years together. On the occasion of an exhibition of her work, Goodman would be found attending to minute details of the installation and arrangements. One of his last official matters of business was to establish a permanent repository for the care and display of the works of Katharine Sturgis at the Cape Ann Historical Association in Cape Ann, Massachusetts.” (C. L. Carter, “A Tribute to Nelson Goodman”, Journal of Aesthetics and Art Criticism 58 (2000), 251–3, 253). “It was at the art gallery that he met his future wife Katherine Sturgis, a talented Cambridge watercolor artist, who had come to the gallery to arrange an exhibition. Nelson and Kay, as she was usually called, couldn’t be more different in temperament. Nelson, both in public and private, was precise, demanding, and reserved – always ready with an acerbic quip or parry, often serving more as a defense of his shyness than a sign of indifference. In contrast, Kay, was easygo-
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Notes
5.
6. 7.
8. 9.
ing, warm, ready to tell you what she felt, and never quite sure where she had put her checkbook or some important document.” (R. Schwartz, “In Memoriam Nelson Goodman (August 7, 1906–November 25, 1998)”, Erkenntnis 50 (1999), 7–10, esp. 8) With Goodman’s car, Quine took almost all of his students from his seminar on Carnap’s Logische Syntax to Baltimore. The trip was remarkable in various respects. On the one hand, the Baltimore visit is nowadays transfigured into the official origin of analytic philosophy (e.g. by Ernest LePore; see A. Beckermann, Analytische Einführung in die Philosophie des Geistes, 2nd edn (Berlin: DeGruyter, 2001), VIII), especially in the story Quine tells: “We moved with Carnap as henchmen through the metaphysician’s camp. We beamed with partisan pride when he encountered a diatribe of Arthur Lovejoy’s in his characteristically reasonable way, explaining that if Lovejoy means A then p, and if he means B then q” (The Ways of Paradox and Other Essays, revised and enlarged edn (Cambridge, MA: Harvard University Press, 1976), 42; The Time of My Life: An Autobiography (Cambridge, MA: MIT Press, 1985), 122). On the other hand, it initiated the close cooperation between Quine and Goodman. On the way back to Harvard, Leonard and Goodman told Quine for the first time about their project and Quine recognized it to be Leśniewski’s so-called “mereology” (see Quine, The Time of My Life, 122). Quine cooperated closely with Goodman from then on. These are reprinted in R. Creath (ed.), Dear Carnap, Dear Van: The Quine–Carnap Correspondence and Related Work (Berkeley, CA: University of California Press, 1990). Scholz, “In Memoriam Nelson Goodman”, suggests that Goodman learnt of Carnap’s work from either C. I. Lewis or Leonard, who visited Munich in 1929. It was unlikely to have been Leonard. It seems that Leonard would have included a reference to Carnap’s work in his own thesis in 1930 had he known about Carnap. Instead Leonard solely refers to Whitehead’s work in that area. Carnap’s work is first mentioned in H. S. Leonard & N. Goodman, “The Calculus of Individuals and its Uses”, Journal of Symbolic Logic 5 (1940), 45–55. There appears to be no evidence that Goodman knew of Carnap’s work until the discussion with Quine on the occasion of the trip to Baltimore. It also seems likely that Leonard and Goodman would have mentioned something about Carnap to their peer Quine, but Quine writes that he had not heard of Carnap before 1932 (Quine, The Time of My Life, 86). See www.davidalpher.com/ (accessed Nov. 2005). The website contains more quotes from reviews of Variations. Elgin, for example, reports: “I was never Nelson Goodman’s student. I did not attend Harvard; even if I had, I probably would have lacked the courage to study with him. Goodman had a fierce public persona. His lectures made it clear that he did not suffer fools gladly, and given the choice would not suffer them at all. He refused to allow auditors in his seminars, reasoning that there was no way to insure that they would do the work, and he had no time to waste on idlers. He was a remote, daunting figure. The lines in his face looked as though they were etched in stone. So when I began to work on Goodman’s philosophy, I fully intended never to meet the man. I mentioned my research to Jay Hullett, a friend of mine who was a former student of Goodman’s. He encouraged me to contact Goodman, insisting that Goodman would be interested in my project. Naturally, I ignored this advice. My instinct for self-preservation was too strong. Hullett, however, contacted Goodman, who then invited me to his office to discuss my work. With trepidation verging on terror, I went. To my astonishment, I discovered that the public persona was a facade. Nelson Goodman turned out to be a warm, witty, generous man who was enthusiastic about my project and flattered by my interest in his work. … He was as exacting and demanding as his reputation made him out to be. But he was not motivated by
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10.
11.
12.
13.
14. 15.
16.
nastiness. He insisted that only by hard work and meticulous attention to detail could progress in philosophy be made” (“Worldmaker: Nelson Goodman (1906– 1998)”, Journal for General Philosophy of Science 31 (2000), 1–18, esp. 1–2). On the other hand, close friendship did not help much when one found oneself involved in a philosophical dispute with Goodman. As his friend Israel Scheffler remembers: “Anyone familiar with Nelson Goodman’s philosophical career knows that to have quarrelled with him was a hazardous enterprise. For aside from his creative brilliance and analytic subtlety, he was also one of the foremost dialecticians of the age. Seeing through the flaws of rival views and rebutting putative counterarguments to his own came as easily to him as breathing. … To take issue with him was in fact to take one’s philosophical life in one’s hands and many are those over his career who rued the venture … A week or so after I presented the book [I. Scheffler, Inquiries: Philosophical Studies of Language, Science, and Learning (Indianapolis, IN: Hackett, 1986), which contains a critique of Goodman’s constructionalism] to Goodman at a small party celebrating his birthday, he phoned to thank me for the book, which he said he had liked ‘except for one bad patch.’ He then cautioned me, saying, ‘Don’t think that because you dedicated the book to me, I won’t reply to you.’ ‘Nelson’, I said, ‘the thought never crossed my mind’” (I. Scheffler, “My Quarrels with Nelson Goodman”, Philosophy and Phenomenological Research 62 (2001), Harvard Symposium for Nelson Goodman, 665–77, esp. 665, 670). According to L. Lawlor & V. Moulard, “Henri Bergson”, in The Stanford Encyclopedia of Philosophy (summer 2004), E. N. Zalta (ed.) (http://plato.stanford. edu/archives/sum2004/entries/bergson/). As Oliver Scholz informed us, Bergson was also considered at Harvard for the position that was eventually filled by Alfred North Whitehead (Bertrand Russell was another candidate). Wittgenstein, who seems to be Goodman’s main target here, would probably have rather said that philosophers cannot stop doing philosophy, since they feel, almost pathologically, compelled to philosophize. Philosophers are themselves the poor souls that are tantalized by the language puzzles. In the preface to Languages of Art: An Approach to a Theory of Symbols, 2nd edn (Brighton: Harvester, 1981), for instance, Goodman writes: “Layman or not, the reader must be prepared to find his convictions and his common sense – that repository of ancient error – often outraged by what he finds here” (LA: xii). In his comments on a paper by Hilary Putnam in which the latter draws on common sense for the support of his argument, Goodman replies: “On ‘presystematic discourse’ as a background for construction of systems, see A Study of Qualities [New York: Garland, 1990]. I do not share Putnam’s affection for common sense. It has no sharp or stable boundaries, and is often at odds with itself. In such cases, does ‘common sense’ call for ‘taking it at face value’ or for demanding consistency?” (“Comments”, in Starmaking: Realism, Anti-Realism, and Irrealism, P. J. McCormick (ed.), 203–13 (Cambridge, MA: MIT Press, 1996), 203–13, esp. 206, n.3). Goodman himself speaks of his philosophy as “skeptical” (WW: 1), but presumably he means something close to what we sketch here. That Frege was recognized as an important philosopher later is due to Russell, Wittgenstein and Carnap, who kept emphasizing Frege’s influence. The content of Frege’s lectures of these years, for example, survived only because of the lecture notes that Carnap took when attending them. See G. Frege, Frege’s Lectures on Logic: Carnap’s Student Notes 1910–1914, E. H. Reck & S. Awodey (eds and trans.) (Chicago, IL: Open Court, 2004). The members of the Vienna Circle and the philosophers they were in close contact with are often labelled ‘logical positivists’, ‘neopositivists’ and ‘logical empiricists’. All these labels are inadequate in various ways. For the purposes of this book we shall simplify matters by using these labels interchangeably. For an adequate treatment of this group of philosophers, see F. Stadler, Studien zum
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17. 18.
19.
20. 21.
22. 23. 24.
25.
Wiener Kreis: Ursprung, Entwicklung und Wirkung des Logischen Empirismus in Kontext (Frankfurt: Suhrkamp, 1997). Kant’s reasons for thinking so were actually a little more complex. For a more detailed discussion, see S. Shapiro, Thinking about Mathematics (Oxford: Oxford University Press, 2000), 73–91. It was Frege’s logicist project to reduce all truth of mathematics, and especially arithmetic, to logic (barring geometry, however, which he believed to be synthetic a priori, following Kant here). This project famously failed with Russell’s discovery of the paradox that bears his name. (For a good and fairly easy introduction to Frege’s logicism and Russell’s paradox, see Shapiro, Thinking about Mathematics, ch. 5). Some simple arithmetical statements, such as Kant’s famous example ‘7 + 5 = 12’, can, however, be analysed as truths of logic. Any finite number statement can be expressed in first-order predicate logic. (If we use second-order logic – or Russell’s theory of types, which was the relevant system of logic for Carnap – some even more interesting mathematical statements can be expressed. A number of examples can be found in Shapiro, Foundations without Foundationalism: A Case for SecondOrder Logic (Oxford: Oxford University Press, 1991). ‘There are exactly two Fs’, for example, can be rendered as ‘∃x∃y [Fx ∧ Fy ∧ x ≠ y ∧ ∀z (Fz ⊃ (z = x ∨ z = y))]’; ‘there are exactly three Fs’ becomes ‘∃x∃y∃w [Fx ∧ Fy ∧ Fw ∧ x ≠ y ∧ x ≠ w ∧ y ≠ w ∧ ∀z (Fz ⊃ (z = x ∨ z = y ∨ z = w))]’ – it should be clear how this continues. For ‘7 + 5 = 12’ we just express in this way that if there are exactly 7 Fs and exactly 5 Gs, and none of the Gs are Fs and vice versa, then there are exactly 12 things that are either Fs or Gs. Yes, this formula will get very long and is rather cumbersome, but the crucial point is that the resulting sentence will be a logical truth, provable in logic alone without assuming any mathematics (and no one suggests, of course, actually doing arithmetic in this way). This “recipe” works generally for simple statements like this. In Chapter 4 we shall encounter a similar method proposed by Goodman and Quine. This is also echoed in the foreword to Goodman’s The Structure of Appearance, 3rd edn (Boston: Reidel, 1977): “Perhaps the day will come when philosophy can be discussed in terms of investigation rather than controversies, and philosophers, like scientists, be known by the topics they study rather than by the views they hold” (SA: IL). This is the slogan that is commonly associated with Carnap’s position. See R. Carnap, The Logical Syntax of Language (London: Routledge & Kegan Paul, [1934] 1937), xiii. For our purposes it is convenient to divide Whitehead’s work into two parts: mathematics and philosophy. Whitehead’s life is often partitioned into three parts: the mathematical work, the work on natural philosophy and finally the work on metaphysics (and sometimes the work on metaphysics is divided into an early and a late conception). Such partitioning is then considered to reveal interesting insights into Whitehead’s intellectual development. We do not endorse any such thesis here. See M. Hampe, Alfred North Whitehead (Munich: Beck, 1998), 26. For a study of Whitehead’s mereology see L. Ridder’s Mereologie (Frankfurt: Klostermann, 2002), 193–215, and P. Simons, Parts: A Study in Ontology (Oxford: Oxford University Press, 1987), 81–6. Leśniewski had published his mereology in 1916, at about the same time Whitehead was working on his An Enquiry Concerning the Principles of Natural Knowledge, which appeared in 1919. Russell knew of Whitehead’s method already in 1914 when he published Our Knowledge of the External World (London: Allen and Unwin, 1914). See Simons Parts, 82. A problem that Whitehead had dealt with, the construction of time points from abstractive classes of durations, was also a topic Goodman dealt with in his thesis.
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Nelson Goodman 26. One more philosopher we have to mention among the allies is Ernst Cassirer (1874–1945). Cassirer is an interesting figure in the German history of philosophy. On the one hand he was interested in many of the problems the logical empiricists were interested in and worked on matters in philosophy of mathematics and the philosophy of physics. He proposed Carnap for a job in Germany (without much success) and wrote a critical response to some of Carnap’s writings on physicalism. Cassirer was also in close contact with Schlick. On the other hand Cassirer failed to appreciate the value of formal logic and clarity, and did not participate in the research programme of logical empiricism. Moreover, he was able to take pleasure in taking Heidegger’s writings seriously, which made him a mediating figure between the analytic and the continental tradition. Cassirer does not concern us much as a possible source of influence on Goodman in his early career. In various ways, however, Cassirer followed a similar programme to Goodman. He also defended the thesis that there are more ways to represent and understand the world than what is embodied in scientific knowledge alone. Cassirer also conceived these differing ways as different symbol systems and also argued that none of them is necessarily privileged. Cassirer’s style makes it difficult for us to evaluate to what degree he would have been in agreement with Goodman’s view. Goodman later saw a connection when he wrote Ways of Worldmaking (Indianapolis, IN: Hackett, 1985). Moreover, Goodman mentions Cassirer in Languages of Art. Cassirer’s Philosophy of Symbolic Forms (New Haven, CT: Yale University Press, 1955) appeared in English translation in 1955 and might have inspired Goodman’s semiotic philosophy, which we discuss in Chapter 6. As Scholz informed us, Goodman was probably also aware of Cassirer’s Language and Myth. In the preface to Languages of Art he writes that he is “by no means unaware of contributions to symbol theory by such philosophers as Peirce, Cassirer, Morris, and Langer” (LA: xii). In the only paragraph in the main text of this book where Goodman mentions Cassirer, however, he grants that his claims (concerning metaphor) are illuminating and even true in some cases, but finds them not obviously explanatory in general (LA: 77).
Chapter 2. If this were an emerald it would be grue: problems and riddles of induction
1. ‘De re’ means here that you know of the effect-phenomenon, but not under the description that it is an “effect” of anything. (‘De re’ contrasts with ‘de dicto’ knowledge, which is knowledge under a certain description.) Of course, if you know of a phenomenon, for example a terrible headache, under the description ‘the effect of my heavy drinking the other day’ you could deduce the cause of the headache a priori. To emphasize this, we always write “cause” and “effect” in double quotation marks, indicating that we talk about the phenomenon itself and not the phenomenon already known under the label ‘effect’ or ‘cause’. 2. In these semi-formalized sentences, we follow the conventions of standard predicate logic in using upper case letters for predicates and lower case letters for names. Thus ‘Raven(paul)’ corresponds syntactically to ‘Rp’ or ‘R(p)’. 3. The label ‘reflective equilibrium’ for this method stems from J. Rawls, A Theory of Justice (Cambridge, MA: Harvard University Press, 1971), 20. In “Logic, Normative or Descriptive? The Ethics of Belief or a Branch of Psychology?”, Philosophy of Science 52 (1985), 221–38, M. D. Resnik develops an account of logic based on Goodman’s notion of a reflective equilibrium. C. Z. Elgin’s Considered Judgement (Princeton, NJ: Princeton University Press, 1996) contains an intensive study of reflective equilibria in general (see esp. ch. IV). See also N. Daniels’s “Reflective Equilibrium”, in The Stanford Encyclopedia of Philosophy (summer 2003) (http://plato.stanford.edu/archives/sum2003/entries/reflective-equilibrium/). An in-depth study of Goodman’s notion of reflective equilibrium and a comparison
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4. 5.
6.
7.
8.
9.
10.
with Rawls can be found in S. Hahn, Überlegungsgleichgewicht(e): Prüfung einer Rechtfertigungsmetapher (Freiburg: Alber, 2000). This has nothing to do with, for example, Kantian intuitions here; rather, read ‘intuitive’ as something in the vicinity of some pre-systematic inclination to judge this way. No special faculty called ‘intuition’ or anything like it is presupposed. Stich and Nisbett argue that this picture is inappropriate for the justification of inductive inference rules, but we guess they would take empirical results concerning the capability to draw valid deductive inferences as similarly damaging. Their argument is that people have inference rules that are in a reflective equilibrium but are not valid at all. It is pretty unclear what that is supposed to prove. Goodman did not say that there could be only one reflective equilibrium; therefore to show that some person (or a group) uses inference rules that are in a reflective equilibrium but invalid with respect to some other system that perhaps is also in a reflective equilibrium is utterly uninteresting. It would be somewhat interesting if the rules were not necessarily in a reflective equilibrium, but nevertheless used by normal folk (which, anyway, seems to be the case). Then the argument by Stich and Nisbett should rather be this: “Look, there are people who make these intuitive judgements that are light-years away from what (deductive or inductive) logic accepts as a valid inference. How can that happen?” Why this latter argument poses no problem for Goodman is explained in this chapter. Basically, their suggestion goes back to the method famously introduced by the Polish logician Alfred Tarski to characterize logical consequence; see A. Tarski, “On the Concept of Logical Consequence”, in Logic, Semantics, Metamathematics, J. Corcoran (ed.), 409–20 (Indianapolis, IN: Hackett, [1936] 1983). Tarski was dissatisfied with the deductive characterization of logical consequence, partly because it did not seem general enough to him. He proposed a way of characterizing logical consequence semantically. His method gave rise to the model-theoretic semantics common today. Specific deductive systems are taken to allow for valid inferences only if it can be shown that they agree with Tarski’s general semantic characterization. Regarding our topic here, the Goodmanian observation would be that a general semantic characterization of logical consequence must reach a reflective equilibrium with the pretheoretic notion of logical consequence. This is also discussed in the main text that follows and in note 8. A point similar to this – concerning the relationship between deductive systems and model-theoretic semantics with respect to logical inference – is developed and discussed in detail by M. Rossberg in “First-Order Logic, Second-Order Logic, and Completeness”, in First-Order Logic Revisited, V. Hendricks, F. Neuhaus, S. A. Pedersen et al. (eds), 303–21 (Berlin: Logos, 2004). There are, of course, other approaches to characterize the valid inference rules, for example, in terms of the so-called ‘logical constants’. Since the whole debate is only a side issue for us, we will not try to give a comprehensive picture of the entire landscape here. The Goodmanian thought would be that all accounts, no matter in which way they try to solve the problem, must eventually rely on some sort of reflective equilibrium between the rigorous formal rules, rigorous formal semantics or some other rigorous formal characterizations it might be, and the “intuitive” conception. In the case of a logical-constants approach, for instance, it would be a reflective equilibrium between what we take ‘and’, ‘not’, ‘if … then’, ‘all’ and so on to mean, and how these terms are regimented and what inferences are allowed according to this regimentation. In the foreword to Chapter VIII “Induction” in Problems and Projects (Indianapolis, IN: Bobbs-Merrill, 1972), Goodman deals (slightly differently) with a similar objection by J. J. Katz (The Problem of Induction and its Solution (Chicago, IL: University of Chicago Press, 1962), 46–9). We already mentioned this in note 5.
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Nelson Goodman 11. Earman and Salmon seem to interpret Carnap and Goodman as if they would think that for an explication to be satisfying the intuitive judgements only matter, which is why they find Goodman’s and Carnap’s solution of Hume’s problem unconvincing. This is clearly wrong, as can be seen in Goodman’s notion of reflective equilibrium in which intuitions play only a partial role in determining the right system, as well as in Carnap’s notion of explication, which will be discussed in Chapter 3. 12. The proof is rather simple: ‘is examined before t and grue’ is by definition equivalent to ‘is examined before t and ((green if examined before t) and (blue if not examined before t))’. This, in turn, is equivalent to ‘(is examined before t and green) and (is examined before t or blue)’, which, eventually, is equivalent to ‘is examined before t and green’. To check the proof, it can be formalized in predicate logic. 13. Examples of such properties are the logical dependence and independence relations between sentences that secure that each sentence of one language has a logically equivalent mirror sentence in the other language. 14. To be more precise, this does not mean that a grue-ified science is completely indistinguishable from some original science. They are analytically and empirically equivalent up to t, but then both sciences make predictions that are incompatible (from both points of view). This is why that result is so problematic. 15. This principle, also sometimes called ‘ex contradictione quodlibet sequitur’ or ‘principle of explosion’, holds in standard deductive logic. 16. David Lewis would be such a philosopher. See his Counterfactuals (Oxford: Basil Blackwell, 1973) for his analysis of counterfactuals and On the Plurality of Worlds (Oxford: Basil Blackwell, 1986) for a more detailed discussion of his “modal realism”. See D. Nolan’s David Lewis (Chesham: Acumen, 2005), esp. chs 3 & 4, for an excellent introduction. For a general introduction to the contemporary discussion about possible worlds see J. Divers’s Possible Worlds (London: Routledge, 2002). For an alternative analysis of counterfactuals within the possible worlds framework, see R. Stalnaker’s “A Theory of Conditionals”, in Ifs: Conditionals, Belief, Decision, Chance, and Time, R. Stalnaker, W. L. Harper & G. Pearce (eds), 41–55 (Dordrecht: Reidel, 1968). 17. Alas, he never really tries to show that the possibilities we get this way are really sufficient for these purposes. 18. However, not all things that once burned are still inflammable.
Chapter 3. The big picture
1. ‘Esoteric’ here means “dealing with very special problems”. In contrast to broader topics that connect with things from other sciences or society these are “of special, rare, or unusual interest”. 2. In a less technical way the paradox also arises for Goodman’s notion of philosophical analysis. In The Structure of Appearance he notes: “Any effort in philosophy to make the obscure obvious is likely to be unappealing, for the penalty of failure is confusion while the reward of success is banality. An answer, once found, is dull; and the only remaining interest lies in a further effort to render equally dull what is still obscure enough to be intriguing” (SA: L). 3. For a detailed discussion of this principle see D. Cohnitz, “Is Compositionality an a priori Principle?”, in The Compositionality of Concepts and Meanings: Foundational Issues, M. Werning, E. Machery & G. Schurz (eds), 23–58 (Frankfurt: Ontos, 2005). 4. For (P7) to be true, quotation must be such that the expressions within the quotation marks are still proper syntactical parts of the complex sentence. Otherwise the problem could not arise. 5. For the letters see M. White, A Philosopher’s Story (University Park, PA: Pennsylvania State University Press, 1999).
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Notes 6. See Chapter 5 for a qualification of this. 7. For a more detailed analysis see D. Cohnitz, Gedankenexperimente in der Philosophie (Frankfurt: Ontos, forthcoming). 8. We discuss Goodman’s theory of reference further in Chapter 7. An elaboration of Goodman’s ideas on extensional semantics can be found in R. A. Eberle, “Semantic Analysis without Reference to Abstract Entities”, The Monist 61 (1978), 363–83 and “Goodman on Likeness and Difference of Meaning”, Erkenntnis 12 (1978), The Philosophy of Nelson Goodman Part I, 3–16.
Chapter 4. Particulars and parts
1. A very useful starting-point for readers who want to know more about this, or about Ockham and medieval nominalism in general, can be found online in P. V. Spades’s “William of Ockham”, in The Stanford Encyclopedia of Philosophy (autumn 2002), E. N. Zalta (ed.) (http://plato.stanford.edu/archives/fall2002/ entries/ockham/) (accessed Nov. 2005); see also Spades’s “Ockham’s Nominalist Metaphysics”, in The Cambridge Companion to Ockham, P. V. Spade (ed.), 100–117 (Cambridge: Cambridge University Press, 1999). 2. B. Hale, Abstract Objects (Oxford: Oxford University Press, 1987), for example, rejects a whole battery of definitions before he presents his own. Needless to say, despite Hale’s careful and detailed formulation, this definition has its opponents too. 3. Incidentally, something very similar to this might have been one of Ockham’s reasons to reject universals; see Spades, “Ockham’s Nominalist Metaphysics” and “William of Ockham”. 4. Of course, there are very few positions in philosophy that nobody has held, and sure enough there are philosophers who have defended positions very much like this one. Penelope Maddy in Realism in Mathematics (Oxford: Oxford University Press, 1990), for instance, argues that one kind of mathematical object can at least be perceived; namely, sets or, more precisely, sets of medium-sized physical objects. Note that the claim is not merely that we perceive the members of the set, but that, on top of them, we also perceive the set. 5. Quine famously explains his views in “On What There Is”, Review of Metaphysics 2 (1948), 21–38. 6. Platonism in this sense has little to do with the historical philosopher Plato, but merely refers to the position that abstract objects exist, and hence the denial of our (N3)-nominalism as defined above. Note that one could probably also distinguish various doctrines that come under the label ‘platonism’. 7. Hao Wang, “What is an Individual?”, Philosophical Review 6 (1953), 413–20, claimed to have found a way to turn any platonistic system into a nominalistically acceptable one, but Goodman (among others) rejects this in “A World of Individuals” (PP: 161). 8. Actually, ‘⊃’, the sign for the conditional, does not occur in Goodman and Quine’s construction. We picked it here anyway because it is much more common than the sign of alternative denial ‘|’ (the Sheffer-stroke) that they use. So ‘p | q’ is false if both ‘p’ and ‘q’ are true, and true otherwise. (In Goodman and Quine’s construction, ‘|’ is characterized not semantically, by ascriptions of truth-conditions, but syntactically, by axioms and rules of inference.) With ‘|’ as the only sentential connective, all the usual connectives of propositional logic can be defined. ‘¬ p’, for example, is defined as ‘p | p’, and ‘p ⊃ q’ as ‘p | ¬ q’. (We leave ‘∧’, ‘∨’ and so on as an exercise for the reader.) Goodman and Quine need only a small number of primitives signs as the basis for their object language, but as mentioned above they choose a platonistic object language containing the membership symbol ‘∈’. These two signs (‘|’ and ‘∈’), together with the signs to form variables, ‘v’ and ‘′’, and the parentheses, ‘(’ and ‘)’, are the only six signs needed to form the whole object language. One might think
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9.
10. 11.
12. 13. 14.
15.
16.
17.
18. 19.
that there is a problem connected to the parentheses, since the left and the right one are alike in shape, but this can be disregarded as a mere “typographical idiosyncrasy”, as Goodman and Quine point out. Nevertheless, they provide a fix for it in “Steps Toward a Constructive Nominalism” (PP: 184). This does not seem to be true of nominalists today, however. H. H. Field, Science without Numbers (Princeton, NJ: Princeton University Press, 1980) accepts uncountably infinitely many spacetime points; C. Chihara, Constructibility and Mathematical Experience (Oxford: Oxford University Press, 1990) accepts infinitely many possible inscriptions of open sentences (also note the modality here); and G. Hellman, “On Nominalism”, Philosophy and Phenomenological Research 62 (2001), Harvard Symposium for Nelson Goodman, 691–705, is willing to go all the way (see also Hellman’s Mathematics without Numbers: Towards a ModalStructural Interpretation (Oxford: Oxford University Press, 1989)). Another class theory can be found in W. V. Quine’s Mathematical Logic (Cambridge, MA: Harvard University Press 1951 [1940]). It would be better to just speak of “constructional systems” here, and leave the “of the world” out, but we have not yet introduced Goodman’s constructionalism. We shall do so in Chapter 5. Why saying “of the world” might be problematic will become clear in Chapter 8. Goodman’s hostility towards intensionality, or to put it a more positive way, his extensionalism, has already surfaced in Chapters 2 and 3; the theme will reoccur in the following chapters. In The Structure of Appearance, however, Goodman suggests an explication of the abstract–concrete distinction (SA: 177–8). A proviso needs to be made at this point: the mereology discussed here is classical extensional mereology, as exemplified by Leonard and Goodman’s calculus of individuals. We shall raise and explain this point further below, after we have introduced the calculus. Goodman was known to tell fellow philosophers, including, for instance, David Lewis, that he could prove that the universe was odd. Assuming that the universe is composed of finitely many atoms, where n is the number of atoms, the number of things in the universe, 2n – 1, has to be odd since any power of 2 is even. (This anecdote was reported to us by Daniel Nolan who heard it from Lewis himself. Many thanks to him for this gem!) Józef Maria Bocheński was Goodman’s contemporary. Goodman is not (or not just?) mocking him by calling him “Father”: Bocheński was a Dominican, and also often called “Father Bocheński” by his peers. He was a prominent member of the Cracow Circle, which was a “group of scholars who decided to try and introduce into the Catholic School of Philosophy and Theology the methods developed and practised by the Warsaw logicians” (J. M. Bocheński, “The Cracow Circle”, in The Vienna Circle and the Lvov-Warsaw School, K. Szaniawski (ed.), 9–18 (Dordrecht: Kluwer, 1989), 9). Bocheński was (among many other things) a philosopher and logician. He also attended lectures by Leśniewski and Łukasiewicz, and was a vehement critic of nominalism. Goodman’s “A World of Individuals” was first published in a volume called The Problem of Universals, which also contains a paper by Bocheński and one by Alonzo Church. All three papers were presented at the Aquinas Symposium sponsored by the Department of Philosophy of the University of Notre Dame on 9–10 March 1956. Father Bocheński, therefore, must have been in the audience when Goodman read this passage. See also A. Orenstein, W. V. Quine (Chesham: Acumen, 2002), ch. 3, for an easy introduction, and Shapiro, Thinking about Mathematics, ch. 9, for an equally approachable introductory discussion of Quine’s indispensability argument in the context of nominalistic positions in the current philosophy of mathematics. Goodman very briefly comments on Field in MM: 53. We chose the more careful formulation since it is at least not obvious that the
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20.
21. 22.
23. 24. 25. 26.
27. 28.
numerous criticisms can be overcome, and, of course, a nominalistically acceptable version of Newtonian gravitational theory does not guarantee that the same can be done for the vast remainder of physics. This criticism was, to our knowledge, first formulated by D. Malament in “Review of Hartry Field’s Science without Numbers”, Journal of Philosophy 19 (1982), 523–34. Some advances into quantum mechanics have since been made by M. Balaguer in Platonism and Anti-Platonism in Mathematics (Oxford: Oxford University Press, 1998); Einstein’s special and general theories of relativity have very recently been tackled, too: some results and further literature can be found in H. Andréka, J. X. Madarász & I. Németi, “Logical Axiomatizations of Space-Time: Samples from the Literature”, in Non-Euclidean Geometries, A. Prekopa & E. Molnár (eds) (Dordrecht: Kluwer, forthcoming) and J. X. Madarász, I. Németi & C. Töke, “On Generalizing the Logic-Approach to SpaceTime towards General Relativity: First Steps”, in First-Order Logic Revisited, V. Hendriks et al. (eds). In Of Mind and Other Matters, Goodman also tells this parable that we cannot resist quoting: “In a certain village, Maria’s sign reads ‘All clothes washed’ while Anna’s counters ‘Clothes washed in clean water.’ Anna always returns a wash with many articles untouched; for her spring gives clean water but not fast enough. Maria always finishes much more of the wash, but never all; for although her creek provides plenty of rather muddy water, there is always too much work to do. Whenever a traveller inquires at the inn for a laundress, he is asked whether he is a nominalist or a platonist” (MM: 50). See note 7 above. See Ridder’s Mereologie, ch. IV.3, for an exposition and discussion of Whitehead’s mereological studies, which were independent of Leśniewski’s. For a more detailed discussion of the historical development of mereology and the interaction of the main players see our “Individuals: Russell, Whitehead, Leonard, Goodman and the Origins of Mereology”, forthcoming. A historical investigation of Leonard’s and Goodman’s development of the calculus of individuals is presented in D. Cohnitz and M. Rossberg, “Individuals: Russell, Whitehead, Leonard, Goodman and the Origins of Mereology”, forthcoming. For details see the first chapters of Ridder, Mereologie. See Ridder, Mereologie for the equivalence proofs. One can have mereological systems without atoms, too. Every individual has a proper part in such systems. After D. Lewis, Parts of Classes (Oxford: Blackwell, 1991) it has become common to call atomless stuff “gunk”. See also T. Sider’s “Van Inwagen and the Possiblity of Gunk”, Analysis 53 (1993), 285–9, for such a “gunky” mereology. See Lewis, Parts of Classes, §§3.5 & 3.6, for a passionate defence. A number of good publications advance in that direction. See for example Simons, Parts; R. Kleinknecht, “Mereologische Strukturen der Welt”, Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin, Reihe Geistes- und Sozialwissenschaften 41 (1992), 40–53; B. Smith & A. C. Varzi, “Fiat and Bona Fide Boundaries: Towards an Ontology or Spatially Extended Objects”, in Spatial Information Theory, S. C. Hirtle & A. U. Frank (eds), 103–19 (Berlin: Springer, 1997); Ridder, Mereologie, ch. IV. Of course, this is not to say that there are no further interesting philosophical questions here. See, for example, R. Casati & A. C. Varzi, Parts and Places: The Structures of Spatial Representation (Cambridge, MA: MIT Press, 1999) and, for a discussion in a wider setting of philosophical issues, T. Sider, Four-Dimensionalism (Oxford: Oxford University Press, 2001), ch. 5, esp. §7. Sider also discusses a doctrine called ‘mereological nihilism’: no two individuals have a sum – there are no composite objects. Peter van Inwagen, Material Beings (Ithaca, NY: Cornell University Press, 1990) holds a slightly less radical view. According to him, the only things that exist, except for atoms, are living things.
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Nelson Goodman 29. To be really nitpicking, to speak even more strictly, everything is fine with this. ‘Nominalism’ and ‘nominalistic’ are two distinct terms of art. We might be inclined to see a connection between them, because they sound similar (but then, so do ‘cat’ and ‘cattle’), and there also is a connection, but it is not as straightforward as one might think. ‘Nominalism’ refers to an ontological doctrine: the denial of the existence of classes (or maybe the prohibition of using classes in constructional systems or world versions; see Chs 5 & 8). ‘Nominalistic’, on the other hand, is a predicate that classifies systems. It labels those that have a generating relation that obeys Goodman’s sameness-of-content criterion, and hence rules out class formation as well as non-extensional mereological summation, and possibly more. There is no tension, since the two are different kettles of fish that really strictly speaking must not be identified.
Chapter 5. From Vienna Station to Boston Terminus
1. This is done, for example, in G. Abel’s “Logic, Art, and Understanding in the Philosophy of Nelson Goodman”, in The Philosophy of Nelson Goodman Vol. 1: Nominalism, Constructivism, and Relativism, C. Z. Elgin, 1–11 (New York: Garland, 1997). 2. These are taken from Hellman’s introduction to the third edition of The Structure of Appearance. 3. We can only highlight some of the interesting historical issues connected with Goodman’s A Study of Qualities and The Structure of Appearance. For a more detailed treatment of the history of the calculus of individuals, see our “Individuals: Russell, Whitehead, Leonard, Goodman”. 4. Russell informed Frege about the problem in a personal letter dated 16 June 1902. See B. Russell, “Letter to Frege”, in From Frege to Gödel: A Source Book in Mathematical Logic, J. van Heijenoort (ed.), 124–5 (Cambridge, MA: Harvard University Press, 1967). 5. Strictly speaking, the objects in Frege’s system of the Grundgesetze are extensions of concepts, not classes, but such subtleties need not worry us here. 6. It is doubtful whether Whitehead really succeeded in this. T. Mormann, “Description, Construction and Representation: From Russell and Carnap to Stone”, in On Denoting 1905–2005, B. Loinsky & G. Imaguire (eds) (Munich: Philosophia, forthcoming) argues that it took until the 1970s and 1980s to accomplish a proper “pointless topology”. See also P. T. Johnstone, Stone Spaces (Cambridge: Cambridge University Press, 1982). 7. Indeed, Carnap’s (unpublished) manuscript from 1923, “Die Quasizerlegung: Ein Verfahren zur Ordnung nichthomogener Mengen mit den Mitteln der Beziehungslehre [Quasi-Division: A Method for Ordering Non-Homogeneous Sets by Means of the Theory of Relations]” was arguably much closer to Russells’s project than the later Aufbau. See Mormann, “Description, Construction and Representation”. 8. In §5, however, Carnap declares that the Aufbau is neutral with respect to the conflict between rationalism and empiricism. A clearly non-empiricist statement is formulated in §10 and §12, when Carnap explains that science is only concerned with the structural relations between things and that it does not talk about the concrete relations and nodes of those structures (T. Mormann, Rudolf Carnap (Munich: Beck, 2000)). These structural relations are also deemed responsible for the objectivity of science, which is why providing an object-level domain is unnecessary. Such statements cannot be read as belonging to an empiricist programme. Finally, in §176 Russell is accused of metaphysical leanings just because of his empiricism. See Mormann, Rudolf Carnap and M. Friedman, “Carnap’s Aufbau Reconsidered”, Noûs 21 (1987), 521–45. For the influence of Russell on Carnap see also C. Pincock, “Russell’s Influence on Carnap’s AUFBAU”, Synthese 131 (2002), 1–37, and “Carnap, Russell and the External World”, in Cambridge Companion
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9.
10. 11. 12.
13.
14.
15.
16. 17.
to Carnap, M. Friedman & R. Creath (eds) (Cambridge: Cambridge University Press, forthcoming). ‘In der Krim’ is the bus stop near the house in which Carnap was born: In der Krim 42. This house still exists. It is a very beautiful villa built in 1890 (the year before Carnap was born) and displays a plate indicating that the Carnap family lived there. We should like to thank the Verkehrsverbund Rhein-Ruhr for the kind permission to reprint this partial map. This is argued at length in R. Naumann, Das Realismusproblem in der analytischen Philosophie: Studien zu Carnap und Quine (Freiburg: Alber, 1993) against Quine’s criticism. Both points were overlooked by Dummett in his criticism of Goodman’s The Structure of Appearance. See M. Dummett, “Constructionalism”, in Truth and Other Enigmas, 50–65 (London: Duckworth, 1978 [1957]) and R. Farrell, “Michael Dummett on The Structure of Appearance”, in Elgin’s The Philosophy of Nelson Goodman Vol. 1, 49–65. Some historians have convincingly argued that the Aufbau is thus a synthesis of positivism and neo-Kantianism that is closer in emphasis to neo-Kantianism than to empiricism (Friedman, “Carnap’s Aufbau Reconsidered”; A. Richardson, Carnap’s Construction of the World: The Aufbau and the Emergence of Logical Empiricism (Cambridge: Cambridge University Press, 1998); Mormann, Rudolf Carnap; Pincock, “Russell’s Influence on Carnap’s AUFBAU”). If the Aufbau is considered a general theory of constitution systems, a critique of Carnap’s work should not judge its merits and mistakes on the basis of a specific constitution. Hence a refutation of Carnap’s early kind of phenomenalism is not necessarily also a refutation of the Aufbau (as many have mistakenly tried to argue). As we shall explain in more detail below, Carnap aimed only at a rational reconstruction. In other words, the question of whether or not the process of actual knowledge acquisition resembles the steps of construction explicated in the Aufbau was not a real issue for him. The Aufbau does not attempt to describe the real psychological processes. We agree with Richardson, Carnap’s Construction of the World, and Mormann, Rudolf Carnap, that such a reading misrepresents the intended generality of constitution theory. However, in the light of puzzling remarks by Carnap from 1931 that are left unexplained by Mormann and Richardson, we feel unable to ascribe to Carnap a strong early “principle of tolerance” with respect to the basis of the constitution system. You find these remarks in the protocols of the Vienna Circle. On 12 March 1931 Carnap discussed the ways in which his views had changed since the Aufbau. Concerning “matters of content” he remarked that “The problem of the basis is problematic (form of atomic sentences). The point of view of methodological solipsism remains the only possible alternative to me.” During this presentation Hans Hahn asked whether this new view meant that there was only one starting-point for a constitutional system. Carnap answered: “Essentially there is only one way, but in practice there might be more alternatives which can easily be transformed into each other. However, of the possibilities sketched it seems that only one really is possible” (Stadler, Studien zum Wiener Kreis, 297–302). These remarks can be interpreted in various ways. Prima facie, however, they seem to delimit a principle of tolerance considerably. Such misunderstandings are in part due to Carnap’s own use of ‘phenomenalism’. For Whitehead’s use of this in An Enquiry Concerning the Principles of Natural Knowledge (Cambridge: Cambridge University Press, 1919), see Ridder, Mereologie, ch. IV, and A. Grünbaum, “Whitehead’s Method of Extensive Abstraction”, British Journal for the Philosophy of Science IV(15) (1953), 215–26. The first presentation of the method of quasi-analysis seems to be in Russell’s Our Knowledge
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18.
19. 20.
21.
22.
23.
24.
25.
of the External World, where Russell constructs instants of time from a basis of events. For a discussion of Russell’s construction and its relation to Carnap’s quasianalysis see R. Kleinknecht, “Zeitordnung und Zeitpunkte”, Erkenntnis 54 (2001), 55–75; Mormann, “Description, Construction and Representation”; and H. Leitgeb, “Under what Conditions does Quasianalysis Succeed?” (forthcoming). T. Mormann, “Synthetic Geometry and Aufbau”, in Language, Truth, and Knowledge: Contributions to the Philosophy of Rudolf Carnap, T. Bonk (ed.), 45–64 (Dordrecht: Kluwer, 2003) argues that Carnap’s project started with his doctorate thesis, Der Raum: Ein Beitrag zur Wissenschaftslehre [Space] (Berlin: Reuther & Richard, 1922), and was rather influenced by synthetic geometry than Whitehead’s project. This is not quite accurate, but for our discussion more than sufficient. For the notions of part similarity and part identity see SA: ch. V. Carnap uses similarity relations other than the part-identity relation because similarity comes in degrees and thus makes possible an ordering of the quasi-qualities. However, the problems arising for the identity relation (discussed later in this chapter) are analogous to the problems of any similarity relation. The difference between analyses on the basis of part-identity and part-similarity relations is the difference between what Leitgeb calls “quasianalysis I” and “quasianalysis II” (“Under what Conditions does Quasianalysis Succeed?”). However, quasianalysis II presupposes quasianalysis I, which is why it seems sufficient to concentrate on the latter (see ibid.). For a discussion of quasi-analysis II and the relevance of Goodman’s negative results for it (which we shall discuss further below) see R. A. Eberle, “A Construction of Quality Classes Improved upon the Aufbau”, in Rudolf Carnap, Logical Empiricist, J. Hintikka (ed.), 55–73 (Dordrecht: Reidel, 1975); and R. Kleinknecht, “Quasianalyse und Qualitätsklassen”, Grazer Philosophische Studien 11 (1980), 23–43. For this idea we are indebted to Thomas Mormann. T. Mormann, “A Quasi-analytical Constitution of Space”, in Carnap Brought Home: The View from Jena, S. Awodey & C. Klein (eds), 79–99 (Chicago, IL: Open Court, 2004) argues that Carnap’s project could nevertheless be reconciled with a pure quasi-analytic constitution if space as a purely mathematical object is not just presupposed (such that it is necessary to “map” the subjective world onto this mathematical structure) but also constituted by means of quasi-analysis. Mormann, Rudolf Carnap, points out that Carnap refers to his conventionalistminded paper, ‘Über die Aufgabe der Physik und die Anwendung des Grundsatzes der Einfachstheit [The Aim of Physics and the Application of the Basic Principle of Simplicity]”, Kant-Studien 28 (1923), 90–107, when explaining this mapping relation. This is evidence that Carnap had a programme in mind that differed in important respects from Russell’s. But see Mormann, “A Quasi-analytical Constitution of Space” (and the previous footnote) for second thoughts. It is questionable whether this solipsistic concept conforms to intersubjectivity as it is normally understood (see Mormann, Rudolf Carnap, 104). Moreover it is unclear how the original idea to preserve objectivity by structure (remember the railway map example given above) fits with this solution presented at the end of the Aufbau. This is problematic in the light of the normativity of explication. If explication is a normative enterprise, a different decision might well lead to the revision of sentences. See the detailed discussion of this problem in Naumann, Das Realismusproblem in der analytischen Philosophie. For the protocol sentence debate see A. Coffa, The Semantic Tradition from Kant to Carnap: To the Vienna Station (Cambridge: Cambridge University Press, 1991); O. Neurath, “Protokollsätze”, Erkenntnis 3 (1932), 204–14; and R. Carnap, “On Protocol Sentences”, R. Creath & R. Nollan (trans.), Noûs 21 (1987 [1932]), 457–70. The interesting similarities of the Carnap–Neurath position and Goodman’s views, as well as their differences, are also discussed in I. Scheffler, Symbolic Worlds: Art,
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26.
27. 28.
29.
Science, Language, Ritual (Cambridge: Cambridge University Press, 1997) and C. G. Hempel. “Comments on Goodman’s Ways of Worldmaking”, Synthese 45 (1980), A Symposium on Nelson Goodman, Ways of Worldmaking, 193–9. Carnap’s work of the early 1930s should be seen in the light of the unity of science movement. On the one hand the Aufbau was concerned with the justificatory problems of our knowledge: how our scientific knowledge is related to our experiences, this being the reading that survived in the early history of analytic philosophy. The Aufbau, however, is mainly concerned with questions of intersubjectivity and intertranslatability, and it was on this latter issue that Carnap continued to work. In the Aufbau it is shown how the different aspects of science are nevertheless aspects of the same enterprise: to understand the world. In the Aufbau this case is made by demonstrating how all that is said by the sciences is based on the same foundation. In his paper on physicalism, “Die physikalische Sprache als Universalsprache der Wissenschaft”, Erkenntnis 2 (1932), 432–65 (revised edition published in English as The Unity of Science, M. Black (trans.) (London: Kegan Paul, Trench, Truebner, 1934)), which marked the next phase of his intellectual development, Carnap tried to show how sciences as diverse as physics and psychology might nevertheless be talking about the same things. Recalling what we said in Chapter 4 about the purpose of explications, this might seem puzzling. Goodman’s criterion for adequacy evidently presupposes that the extensions of the explicanda are precisely specified: a condition that is rarely satisfied in situations requiring philosophical analysis. In general, the terms around which philosophical perplexities centre are beset with obscurity, vagueness and ambiguity, and the classes of instances to which they apply are therefore anything but precisely determined. As C. G. Hempel, “Reflections on Nelson Goodman’s The Structure of Appearance”, in The Philosophy of Nelson Goodman, 66–74, points out, Goodman’s criterion presupposes a preconstructional clarification of the explicanda under investigation. Such a preconstructional analysis would have three tasks: (i) to disentangle the various modes of usage of the explicanda; (ii) to explore the rationale of each of the various patterns of use and to appraise its value for descriptive and theoretical purposes; and then (iii) to assign precise meanings to the explicanda in such a way that they permit a clear description and a fruitful theoretical treatment of the issues under analysis. In Chapter 3 we hinted at how this can be achieved and indicated that the project of ordinary-language analysis, as undertaken by British ordinary-language philosophy, could be seen as the first step in such a preconstructional analysis. The best analysis of Goodman’s isomorphism criterion still seems to be G. Hellman, “Accuracy and Actuality”, Erkenntnis 12 (1978), The Philosophy of Nelson Goodman Part II, 209–28. On these and related arguments against thought experiments in philosophy, see Cohnitz, Gedankenexperimente in der Philosophie. Carnap anticipated and dealt with the companionship difficulty in his unpublished “Die Quasizerlegung” and also in the Aufbau itself. For recent discussions of Carnap’s solution, see Leitgeb, “Under what Conditions does Quasianalysis Succeed?”. Note that this problem arises although Goodman concedes to Carnap his extensionalism (Goodman’s criterion of “extensional isomorphism” is, as we have seen, even more radical in this respect). The companionship problem should, however, not be confused with a worry that can occur only within an intensional account. Two properties (if conceived as being intensional objects) could well be different although they are instantiated by the exact same individuals. In this case a quasiproperty, that is, a property reconstructed by way of quasi-analysis, could represent more than one property. (See Kleinknecht, “Quaisanalyse und Qualitätsklassen”, and Eberle, “A Construction of Quality Classes” for this objection against quasianalysis.) If extensionalism (or extensional isomorphism) is accepted as the criterion of adequacy this objection can no longer be raised. See G. Rodriguez-Pereyra,
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30.
31.
32. 33. 34. 35.
Resemblance Nominalism: A Solution to the Problem of Universals (Oxford: Clarendon Press, 2002), ch. 8, and Leitgeb, “Under what Conditions does Quasianalysis Succeed?”. Recent commentators have argued that it is not so clear that these are really grave problems for Carnap. After all, the erlebs in Carnap’s Aufbau are primitive, they have no “real” colours, and hence there is no “right” way of doing quasi-analysis. What quasi-parts are obtained from the Pi ordering of ground-elements is, arguably, unimportant as long as the system of science can be constructed from it. For Richardson, “Goodman’s particular concerns dissolve when we respect the constitutional difference between analysis and quasi analysis. In cases of quasi analysis, there is no external perspective against which to check the construction for correctness; quasi analysis is not constrained by antecedent or independent matters of fact about the qualities of the objects related by the similarity relations. Indeed, to think it was so constrained would be to obviate the need for quasi analysis at the outset and to dismiss Carnap’s methodological priority of relations over primitive properties for the basis elements” (Carnap’s Construction of the World, 64). For the same argument see also J. Proust, Questions of Form: Logic and the Analytic Proposition from Kant to Carnap (Minneapolis, MN: University of Minnesota Press, 1989) and Mormann, “Synthetic Geometry and Aufbau”. As Leitgeb, “Under what Conditions does Quasianalysis Succeed?”, argues, the question is one of priority. Goodman, in any case, considers qualities to be prior to the similarities they give rise to, such that the road in the other direction is one of reconstruction. Carnap’s view on the matter is less clear. However, “[w]hen Carnap discusses the intended results of quasianalysis (see §81, 72) and distinguishes them from unintended ones that might occur under unfavourable circumstances, he takes the extrasystematic standpoint” (ibid.). In other words, Carnap seems to assume that qualities are extrasystematically prior to the obtaining similarities, but treats the similarities as prior within the phenomenalistic constitution system. We refer to Leitgeb, “Under what Conditions does Quasianalysis Succeed?”, for a detailed assessment of Carnap’s quasi-analysis. Leitgeb also presents necessary and sufficient conditions for the success of quasi-analysis. As Hempel, “Reflections on Nelson Goodman’s The Structure of Appearance” argues, Goodman cannot turn to incomplete definitions in Carnap’s sense, for this move would violate Goodman’s own criterion for the adequacy of a constructional system. Nor can he make use of modal or counterfactual expressions, since these fail to meet Goodman’s standards of intelligibility. We return to this in Chapter 8. The details can be found in SA: 47–84. Note that symmetry of ‘intersects’ means that ∀x∀y(Intersects(x, y) ⊃ Intersects(y,x)). Assume that some a intersects some b. By definition, a cuts b or b cuts a. If b cuts a or a cuts b, however, b intersects a, again by definition. QED. The earliest connection between the calculus of individuals and the Aufbau is the solution to Carnap’s difficulty of imperfect community in Leonard & Goodman, “The Calculus of Individuals”, presented as early as 1936 to the Association for Symbolic Logic. This leaves open the possibility, considered in Chapter 1, that Goodman and Leonard learnt of Carnap’s Aufbau from Quine, and that he might have drawn the connection between their calculus and Carnap’s project in December 1935 on the way back from Baltimore. As Quine reports in his autobiography: “Goodman, Leonard, and I drove back to Cambridge, stopping in New York at the Lafayette, a French hotel off Washington Square. On the way they told of a project of theirs. They broached it diffidently, for I had seemed unsympathetic when Henry spoke of it on an earlier occasion. I became interested as I heard more, and I was able to help them on a technical problem. We talked in our hotel room until four in the morning. They were concerned with constructing a systematic theory of sense qualities, and their effort had much in common with
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36. 37. 38. 39.
Carnap’s Logischer Aufbau der Welt. As an auxiliary they had developed a logic of part–whole relation, which I recognized as Leśniewski’s so called mereology” (Quine, The Time of My Life, 122). This leaves open the question of who drew the connection to Carnap (but not who drew the connection to Leśniewski). However, if the project was a sequel to Leonard’s Singular Terms, the idea to construct a system of sense qualities might well have been taken from Whitehead (as it is in Singular Terms). For details see The Structure of Appearance (SA: ch. III). For details see The Structure of Appearance (SA: 154). We have already emphasized that Carnap also considered other bases in the Aufbau. See, for example, Leitgeb, “Under what Conditions does Quasianalysis Succeed?”; Kleinknecht, “Zeitordnung und Zeitpunkte”; G. Rodriguez-Pereyra, “Resemblance Nominalism and the Imperfect Community”, Philosophy and Phenomenological Research 59 (1999), 965–82, and Resemblance Nominalism.
Chapter 6. Follow the sign
1. Scheffler, Symbolic Worlds, adds religion to the list, and undoubtedly one can think of more. 2. Goodman trusts that such platonistic-sounding talk can be nominalized, and that the theory especially could be presented without the use of classes (LA: xiii). We shall come back to this later in the chapter; see also MM: 51. 3. In MM: 77–80, Goodman discusses how these predicates could also, contrary to his initial suggestion, be taken to be composed without threatening his position. He reacts here to the work of Rolf Eberle (see “Semantic Analysis without Reference to Abstract Entities” and “Goodman on Likeness and Difference of Meaning”). The predicate ‘picture of a unicorn’, for example, can be taken to be composed of ‘picture’ and ‘of a unicorn’. More generally, ‘picture of an x’ would be composed of ‘picture’ and the modifier ‘of an x’. This allows, for example, the inference from ‘a is a picture of a unicorn’ of both the statements ‘a is a picture’ and ‘a is of a unicorn’. The statement ‘a is of a unicorn’ still does not require that there are unicorns: ‘of a unicorn’ has pictures and descriptions in its extension. Since ‘picture of a unicorn’ is also a compound of ‘unicorn’ (predicates can be analysed into compounds in different ways according to the purpose at hand), the primary extension of ‘picture of a unicorn’ is part of the secondary extension of ‘unicorn’, whose primary extension is empty. (We introduced primary and secondary extensions in Chapter 2.) Talking about modifiers in predicates also allows us to characterize the difference between the occurrence of ‘unicorn’ in ‘unicorn-picture’, and that of ‘bat’ in ‘battle’. Only those compounding terms that function as a modifier are semantically relevant. ‘Bat’ is not a modifier of ‘tle’, nor vice versa. The same goes for ‘detergent’ and ‘determine’: they are not cases of things that deter. 4. Note the similarity of this question with that discussed in Chapter 2 concerning how we manage to project disposition predicates. The answer given there is essentially the same as the one Goodman gives here. 5. There might be symbols that are not conventional; those that are caused by what they stand for are probably the best candidates. These are sometimes called signs (LA: 65). Smoke, to use a common example, is a sign for fire. So-called symptoms of a disease are another case of caused signs. One might try to argue – which Goodman does not – that taking smoke as a sign of fire is in fact conventional. However that might be, at least background knowledge that fire does cause smoke, and that such-and-such symptoms typically occur with this-and-that disease, will be needed even in these cases. 6. Other languages, such as Italian, do better since they have fewer “exceptions” when it comes to the notations of the spoken language. English massively violates
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7.
8.
9.
10. 11. 12. 13.
14.
15. 16.
17.
the uniqueness requirement for a notation. For example, it allows an f-sound to be denoted as ‘gh’ as in ‘tough’; a sound like the ‘i’ in ‘in’ can sometimes be denoted as ‘o’, namely in ‘women’; and the ‘ti’ in ‘station’ denotes the same sound as the ‘sh’ in ‘shine’. So, how do you pronounce ‘ghoti’? Also, consider the different ways the letter combination ‘ough’ can be pronounced in English, as in ‘thought’, ‘though’, ‘cough’, ‘tough’, ‘plough’, ‘through’, ‘thorough’ and ‘hiccough’. Goodman remarks that not everything that is ordinarily called a score fulfils this criterion: “here, as with most familiar words, systematic use involves a specialization from ordinary usage” (LA: 128, n.1). In other words, Goodman is offering an explication of ‘score’. This does not mean that ordinary scores are useless but merely says that they are not notations. On this point, see also LA: ch. V, §2. To call utterances, which are sound waves, ‘inscriptions’, is merely a piece of terminology, however; little hangs on the word. If one prefers to reserve ‘inscription’ for visual marks rather than distinguish between visual and auditory inscriptions (the latter including utterances), one is free to invent a new term that covers both. Nothing substantial will change. Occasionally Goodman hints at how platonist talk can be eliminated for a “clean” nominalist version; compare, for example, “The seemingly shameless platonism exhibited here will be corrected shortly” (LA: 46, n.1 – he is referring to LA: 54–7; or LA: 156, n.15). Advances into a nominalistically acceptable version of semantics are made in Eberle, “Semantic Analysis without Reference to Abstract Entities”. Goodman discusses more tricky cases, for example, the same mark being used simultaneously as an inscription of two different characters in different contexts (LA: 138–9). Density is with respect to an ordering, and ‘dense’ is short for ‘densely ordered’ (see LA: 137, n.6). One might wonder what happens if we refine our measuring technique to the extent that we hit the quantum level. The answer is that this changes the example. If it is determined whether an inscription belongs to a character by the number of quanta lined up one after the other, it is no longer the case that any difference in length no matter how small determines belonging to a character. The scheme that counts quanta is articulate, thereby contradicting the original description. Yes, it is. Any inscription of an Arabic fractional numeral can be determined to belong to exactly one character. The fractional lengths or fractional quantities or indeed numbers they might stand for are not as we just discussed: they are dense. Compare note 12 above. A. Kirsch, “Venn-Diagramme und freie Boolesche Verbände”, Der Mathematikunterricht 18 (1971), 15–33 proved that Venn diagrams can be used as a decision procedure for monadic predicate logic; see also S.-J. Shin, The Logical Status of Diagrams (Cambridge: Cambridge University Press, 1994). Shin, The Logical Status of Diagrams and M. Greaves, The Philosophical Status of Diagrams (Stanford, CA: CSLI Publications, 2002) contain detailed investigations of the rigorous use of diagrams for mathematical purposes. Note that this is not quite the standard “notation” for chess. The standard “notation” does not fulfil Goodman’s requirements for a proper notation: it is not semantically disjoint, that is, there is a certain “flexibility” as to how moves are recorded. Also, the recorder has a range of additional symbols at hand that provide redundant information, such as ‘x’ for indicating capture of a piece, or ‘+’ for check (both of these states of the game can determinately be read off the notation we provide), and even some symbols to provide a personal comment on the game, such as ‘!’ for “This was an excellent move”, ‘+/-’ for “White has a clear advantage”, or ‘?’ for “This was a blunder”. It should be clear how the standard “notation” does not fulfil the strict requirements for a notation in Goodman’s sense.
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Notes Chapter 7. Diagnosing art
1. Interestingly enough, E. Gombrich’s Art and Illusion (New York: Pantheon, 1960) was based on a lectures series he gave in 1956 called “The Visible World and the Language of Art”. There are a few places in Languages of Art and elsewhere in Goodman’s writings, where he acknowledges the influence Gombrich’s books had on him. 2. For Goodman’s views on perception see also WW: ch. V. 3. See also MM: 128; for a treatment of “the given” see § “The roots at Harvard”, p. 21 and Chapter 5; SA: 97–9; and PP: 60–68. 4. Leonardo even noticed that the horizontal lines of the bases and so on of the columns were not only to be represented converging, to accord to the “right” perspective, but also they had to be curved, thus, in a sense, foreshadowing projective geometry. (The retina is concave!) 5. An excellent paper concerning the conventionality of perspective is that of the art historian Erwin Panofsky, translated as Perspective as Symbolic Form, C. S. Wood (trans.) (New York: Zone Books, 1925). More discussion of perspective by Goodman can be found in MM: 9–14 and “Perspective as Convention – on the Views of Goodman and Gombrich”, Leonardo 14 (1981), 86. 6. Some kind of so-called reverse perspective is indeed often found in Byzantine and medieval painting, and is thus not only an academic idea (see LA: 15, and n.15 on the same page for references to relevant literature on reverse perspective). What happens here is basically that lines that converge in standard perspective diverge in reverse perspective. As a simple example, the box on the left is presented in standard perspective, and the one on the right in reverse perspective:
7.
8.
9. 10.
Both boxes are represented with the square as the front side. Actual examples of paintings in reverse perspective from Byzantine and medieval times do not carry this perspective through stringently enough to comply with Goodman’s thought experiment, but he believes that reverse perspective can be consistently applied (MM: 10). Coming up with an algorithm to translate standard perspective into reverse perspective might merely be a weekend’s fun for a graduate student in computer science. (Should one of our readers come up with such an algorithm and implement it in suitable software, we would be grateful if she or he contacted us.) Obviously, some symbol systems are easier to read than others. Notations that are very complicated to parse include systems we commonly call ‘codes’. Gödel numberings are impressive examples of notations that outrun our mental capacities already in the basic cases; this is especially true of the one Gödel himself proposed. Why this does not constitute a counter-argument against Goodman becomes clear in what follows in the main text. Goodman adds a footnote here: “Indeed, there are usually many such systems. A picture that under one (unfamiliar) system is a correct but highly unrealistic representation of an object can under another (the standard) system be a realistic but very incorrect representation of the same object. Only if accurate information is yielded under the standard system will the picture represent the object both correctly and literally” (LA: 38, n.30). Goodman jokingly attributes this to Immanuel Tingle and Joseph Immersion, c.1800. Goodman’s own partial definition uses the primitive terms only: “if a expresses b then: (1) a possesses or is denoted by b; (2) this possession or denotation is metaphorical; and (3) a refers to b” (LA: 95). It is an easy exercise to show that Goodman’s formulation is equivalent to ours.
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Nelson Goodman 11. Also recall in this context the discussion of the question of coextensionality for explications (see Ch. 3). 12. This is not entirely unlike Goodman’s argument that philosophers should proceed nominalistically while scientists can use classes and as much mathematics as they like; we discussed this in Chapter 4. Goodman’s generous pluralism, which we discuss in detail in Chapter 8, is exemplified in these two positions. 13. See also F. E. Sparshott’s “Goodman on Expression”, Monist 58 (1974), Languages of Art, 187–202, for a discussion of Goodman’s explication of expression and of how it squares with traditional conceptions of expression. 14. We mention songs in the title of this section, but do not present their identity conditions. After a careful reading of the section, it should be an easy exercise to state these in Goodmanian fashion; it is left to the reader. 15. Obviously, there is a problem with restoration here. See C. Z. Elgin’s Between the Absolute and the Arbitrary (Ithaca, NY: Cornell University Press, 1997), ch. 5, for a discussion of this. 16. That all artworks (and works of music in particular) actually are abstract objects, exactly because a work of music is neither the score nor the performance(s) is argued in M. E. Reicher’s Einführung in die philosophische Ästehtik (Darmstadt: WBG, 2005), ch. IV. See also R. Schmücker’s Was ist Kunst? Eine Grundlegung (Munich: Fink, 1998), ch. 5.4. 17. For more on the Halberstadt performance of Organ2/ASLSP, see www.john-cage. halberstadt.de (accessed Dec. 2005). 18. One might think that the presence of singing in Hotel California but not in the Fifth, or even merely the difference in instrumentation between the two, might cause trouble for this example, but the point it is meant to illustrate should be sufficiently clear however that might be. Identifying Hotel California with Bach’s Coffee Cantata, or Beethoven’s Fifth with his Sixth, certainly would be bad enough. 19. There is an interesting debate concerning this point between Arthur C. Danto on the one side, and Elgin and Goodman on the other. The discussion focuses on the example of the character called Pierre Menard in Jorge Luis Borges’s short story named after that character: “Pierre Menard: Author of the Quixote”, in Labyrinths: Selected Stories and Other Writings, 36–44 (New York: New Directions, 1962). Menard is an author who writes Cervantes’s Don Quixote long after Cervantes has written it. See Danto’s The Transfiguration of the Commonplace: A Philosophy of Art (Cambridge, MA: Harvard University Press, 1981), ch. 2, and RP: ch. III. 20. We do not want to suggest that playing a piece of music much too fast or much too slow is a particularly subtle offence, of course. Note that the tempo of a piece is also an important feature that will not be part of a possible notation for dance. 21. Goodman gives a sample of Labanotation (LA: 125), and also provides references to publications by Laban, some secondary literature for his notation, and a reference to a book by Rudolf and Joan Benesh who propose an alternative notation for dance (LA: 213, n.21).
Chapter 8. Starmaking
1. Such a system can comprise axioms as well, of course. Indeed, axiomatizations of, say, propositional logic constitute very important steps in the history of logic. Note that axioms and axiom schemata are easily construed as rules of this form: at any line of the proof the axiom (or an instance of the axiom schema) can be added as the next line, and it can also be the first line of a proof. 2. We return to starmaking in § “Metaphysics”, p. 212. 3. “Let it be clear that the question here is not of the possible worlds that many of my contemporaries, especially those near Disneyland, are busy making and manipulating. We are not speaking in terms of multiple possible alternatives to a single actual world but of multiple actual worlds” (WW: 2). Also: “The multiple worlds
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Notes I countenance are just the actual worlds made by and answering to true or right versions. Worlds possible or impossible supposedly answering to false versions have no place in my philosophy” (WW: 94). Compare also WW: 104 and MM: 31. 4. We return to this discussion in § “Metaphysics”, p. 212. 5. For this and what follows see also the brilliant exposition in W. Künne, “Truth, Rightness and Permanent Acceptability”, Synthese 95(1) (1993), Probing into Reconceptions, 107–17.
Chapter 9. Never mind mind, essence is not essential and matter does not matter
1. Kripke mentions Goodman’s new riddle of induction in particular in Wittgenstein on Rules and Private Language (Oxford: Blackwell, 1982), 58–9, esp. nn. 44, 46. 2. C. Wright, Rails to Infinity (Cambridge, MA: Harvard University Press, 2001), 176–7, and W. Goldfarb, “Kripke on Wittgenstein on Rules”, in Rule-Following and Meaning, A. Miller & C. Wright (eds), 92–107 (Chesham: Acumen, 2002), 95, argue that the premise of Kripke’s argument, which is (2) in our reconstruction above, leads to a challenge that should not be accepted, since it would not be answerable. The conception of meaning that Kripke presupposes, so goes the criticism, is begging the question in favour of the Kripkensteinian sceptic. 3. For an overview see M. Bremer, Einfachheit (www.mbph.homepage.t-online.de/ einfachheit.pdf ) (accessed Nov. 2005). 4. It should also be simpler by Quine’s criterion. 5. See SA: ch. IX.5 for Goodman’s treatment of kinds. 6. To be more precise, since the Big Dipper is part of the constellation Ursa Major (the Great Bear), it is technically not a constellation. It is what is called an ‘asterism’, which is the name given to interesting star patterns that are easily recognizable, but do not belong to the “official” constellations. 7. In his very readable comment on Putnam in P. J. McCormick (ed.), Starmaking, Goodman writes: “the characterization of my philosophy as extreme idealism seems to be a negative reaction against some of what I write about the relationship between versions and worlds. After all, statements like ‘there is no unique right version or world’; ‘versions make worlds’; and ‘conflicting right versions are of different worlds if any’; are likely to strike the realistically minded thinker as hostile, and to provoke in return an indictment of my philosophy as ‘extreme idealism’. But on two scores, I plead ‘not guilty’. In the first place, I have not said that there are no worlds, but only that conflicting right versions are of different worlds if any. My nihilism and my pluralism are complementarily conditional; and that, I submit, has more the flavor of irrealism than of idealism. In the second place, I do not see why even saying that there are no worlds but only versions would be idealistic, for I do not think of versions, verbal or pictorial, as mental or as being or in general referring to ideas or Ideas, but as objects functioning as symbols” (Goodman, “Comments”, 204). 8. See also D. Lewis, “Mathematics is Megethology”, Philosophica Mathematica 1 (1993), 3–23. Ridder, Mereologie, 331–74, contains a formal axiomatization of Lewis’s system of Parts of Classes, as well as a technical and philosophical discussion. 9. Another question is whether Goodman actually thought that. In “On Relations that Generate”, Philosophical Studies 9 (1958), 65–6, he writes that “notation aside, the proper-part relation may itself be regarded as a subrelation of the ancestral of membership … there are no generating relations other than subrelations of the latter” (p. 66). Note that this passage does not occur in the revised reprint of the paper in PP. 10. He also needs some choice principle (Lewis, Parts of Classes, 71–2), but we will not get into that here.
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Nelson Goodman 11. The current “bible” of second-order logic is Shapiro, Foundations without Foundationalism. 12. The derivation of standard axioms of set theory in Lewis’s megethology can be found in Lewis’s Parts of Classes, 100–107, and “Mathematics is Megethology”, 21–2. Ridder, Mereologie, 351–7, fills in formal details. 13. Lewis also accepts mixed fusions, that is, fusions of classes and individuals, since he believes in unrestricted composition: you can take a fusion of whatever you will. But he rejects that such mixed things can be members of classes. Unrestricted composition, he contends, forces him to accept fusions of classes with individuals, but there is no principle of unrestricted class formation, that forces classes of these mixed things upon him. In fact, as we also have seen in Chapter 5, assuming such a principle is inconsistent (Lewis, Parts of Classes, 7–8). 14. We have to insert a disclaimer: Lewis does not like the idea of a null individual, and nor does Goodman. There are mereologists, however, who posit such an entity; see, for example, R. M. Martin, “Of Time and the Null Individual”, Journal of Philosophy 62 (1965), 723–35; cf. Lewis Parts of Classes, 10, for further references. 15. Also, Lewis does not allow formation of singletons of the mixed things mentioned in note 13. 16. See note 12. Strictly speaking, Lewis also needs three different assumptions about the size of Reality to prove the set theoretical axioms. In order to fulfil them all, Reality has to comprise inaccessibly many atoms. We return to considerations about this size of Reality shortly. 17. To put the natural numbers into one-to-one correspondence, just order the integers in such a way that you start with 0, and then insert all the negative numbers right behind their positive counterpart. The list you get starts: 0, 1, –1, 2, –2, 3, –3, and so on (it is infinite, of course). Now you can write the natural numbers below that list, starting with 0, 1, 2, 3, and so on. You can see that there is a natural number for every integer. The natural numbers get bigger more quickly, of course (e.g. the integer 158 corresponds to the natural number 316), but that does not matter since there are infinitely many of them. (Nominalistic scruples have to be switched off for this exercise.) 18. This proof is a bit more complicated, but it is not too hard to understand it on an “intuitive” level. It is rather lengthy though, so it is omitted here. A version of Cantor’s proof can be found in any standard introductory book to set theory or mathematical logic. 19. Catherine Elgin gave us this information in personal communication. We are indebted to her. Goodman also told Lewis how impressed he was with his accomplishment. 20. In the same place, Lewis explains why he thinks himself justified to assume Reality to be of inaccessible size. See also Lewis, Parts of Classes, 57–9 (also cf. Lewis, “Mathematics is Megethology”, 14–15) for his famous “credo”: how he is “moved to laughter at the thought how presumptuous it would be to reject mathematics for philosophical reasons. How would you like the job of telling the mathematicians that they must change their ways, and abjure countless errors, now that philosophy has discovered that there are no classes? Can you tell them, with a straight face, to follow philosophical argument wherever it may lead? If they challenge your credentials, will you boast of philosophy’s other great discoveries: that motion is impossible, … that it is unthinkable that anything exists outside the mind, that time is unreal, … and so on, and on, ad nauseam? Not me!” (Parts of Classes, 59). As an antidote to a sentiment like this, which one might be tempted to call “philosophobic” (and perhaps a bit irresponsible: does Lewis suggest that philosophy should be uncritical?), it is advisable to recall what was said about Goodman’s view concerning the purpose of philosophy and its relation to science in Chapter 3 and Chapter 4.
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Bibliography
We have listed in this bibliography all the works referred to in the text as well as all publications by Goodman that we know of. John Lee from the University of Edinburgh has put online an enormously helpful “International Bibliography of Works by and Selected Works about Nelson Goodman” (www.hcrc.ed.ac.uk/~john/GoodmanBib. html). It is based on Sigrid Berka’s bibliography which appeared in the Journal of Aesthetic Education in 1991; we have profited from both. For additional material on Goodman’s philosophy, we recommend one of those. Goodman’s works are listed in chronological order of first publication, but quotations are taken from the more recent editions given. Occasionally, Goodman reprinted chapters of earlier books in later books (especially in PP); where this is the case we provide page references to the collected volume, except for A Study of Qualities and The Structure of Appearance, which we treat as different books for reasons given in the text.
Writings by Nelson Goodman Books 1941. A Study of Qualities, PhD thesis, Harvard University. First published New York: Garland, 1990 (Harvard Dissertations in Philosophy Series). 1951. The Structure of Appearance. Cambridge, MA: Harvard University Press. Third edition (Boston, MA: Reidel, 1977). 1954. Fact, Fiction, and Forecast. London: Athlone Press, 1954. Fourth edition (Cambridge, MA: Harvard University Press, 1983). 1968. Languages of Art: An Approach to a Theory of Symbols. Indianapolis, IN: BobbsMerrill. Second edition (Brighton: Harvester, 1981). 1972. Problems and Projects. Indianapolis, IN: Bobbs-Merrill. 1972. Basic Abilities Required for Understanding and Creation in the Arts: Final Report (with David Perkins, Howard Gardner, and the assistance of Jeanne Bamberger et al.), Harvard University, Graduate School of Education: project no. 9-0283, grant no. OEG-0-9-310283-3721 (010). Reprinted (in part and with changes) MM, V, ch. 2. 1978. Ways of Worldmaking. Indianapolis, IN: Hackett. Paperback edition (Indianapolis, IN: Hackett, 1985).
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Nelson Goodman 1984. Of Mind and Other Matters. Cambridge, MA: Harvard University Press. 1988. Reconceptions in Philosophy and other Arts and Sciences (with Catherine Z. Elgin). London: Routledge, 1988. Paperback edition (London: Routledge, 1990).
Articles by Nelson Goodman Many of Goodman’s articles have been reprinted as chapters of his books or in volumes that are easier to access than the original publication. In these cases we have usually referred to the reprinted versions. 1931. “The Truth-Tellers and the Liars” [published anonymously], Boston Post, 8 June 1931, 1, cols 1 & 2. [Goodman’s solution with explanation was published in the same paper, 9 June 1931, 15, cols 6 & 7.] Reprinted PP, 451 (and at the end of Chapter 9 of this book). 1940a. (with Henry S. Leonard) “The Calculus of Individuals and Its Uses”. Journal of Symbolic Logic 5, 45–55. Reprinted in Elgin (1997b: 129–39). 1940b. (with W.V. Quine) “Elimination of Extra-Logical Postulates”. Journal of Symbolic Logic 5, 104–9. Reprinted PP, 325–33. 1941. “Sequences”. Journal of Symbolic Logic 6, 150–53. 1943. “On the Simplicity of Ideas”. Journal of Symbolic Logic 8, 107–21. 1944. “Rev. of Outline of a Logical Analysis of Law, by Felix Oppenheim”. Philosophy of Science 11, 142–60. 1946a. “Descartes as Philosopher” (mimeographed). Boston: Cartesian Research Bureau. Reprinted PP, 45–8. 1946b. “A Query on Confirmation”. Journal of Philosophy 43, 383–5. Reprinted PP, 363–6. 1946c. “Review of ‘Definition and Specification of Meaning,’ by David Kaplan”. Journal of Philosophy 43, 281–8. 1947a. “On Infirmities of Confirmation-Theory”. Philosophy and Phenomenological Research 8, 149–51. Reprinted in Elgin (1997c: 17–19) and PP, 367–70. 1947b. (with W. V. Quine) “Steps Toward a Constructive Nominalism”. Journal of Symbolic Logic 12, 105–22. Reprinted PP, 173–98. 1947c. “The Problem of Counterfactual Conditionals”. Journal of Philosophy 44, 113– 20. Reprinted FFF, 3–27. 1948. “Review of Elements of Symbolic Logic, by Hans Reichenbach”. Philosophical Review 58, 100–102. Reprinted PP, 413–15. 1949a. “The Logical Simplicity of Predicates”. Journal of Symbolic Logic 14, 32–41. 1949b. “On Likeness of Meaning”. Analysis 10, 1–7. Reprinted PP, 221–30. 1949c. “Some Reflections on the Theory of Systems”. Philosophy and Phenomenological Research 9, 620–26. Reprinted PP, 33–40. 1950. “An Improvement in the Theory of Simplicity”. Journal of Symbolic Logic 14, 228–9. 1952a. “New Notes on Simplicity”. Journal of Symbolic Logic 17, 189–91. 1952b. “On a Pseudo-Test of Translation”. Philosophical Studies 3, 81–2. Reprinted PP, 239. 1952c. “Sense and Certainty”. Philosophical Review 61, 160–67. Reprinted in Elgin (1997b: 120–27) and PP, 60–68. 1953. “On Some Differences about Meaning”. Analysis 13, 90–96. Reprinted PP, 231–8. 1955. “Axiomatic Measurement of Simplicity”. Journal of Philosophy 52, 709–22. 1956a. “Definition and Dogma”. Pennsylvania Literary Review 6, 9–14. Reprinted PP, 49–55. 1956b. “The Revision of Philosophy”. In American Philosophers at Work, S. Hook (ed.), 75–92. New York: Criterion. Reprinted PP, 5–23.
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Bibliography 1956c. “A Study of Methods of Evaluating Information Processing Systems of Weapons Systems”. University of Pennsylvania: The Institute for Cooperative Research. Project Wescom DA36-039 SC 63143. 1956d. “A World of Individuals”. In The Problem of Universals: A Symposium, J. M. Bocheński, A. Church & N. Goodman (eds), 13–31. Notre Dame, IN: University of Notre Dame Press. Reprinted PP, 155–72. 1957a. “Review of ‘Reds, Greens, and Logical Analysis’ by Hilary Putnam”. Journal of Symbolic Logic 22 (1957): 318–19. 1957b. “Determination of Deficiencies in Information Processing”. University of Pennsylvania: The Institute for Cooperative Research. Project Wescom DA 36-039 SC 63143. 1957c. Letter to the Editor. Mind 66, 78. 1957d. “Parry on Counterfactuals”. Journal of Philosophy 54, 442–5. 1957e. “Reply to an Adverse Ally”. Journal of Philosophy 54, 531–3. Reprinted PP, 398–402. 1957f. “Review of ‘Replacement of Auxiliary Expressions’ by William Craig”. Journal of Symbolic Logic 22, 317–18. Reprinted PP, 322–4. 1958a. “On Relations that Generate”. Philosophical Studies 9, 65–6. Reprinted PP, 171–2. 1958b. “The Test of Simplicity”. Science 128, 1064–9. Reprinted PP, 279–94. 1958c. “Review of Philosophical Analysis, by J. O. Urmson”. Mind 67, 107–9. Reprinted PP, 41–4. 1959. “Recent Developments in the Theory of Simplicity”. Philosophy and Phenomenological Research 19, 429–46. Reprinted PP, 295–318. 1960a. “The Way the World Is”. Review of Metaphysics 14, 48–56. Reprinted PP, 24–32. 1960b. “Positionality and Pictures”. Philosophical Review 69, 523–5. Reprinted in Elgin (1997c: 71–3) and PP, 402–4. 1960c. “Review of Art and Illusion, by Ernst H. Gombrich”. Journal of Philosophy 57, 595–9. Reprinted PP, 141–6. 1961a. “About”. Mind 70, 1–24. Reprinted PP, 246–72. 1961b. “Condensation versus Simplification”. Theoria 27, 47–8. Reprinted PP, 319– 21. 1961c. “Graphs for Linguistics”. Proceedings of Symposia in Applied Mathematics. American Mathematical Society 12, 52–5. 1961d. “Safety, Strength, Simplicity”. Philosophy of Science 28, 150–51. Reprinted PP, 334–6. 1962. “Review of Berkeley’s Theory of Vision, by David M. Armstrong”. Philosophy and Phenomenological Research 23, 284–5. Reprinted PP, 80–81. 1963a. “Faulty Formalization”. Journal of Philosophy 50, 578–9. Reprinted PP, 404– 5. 1963b. “Science and Simplicity”. Voice of America Philosophy of Science Series 16. Reprinted PP, 337–46. 1963c. “The Significance of Der logische Aufbau der Welt”. In The Philosophy of Rudolf Carnap, P. A. Schilpp (ed.), 545–58. La Salle, IL: Open Court. 1965. “‘About’ Mistaken”. Mind 74, 248. Reprinted PP, 273. 1966a. “Merit as Means”. In Art and Philosophy, S. Hook (ed.), 56–7. New York: New York University Press. Reprinted PP, 120–21. 1966b. “Three Replies”, consisting of “Foreword” and “Comments”. Journal of Philosophy 63, 328–31. Reprinted PP, 405–10. 1967a. “The Epistemological Argument”. Synthese 17, 23–8. Reprinted PP, 69–75. 1967b. “Two Replies”. Journal of Philosophy 64, 286–7. Reprinted PP, 410–12. 1967c. “Uniformity and Simplicity”, 75th Anniversary Lecture (1963), Geological Society of America. GSA Special Paper 89, 93–9. Reprinted PP, 347–54. 1968a. “Art and Inquiry”, Presidential Address. In Proceedings and Addresses of the
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Nelson Goodman American Philosophical Association, Eastern Division. XLI (October 1968), 5–19. Reprinted PP, 103–19. 1968b. “Reality Remade”. L’Age de la Science 1, 19–40. 1969a. “The Emperor’s New Ideas”. In Language and Philosophy, S. Hook (ed.), 138– 42. New York: New York University Press. Reprinted PP, 76–9. 1969b. “Memorial Note” (on Henry Leonard). In The Logical Way of Doing Things, K. Lambert (ed.), ix–x. New Haven, CT: Yale University Press. 1969c. “A Revision in the Structure of Appearance”. Journal of Philosophy 66, 383–5. Reprinted PP, 199–200. 1969d. “Misinterpretation”. Science 164, 1343. Reprinted PP, 140. 1970a. “Some Notes on Languages of Art”. Journal of Philosophy 67, 563–73. Reprinted PP, 122–32 and (in part) in Elgin 1997d (reply to Boretz). 1970b. (with Robert Schwartz and Israel Scheffler) “An Improvement in the Theory of Projectibility”. Journal of Philosophy 67, 605–8. Reprinted PP, 389–93. 1970c. (with Howard Gardner) “The Randolph Museum Case”. Prepared for the Institute in Arts Administration, Harvard University. 1970d. “Seven Strictures on Similarity”. In Experience and Theory, L. Foster & J. W. Swanson (eds), 19–29. Amherst, MA: University of Massachusetts Press. Reprinted PP, 437–46. 1971. “On J. J. Gibson’s New Perspective”. Leonardo 4, 359–60. Reprinted (with changes) MM, I, ch. 3. 1972a. “Art and Understanding: The Need for a Less Simple-Minded Approach”. Music Educators Journal 58(5) (Feb), 43–5, 85–8. 1972b. (with Israel Scheffler) “Selective Confirmations and the Ravens: A Reply to Foster”. Journal of Philosophy 69, 78–83. 1972c. “On Kahane’s Confusions”. Journal of Philosophy 69, 83–4. 1973. “‘That is’: A Reply to Isaac Newton Nozick”. Journal of Philosophy 70, 166. Reprinted in Elgin (1997d: 110) and (with changes) MM, IV, ch. 7. 1974a. “Much Ado”. Synthese 28, 259. 1974b. “Some Questions Concerning Quotation”. The Monist 58, 294–306. Reprinted WW, 41–56. 1974c. “On Reconceiving Cognition”. The Monist 58, Supplement: Symposium on Skills and Symbols in the Arts, 339–42. Reprinted (with changes) MM, I, ch. 4. 1975a. “The Status of Style”. Critical Inquiry 1, 799–811. Reprinted WW, 23–40. 1975b. “Words, Works, Worlds”. Erkenntnis 9, 57–73. Reprinted WW, 1–22. 1975c. “A Message from Mars”. The Arts Spectrum 2, 4. Reprinted (with changes) MM, V, ch. 3. 1975d. (with Joseph Ullian) “Bad Company: A Reply to Mr. Zabludowski and Others”. Journal of Philosophy 72, 142–5. 1977a. “The Trouble with Root”. Linguistics and Philosophy 1, 277–8. 1977b. “Predicates without Properties”. Midwest Studies in Philosophy 2, 212–13. Reprinted (with changes) MM, II, ch. 4. 1977c. (with Joseph Ullian) “Truth about Jones”. Journal of Philosophy 74, 317–38. Reprinted in Elgin (1997e: 197–218) and (with changes) MM, III, ch. 7. 1977d. “When Is Art?” In The Arts and Cognition, D. Perkins & B. Leondar (eds), 11–19. Baltimore, MD: Johns Hopkins University Press. Reprinted WW, 57–70. 1978a. (with Joseph Ullian) “The Short of It”. Journal of Philosophy 75, 263–4. 1978b. “Comments on Wollheim’s Paper: ‘Are the Criteria of Identity that Hold for a Work of Art in the Different Arts Aesthetically Relevant?’”. Ratio 20, 49–51. Reprinted in Elgin (1997d: 93–5) and (with changes) MM, IV, ch. 8. 1978c. “In Defense of Irrealism (Letter to the Editor)”. New York Review of Books 25(20), 58. 1978d. “Review of Remarks on Color, by Ludwig Wittgenstein”. Journal of Philosophy 75, 503–4. 1978e. “Replies”. Erkenntnis 12, The Philosophy of Nelson Goodman Part I, 153–79.
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Bibliography Reprinted in Elgin (1997d: 93–5) (reply to Beardsley) and Elgin (1997e: 152–4) (reply to Eberle) and (with changes) MM, I, chs 2–3; III, chs 3–6. 1978f. “Replies”. Erkenntnis 12, The Philosophy of Nelson Goodman Part II, 281–91. Reprinted (in part and with changes) in Elgin (1997b: 95–8) and MM, II, ch. 3. 1979a. “On Matter over Mind (Letter to the Editor)”. New York Review of Books 26(8), 42. 1979b. “Metaphor as Moonlighting”. Critical Inquiry 6, 125–30. Reprinted in Elgin (1997e: 53–8) and (with changes) MM, III, ch. 2. 1979c. “J. J. Gibson’s Approach to the Visual Perception of Pictures”. Leonardo 12, 175. 1979d. “Credence, Credibility, Comprehension”. Journal of Philosophy 76, Symposium: Goodman’s Ways of Worldmaking, 619. 1980a. “Twisted Tales – or, Story, Study, and Symphony”. Critical Inquiry 7, 103–19. Reprinted (with changes) MM, IV, ch. 1. 1980b. “On Starmaking”. Synthese 46, 211–16. Reprinted (with changes) MM, II, ch. 2. 1980c. “Science and Sin”. Communication & Cognition 13 (1980), 169–72. Reprinted (with changes) MM, I, ch. 1. 1981a. “The Telling and the Told”. Critical Inquiry 7, 799–801. Reprinted (with changes) MM, IV, ch. 2. 1981b. “Perspective as a Convention – on the Views of Goodman and Gombrich”. Leonardo 14, 86. 1981c. “Routes of Reference”. Critical Inquiry 8, 121–32. Reprinted (with changes) MM, III, ch. 1. 1981d. “Ways of Worldmaking”. Leonardo 14, 351. 1981e. “Replies”. Journal of Aesthetics and Art Criticism 39, Aesthetics and Worldmaking: An Exchange with Nelson Goodman, 273–80. Reprinted (with changes) MM, I, chs 2 & 5; III, chs 4 & 5; IV, chs 4 & 6. 1982a. “The Fabrication of Facts”. In Relativism: Cognitive and Moral, J. W. Meiland & M. Krausz (eds), 18–29. Notre Dame, IN: University of Notre Dame Press. 1982b. “Implementation of the Arts”. Journal of Aesthetics and Art Criticism 40, 281–3. Reprinted (with changes) MM, IV, ch. 9. 1982c. “On Thoughts without Words”. Cognition: International Journal of Cognitive Psychology 12, 211–17. Reprinted (with changes) MM, I, ch. 6. 1982d. “Fiction for Five Fingers”. Philosophy and Literature 6(1–2), 162–4. Reprinted (with changes) MM, IV, ch. 3. 1982e. “Notes on the Well-Made World”. In Language and Ontology, W. Leinfellner, E. Kraemer & J. Schank (eds), 31–6. Vienna: Holder-Pichler-Tempsky. Reprinted (with changes) MM, II, ch. 1. 1983a. “Realism, Relativism, and Reality”. New Literary History 14, 269–72. Reprinted (with changes) MM, IV, ch. 5. 1983b. “Semiotische Ästhetik und pragmatischer Irrealismus”. Zeitschrift für Semiotik 5, 256–7. 1983c. “Modes of Symbolization” and “Afterword: An Illustration”. In What Is Dance?, R. Copeland & M. Cohen (eds), 66–85. Oxford: Oxford University Press. Reprinted (in part and with changes) MM, III, ch. 1. 1983d. “The Role of Notations”. In What Is Dance?, R. Copeland & M. Cohen (eds), 399–410. Oxford: Oxford University Press. 1983e. “Notes on the Well-Made World”. Erkenntnis 19, 99–108. 1983f. (with Menachem Brinker) “Yitzog v’ realizem b’omanut [Representation and Realism in Art]”. Iyyun 32, 216–22 [in Hebrew]. 1983g. “Notes from the Underground”. Art Education 36, 34–41. Reprinted MM, V, ch. 1. 1983h. “Art and Ideas”. In Past, Present, East and West, S. Lee, 17–18. New York: George Braziller. Reprinted (with changes) MM, V, ch. 4.
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Nelson Goodman 1983–84. “The End of the Museum”. The New Criterion 2, 9–14. Reprinted (with changes) MM, V, ch. 5. 1984a. “Implementation of the Arts”. Communication and Cognition 17, 11–14. 1984b. “Relativism Awry: Response to Feyerabend”. New Ideas in Psychology 2, 125. 1985a. “Statement and Pictures”. Erkenntnis 22 , 265–70. 1985b. “How Buildings Mean”. Critical Inquiry 11, 642–53. Reprinted RP, ch. II. 1985c. “The End of the Museum?”. Journal of Aesthetic Education 19(2), 53–62. Reprinted MM, pt V, ch. 5. 1986a. (with Catherine Z. Elgin) “Interpretation and Identity: Can the Work Survive the World?”. Critical Inquiry 12, 564–75. Reprinted RP, ch. III. 1986b. “A Note on Copies”. Journal of Aesthetics and Art Criticism 44, 291–2. 1986c. “Nominalisms”. In The Philosophy of W.V. Quine, L. E. Hahn & P. A. Schilpp (eds), 159–61. La Salle, IL: Open Court. 1986d. “The Nature and Function Of Architecture”. Domus 672, 17–28. 1987a. (with Catherine Z. Elgin) “Changing the Subject”. Journal of Aesthetics and Art Criticism 46, 219–23. 1987b. “Variations on Variation – or Picasso Back to Bach”. Acta Philosophica Fennica 43, Essays in the Philosophy of Music, V. Rantala, L. Rowell & E. Tarasti (eds), 167–78. Reprinted RP, ch. IV. 1988a. “On Some Worldly Worries” (reply to Scheffler). Published by the author, 1 September 1988. Cambridge, MA: Emerson Hall, Harvard University. 1988b. “Introduction, ‘Aims and Claims’”. Journal of Aesthetic Education 22(1), 1–2. 1988c. “On What Should Not Be Said about Representation”. Journal of Aesthetics and Art Criticism 46, 419. 1989a. “Just the Facts, Ma’am!”. In Relativism: Interpretation and Confrontation, M. Krausz (ed.), 80–85. Notre Dame, IN: University of Notre Dame Press. Reprinted RP, ch. VI. 1989b. (with Catherine Elgin) “Savoir et Faire”, J. Riche (trans.). In Encyclopedie Philosophique Universelle 1: L’Univers Philosophique, A. Jacob (ed.), 520–28. Paris: Presse Universitaire de France. Reprinted RP, ch. I. 1990. “Pictures in the Mind?”. In Images and Understanding, H. B. Barlow, C. Blakemore & M. Weston-Smith (eds), 358–64. Cambridge: Cambridge University Press. Reprinted RP, ch, V. 1991a. “On Capturing Cities”. Journal of Aesthetic Education 25, More Ways of Worldmaking, 5–9. 1991b. “Retrospections”. Journal of Aesthetic Education 25, More Ways of Worldmaking, 97–8. 1992. “Contraverting A Contradiction, A Note On Metaphor And Simile, Reply To Kulka, Tomas”. Poetics Today 13(4), 807–8. 1993a. “Status and System: from the 1st Part of the Author’s Doctoral Thesis A Study Of Qualities”. Revue Internationale de Philosophie 47(185), 99–139. 1993b. “On Some Worldly Worries”. Synthese 95(1), Probing into Reconceptions, 9–12. 1994. (with T. Kulka) “How Metaphor Works its Wonders”. Filosoficky Casopis 42(3), 403–20 [in Czech]. 1988. “Eine Neukonzeption der Philosophie”, L. Schmeiser (trans.). In Bewusstsein, Sprache und die Kunst: Metarmorphosen der Wahrheit, M. Benedikt (ed.), 107–114. Vienna: Edition S. Reprinted RP: ch. X. 1996a. “Authenticity”. In The Dictionary of Art, J. S. Turner (ed.), 834–5. London: Macmillan. 1996b. “On Some Worldly Worries”. In Starmaking: Realism, Anti-Realism, and Irrealism, P. J. McCormick (ed.), 165–8. Cambridge, MA: MIT Press. 1996c. “Comments”. In Starmaking: Realism, Anti-Realism, and Irrealism, P. J. McCormick (ed.), 203–13. Cambridge, MA: MIT Press. 1997. “Some Reflections on my Philosophy”. Philosophia Scientiae 2, Actes du Colloque Nelson Goodman 1997, “Manières de faire les mondes”, 15–20.
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Bibliography Miscellaneous Script for Hockey Seen: multimedia production (choreography by Martha Armstrong Gray; electronic score by John Adams). Script for Rabbit, Run: dance version of John Updike’s novel (choreography by Martha Armstrong Gray; score by Joel Kabakov). Conceptual design for Variations: An Illustrated Lecture Concert: including live or taped performance of David Alpher’s “Las Meninas” Theme and Variations for piano, guitar, oboe and cello, synchronized with presentation of slides of Las Meninas by Velazquez and of Picasso’s painted variations on it.
References and further reading Abel, G. [1977] 1997. “Logic, Art, and Understanding in the Philosophy of Nelson Goodman”. See Elgin (1997b), 1–11. Ayer, A. J. 1956. The Problem of Knowledge. New York: St Martin’s Press. Andréka, H., J. X. Madarász & I. Németi forthcoming. “Logical Axiomatizations of Space-Time: Samples from the Literature”. In Non-Euclidean Geometries, A. Prekopa & E. Molnár (eds). Dordrecht: Kluwer [preprint available at: www.math-inst. hu/pub/algebraic-logic/Contents.html]. Armstrong, D. M. 1978a. Universals and Scientific Realism. Volume I: Nominalism & Realism. Cambridge: Cambridge University Press. Armstrong, D. M. 1978b. Universals and Scientific Realism. Volume II: A Theory of Universals. Cambridge: Cambridge University Press. Armstrong, D. M. 1989. Universals: An Opinionated Introduction. Boulder, CO: Westview. Armstrong, D. M. 1997. A World of States of Affairs. Cambridge: Cambridge University Press. Balaguer, M. 1998. Platonism and Anti-Platonism in Mathematics. Oxford: Oxford University Press. Beckermann, A. 2001. Analytische Einführung in die Philosophie des Geistes, 2nd edn. Berlin: DeGruyter. Benacerraf, P. & H. Putnam 1964. Philosophy of Mathematics: Selected Readings. 1st edn. Englewood Cliffs, NJ: Prentice-Hall. Berka, S. 1991. “An International Bibliography of Works by and Selected Works about Nelson Goodman”. Journal of Aesthetic Education 25(1), More Ways of Worldmaking, 99–112. Bieri, P. & O. R. Scholz 1993. “Probing into ‘Reconceptions’”. Synthese 95, 1. Bishop, M. A. & J. D. Trout 2005. Epistemology and the Psychology of Human Judgment. Oxford: Oxford University Press. Black, M. 1962. Models and Metaphors: Studies in Language and Philosophy. Ithaca, NY: Cornell University Press. Bocheński, J. M. 1989. “The Cracow Circle”. In The Vienna Circle and the Lvov-Warsaw School, K. Szaniawski (ed.), 9–18. Dordrecht: Kluwer. Boolos, G. 1984. “To Be is To Be the Value of a Variable (Or Some Values of some Variables)”. Journal of Philosophy 81, 430–49. Reprinted in Boolos (1998), 54–72. Boolos, G. 1985. “Nominalist Platonism”. Philosophical Review 94, 327–44. Reprinted in Boolos (1998), 73–87. Boolos, G. 1998. Logic, Logic, and Logic, R. Jeffrey (ed.). Cambridge, MA: Harvard University Press. Borges, J. L. 1962. “Pierre Menard: Author of the Quixote”. In Labyrinths: Selected Stories and Other Writings, 36–44. New York: New Directions.
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Nelson Goodman Bremer, M. 2005. Einfachheit [www.mbph.homepage.t-online.de/einfachheit.pdf]. Burgess, J. 1983. “Why I Am Not a Nominalist”. Notre Dame Journal of Formal Logic 24, 93–105. Burgess, J. & G. Rosen 1997. A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. Oxford: Clarendon Press. Carnap, R. 1922. Der Raum: Ein Beitrag zur Wissenschaftslehre. Berlin: Reuther & Richard. Carnap, R. 1923a. “Über die Aufgabe der Physik und die Anwendung des Grundsatzes der Einfachstheit”. Kant-Studien 28, 90–107. Carnap, R. 1923b. “Die Quasizerlegung: Ein Verfahren zur Ordnung nichthomogener Mengen mit den Mitteln der Beziehungslehre”. Unpublished manuscript RC-08104-01, University of Pittsburgh. Carnap, R. 1932a. “Die physikalische Sprache als Universalsprache der Wissenschaft”. Erkenntnis 2, 432–65. Revised edition published in English as The Unity of Science, M. Black (trans.) (London: Kegan Paul, Trench, Truebner, 1934). Carnap, R. 1932b. “Über Protokollsätze”. Erkenntnis 3, 215–28. Published in English as “On Protocol Sentences”, R. Creath & R. Nollan (trans.), Noûs 21 (1987), 457–70. Carnap, R. 1935. Philosophy and Logical Syntax. London: Kegan Paul. Carnap, R. [1934] 1937. The Logical Syntax of Language. London: Routledge & Kegan Paul. Carnap, R. 1945a. “On Inductive Logic”. Philosophy of Science 12, 72–97. Carnap, R. 1945b. “The Two Concepts of Probability”. Philosophy and Phenomenological Research 5, 513–32. Carnap, R. [1939] 1949. “Wahrheit und Bewährung”. In Readings in Philosophical Analysis. H. Feigl, & W. Sellars (eds), 119–27. New York: Appleton-CenturyCrofts. Carnap, R. 1950. “Empiricism, Semantics, and Ontology”. Revue internationale de philosophie 4e année, no 11, 20–40. Carnap, R. [1950] 1956. Meaning and Necessity: A Study in Semantics and Modal Logic, 2nd edn. Chicago, IL: University of Chicago Press. Carnap, R. [1928] 1961. Der logische Aufbau der Welt: Scheinprobleme in der Philosophie. Hamburg: Meiner. Carnap, R. 1963. “Intellectual Autobiography”. See Schilpp (1963), 3–84. Carnap, R. 1967. Logical Foundations of Probability. Chicago, IL: University of Chicago Press. Carnap, R. [1947] 1997. “On the Applications of Inductive Logic”. See Elgin (1997a), 1–15. Carter, C. L. 2000. “A Tribute to Nelson Goodman”. Journal of Aesthetics and Art Criticism 58, Symposium: The Legacy of Nelson Goodman, 251–3. Casati, R. & A. C. Varzi 1999. Parts and Places: The Structures of Spatial Representation. Cambridge, MA: MIT Press. Cassirer, E. 1955. The Philosophy of Symbolic Forms. Volume One: Language. New Haven, CT: Yale University Press. Chihara, C. 1990. Constructibility and Mathematical Existence. Oxford: Oxford University Press. Cirera, R. 1994. Carnap and the Vienna Circle: Empiricism and Logical Syntax. Amsterdam: Rodopi. Coffa, A. 1977. “Carnap’s Sprachanschauung Circa 1932”. In Proceedings of the 1976 Biennial Meeting of the Philosophy of Science Association, vol. 2, F. Suppes & P. D. Asquith, 205–41. East Lansing: MI: Philosophy of Science Association. Coffa, A. 1991. The Semantic Tradition from Kant to Carnap: To the Vienna Station. Cambridge: Cambridge University Press. Cohnitz, D. 2005a. “Why Consistentism Won’t Work”. In Modal Epistemology, E. Weber & T. De Mey (eds), 33–51. Brussels: Contactforum.
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Index
a priori 19, 25, 30–31, 78, 244 n.1 synthetic a priori 19, 243 n.18 A Study of Qualities 3–8, 16, 76, 86–9, 91, 99, 113–16, 120–25, 130–31, 136–9, 191, 198–9, 230, 232, 234, 238 Abel, G. 250 n.1 absolutism 12–13, 19, 166, 170, 191, 199, 217 abstractum see object, abstract accent 84–5 actor 74–5 Adams, D. 154 Adams, J. 9 adoption 33, 66, 135, 187, 212 aesthetic 4, 6, 175, 204 difference 178–9 experience 164 symptoms of 187–90 algebra 21, 57, 61 allographic see art, allographic Alpher, D. 9, 241 n.8 alternative denial see Sheffer stroke ambiguity 60–61, 143–4, 253 n.26 of characters 155, 156–8, 182, 185, 189 analytic philosophy see philosophy, analytic analyticity 19, 42–3, 66–7, 70, 73–4, 237, 246 n.14 Andréka, H. 249 n.19 animals 10, 64, 81–2, 145, 157 anti-realism 218 anti-foundationalism 4, 22, 99, 120, 191 anti-scientific attitude 12 anti-systematicity 15 Antoinett, M. 142
arbitrariness 53, 105, 124, 192, 199, 203, 214, 217 architecture 168–9, 177 argument deductive 29, 35–8, 192, 245 n.5 inductive 33–4, 39–40, 43, 192, 245 n.5 Aristotle 17, 19, 36, 70 arithmetic 57, 104, 112, 243 n.18 Armstrong Gray, M. 9 Armstrong, D. 77, 79 art 1–2, 4–9, 24, 54–6, 66, 140–41, 145, 150, 161, 164–90, 192, 198, 240 n.4 allographic 180–81 appreciation of 6–7, 164 autographic 180–81 Goodman’s collection of 7 history of 6 one-stage/two-stage 180–81 presentation of 6 art gallery 6, 7, 172, 178, 188, 240 n.4 articulateness see finite differentiation asterism 259 n.6 atom, of a system 87–9, 95, 97, 106, 118–20, 131–7, 218, 222–6, 230, 248 n.15, 249 nn.26 & 28, 260 n.16 attenuation 188 Aufbau (Carnap) 4, 6–8, 18, 21, 100, 102–13, 116, 120, 130, 132, 135, 137–9, 198–9, 250–55 Austin, J. L. 233 autographic see art, autographic Awodey, S. 242 n.15 axiom 85, 230, 259 n.1 Ayer, A. J. 32 Bach, J. S. 56, 175, 258 n.18
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Nelson Goodman Balaguer, M. 248 n.19 ballet 84; see also dance Baltimore 7, 241 n.5, 254 n.35 basic relation 105–6, 118–20, 131–2, 135, 232 basis 86–7, 90, 96, 104–6, 111–14, 118, 124–9, 136, 138, 165, 221, 225, 230, 231, 247 n.8, 251 n.15 Beethoven, L. van 156, 179, 180, 182–3, 258 n.18 Benesh, J. and R. 258 n.21 Bergson, H. 12–13, 242 n.11 Berka, S. 262 Berkeley, G. 6 bicomplex of qualia 133–4 Big Dipper 212–15, 259 n.6 Bishop, M. A. 115 Black, M. 148 bleen 43, 63, 205, 207, 210 definition of 43 blue, definition of 43 Bocheński, J. M. 89, 248 n.16 Boolos, G. 220 Borges, J. L. 258 n.19 boundary conditions 46–7 Brandeis University 8 Bremer, M. 211, 259 n.3 Burgess, John 90, 223, 225, 238 burning 50–51 book 48–9 match 45–7 score 180 Cage, J. 182–3, 258 n.17 score 183 calculus of classes 92, 122–5, 130–31, 136–7, 230 calculus of individuals 3–4, 8, 21, 76, 92–8, 121–4, 125, 130–37, 218, 230, 238, 248 n.14, 249 n.23, 250 n.3, 254 n.35 calculus of simplicity 128–30, 211 calculus of singular term 123 Cantor, G. 224, 226, 234, 260 n.18 cardiogram 159, 161, 188 caricature 144 Carnap, R. 4–8, 14, 17–32, 26, 40, 43, 60, 99–126, 130, 191, 198–200, 232, 238, 241–6, 250–55 Carter, C. L. 7–9, 11 Casati, R. 249 n.28 Cassirer, E. 244 n.26 category of qualia 119, 132 causal relations 30–31, 49, 78 causal theory of expression see expression, causal theory of
278
centaur 72, 143–4 certainty 65–6 Cervantes, M. de 258 n.19 character 85, 151–61, 181, 184–5, 256 nn.13–14 character indifference 151–2, 156–7, 240 n.4 chess 160–62, 256 n.17 Chihara, C. 248 n.9 Chopin, F. 184 Church, A. 67, 69, 248 n.16 Churchill, W. 143–4, 146 circularity see vicious circle Cirera, R. 110 clairvoyance 34 clarity 3, 13, 17, 22, 61, 62, 74, 89, 91, 93, 177, 231, 244 n.26, 253 n.26 class 81–93, 97–8, 112, 114, 122–5, 130–37, 137, 143, 218–26, 230 abstractive 23, 243 n.25 proper 222–4, 230 coextensionality 51, 62–6, 230 of definitions 63–6 Coffa, A. 110, 113, 238, 252 n.24 Cohns, C. 161 cointensionality 230, 235 companionship difficulty 117, 130, 136, 192, 253 nn.28–9 complex of qualia 133–7 complexity value of predicates 127–8, 136–7 compliance-class 155–60, 181, 185–6 compliant 155–7, 181, 184–6 composition mereological 88, 96, 219; see also sum suprematist 144 unrestricted 96, 219, 260 n.13 compositionality 68–9, 246 n.4 concatenation 85 conceivability 71–2 conceptual analysis 62, 67, 115 conclusion 35–7, 230 concretum see object, concrete conditional counterfactual 41, 45–9, 53, 231, 246 n.16 material 45–6, 229, 232 constant, logical 39, 121, 230–31, 245 n.8 constellation 212–14, 259 n.6 constitutional system 18–19, 23, 102–8, 111–15, 136, 139, 231, 251 n.15 constructional system see constitutional system
Index constructionalism 2, 4, 16, 99, 120–21, 125, 191, 203, 215, 239, 242 n.10 content see sameness-of-content criterion convention 4, 13, 105, 111–12, 140, 146–7, 170, 175–7, 190, 212–18, 252 n.21, 255 n.5, 257 n.5 conventional system 111 Cooley, J. 7–8, 21 corroboration 34, 42, 44 counterfactual see conditional, counterfactual counterpart 49 Cracow Circle 248 n.16 creativity 62, 171 cubism 142 custom 31, 39, 147, 172, 176; see also habit, convention dance 174, 176, 186–7 Dance Center (Harvard) 8 Daniels, N. 244 n.3 Danto, A. C. 239, 258 n.19 David, J.-L. 142 de re/de dicto 30, 231, 244 n.1 deception 140, 171–2, 177 deduction, justification of 35–8 definiendum 58–60, 67, 69, 114, 231 definiens 231 definientia 231 definite description see description, definite definition 58–73, 231 accuracy of 114 adequacy of 58–62, 69–70 nominal 58–61, 231 real 58–60, 231 Deleuze, G. 12 demarcation criterion 104 Demuth, C. 239 denotation 65, 71, 141–63, 165, 172, 184, 257 n.10 pictorial see depiction density 153–61, 189, 198, 256 n.12 semantical 157–8 syntactical 153–4 throughout 153 depiction 65, 142–50, 165–7, 171–2, 188 Descartes, R. 87, 227 description 73, 144, 189 definite 95 structural 103–4 Dewey, J. 24 diagram 140–41, 146, 159–63, 188
Venn 160, 256 n.16 graphic 160, 188 difficulty of imperfect community 118, 130, 133–6, 192, 254 n.35, 255 n.39 discreteness 93–4, 125, 134–5, 229 disjointness 158, 159, 182–5, 229, 256 n.17 of characters in a notational scheme 152 of compliance classes 156 requirement for notations 157 disposition 45–50, 53, 64, 120, 138, 207, 255 n.4 Divers, J. 246 n.16 division problem 209–12 dogma 56–8, 112, 187 domain 23, 64, 220, 231, 250 n.8 Don Quixote 258 n.19 drama 176, 185–6 Dudau, R. 194 Dummett, M. 14, 203, 251 n.12 Eagles, The 156, 183 Earman, J. 33, 37–9, 246 n.11 Eberle, R. A. 237, 248 n.9, 252 n.18, 253 n.29, 255 n.3, 256 n.10 economy 93, 130, 211 Egan, F. J. 213, 215 Einstein, A. 19, 198, 248 n.19 Elementarerlebnis see erlebs elementary experience see erlebs Elgin, C. Z. 1, 4, 6–7, 10–11, 23, 65, 92–3, 120, 149, 164, 202–3, 226–7, 237–9, 241 n.9, 244 n.3, 258 nn.15 & 19, 260 n.19 eliminability 59 eliminativism 93 emerald 42, 51–3, 62, 205 Emin, T. 188 empirical analysis 60, 231 empty class 88, 231 empty set see empty class entrenchment 51–3, 66, 173, 176, 197, 199, 207, 210, 217 epistemic primacy 105 Epistemic Turn, Goodman’s, in the philosophy of art 4, 164 epistemology 1–3, 7, 12, 19, 24–6, 44–5, 50, 53, 99, 102, 121, 191 erleb 106–11, 114–20, 124, 135–8, 191, 231, 254 n.30 etching 174, 180–81 ex falsum quodlibet sequitur 46 exactness see explication, exactness exemplification 74, 145–9, 154, 158, 176–7, 187, 197–9
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Nelson Goodman metaphorical 147–9, 187 existence 18, 29, 55, 59, 75–82, 89, 102, 115, 193, 197–9, 213, 247 n.6, 250 n.29 explanation 42–3, 48–9, 77 explicandum 61–4, 177, 231 explication 3, 23, 26, 39, 40, 48, 52–3, 58, 61–5, 69–70, 74–5, 92, 114–15, 127, 131, 139, 144, 176–7, 184, 200–201, 231, 246 n.11, 253 n.26 exactness of 62, 184 fruitfulness 62–4, 184 simplicity 62 explicatum 61–4, 115, 177, 231 expression in art 174–7, 189, 204, 257 n.10, 258 n.13 causal theory of 174–5 extension 63–5, 71–4, 232 null-extension 72–3, 143–4, 232 primary 72–3, 255 n.3 secondary 73, 143, 232, 235, 255 n.3 extensional isomorphism 114–16, 253 n.29 extensional ordering of erlebs 108 extensionalism 71–4, 98, 145, 200, 253 n.29 extensive abstraction 6, 18, 101–2, 106, 147, 251 n.17 Fact, Fiction, and Forecast 10, 40, 45, 48, 53 fake see forgery falsifiability 129–30 familiarity 62, 93, 147, 171–3, 257 n.8; see also naturalness Farrell, R. 251 n.12 Feigl, H. 21 Feyerabend, P. 2, 44 Field, H. H. 90–91, 248 nn.9 & 18 film 9, 175, 185 Japanese 175 finite differentiation of a notation semantic 153–4, 179, 184, 187 syntactical (also articulateness) 157–8, 179, 182, 184–5, 187 finitism 84, 225 first-order logic see predicate logic first-order quantification see quantification, first-order forgery 177–81 formal mode 26 formation rule 83 formula 46, 83, 85 foundationalism 4, 15–17, 22, 99, 120, 123, 191; see also mathematics, foundation of
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Frege, G. 14, 17, 69, 79, 99, 100, 216, 232, 234, 242 n.15, 243 n.18, 250 nn.4 & 5 Fregean sense 69 Friedman, M. 250 n.8 fusion, mereological 221–2, 225–6, 260 n.13; see also sum, mereological gallery see art gallery gauge, pressure 158–9 gemmology 42 gemstone 42, 248 n.15 general statements accidentally true 47, 120 lawlike 41–4 generating relation 87–8, 95–7, 218–20, 225–6, 250 n.29, 259 n.9 geocentric system 195, 198 geometrical point see point, geometrical geometry 15, 21–5, 101, 106, 115, 168, 173, 216, 243 n.18, 251 n.17, 257 n.4 Euclidean 19 Gestalt-psychology 105–6 gesture 146 ghost 88 given, the (in experience) 24–6, 104, 111, 113, 120–21, 166, 196–8 Gödel numbering 257 n.7 Gödel, K. 21, 257 n.7 Goldfarb, W. 259 n.2 Gombrich, E. 175–6, 257 n.1 Goodman, E. (Woodbury) 5 Goodman, H. L. 5 Gosselin, M. 238 Goya, F. J. de 56, 174 graph 108, 117–18 Great Bear see Ursa Major Greaves, M. 256 n.16 green, definition of 43 green-sayer 205–6 grue 1, 3, 41–4, 51, 53, 62–3, 138, 192, 205–11 definition of 42 grue-speaker 215–16 Grünbaum, A. 251 n.17 Grünfeld Defence 161–2 Gsell, P. 170 gunk 218, 249 n.26 habit 31, 39, 52, 57, 66, 172–3; see also convention; custom Hahn, H. 251 n.15 Hahn, S. 244 n.3 Hale, B. 247 n.2
Index Hampe, M. 23–4, 243 n.22 Harvard University 5–11, 19, 21–4, 55, 67, 122, 239, 241 n.5, 242 n.11 Hazen, A. P. 223, 225 Heidegger, M. 14, 49, 55, 244 n.26 heliocentric system 195, 198 Hellman, G. 237, 238, 248 n.9, 250 n.2, 253 n.26 Hempel, C. G. 40, 193–4, 252 n.25, 253 n.6, 254 n.31 Herbrand, J. 21 Herodotus 195 higher-order logic see predicate logic, second-order Hirsch, E. 209–11 Hockey Seen 9, 267 Hocking, W. E. 5 Hokusai, K. 161, 188 homomorphism 114 Hullett, J. 44, 241 n.9 Hume, D. 29–34, 39–40, 43, 208, 246 n.11 Humphrey, D. 176 hypothesis exhausted 51 falsified 34, 51 nonprojectible, definition of 51 overridden 51, 62 projected 50–2 projectible 40–53 unprojectible 50–52 idea mental 71 Platonic 24, 71 ideal language see language, ideal idealism 5–6, 105, 212, 218, 259 n.7 identity of classes 81, 234 identity criteria for works of art 156, 177–80 defined mereologically 94 imaginability 71 Immersion, J. 175, 257 n.9 inaccessible set 224–5, 260 nn.16 & 20 incorrigibility of the given in experience 121 independence, logical 77, 79, 84, 158, 199, 232 indispensability, of mathematics 85, 89–90, 248 n.17 individual 64, 86–98, 106–10, 118–19, 121–5, 130–38, 143, 193, 221–3, 227, 230, 232, 257–60, 253 n.29, 260 n.13–14
indubitability of the given in experience 25–6, 121 induction 3–4, 28–53, 54, 58, 62–4, 72, 173, 192, 204–8, 237 Hume’s problem of 29–34 new riddle of 40–45 ordinary language justification of 32 pragmatic justification of 39 validation of 33 vindication of 33 ineffability of experience 103 inference rules see rules of inference infinity 18, 31, 42, 84, 88, 101, 114, 115, 152–3, 182, 221–5, 234–5, 257 n.9, 260 n.17 information 36, 78, 103–8, 116, 140, 163, 172–3, 185, 257 n.8 inner part see part innocent eye 165–7, 175 inscription 84–5, 149, 151–61, 180–85, 248 n.9, 256 nn.8, 11, 13 & 14 instantiation of properties 79–80, 145, 152, 253 n.29; see also possession Institute for Arts Administration (Harvard) 8 intension 69, 71–5, 86, 109, 114, 122, 145, 200, 210, 232, 248 n.12, 253 n.29 intertranslatability of scientific theories 20, 193, 252 n.25 intuition 13, 35, 37, 39, 212, 245 n.4, 246 n.11 Inwagen, P. van 249 nn.26 & 28 irrationalism 2, 12, 191, 197, 203, 240 n.1 irrationality 112, 209–11; see also irrationalism irrealism 191, 194, 212, 218, 239, 259 n.7 irreflexivity 128, 132, 134, 232 isomorphism 232; see also extensional isomorphism James, W. 24 Johnstone, P. T. 250 n.6 Kabakov, J. 18, 267 Kant, I. 19, 166, 233, 243 nn.17–18, 245 n.4 Katz, J. J. 245 n.9 Kemp, M. 168 kind artificial 214 natural 211, 214 Kirsch, A. 256 n.16 Klee, P. 168
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Nelson Goodman Klein, C. 242 n.15 Kleinknecht, R. 249 n.28, 251 n.17, 252 n.8, 253 n.29, 255 n.39 knowledge 12–18, 20–30, 62, 65–6, 78, 93, 101–5, 110–13, 115, 120–21, 146, 165, 171, 175, 186 causal theory of 78 Kornblith, H. 115 Kripke, S. 206–8, 259 n.1–2 Küng, G. 197 Künne, W. 200–203 Laban, Rudolf 186–7, 258 n.21 Labanotation 186–7, 258 n.21 label 145–9, 171, 173, 178, 187, 214 Langford, C. H. 67–9 language formal 17, 83–5, 198 ideal 3, 17, 20 ordinary, natural 15, 20, 23, 64, 210, 233–4 spoken 150, 186, 255 n.6 vocabulary of 83, 85, 132, 155, 185, 193, 211 Languages of Art 4, 140, 164, 244 n.26, 257 n.1 Las Meninas 9, 267 law of nature or physics 29, 61, 77, 90, 120, 126, 166, 170, 235 lawlikeness 41, 43–5, 52, 126, 208, 233 Lawlor, L. 242 n.11 Lee, J. 262 Leitgeb, H. 251 n.17, 253 n.28, 253 n.29, 254 n.30, 255 n.39 Leonard, H. S. 3, 6–8, 21–4, 92–3, 122–5, 130–31, 138, 218, 227, 230, 238, 241 nn.5 & 7, 248 n.14, 249 nn.22–3, 250 n.3, 254 n.35 Leonardo da Vinci 142, 168, 174, 178, 257 n.4 Leśniewski, S. 8, 22–3, 92–3, 233, 241 n.5, 243 n.24, 248 n.16, 249 n.22, 254 n.35 Lewis, C. I. 5–6, 21, 24–6, 121, 241 n.7 Lewis, D. 97, 218–26, 246 n.16, 248 n.15, 249 nn.26–7, 259 nn.8 & 10, 260 nn.12–16 & 19–20 liars 227 likeness of meaning see meaning, likeness of limitation of size 223 logic 1–2, 4–7, 16–26, 29, 31, 35–41, 67, 71, 78, 81–3, 102, 111, 122–4, 129, 160, 192, 204, 218–19, 243 n.18, 244 n.26, 244 n.3, 245 nn.5–7,
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246 nn.12, 13 & 15, 247 n.8, 259 n.1; see also predicate logic modal logic 24 term logic 92 logical constants see constants, logical logical empiricism 17, 20–21, 26, 44, 60, 66, 110–11, 244 n.26 logical independence see indepencence logical positivism see logical empiricism logical truth see truth, logical logicism 17, 100–1, 243 n.18 Lovejoy, A. 241 n.5 Łukasiewicz, J. 248 n.16 Mach, E. 105 Madarász, J. X. 248 n.19 Maddy, P. 247 n.4 Malament, D. 248 n.19 Malevich, K. 144 mark 83–4, 86, 149–55, 189, 256 nn.8 & 11 Martin, R. M. 260 n.14 Martin-Löf, P. 236 material conditional see conditional mathematical truth see truth, mathematical mathematics 5, 17, 19–21, 24, 26, 29, 79, 80, 83, 89–91, 100–2, 123, 159, 160, 173, 200, 224–6, 243 n.21, 258 n.12, 260 n.20 foundations of 17, 90, 173, 233, 235; see also logicism philosophy of 19, 75, 238, 244 n.26, 247 n.4, 248 n.17 McCormick, P. J. 193, 115, 239 McKinsey, J. C. C. 6 meaning 54–5, 59–75, 83, 112, 115, 140, 143, 145, 217, 232, 259 n.2 likeness of 71–3, 143, 145 sameness of see synonymy meaning analysis 23, 60–62, 66–7, 69, 231 Meegeren, H. van 179 megethology 219, 223, 225, 259 n.8 member 81–2, 87–8, 100–1, 117, 130, 181, 184, 205, 221–6, 229, 232–3, 247 nn.4 & 8, 260 n.13 membership see member membership relation, ancestral of 218–19, 225, 259 n.9 Menard, Pierre 258 n.19 mereological composition see composition mereological sum see sum mereology 8, 22–3, 82, 88, 92–8, 136–7,
Index 218–26, 233, 241 n.5, 243 nn.23–4, 249 nn.22–3 & 26, 254 n.35; see also calculus of individuals non-extensional 97, 219, 250 n.29 meta-induction 33 metaphor 147–9, 171, 176–7, 244 n.26, 248 n.10 effectivity of 149 fading 147 metaphysics 1, 15, 20, 22, 75, 99, 101, 112, 122, 191–203, 204, 212–18 metatheory 38, 94, 114, 216, 233 methodology 2, 18, 33, 92, 99, 126, 251 n.15, 254 n.30 middle level of a constitutional system 109 Mitchell, W. J. T. 9 modal logic see logic, modal modality 45, 49, 53, 246 n.16, 248 n.9, 254 n.31 model theory 38–9, 233, 245 nn.6–7 modern logic 19, 21–2, 36, 61, 92; see also logic and predicate logic modus ponens 35, 38, 232 modus tollens 34, 38, 233 Molnár, E. 248 n.19 Mondrian, P. 175 monism 138, 192–6 monistic reductionism 194 Mormann, T. 104, 106, 110, 250 nn.6–8, 251 n.17, 252 nn.19–22, 254 n.30 Morris, C. 19, 244 n.26 Moulard, V. 242 n.11 museum 6, 7, 172, 184, 187 music 1, 9, 150–51, 156, 172, 174, 179–86, 189, 258 nn.16 & 20 mysticism 12–13 myth of the given see given, the naturalness 140 of predicates 173, 176 of representations 167, 170, 176 unnaturalness of nominalist systems 90 Naumann, R. 251 n.11, 252 n.23 necessity 31, 60; see also modality Németi, I. 248 n.19 neo-Kantianism 110–11, 233, 251 n.13 Neurath, O. 4, 113, 198, 252 n.24–5 Neurath’s ship 198 Newtonian gravitational theory 90, 248 n.19 nihilism 259 n.7 mereological 249 n.28 Nisbett, R. E. 36, 39, 245 n.5
Nolan, D. 246 n.16, 248 n.15 nomic 109, 233, 235 nominal definition see definition, nominal nominalism 3, 70, 75–98, 121–5, 130–31, 136–9, 151, 192, 199–200, 219–20, 232–4, 247–50, 256 nn.9–10, 258 n.12 nomological supervenience see supervenience, nomological normal viewing conditions 165–9, 172, 178 notation 140, 150–63, 179–87, 190, 255 n.6, 256 n.7 & 17, 257 n.7, 258 nn.20–21 for chess see chess for dance 186–7 for paintings 194–5 semantic condition for 155–8 syntactic condition for 151–4 novel see literature null individual 222, 260 n.14 null set 222; see also empty class null-extension see extension, null number as an entity 18, 75, 77, 79, 81, 84, 90–91, 104, 112, 147, 173, 243 n.18 object abstract 18, 69–70, 75, 77–87, 106–7, 112, 119, 125, 131, 137, 180, 247 nn.2 & 6, 248 n.13, 258 n.16 autopsychological 109–10 concrete 18, 48–9, 76–9, 83–7, 101–2, 118–9, 123–4, 137, 193, 216, 248 n.13 geometric 22–3, 101, 106 of second order 108 of third order 108 physical 79–80, 84, 86, 102, 109, 118–19, 137–8, 161, 179–80, 191, 247 n.4 psychological 109 quasi-object 107 observation report see protocol sentence Ockham, William of 76–7, 247 nn.1 & 3; see also Ockham’s razor Ockham’s razor 18, 76–7, 87, 89 Of Mind and Other Matters 86, 164, 202, 237, 238, 249 n.20 ontological commitment 112, 208 ontological parsimony see parsimony ontology 22, 24, 45, 75, 77, 85, 89, 96, 99, 101, 107, 112, 194, 208–9, 211; see also nominalism; platonism
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Nelson Goodman optics 166, 170 ordered pair 107, 132, 223, 229 ordinary language see language, ordinary Orenstein, A. 238, 249 n.17 original in art 7, 177–81, 185; see also forgery ostensive learnability 44 overlapping 4, 23, 93–5, 98, 102, 134, 229 painting 7, 9, 141, 160–61, 167–8, 172, 175, 177–80, 184–5, 186–9, 198, 257 n.6 Panofsky, E. 257 n.5 parsimony, ontological 76–7, 134, 197, 208–9; see also Ockham’s razor part 4, 82, 88, 94–9, 116–17, 123, 125, 134–5, 218–22, 229, 254 n.35 inner 97 proper 87–8, 94, 97, 135, 218–19, 222, 229, 249 n.26 quasi-part 108–9, 254 n.30 particularism 118–19, 124, 130, 135–8, 193 particulars 16, 76–81, 83, 87, 124, 131 part-identity, the relation Pi 106–8, 116, 118, 252 n.18, 254 n.30 Pedretti, C. 168 Peirce, C. S. 21, 24, 244 n.26 perception 6–7, 12, 19, 22, 25, 109, 151–2, 165, 167, 169, 171, 175, 247 n.4, 257 n.2 performance 1, 9, 150–51, 179–86, 258 n.16, 267 Perry, R. B. 5 perspective reverse 172, 257 n.6 standard 166, 168–70, 172, 192, 257 nn.4–6 Petrozino, P. 7 phenomenal experience 26, 102–3, 118–20 phenomenalism 105, 113, 119–20, 124, 138, 251 nn.13 & 16, 254 n.30 phenomenalistic fundamentalism 113 phenomenology 12 Phi Beta Kappa 6, 240 n.3 philosophy aim of 3, 16, 54, 58, 60, 66, 74 ambulance model of 14 analytic 2, 11–2, 14–5, 17, 19, 20, 22, 57–8, 61, 73, 99, 141, 241 n.5, 244 n.26, 252 n.25 ideal language 3, 17, 20 method of see methodology
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ordinary language (British) 14–15, 62, 233–4, 253 n.26 purpose of 3, 54–8, 61, 74, 261 photography 168, 170, 178 physicalism 77–8, 138, 193–4, 244 n.26, 252 n.25 Pi see part-identity Picasso, P. 7, 9, 171, 267 pictorial denotation see depiction picture 56, 72–3, 140–50, 159–60, 165–76, 179, 181, 184–5, 188–9, 255 n.3, 257 n.8 Pincock, C. 250 n.8 Plato 6, 76, 247 n.6 platonism 81–6, 90–93, 97, 112, 122, 124, 136–7, 199, 224, 247 nn.6–8, 248 n.8, 249 n.20, 255 n.2, 256 n.9 play see drama plural quantification see quantification, plural pluralism 138, 191–2, 196–7, 218, 239, 258 n.12, 259 n.7 pluralism logical 5 methodological 99 ontological 22, 99, 107 poetry see literature point, geometrical 23, 101, 106, 115 Popper, K. 33–4, 44, 113, 129 Popperian deductivism 33 portrait 141–2, 164–5, 170–71 positionality of predicates 40, 43–4, 63, 205 positivism see logical empiricism possession of properties 145, 148–9, 176, 257 n.10 possibility 49–50, 71–2, 246 n.17; see also modality possible states 48 possible worlds 58, 196, 246 n.16, 259 n.3 postmodernism 2, 12, 164, 197, 199, 203 postulate, extralogical see statement, extralogical powerset 224, 234 pragmatism 19, 24, 26 Prall, D. 7 predicate 3, 40–5, 48–53, 63–6, 70, 72–3, 80–82, 84–5, 87, 92–8, 119, 125, 127–9, 143–9, 173, 176, 192, 197, 199, 207–11, 217, 234 predicate logic 17, 35–7, 41, 81–2, 85, 92, 94, 160, 243 n.18, 244 n.2, 246 n.12, 256 n.16 second-order 219–20, 243 n.18, 245 n.7, 260 n.11
Index predicate basic 205, 207 dispositional see disposition extralogical 126, 128–9 manifest 48–50 positional see positionality projectible see projectibility qualitative 43 prediction 28–9, 31–4, 39, 42, 51–2, 58, 62–3, 199, 207, 246 n.14 Prekopa, A. 248 n.19 premise 29, 36–8, 111, 230 Principia Mathematica (Russell & Whitehead) 17, 21–2, 100, 122–3, 236 principle of tolerance Carnap’s 4, 111–12, 251 n.15 Leonard’s 124 problem of abstraction 131, 135 problem of concretion 119, 131 problem of intersubjectivity for constructional systems 110, 114, 252 n.25 Problems and Projects 53, 139, 226, 237, 245 n.9 progressive shift 64, 140, 187 Project Zero 8, 55 projectibility 40, 43–5, 48, 50–3, 62–4, 70, 208, 210 Prokofiev, S. 179 proof 37–9, 80, 83, 85, 160 proof theory 37, 83 proper analysis 107, 116 property 52, 80, 106, 145, 148, 219, 253 n.29 quasi-property 110, 253 n.29 protocol sentence 26, 113 protocol sentence debate 113, 252 n.24 Proust, J. 254 n.30 pseudoproblems 20 Putnam, H. 10–11, 89–90, 193, 200, 215–16, 218, 242 n.13, 259 n.7 quaddition 206–7 quale/qualia 77, 79–80, 86–7, 114, 118–19, 121, 123–4, 131–8, 191, 234 quality 101–2, 107, 110, 123–4, 130, 132, 135 quality stretch 135 quality whole 130, 135 phenomenal see quale quantification 89, 201, 208 first-order 220 plural 219–21, 223–4 second-order 219–20; see also predicate logic
quantifier 85, 125, 201, 208, 220, 229, 234 quasi-analysis 106–7, 110, 116–18, 130, 132, 253 n.29, 254 n.30 quasi-object see object quasi-part see part quasi-property see property Quine, W. V. 6–8, 19, 21–2, 41, 67, 69–70, 73, 79–93, 97, 100, 102, 129, 138, 193, 208–9, 216, 241 nn.5 & 7, 247 nn.5 & 8, 248 nn.10 & 17, 251 n.11, 254 n.35, 259 n.4 quus see quaddition railway map 103, 108, 252 n.22 rational reconstruction 62, 104–5, 111, 121, 251 n.14 Rawls, J. 244 n.3 real definition see definition, real realism 5, 75, 124, 137–8, 173, 193, 212, 218 logical 36, 39 modal 49, 246 n.16 concerning representations 165–8, 170–78, 192, 257 n.8 tolerant 197 reality 13, 20, 65, 200, 209–10, 212, 216–17 Reality (D. Lewis) 222, 224–5, 260 nn.16 & 20 Reality (Goodman) 65, 191, 194, 196–7 reception 166, 168, 171; see also perception and vision Reck, E. H. 242 n.15 recollection of similarity see similarity, recollection of Reconceptions in Philosophy 10, 23, 203 reductive empiricism 102 redundancy of a symbol system 156–8, 181 reference 4, 48, 52, 60, 80, 67, 141–9, 154, 158, 173, 176, 188–90, 241 n.7, 247 n.8 reflective equilibrium 36–7, 39–40, 192, 244 n.3, 245 nn.5–6 & 8, 246 n.11 reflexivity 128, 234 region 94 Reichenbach, H. 32 Reicher, M. E. 258 n.16 relational system 105 relativism 2, 4, 191, 197, 199, 203, 211 ontological 99 religion 12, 24, 57, 255 n.1 repleteness 188–9
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Nelson Goodman representation 12–13, 24–5, 62, 140–44, 160–61, 165–79, 188–90, 257 nn.4, 6 & 8 resemblance 37, 97, 141–2, 148–9, 165, 198, 214, 251 n.14 Resnik, M. D. 244 n.3 restoration of artworks 258 n.15 reverse perspective see perspective, reverse Richardson, A. 110, 238, 251 n.13, 254 n.30 Ridder, L. ix, 22–3, 238, 249 nn.22–3, 25 & 28, 251 n.17, 259 n.8, 260 n.12 Riggs, L. A. 167 rightness 13, 52, 65–6, 104, 193, 196–9, 203, 216–17, 259 n.5 Rodin, A. 170 Rodriguez-Pereyra, G. 253 n.29, 255 n.39 Romanticism 174–5 Rorty, R. 2 Rosen, G. 90, 238 Rothko, M. 178 Royce, J. 21 Rs see similarity, recollection of Rubens, P. P. 142 rules of inference 33–40, 53, 85, 232 soundness of see soundness validity of 35–7, 203 Russell class 100, 222, 236 Russell, B. 17–19, 21, 33, 100–102, 106, 110, 115, 122, 222, 230, 236, 242 nn.11 & 15, 243 nn.18 & 24, 249 nn.22–3, 250 nn.3–4 & 6–8, 251 nn.13 & 17, 252 n.21 Russell’s paradox 100–101, 236, 243 n.18 Sachs, P. J. 6–7 Salmon, W. C. 33, 37–9, 246 n.11 sameness of meaning see meaning, sameness of sameness-of-content criterion 97, 125, 218, 225, 250 n.29 sample 145–6, 149 scepticism 56–7, 115, 207–8, 226–7, 242 n.14, 259 n.2 Scheffler, I. 1, 197, 212, 238–9, 242 n.10, 252 n.25, 255 n.1 scheme see symbol scheme Schlick, M. 18, 244 n.26 Schmidt, S. J. 11 Schmücker, R. 258 n.16 Scholz, O. R. 5–8, 11, 240 n.2, 241 n.7, 242 n.11, 244 n.26 Schwartz, R. 1, 6, 44, 240 n.4
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science 13, 17–20, 22, 24, 28–9, 31–4, 66, 73–5, 84, 89–91, 102–4, 112–14, 125–6, 141, 150, 159, 164, 171, 189, 192–3, 198, 200, 205, 246 n.14, 250 n.8, 252 n.25, 254 n.30 esoteric 56–7 philosophy of 1, 3, 18, 40, 42, 44–5, 50, 53 125, 204 purpose of 55–6, 60–61 score 150–51, 156, 172, 179–85, 189, 256 n.7, 258 n.16, 259 n.7 script 185–6, 189 sculpture 7, 170, 174–5, 180, 189 second-order logic see predicate logic, second-order second-order quantification see quantification, second-order seismogram 160 self-completeness 128 semantics 20, 38–9, 44–5, 49–51, 150, 154–8, 160, 164, 181–2, 184–7, 189, 234, 245 nn.6–8, 247 n.8, 256 n.10 formal 45; see also model theory sense data 25, 101, 105, 110, 115 sense realm 131–4, 136 sense-class 109 sensory experience 102 set 1, 18, 77, 81, 83–4, 87, 114–15, 132, 173, 199, 220–26, 229, 234, 247 n.4; see also class structured 105 set theory 83, 87, 90, 97–8, 131, 136–7, 218–26, 234–5, 260 nn.12 & 16 shape 75, 77, 84–5, 119, 152, 188, 214, 247 n.8 V-shape 84–5, 146 Shapiro, S. 238, 243 nn.17–18, 248 n.17 Sheffer, H. M. 5, 21 Sheffer stroke 229, 236, 247 n.8 shift see progressive shift Shin, S.-J. 256 n.16 Shostakovich, D. 183 Sider, T. 249 nn.26 & 28 sign 83, 85, 88, 140, 146, 255 n.5; see also symbol signal 140, 160; see also symbol similarity relation 106–9, 135, 252 n.18, 254 n.30 similarity, recollection of, the relation Rs 106–8, 116 simile 148 Simons, P. 22, 97, 243 n.23, 249 n.28 simplicity see calculus of simplicity; explication; parsimony singleton 219–26, 260 n.15
Index Singular Terms (Leonard) 8, 22–3, 93, 122–5, 131, 138, 254 n.35 Sinsi, V. F. 23 Smith, B. 249 n.28 solipsism 105, 110, 251 n.15, 252 n.22 soundness 37–9, 233 Spade, P. V. 247 nn.1 & 3 Sparshott, F. E. 258 n.13 spoken language see language, spoken Stadler, F. 106, 242 n.16, 251 n.15 stages of artwork see art Stalker, D. 40, 205, 237 Stalnaker, R. 246 n.16 starmaking 5, 193, 197, 212–18 state space 110 statement extralogical 128–9 general 28–31, 41, 43, 47 synthetic 66–7 counterfactual see conditional, counterfactual indicative 47 Stein, G. 171 Steinbrenner, J. 240 n.2 Stevenson, C. 7 Stich, S. P. 36–7, 39, 245 n.5 stipulation 58–9, 62, 155, 184, 218, 226, 231 Strawson, P. F. 32, 233 stream of experience 24, 106–7, 128–9, 231, 236 structuralism 225–6 structure as the object of science 102–3 Structure of Appearance, The 4, 8, 18, 21, 76, 80, 82, 86–7, 90–3, 98–9, 113–39, 199–200, 215 Sturgis, K. 7, 9, 240 n.4 subclass 81–2, 136, 221–2 proper 81–2 subset 126, 224, 235; see also subclass sum arithmetical 207 mereological 4, 95–7, 119, 123, 125, 132–6, 221–6, 229, 235, 249 n.28 supervenience, nomological 60, 235 suprematism 144 swatch 145–6 syllogistic 19, 36 symbol 4–5, 65–6, 140–63, 164–5, 172–3, 176–7, 180, 185–90, 203 conventional 140, 255 n.5 natural 140, 255 n.5 theory of 65, 140–63, 176, 190 symbol scheme 151–60
symbol system 4–5, 141, 149–63, 172–3, 177, 179, 185–6, 188, 192, 198, 203, 244 n.26, 257 n.7 categorization (taxonomy) of 4, 150 symbolic function, rightness of 65 symbolic logic see logic and predicate logic symmetry 40, 44, 106, 128–9, 131, 134, 136, 141, 235, 254 n.34 symptom 255 n.5; see also symbol of the aesthetic see aesthetic, symptoms of synonymy (sameness of meaning) 54, 58–60, 63, 66–73, 114–15, 235 syntax 80, 83–5, 151, 154, 235 synthetic a priori see a priori Tarski, A. 21, 23, 92–3, 245 n.6 term logic see logic term abstract 122–3 basic 127, 208–9; see also basis concrete general 122 singular 122–3 universal 122 theorem 80, 85, 93 theory 235–6 theory-ladenness 113, 198 theory of meaning extensional 72–3 intensional 71 theory of relations 102 theory of types 100–101, 236, 243 n.18; see also Principia Mathematica thought experimentation 115, 172, 253 n.27, 257 n.6 Thucydides 195 time slice 106–7, 114, 118–19, 131–2, 236 Tingle, I. 175, 257 n.9 togetherness, the relation Wh, W and Wt 119, 131–7 Tîke, C. 248 n.19 token 84 Tolstoy, L. 185 totalitarian propaganda 56–7 transcendental idealism 19, 105 transitivity 104, 106, 128, 134, 221, 236 tricomplex of qualia 133–4 Trout, J. D. 115 truth correspondence theory of 65, 194, 196, 200 epistemic conception of 200–202 logical 19, 29, 38, 111, 243 n.18
287
Nelson Goodman mathematical 19, 29, 111, 243 n.18 metaphorical 147; see also metaphor as rightness of symbolic function 65 as permanent acceptability 200–203 truth-conditions 45–6, 202, 217, 247 n.8 truth-functional connective 45, 125, 236; see also constant, logical Tufts College 8 type logical see theory of types of event 31 type–token 84 Ullian, J. S. 5 unambiguosness of a symbol system 155–6, 158 understanding 3–5, 14–15, 20, 23, 54, 56–8, 66, 70, 74–6, 89, 91, 103, 164–5, 177, 190, 192, 198, 208, 244 n.26, 252 n.25 unfavourable circumstances for quasianalysis 116, 254 n.30 unicorn 72–3, 143–4, 255 n.3 union operation see union set union set 224, 236 unity of science 20, 193, 243 n.25 universals 75–80, 86–7, 118, 131, 247 n.3 universe 84, 219, 222–5, 236 oddity 248 n.15 universe of discourse 49 University of Chicago 6, 9, 19 University of Pennsylvania 8, 11, 67 unrestricted composition see composition Updike, J. 9, 267 upper level of a constitutional system 109, 120 Ursa Major 259 n.6; see also Big Dipper utterance 151, 185, 256 n.8 vacancy of characters and inscriptions 155 validity see argument; deduction; induction; rules of inference variable 84–5, 123, 125, 247 n.8
288
Variations 9, 241 n.8, 267 Varzi, A. C. 249 n.28 Velázquez, D. 9, 267 Venn diagram see diagram, Venn verbal analysis see conceptual analysis Vermeer, J. 179 version see world version vicious circle see circularity Vienna Circle 18–19, 21, 242 n.16, 251 n.15 Vigée-Lebrun, E. 142 vision 164–8 vocabulary see language, vocabulary of W see togetherness Walker-Goodman Art Gallery 7 Wang, H. 247 n.7 Ways of Worldmaking 5, 98, 164, 189, 191–203, 244 n.26 Wh see togetherness White, M. 67–70, 73 Whitehead, A. N. 5–6, 11, 17–18, 21–4, 92, 100–102, 106–7, 122–3, 236, 241 n.7, 242 n.11, 243 nn.21–5, 249 nn.22–3, 250 nn.3 & 6, 251 n.17, 254 n.35 whole 82–5, 88, 94, 96, 107, 135, 140; see also quality whole whole meal 3 Wittgenstein, L. 14–17, 206, 233, 242 n.12 Woods, J. H. 5–6 world 4, 12–13, 52, 65–6, 80, 86, 108–10, 123–6, 140, 171, 191–200, 209, 211–12, 216–18, 248 n.11, 259 n.7; see also Reality autopsychological 110; see also solipsism physical 89, 110 solipsistic see solipsism world version 5, 124, 164, 170–71, 191–200, 208, 212–18, 239, 250 n.29, 259 nn.3 & 7 worldmaking 4–5, 171, 197–200, 212–18, 239 Wright, C. 258 n.2 Wt see togetherness Wuppertal-Ronsdorf 17, 103–4
