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The Structure of Arguments
human cognitive processing is a forum for interdisciplinary research on the nature and organization of the cognitive systems and processes involved in speaking and understanding natural language (including sign language), and their relationship to other domains of human cognition, including general conceptual or knowledge systems and processes (the language and thought issue), and other perceptual or behavioral systems such as vision and nonverbal behavior (e.g. gesture). ‘Cognition’ should be taken broadly, not only including the domain of rationality, but also dimensions such as emotion and the unconscious. The series is open to any type of approach to the above questions (methodologically and theoretically) and to research from any discipline, including (but not restricted to) different branches of psychology, artificial intelligence and computer science, cognitive anthropology, linguistics, philosophy and neuroscience. It takes a special interest in research crossing the boundaries of these disciplines.
Editors Marcelo Dascal, Tel Aviv University Raymond W. Gibbs, University of California at Santa Cruz Jan Nuyts, University of Antwerp Editorial address Jan Nuyts, University of Antwerp, Dept. of Linguistics (GER), Universiteitsplein 1, B 2610 Wilrijk, Belgium. E-mail:
[email protected] Editorial Advisory Board Melissa Bowerman, Nijmegen; Wallace Chafe, Santa Barbara, CA; Philip R. Cohen, Portland, OR; Antonio Damasio, Iowa City, IA; Morton Ann Gernsbacher, Madison, WI; David McNeill, Chicago, IL; Eric Pederson, Eugene, OR; François Recanati, Paris; Sally Rice, Edmonton, Alberta; Benny Shanon, Jerusalem; Lokendra Shastri, Berkeley, CA; Dan Slobin, Berkeley, CA; Paul Thagard, Waterloo, Ontario
Volume 7 The Structure of Arguments by Izchak M. Schlesinger, Tamar Keren-Portnoy and Tamar Parush
The Structure of Arguments
Izchak M. Schlesinger Tamar Keren-Portnoy Tamar Parush Hebrew University of Jerusalem
John Benjamins Publishing Company Amsterdam/Philadelphia
8
TM
The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences – Permanence of Paper for Printed Library Materials, ansi z39.48-1984.
Library of Congress Cataloging-in-Publication Data Schlesinger, I.M. The Structure of Arguments / Izchak M. Schlesinger, Tamar Keren-Portnoy, Tamar Parush. p. cm. (Human Cognitive Processing, issn 1387–6724 ; v. 7) Includes bibliographical references and index. 1. Persuasion (Rhetoric) 2. Reasoning. I. Keren-Portnoy, Tamar. II. Parush, Tamar. III. Title. IV. Series. P302.S337 2001 168--dc21 isbn 90 272 2359 9 (Eur.) / 1 58811 0702 (US) (Hb; alk. paper)
2001035012
© 2001 – John Benjamins B.V. No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher. John Benjamins Publishing Co. · P.O. Box 36224 · 1020 me Amsterdam · The Netherlands John Benjamins North America · P.O. Box 27519 · Philadelphia pa 19118-0519 · usa
To our families, who taught us much about arguing
Contents
Preface xi Introduction xiii Chapter 1. Reasoning and arguing 1 1. Underlying structures 2 2. Progressive and regressive modes 7 3. Phases of reasoning 9 Chapter 2. Arguments as operations 13 1. Some basic terms 13 2. The nature of formalizations 17 3. From argument to discussion 20 4. Classes of operations 20 5. Basic concepts — a summary 22 Chapter 3. Operators, targets, outcomes 25 1. Operators 25 2. Targets 44 3. Outcomes 51 4. The symbols of the notation — a summary 62 Chapter 4. Compounds 65 1. Implications 65 2. Disjunctions 70 3. Conjunctions 71 4. Compound targets 74 5. Dependent and independent eVects 75
viii The Structure of Arguments
Chapter 5. Justifications 79 1. The nature of JustiWcation 79 2. The formalization of JustiWcations 84 3. Some common JustiWcations 90 4. JustiWcations as targets 98 5. Dependent and independent eVects 100 6. Deciding on the appropriate analysis 104 Chapter 6. Conflations 109 1. The concept of conXation 109 2. Outcomes of conXations and conXations as targets 110 3. ConXating operators 116 4. ConXating Designations 122 5. ConXations with compounds and with sequences 127 Chapter 7. Questions 129 1. Question operators and outcomes 2. Backdrops 134 3. Questions in conXations 136 4. Questions as targets 140 5. Answers 143 6. ‘Don’t know’ 145
130
Chapter 8. Connections 147 1. A notation for connections 148 2. “Unrestricted” connections 149 3. Between-argument connections 157 4. Connections as toned-down operations 159 5. Summary 161 Chapter 9. Relations within and between arguments 163 1. ‘Argument’ defined 163 2. Relations between arguments 175 3. “Encapsulated” dialogues 180 4. Toward a typology of arguments 182 Chapter 10. Expressed arguments 191 1. Arguing and understanding arguments 191
Contents
2. An experimental study of omissions 198 3. Experimental studies of précis writing 203 4. Targeting the expressed argument 208 Notes
223
References 239 Appendices 247 Author index 253 Subject index 257 List of symbols 261
ix
Preface
This book originated in the Wrst author’s interest in Talmudic argumentation. It seemed self-evident that a description of this kind of argumentative discourse requires a taxonomy of steps in arguments and discussions, but the literature in the Weld did not oVer anything that came near doing justice to the varieties and complexities of such debates. So he set out to develop a notational system that would be appropriate for descriptive purposes. After a Wrst version of the system had been developed, the second and third authors became involved in the project, and in the course of countless exerting, but enjoyable, sessions we thoroughly revised and greatly expanded the system. Several research seminars aVorded opportunities for trying out our method of analysis, and thanks are due to some of the students, who made astute remarks that led to some reformulations. We are indebted to more persons and institutions than can be listed here. Some of the ideas were developed in the course of a project carried out by the Wrst author, sponsored by the Religious Education Administration of the Ministry for Education and Culture, devising a method for grading the diYculty of materials for Talmud study in Israeli schools, and thanks are due to Abraham Ron, then head of the Administration, for his support and encouragement. Work on the notational system and some empirical studies were supported for two years, by a grant from the Israel Science Foundation. Smadar Sapir-Yogev cooperated on the project in its earliest stages. Hadas Shintel, Gazit Kahana, and Meirav Arieli-Attali read parts of the manuscript, detected errors and made some suggestions concerning presentation of the material. Gazit and Hadas also conducted some of the experiments described in Chapter 10; and Gazit compiled the index. Many thanks to them all. At various stages of our work we circulated outlines and drafts of chapters. We beneWted greatly from the responses we received, some very brief, others that developed into a correspondence. Among the persons to whom we are greatly indebted for comments. criticisms, suggestions and support we want to mention especially Moshe Anisfeld, Marcelo Dascal, Frans van Eemeren,
xii The Structure of Arguments
Maurice Finocciaro, David Green, Norbert Groeben, Theo Herrmann, Mike Inbar, Philip Johnson-Laird, Manfred Kienpointer, Eli Kuzminsky, Brian MacWhinney, Dan Nesher, Moti Rimor, Helmut Schnelle, M. Schreier, Catherine Snow, Benny Shanon, Michael Tomasello, Edy Veneziano, and several anonymous reviewers. Finally, we are grateful to the editor, Jan Nuyts, for his sympathetic approach. I. M. S. T. K.-P. T. P.
Introduction
The last thing one settles in a book is what one should put in Wrst. – Pascal, Pensèes
This book deals with the cognitive structure of arguments. A formal system of analysis will be proposed that reXects the reasoning processes leading to an argument. It is argued that behavioral studies of argumentation can be fruitfully conducted on the basis of this system.
1.
The nature of the present approach
The objectives of this work diVer in various aspects from those of previous ones in this Weld. What characterizes our approach can be summed up as follows: a. The objective of our analyses is descriptive rather than normative. b. Our analyses are focused on propositional content rather than on illocutionary force. c. We introduce more Wne-grained analyses than those in previous work. d. Our analyses include implicit steps of reasoning rather than only explicit ones. e. The unit of analysis is a diVerently deWned notion of ‘argument’. These points will now be elucidated, each in its turn. a. Descriptive rather than normative Traditionally, studies of argumentation have been normative, concerning themselves with the formal validity of arguments. For some decades now it has been increasingly realized (primarily due to the seminal work of Perelman — e.g., Perelman and Olbrechts-Tyteca 1969 — and Toulmin 1958) that there is
xiv The Structure of Arguments
more to argumentation than formal logical validity, and that soundness, plausibility, and acceptability of arguments are important normative criteria. Some recent work abandons the focus on normative issues for a more descriptive approach (e.g., Jacobs and Jackson 1983, 1982; Freeman 1991; Rips 1998). As Freeman (1991: 31) has justly remarked, “… any theory of argument should allow for there to be bad arguments, even spectacularly bad arguments.” An integration of normative and descriptive purposes has been proposed by van Eemeren and his colleagues (van Eemeren et al. 1993). The analytic system developed in the present book is descriptive rather than evaluative. Neither logical validity nor soundness of arguments comes within the purview of our study, and problems of logic will be skirted. Questions of integrity or fairness of arguments (Schreier, Groeben, and Blickle 1995) and criteria of reasonableness — relevance, suYciency, acceptability (Johnson and Blair 1994) — will also not be within the scope of this work. Our system, however, has also a normative facet, since it is based on certain assumptions as to the phenomena that are to be analyzed and the categories deployed in the analyses. Our analysis of an argument resorts to a rational reconstruction of it: we assume that, unless there is evidence to the contrary, the speaker argues in conformity with certain logical norms. Normative studies that evaluate the validity, soundness or acceptability of arguments, we propose, may eventually beneWt from our work, by having at their disposal another tool for formal description, a formal notation in which their hypotheses and generalizations can be stated. b. Focus on propositional content rather than illocutionary force In much current work, argumentation is dealt with in terms of speech acts. The focus of the present work is on the cognitive, rather than the communicative, aspects of arguments. Arguments are conceived of as networks of propositions, and the object of our analyses is the conceptual content of these. Thus, questions like the following are not addressed: Does the speaker intend to appease her partner, provoke her, or threaten her? Does she complain, or suggest something (these categories are from Edmondson 1981), and what emotions are expressed (Hofer, Pikowsky, Spranz-Fogasy, and Fleischmann 1990)? While we agree with van-Eemeren et al. (1995: 277–278) that functional perspectives should not be lost sight of, it seemed to be a fruitful tactic to concentrate, as a Wrst step, on a structural description, which can then be integrated with a functional account in future work. Functional aspects, it should be
Introduction
emphasized, are not disregarded altogether, and in the process of analyzing an argument, attention is paid to the linguistic and extra-linguistic context and to its function in the discussion. Our main objective, however, was to capture the informational structure of discourse rather than its functional aspects, and the outcome of the analysis represents predominantly propositional aspects (it being recognized, though, that there is presumably no sharp dividing line between the latter and those illocutionary acts that are not accommodated in our system). c. A Wne-grained analysis In our system, analyses of propositions are more Wne-grained than those in previous work. Typically, writers on argumentation have deployed categories like ‘claim’ and ‘support’; Freeman (1991) calls this the ‘standard’ approach. Arguably, this is due to a long tradition of viewing arguments through the prism of logic. But much more than making claims and supporting them is going on in argumentation. When trying to make a point, people explain and interpret statements made by others, provide additional information pertinent to these statements, express views about their plausibility (even without providing any reasons that support these views), compare several statements with each other, and so on. Some writers — e.g., Toulmin (1958), Finocchiaro (1987), Freeman (1991), Salmon and Zeitz (1995), Rips (1998) — have sought to enrich the descriptive apparatus by making further distinctions between types of relations, but even these do not go nearly far enough, in our view. The objective of the present work is to develop a descriptive framework for arguments in all their multifariousness. For this purpose a system is needed that is generally much richer than those developed so far. Each argument is analyzed in our system into a number of steps between which certain relations hold. An elaborate classiWcation of such steps (which we call ‘operations’) and the relations between them has been developed and a formal notation system is being proposed. This classiWcation then forms the basis for analyzing the relationships holding between arguments. d. Implicit steps of reasoning rather than only explicit ones Many arguments are expressed in very few words, or even a single word, and it might appear that in such arguments there is not much that can be further broken down in the analysis. It should be noted, though, that our analyses are performed not only on what is explicitly stated but also on what is implicit in
xv
xvi The Structure of Arguments
the speaker’s contribution — the line of reasoning that results in the verbal expression of the argument. The object of our analyses is, as stated, the cognitive, rather than the social and public aspects of argumentation. To a certain extent, then (but only to a certain extent, as will become clear in Chapter 1), what is analyzed is the train of thought leading to the argument. In this respect, too, our approach diVers from that of many other researchers. e. A wider deWnition of ‘argument’ The term ‘argument’ is usually taken to denote only a certain kind of contribution to a discourse. Thus, for Toulmin (1958: 11–12) the primary function of arguments is to defend assertions. Fisher and Sayles (1965: 3; quoted in Cox and Willard 1982: xxi) deWne ‘argument’ as a “statement or series of statements … which requires or rationally authorizes another statement.” Many writers regard as arguments only verbal acts aimed at persuasion. Thus, for Strawson (1952: 12) “the aim of argument is conviction”; for Searle (1969: 66) arguments are “essentially tied to attempting to convince”; Perelman (1963: 155) holds that an argument seeks to evoke assent (“increase adherence,” in his words) to some thesis; Klein (1980) views it as a speech act the purpose of which is to prove a point, to get a thesis accepted; and Chittleborough and Newman (1993) disitinguish between establishing a proposition and persuading as two types of argumentation; cf. also Hamblin (1986: 224V), van Eemeren and Grootendorst (1982), van Eemeren, Grootendorst, and Kruiger (1987), Freeman (1991: 26– 33), and Herrmann and Grabowski (1994: 265–266). Against this approach, Meiland (1989) has argued (persuasively) that in many cases arguments cannot be said to aim at persuasion, unless the meaning of this term is extended unreasonably, but rather at inquiry. An inquiry typically considers possible objections more seriously than persuasion does. Again, an inquiry, unlike persuasion, does not always have to arrive at a conclusion (one might come up with good reasons for more than one possible conclusion). A literature class may try to clarify what possible interpretations can be given to a text; people may argue cooperatively about a course of action they want to take, without holding on to any ‘truth’ they want to persuade each other of. The present work espouses the approach adopting a wider deWnition of ‘argument’: we conceive of arguments as comprising verbal expressions aimed at inquiry as well as those aimed at persuasion. Our primary aim was to develop a system for analyzing arguments. But we soon found that this system lends itself to the analysis of the cognitive structure
Introduction xvii
of any kind of discourse. We therefore use ‘argument’ as a technical term with a much wider sense than the usual one, and refer by it to a single turn in any kind of (written or spoken) text — with discursive, exploratory, or descriptive content — and regardless of the speaker’s purpose. Accordingly, ‘argument’, as the term is generally used, is the prototype of ‘argument’ in our extended sense. Our formal deWnition of ‘argument’ is couched in terms of the constructs of the formal system, and will therefore only be given in Chapter 9, after the system has been presented. The present work has theoretical implications as well as research applications. Our system may lead to theoretical insights that might not have been attained otherwise. Thus, our analyses revealed ambiguities in the use of such pivotal words as ‘reason’, ‘because’, and ‘therefore’ that tend to be glossed over in reading (Chapter 5, Section 1). As for research applications, a few comments will be made in the following section.
2.
Behavioral research based on the present system
The analytic apparatus proposed in this book may serve as a framework for the empirical investigation of discourse. One area in which we have done some experimental research is the processing of arguments. SpeciWcally, we investigated the relationship between the verbal expression of an argument and the chain of reasoning that underlies it. Frequently, this chain of reasoning is much more complex than what appears at the surface, that is, in the verbal expression of the argument. The latter is often more a sort of shorthand version of the reasoning process: the speaker often omits some steps in the chain of reasoning. It would be of interest to go beyond this impressionistic account and investigate regularities in omissions. Is it possible to characterize the types of steps that are more liable than others to be omitted in the presentation of an argument? How do omissions vary with context? An analytic apparatus for categorizing steps in an argument is a prerequisite for dealing with such questions. Within our framework we formulate testable hypotheses concerning the production of arguments and their interpretation. Chapter 10 reports on studies presenting experimental subjects with texts in which the constituent operations were spelled out and few if any were left implicit, and then they were asked to reproduce these texts. In other studies they were asked to prepare a précis of such a text. Predictions as to the kinds of operations more likely to be omitted were formulated in terms of our concep-
xviiiThe Structure of Arguments
tual framework and were experimentally corroborated. The analysis of texts by means of our conceptual apparatus may thus be instrumental in the behavioral study of précis writing and note taking — an area that has not been suYciently investigated so far. The present analytical apparatus may also be of use in comparative research. In what ways do legal texts diVer from others, say, from journalistic or scientiWc writing? Are they more articulated, that is, do they tend to leave fewer operations unexpressed, and if so, which ones? More generally, characterizations of various styles of expression may be formulated and these may be related to genres of writing. Another area where our system may be useful is developmental research: In what ways does the ability of children to express themselves change with age; which kinds of operations tend to be left implicit at various stages of development?
3.
Plan of this book
Chapter 1 introduces a central concept in our system: the underlying structure of an argument. The chapter also discusses brieXy the relationship between reasoning and arguing. The system of notation deployed in our formal framework is explained in Chapters 2–8 at the hand of about 150 examples of formal analyses of arguments. Chapter 9 discusses how arguments may be individuated and how they may be related to each other; we thus proceed from the description of the units of a discussion to that of the discussion as a whole. Chapter 10 discusses the processing of arguments by speakers and hearers and reports on some relevant behavioral research.
*** Let us end on a personal note. Developing the formal notational system for analyzing arguments has been a most rewarding experience for us. We came to realize that apparently simple and straightforward texts may often aVord possibilities of interpretation not surmised previously. Analyzing the internal structure of an argument impels one to submit the text to a much closer reading than one might have done otherwise. Apart from sharpening one’s perceptions, the activity of formalizing arguments may lead to the formulation of empirical hypotheses concerning argumentation, thus providing an important
Introduction xix
tool for theory construction. If one may take one’s cue from the development of other branches of knowledge, like linguistics, some future signiWcant theoretical advances may turn out to have been made possible only by the availability of a formal language. To provide such a formal language is the objective of this book.
Chapter 1
Reasoning and arguing
Thoughts reduced to paper are generally nothing more than the footprints of a man walking in the sand. It is true that we see the path he has taken; but to know what he saw on the way, we must use our own eyes. – Schopenhauer
In this book a notational system is proposed for the analysis of arguments. As stated in the introductory chapter, our system permits the formalization of the line of reasoning underlying the argument rather than its verbal expression. The assumption being made here, and shared by several writers, is that what a speaker or writer says or writes reXects his or her underlying cognitive processes. Reasoning and arguing are indeed closely related. One can reason with oneself and for oneself or one can reason with another person, which is what is called arguing. As Plato has it (in his Theaitetos, 189–190), thinking is dialogue: “The soul in thinking appears to be just talking — asking questions of herself and answering, aYrming and denying. And when she has arrived at a decision… this is called her opinion. I say therefore that to form an opinion is to speak, and opinion is the word spoken — I mean to oneself in silence and not aloud to others”. In fact, in his largely Wctitious dialogues Plato exhibits to us his own trains of thought in grappling with philosophical problems. That thinking may need the support of inner speech has also been observed by the writer Henry Roth (1934/1976: 410): “he muttered, and this he did not so much to populate the silence with ephemeral Wgment selves, but to follow the links of his own, slow thinking, which when he failed to hear, he lost…”. In classical Greek, dialogismos meant both deliberation and conversation, and in Biblical Hebrew `he spoke in his heart’ meant `he thought’. In Developmental Psychology it has been argued that thinking develops in the child through the internalization of speech (Vygotsky 1987). Empirical studies of reasoning have led Green (1995) to conceive of thinking as a form of internal argument (cf. also Kuhn 1991: 1–5).
2
The Structure of Arguments
These observations are mostly based on introspection. But introspection is not an infallible guide, as William James (1890/1981: 236–7) remarked over a century ago: “Let anyone try and cut a thought across in the middle and get a look at its section, and he will see how diYcult the introspective observation of the transitive tracts is. The rush of the thought is so headlong that it almost always brings us up at the conclusion before we can arrest it. Or if our purpose is nimble enough and we do arrest it, it ceases forthwith to be itself.” It has been suggested that, since reasoning and speaking are so closely related, the study of the latter may provide a lever for gaining insight into the former (Collins and Michalski 1989; Kuhn 1991: 274–279; Rips 1998). This approach, however, is not unproblematic. If introspection of one’s own cognitions does not suYce to get a handle on reasoning processes, the verbal output of others may arguably be an even less sure guide. This may have implications for our project of formalizing the trains of thought underlying arguments, and in the present chapter this problem will be discussed.
1.
Underlying structures
A central concept in our system is that of the underlying structure of an argument. In the following we explain what we mean by this term. 1.1
The concept of underlying structure
Compare the following two texts, A and B, and consider the question: Are these the same argument, or are they diVerent ones? A Now might I do it pat, now he is praying; And now I’ll do’t. And so he goes to heaven; And so I am revenged. That would be scann’d: A villain kills my father; and for that, I, his sole son, do this same villain send To heaven. O, this is hire and salary, not revenge. He took my father grossly, full of bread; With all his crimes broad Xown, as Xush as May; And how his audit stands who knows save heaven? But in our circumstance and course of thought, ‘Tis heavy with him: and am I then revenged, To take him in the purging of his soul, When he is Wt and seasoned for his passage? No!
B It would be right to kill him now while he is praying, and this is what I will do, for this would be revenge. But, no, he is a villain, who killed my father and so should be severely punished. If I kill him now, he will go to heaven, and this is a prize, not revenge. He killed my father, who had no chance to repent, and thus may have gone to hell. Revenge should be fair and equitable. To kill him now, when he is praying and has atoned for his sins would not be equitable revenge. So I will not kill him now.
Reasoning and arguing
The text in A is one of Hamlet’s monologues (upon seeing the king at prayer, alone). B is a paraphrase of A. In spite of the diVerences in verbal expression, there is a sense in which A and B are the same argument: under a certain interpretation, they contain the same line of reasoning.1 A and B express the same content, albeit in diVerent verbal garbs.2 It is this content, this line of reasoning leading up to it, that is the object of our analyses. We will call this the underlying structure of the argument.3 It is impossible of course to Wnd out for each argument what cognitive processes in the speaker’s mind gave rise to it, but, as will be shown in detail in Section 1.2, below, one can construe a line of reasoning that might plausibly have resulted in the argument. The object of our analyses, then, is not the verbal form of the argument, but the train of thought that, conceivably, gave rise to it. In this respect the present investigation diVers radically from current work in discourse analysis or text analysis, which almost exclusively concentrates on the written or spoken text; see, for instance, the studies reported in Mann and Thompson (1993). Freeman (1991: 34) states that the purpose of a diagramming technique — another device for formalization — should be to describe the manifest structure of an argument, and none of the “suppressed” premises. Salmon and Zeitz (1995), however, hold that the analysis of arguments should include premises which are only implicit in the argument. An analysis of an argument, in our system, comprises both a verbal description and a formalization of its underlying structure. The verbal description restates the content of the argument, including its implicit steps. Obviously, any such description cannot be identiWed with the underlying structure; it is just another realization of the argument (in the way that B, above, is another realization of the argument in A). The formalization intends to capture the cognitive structure of the argument. It represents the steps in the underlying structure (the ‘operations’, in our terminology) and the relationships between them. The same formalization may be shared by diVerent underlying structures (just as the syntactic structure of quite diVerent sentences — such as “Mary eats a sandwich” and “John cleans the table” — may be identical). In this respect the formalization, like every categorization, entails a loss of information. The formalization deploys a specially devised notation (the formal analysis of the Hamlet monologue is given in Chapter 9, Section 1.4).
3
4
The Structure of Arguments
1.2
Reconstructing the underlying structure
Typically, an underlying structures is more elaborate than the expressed argument. Examples are given in Herrmann and Grabowski (1994: 59–60, 349– 350). As van Eemeren et al. (1987: 13–17; 1993, Chapter 4; see also van Eemeren et al. 1993: 42–44, 1996: 176–177) have pointed out, an argument is often expressed in very few words, or even a single word. And as Meiland (1989: 188) remarks, “In actual cases of argumentation, objections and replies are often stated in fragmentary form and therefore give the appearance of not being arguments”. It has long ago been observed that in stating a syllogism one often tends to omit the major premise — such an argument is called an enthymeme (see Hitchcock, 1998, for discussion) — but the syllogism may be perfectly convincing, because the missing premise is supplied by the hearer (Noordman et al., 1992; Singer et al., 1992). Likewise, an argument from authority (often regarded as a fallacy) is normally enthymematic, the missing premise being: ‘X (the authority cited) is authoritative /an expert in these matters’ (Coleman, 1995: 372). The following Wctitious dialogue may serve to illustrate the “abbreviated” character of expressed arguments. Robert: Sylvia:
What a beautiful picture! You have poor taste.
These are two arguments, in the sense in which we use that term (see Introduction, Section 1). We are concerned here only with the reply “You have poor taste”. Obviously, there are some missing steps here that lead from Robert’s assertion that the picture is beautiful to the conclusion that he has bad taste. It is only because the picture is not beautiful in Sylvia’s eyes that she arrives at this conclusion. But something more has been left implicit, namely, the (quite obvious) assumption that a person’s judgment of a work of art reXects her taste. All this does not have to be made explicit, but it is part of the underlying structure of the reply. This is how one might render a verbal description of the content of this underlying structure: This picture is not beautiful. One’s evaluation of a picture reXects one’s taste. You think this picture is beautiful. Therefore you have poor taste.
Reasoning and arguing
Leave out any one of these implicit steps, and the argument fails to hang together. Of course, the person who makes this reply need not consciously traverse all these steps. However, the underlying structure pertains not only to what the arguer was conscious of, but to whatever mental processes, conscious or not, presumably went into producing the argument.4 Now, one can of course never be quite certain what the arguer’s mental processes were when she advanced this argument in this particular instance. All the analyst can do is propose a possible reasoning process, which may or may not have occurred in exactly this form in the mind of the originator of the argument. The result of his endeavors, then, is a rational reconstruction of the reasoning process; the analysis does not presume to mirror it.5 It will be up to the analyst to decide how far the analysis should be pushed, what hidden links and implied propositions should be included in his reconstruction of the underlying structure. This point will be taken up again in the next chapter. Here is another example of an implied proposition that is contained in the underlying structure, although it is not expressed by the speaker: Sue: Ted:
John has eaten all the cookies in the jar. No, that wasn’t John.6
Ted rejects Sue’s claim, but the way he formulates his answer shows that he concedes that someone has eaten all the cookies in the jar. The latter proposition is implied by his response; presumably, it is part of Ted’s intention to imply it. Hence it is part of the underlying structure that has to be formalized by the analyst.7 In reconstructing the steps of the reasoning process, then, one must look “behind the scenes” of the verbal formulation. There are no general rules that might guide us here. The only “recommendation” to the analyst is that she proceed in a plausible way; this is a version of the “principle of charity” (Scriven 1976: 71). The problem has been discussed by, inter alia, Ennis (1982), Jacquette (1996) and Walton (1996, Chapter 7).8 Given our inability to penetrate the mind of the arguer, we have to start from the assumption that he reasoned rationally. Of course, when there are grounds for assuming that the speaker’s reasoning was faulty, he or she may be credited with an underlying structure involving a fallacy. Thus, while our approach is predominantly descriptive, we do resort to considerations of plausibility and rationality in reconstructing the underlying structure.
5
6
The Structure of Arguments
There is no formal procedure, no algorithm, that takes the expressed argument as input and derives from it its underlying structure. IdentiWcation of the underlying structure depends on the analyst’s interpretation of the expressed argument. The comment about Robert’s artistic taste in our previous example, rather than being prompted by Sylvia’s judgment of that particular picture may have been based on previous acquaintance (‘I know you have poor taste, so it doesn’t surprise me that you say so’). Likewise, one may disagree with the paraphrase of Hamlet’s monologue presented in B and claim that Hamlet has decided from the outset that the king should not be killed (note: “Now might I do it …” rather than “Now will I do it”). Every analysis is dependent on a certain amount of conjecture, and the more the argument has been made explicit in its verbalization, the less conjecture is required. As another example of alternative possibilities of interpretation consider: Evelyn: Abe was at Ben’s party last night. George: I remember that Abe met with Cyril last night in the university library.
The reply might be interpreted as a claim that since Abe met with Cyril, he could not have been at the party. Alternatively, it might be interpreted as conWrming the claim that Abe was at the party and adding that Cyril must have gone with him. If the analyst knows Cyril and Abe to be assiduous students, he may interpret the sentence in one way; if he knows Cyril to be an inveterate partygoer, he may interpret it in another. When all is said and done, the felicity of the analysis will depend on the insight, interpretative skill, and background knowledge of the investigator (see in this connection van Eemeren, de Glopper, Grootendorst, and Oostdam 1995, and Levi 1995). Many arguments, though, are relatively unambiguous and hardly leave room for diverging interpretations. The underlying structure, then, will typically include material that is not verbally expressed. Conversely, some expressed arguments will contain material that is not part of the underlying structure. Here are some examples: a. A literary critic who interprets Hamlet’s monologue, quoted in the foregoing, may detect (as one can certainly detect elsewhere in the play) that the prince is sick of life. This is what motivates Hamlet’s actions, and possibly it is one of the determinants of this monologue. But it is not included in the line of reasoning that is conveyed in the monologue, and hence is not part of the underlying structure.
Reasoning and arguing
b. Comments like “I can’t hear you; could you speak up, please” or “There is a draught here; I’d better close the window” may have an impact on the way the discussion develops, and yet, they are usually not part and parcel of the cognitive “skeleton”, and hence not part of the underlying structure (unless the discussion then continues to revolve around them). c. Felicity conditions, i.e., those conditions that have to be met if the speech act is to be “successful”; for instance, a promise requires that the speaker intends to act as promised, a command — that the speaker has the right and authority to give an order to the addressee, and so on. These conditions will not be part of the underlying structure of the argument. Communication is typically not impeded by omissions of steps in the underlying structure, because this material can easily be reconstructed by the hearer. What is omitted is of course determined partly by the content of the speciWc argument and may be situation-dependent. The question may be raised, however, whether there are any regularities, holding across situations, in respect to the tendency to omit links in the argument. As will be seen in Chapter 10, this problem can be fruitfully studied by testing hypotheses formulated in terms of a formal notation system of the kind developed in this work.
2.
Progressive and regressive modes
Frequently, there are two ways of making the same point. Compare the following two arguments: A Snakes may bite. If you get any nearer to this snake, it may bite you. Therefore you had better keep away. B You had better keep away. This is so because snakes may bite, and if you get any nearer to this snake, it may bite you.
Argument A starts from the premises and draws from them a conclusion; we call this the progressive mode. Argument B, by contrast, states the conclusion Wrst and then “backtracks”, so to speak: it goes on to justify the conclusion by
7
8
The Structure of Arguments
presenting the premises leading to it; we call this the regressive mode of arguing (cf. the distinction made by writers in ArtiWcial Intelligence between forward and backward inferencing). In Chapter 5 we further discuss this and another variant of progressive and regressive arguments. Now, these two modes of arguing correspond to two diVerent modes of reasoning. One may start with the data and attempt to Wnd out what follows from them. But often “[o]ur conclusions run ahead of our power to analyze their grounds”, as William James (1981: 168) pointed out long ago. An example of a regressive mode of reasoning is that of a person who has a strong opinion on some issue and, in a discussion, casts round for considerations that support it. Also, one may have an intuition of a state of aVairs and only subsequently clarify to oneself what justiWes this intuition. The mathematician Gauss once said: “I have had my results for a long time; but I do not yet know how I am to arrive at them”. What may occur in mathematical thinking may also occur, to some extent, in more mundane thinking. A passage from Svevo’s Confessions of Zeno (Svevo 1989: 312) is relevant here: One is often led to say things because of some chance association in the sound of words; and directly one has spoken one begins to wonder if what one has said is worth the breath spent on it, and occasionally discovers that one has started a new idea. I said: “Life is neither good or bad; it is original.” When I thought it over I felt as if I had said something rather important. Looking at it like that I felt as if I were seeing life at the Wrst time, with all its gaseous, liquid, and solid bodies. …
And then he goes on to show why life may be considered original. In reconstructing the underlying structure, one attempts to describe a possible reasoning process that may have resulted in the argument. Accordingly, we recognize two types of underlying structures, one corresponding to the progressive mode and one to the regressive mode.9 The regressive mode may have the eVect of highlighting the conclusion and relegating what supports it to a less salient position. Many arguments consist in a mixture of both modes. The paraphrase of Hamlet’s monologue, B, starts out by a statement — “It would be right to kill him now …” — which is followed by a justiWcation: “for this would be revenge”; this is the regressive mode. But then it goes on with the statement, “he is a villain…”, which leads to a conclusion: “and so should be severely punished” — in the progressive mode.
Reasoning and arguing
3.
Phases of reasoning
Suppose an argument is expressed in the regressive mode. Can one infer from this that its conclusion appeared Wrst in the thinking process of the person who presented the argument, and only subsequently she attempted to justify this conclusion? It should be obvious that there is an additional possibility, namely, the person set out to consider certain facts, then concluded something from these facts — that is, reasoned in the progressive mode — but subsequently formulated the argument in the regressive mode for the purpose of presenting it to the listener or reader. How one arrives at a conclusion is one thing, and how one then “wraps up” the argument so as to present it to the audience is another. In sum, there may have been more than one phase of cognitive processing. (We prefer the term `phase’ to `stage’, because the latter term may suggests a Wxed sequence of stages a process has to go through, and this applies by no means to the generation of all arguments.) In analyzing a given argument, the investigator usually has no clue as to which phases of reasoning the speaker’s mind went through. She may therefore decide to take her cue from the way the argument has been expressed verbally, because this reXects, at least, the last phase of reasoning (that is, if the speaker expressed the argument in, say, the regressive mode, this is how he must have somehow formulated it to himself prior to uttering it). Alternatively, the analyst may decide between an underlying structure in the progressive and one in the regressive mode on the basis of convenience and of perspicuity of the analysis (more about this in Chapter 5, Section 6.1). Here is another example of diVerent phases of reasoning. Suppose someone argues with herself: A I should remodel my house, because it has painful psychological associations for me. But really, I am not sure that remodeling would remove these. Well, even if it doesn’t, I could always resell it, perhaps at a proWt. (Adapted from Freeman, 1991: 163).
Like the Hamlet soliloquy at the beginning of this chapter, this is a kind of internal dialogue. Suppose now that subsequently this argument is verbalized, addressed to someone else. It may now be “wrapped up”, omitting material from the internal dialogue:
9
10
The Structure of Arguments
B I should remodel my house, because it has painful psychological associations for me, and even if remodeling doesn’t remove these, I still could resell it, perhaps at a proWt.
In A, the speaker debates the issue with herself, taking into account conXicting considerations; in B the outcomes of these considerations are presented as leading all to the same conclusion. A and B, then, may represent two phases of reasoning (their underlying structures are analyzed in Chapter 9, Section 3). We are not claiming here, of course, that these two phases are necessary. In a given case, the reasoning may proceed as in A, and the argument be formulated in the same way, as an internal dialogue; in another case, one may start out reasoning as in B and express the argument accordingly. It may also happen (though this is somewhat less likely) that one reasons at Wrst as in B and then reformulates the train of thought as in A, and thus presents it to the hearer. The point being made here is that the expressed argument does not always reveal the course taken by the reasoning process. There are also other reasons why the reasoning process is not always mirrored by the expressed argument. As the literary critic Auguste Bailly has remarked, reasoning is often characterized by simultaneity: “The necessity of recording the Xow of consciousness by means of words and phrases compels the writer to depict it as a continuous horizontal line, like a line of melody. But even a casual examination of our inner consciousness shows us that this presentation is essentially false. We do not think on one plane but on many planes at once. It is wrong to suppose that we follow only one train of thought at a time; there are several trains of thought one above another. … we are also aware, more or less obscurely, of a stream of thought at the lower levels.” (quoted in Gilbert 1955: 15; see also Vygotsky 1987: 281). So far only phases of verbal reasoning have been considered. But a verbal phase of reasoning may be preceded by a non-verbal one. Charles Sanders Peirce (1965: 17, §27; see also p. 107) observed long ago that the thinking process presumably really begins at the very percepts. Percepts (in Peirce’s view) cannot be represented in words, and consequently, the Wrst stage of thinking cannot be represented by any logical form of argument. Instead, “… it is only the self-defense of the [thinking] process that is clearly broken up into arguments.” This, incidentally, may be one of the reasons our thinking is not completely at the mercy of the structure of our language, as an extreme version of the WhorWan hypothesis has it (Schlesinger 1991).10
Reasoning and arguing
Let us return now to the issue raised at the beginning of this chapter: Can the study of argumentation provide a lever for gaining insights concerning reasoning processes? It should be obvious from the discussion in this chapter that there is no straightforward connection between the two. The expressed argument may reXect only one of the phases of the reasoning process. One may decide to model this, or any other phase, by positing an underlying structure of this argument. But in any case, the analysis will only reveal a possible reasoning process. The study of arguments is not ipso facto a study of thought processes. While argumentation thus will not be a keyhole through which we may observe thinking in Xagrante delicto, studying argumentation may be a fruitful way to develop a theory of reasoning. The eVort invested in a Wne-grained analysis of arguments and an understanding of what makes an argument hang together may aVord insights into the mental processes occurring in its production (see also the discussion in Chapter 10, Section 1). Moreover, the investigation of the argumentation process may converge with information gleaned from other kinds of investigation of the reasoning process to yield clues as to the nature of thinking, and may thus be expected to make a contribution to Cognitive Psychology.
11
Chapter 2
Arguments as operations
Argue, v.t., to attentively consider with the tongue. – Ambrose Bierce, The enlarged devil’s dictionary
In the preceding chapter we introduced the concept underlying structure, that is, an idealization of the line of reasoning that leads up to an argument. In this book a system for the formalization of underlying structures will be proposed, and in the present chapter the general principles of such a formalization will be outlined. For the purpose of formalization, an argument is broken down into a series of steps (in the “degenerate” case there will be only one step). Each step is analyzed in a formal language. We now turn to an explanation of the central concepts of the system.
1.
Some basic terms
Each argument has an author; this technical term will be used to refer to a speaker as well as to a writer, that is, to the source of any written or spoken text.1 To describe arguments, some writers (e.g., Freeman 1991, Toulmin 1958, and Thomas 1986) have deployed diagrams in which the various premises and conclusions are connected by lines symbolizing the relation of supporting. As stated in the Introduction, there are many more types of relations between premises and between propositions in an argument, and in our system many of these are included in the analysis. We deploy an inherently relational notion, operation, and distinguish many types of operations of which arguments are constituted. A given argument, then, is broken down into a series of steps, each of which is analyzed as an operation.2 Let us illustrate this by the following dialogue:
14
The Structure of Arguments
Author 1: Abe has a haggard look today. He must have been at one of Ben’s wild parties last night. How disgusting! Author 2: No, I was with him in his apartment last night.
The Wrst step in the analysis is to decide on the underlying structure of the argument. The analyst, of course, has at his or her disposal only the expressed argument (see Chapter 1, Section 1.1), and any decision as to its underlying structure will depend on its interpretation by the analyst. The underlying structure of the argument made by Author 1 contains, on our interpretation, three operations, which may be stated as follows: 1. Abe has a haggard look today. 2. One can infer from this that he has been at Ben’s wild party last night. 3. His attendance at this party is reprehensible.
It would be incorrect to say that 1–3 is the underlying structure. In these lines we have just another expressed argument (equivalent, in a way, to the expressed argument as formulated by its author). However, these lines are intended to reXect the underlying structure, and such formulations are typically more elaborate than the expressed argument (as will be illustrated below, when we deal with Author 2’s response). To explain how this argument is formalized, consider Wrst how Lines 1–3 are related to each other. Line 2 (“One can infer from this…”) refers to Line 1, and Line 3 — to Line 2. Line 1, by contrast, does not refer to any other operation. Instead, it introduces new material that forms the basis of other operations. An operation that does not refer to any previous operation in the discussion will be called a Presentation. In Line 2 a conclusion is drawn from the text in Line 1. Our term for an inference of this kind is Eduction. In Line 3 we have a value judgment pertaining to Line 2; we call this operation an Evaluation. An argument, then, is made up of operations. Each operation is constituted of: a. an operator, which indicates the kind of operation that is performed; b. a target, which indicates to which previous operation it refers; and c. an outcome: the proposition that results from the operation. These concepts can be illustrated by the following example, in which the argument made by Author 1 is formalized.
Arguments as operations
Example 1 Author 1 1. P(p) p 2. E(p1) e 3. Q(e2)
q
Abe has a haggard look today. 〈 One can infer from this that 〉 he has been at Ben’s wild party last night. His attendance at this party is reprehensible.
operator target outcome
The capital letters in this formalization are operators. An operator indicates the kind of operation that is performed. The Presentation operation has a Presentation operator, symbolized by P; the Eduction operation has an Eduction operator, E; and the Evaluation operation — an Evaluation operator, Q. Each operation has an outcome. Outcomes are symbolized by lower-case letters corresponding to the symbol for the respective operators: The outcome of P is p, the outcome of E is e, and so on.3 The outcome of the Presentation can be presented verbally as “Abe has a haggard look today”. The outcome of the Eduction can be represented as “he has been at Ben’s wild party last night” (the phrase “one can infer from this that” in Line 2 does not belong to the outcome; it merely shows how this outcome is connected to the previous line). The outcome of the Evaluation is the proposition in Line 3. The parenthesized letter after the operator symbolizes the target to which the operator refers. An exception is Presentation, which is the operation that introduces a new text, rather than referring to a previous one, and therefore has, strictly speaking, no target; however, for the sake of uniformity of the notational system we assign to each Presentation a “dummy” target, (p). The two targets in Lines 2 and 3 of the present example are each an outcome of the previous operation and are symbolized by lower-case letters. Thus, the Eduction targets the outcome of the Presentation in Line 1, and hence the target is symbolized by (p1) — the subscript always refers to the line in which the targeted outcome has appeared. The outcome of this Eduction is targeted, in its turn, by the Evaluation in Line 3 (the subscript in e2 indicates the Line in which e appears as outcome). As will be seen in the next chapter, the target may also be an operator, rather than an outcome (that is, the operation itself is commented on), and then it is symbolized by a capital letter. The symbolization for an operation, then, can be described schematically as follows:
15
16
The Structure of Arguments
X (y) X (Y)
x x
when an outcome is targeted, when an operator is targeted.
Here X is the operator, y or Y is the target, and x – the outcome. Let us leave now our puritanical Author 1 and analyze the reply made by Author 2: “No, I was with him in his apartment last night”. The following reformulation of Author 2’s argument shows which operations are contained in its underlying structure. 4. 5. 6. 7.
I was with Abe in his apartment last night. Therefore he was not at Ben’s party. Your claim that he was at Ben’s party is false. One can infer from this that one cannot blame Abe for behaving reprehensibly.
The operations in 5 and in 7 do not appear in the expressed argument; that in 6 is merely hinted at — at the beginning of the expressed argument — by one word: “No”. In Example 2 we repeat the analysis of the Wrst author’s argument (Example 1) and add that of the second author. Example 2 Author 1 1. P(p) p 2. E(p1 ) e 3. Q(e2 ) 4. 5. 6. 7.
Author 2 P(p) E(p4 ) T– (e2 ) E(t–6 )
q p e t– e
Abe has a haggard look today. 〈 One can infer from this that 〉 he has been at Ben’s wild party last night. His attendance at this party is reprehensible. I was with Abe in his apartment last night. 〈 One can infer from this that 〉 he was not at Ben’s party. Your claim e2 (that Abe was at Ben’s party) is false. 〈 One can infer from this that 〉 one cannot blame Abe for behaving reprehensibly.
The argument made by Author 2 starts out with another Presentation (Line 4). From the outcome of this Presentation something is inferred by the Eduction operation (Line 5) and the outcome of this Eduction — the inferred proposition — is “He was not at Ben’s party” (“One can infer from this that” is not part of the outcome, which is why it is included in angular brackets). From
Arguments as operations
the outcome in Line 5, e5 , it follows that the claim made in Line 2 of the Wrst argument is false. The operator T in Line 6 stands for Truth value. This is the operation of claiming that a targeted statement is true or false. In this example, e2 is claimed to be deWnitely false, and hence we write T–. (Actually, the formalization in Lines 5–6 is oversimpliWed, as will be seen in the next chapter, Section 3.5.) From the fact that the claim is false it is inferred (in Line 7) that there was nothing wrong with the way Abe behaved.4 Lines 5 and 6 illustrate the need of providing targets with numerical subscripts. The Eduction in Line 5 has the immediately preceding p4 as its target, not p1. The Truth value operator targets e2, not the immediately preceding e5. It should be emphasized that an operation can only target a previous operator or outcome, not a subsequent one. It will be noted that the operations of the two arguments are numbered consecutively; the second argument continues with Line 4 rather than starting with Line 1. This convention permits more convenient cross-referencing by numerical subscripts. The reader should remember, however, that ‘argument’, as used in this book, does not refer to the whole discussion, but rather to a single turn; thus, Lines 1–3 and Lines 4–6 contain two diVerent arguments. The arguments analyzed in the preceding are rather trivial ones; their simplicity makes them suitable for illustrative purposes. Some more interesting cases will be analyzed in later chapters (see especially the analyses in Appendix B and Appendix C). A more detailed explanation of our notational system will be presented in the following chapters. As stated, this notation was developed for the analysis of underlying structures. Expressed arguments and their relations to underlying structures are dealt with in Chapter 10.
2.
The nature of formalizations
2.1 Formalizing the underlying structure In analyzing an argument, one has to determine its underlying structure and one has to formalize it. These are not two consecutively performed tasks; instead, reconstructing the underlying structure is normally carried out in the course of formalizing it. In deciding on the kinds of operations that make up the argument and their relationship to each other, the analyst will become aware of propositions that do not appear in the verbal expression but have to be
17
18
The Structure of Arguments
supplied so as to make the argument hang together. Those who have used our system have repeatedly found that it provides a catalyst for understanding the argument in all its ramiWcations. It should be appreciated that a formalization, like all categorizations, involves a loss of information. In our examples, operations were categorized into types: Presentation, Eduction, Evaluation, Truth value (and there are many others that will be introduced in the next chapter). There is no diVerence between, for instance, the formalization in Line 1 of Example 2 and that in Line 4 — both are: P(p) p. The formalization in Example 1 might be identical to that of some other argument involving an inference and an Evaluation (say, “The cat has milk on her whiskers. She must have jumped on the table again and lapped up the milk. What a monster!”). The verbal description of operations and outcomes is not part of the formalization and would of course be diVerent in the two cases. Our formalizations describe merely the “skeletons” of arguments: the types of operations and the way they are related to each other (see Chapter 1, Section 1.1). The formal analyses deploying this notation may be regarded as a descriptive grammar of arguments. But there is this important diVerence: A grammar entails a distinction between sentences that conform to its rules (are ‘grammatical’) and ‘ungrammatical’ expressions that do not. Our system, by contrast, is not designed to distinguish between “good” and “bad” arguments; it analyzes impartially any contribution of a speaker to a discussion (with the exception of certain extraneous remarks that do not bear on the content of the discussion, see Chapter 9, Section 1.2).5 2.2
The limits of formalization
The limits of the formalization have to be determined by the analyst. It will often be the case that additional steps of arguing might have been included in the formalization. Thus, in inferences, the conclusion often does not follow ineluctably from the premises. For instance, the Eduction in Line 5 of Example 2 might have been bolstered by additional steps like: ‘The party took place at the time I saw Abe in his apartment’, and: ‘Abe cannot have been in both these places at the same time’. And perhaps one may come up with even more steps. It is doubtful, of course, whether there is any sense in which all these steps may be said to have occurred in the author’s thought processes, but this by itself is no reason for not formalizing them. What is true of inferences is true also for certain other operations. Thus,
Arguments as operations
when a reason, X, is adduced for an action or state of aVairs, Y, one can always raise the question why Y follows from X, and when one then gives a reason for this, the same question can be asked again (as parents of small children will have had occasion to Wnd out). It is up to the analyst to decide how much detail the underlying structure of a given argument has to contain, and there can be no hard-and-fast rule to guide her. How Wne-grained the analysis will be may depend on the general objective of the investigation (as pointed out to us by Theo Herrmann). At times, analysts may diVer in the amount of detail they include in their analyses. We posit therefore a Formalization principle, which says that an analysis need not go into all the details; the investigator has to decide which details it is reasonable to include in the analysis. This does not mean, of course, that the analyst has complete license in determining which operations are to be included in the analysis and which are to be omitted. Thus, when the author expressly states a link in the argument, this has to be included in the formalization. Further, any link that is referred to later on in the argument has to be formalized as an operation, so that it can subsequently be targeted. 2.3
Alternative formalizations
Some arguments can be formalized in more than one way. The question then arises whether the resulting formalizations represent diVerent underlying structures or are merely alternative notations of the same underlying structure, just as in arithmetic there may alternative notations of the same expression. The diVerence between progressive and regressive analyses of an argument, discussed in the previous chapter (Section 2), appears to be an example of diVerent, though similar, alternative underlying structures, because, as argued there, these modes correspond to diVerent ways of reasoning. The following example also permits of alternative formalizations in our system: The sentence “The measures have not been approved by the Council” may be analyzed with a Truth value operation: T –(xi ), where xi stands for the proposition “The measures have been approved by the Council”.6 Alternatively, the whole sentence, negation included, can be a single operation, say, a Presentation P(p). The same options exist for the positive sentence “The measures have been refuted by the Council”, which may be analyzed as T –(xi ) — “It is false that the measures have not been approved by the Council” — or as P(p). The form in which the sentence appears in the verbally expressed argument — “not
19
20
The Structure of Arguments
approved” or “refuted” — does not entail a preference for any one of these alternatives.7 Besides these relatively clear-cut cases, there may be intermediate ones that may be conceived of either as alternative formalizations of the same underlying structure or as formalizations of two diVerent, though equivalent, underlying structures.
3. From argument to discussion In the Introduction (Section 2) we mentioned some empirical questions involving arguments that deserve to be investigated. An analytic framework that permits concise formalizations of arguments is an important tool for such investigations. Let us deal here brieXy with an additional empirical issue that lends itself to investigation within the present conceptual framework. An argument may be part of a conversation, discussion, or debate. In the conversation between Author 1 and Author 2 (Section 1), an operation in the argument made by Author 2 refers back to the Wrst argument. Referring back to previous arguments is what makes a discussion cohesive (at least minimally so); when each discussant talks about something else without relating to the contribution of others, this will hardly be considered a discussion in any serious sense. We can therefore explicate the notion of cohesion of a discussion in terms of the degree to which individual arguments relate to other arguments in it. This issue will be dealt with in Chapter 9, Section 2 (a proposal for quantifying this property is made in Schlesinger 1974). Further, we can identify arguments that do not “belong” to the discussion, that is, they are asides, fulWlling no function in it or belong to a diVerent discussion that is being conducted in parallel. These are arguments that neither refer to nor are referred to by any other argument in the discussion; see Chapter 9, Section 2.2, for a fuller treatment.
4.
Classes of operations
In the preceding we have introduced four types of operations: Presentation, Eduction, Evaluation, and Truth value. Many more are needed for the analysis of arguments, and the next chapter presents a list of operations. Here we deal
Arguments as operations
brieXy with categories into which all types of operations fall. Presentation is a category by itself, since it introduces new material and does not refer to a previous operation. Among operations that do target other operations a further distinction can be made between: 1. the operation of interpreting a statement; the author of such an Interpretation does not intend to add anything to the information contained in the statement, but merely to restate it; 2. operations intending to add something to the targeted operation or to its outcome — to infer something from it (e.g., Eduction, discussed in this chapter), comment on its Truth value or otherwise evaluate it (Evaluation), etc. Operations under (2), again, fall into several classes of operations. This becomes clear on considering the various ways in which an operation may relate to others; these will be enumerated here along with the name we have given to the class. An operation can — a. elaborate on the outcome of a previous operation: Elaboration; b. state what is the cause, reason, purpose, or motive of an event, action or state of aVairs, or what is its result: Cause; c. infer a statement from another one (as in an Eduction): Inference; d. justify a previous operation: JustiWcation; e. add certain kinds of comments on the nature of a statement: evaluate it, comment on its truth value, compare it to another statement, or state who is its author, at what the time or place it was made, etc.: Adjudgement; f. ask a question or state that one does not know something: Nescience. These considerations, then, deWne eight classes of operations, as shown in the Wgure below. Within each of these eight classes there may be several types of operations. Thus, Eduction falls under Inference, a class which, as will be shown in the next chapter, also contains several other types of operations; and Truth value and Evaluation are types of Adjudgment, which also contains several other types of operations. In drawing up a list of types, one may be guided by various alternative criteria of categorization; furthermore, the question arises of how Wne one should make the distinctions. One might decide on a broadly deWned type, lumping together various kinds of “steps” in an argument, or else one might decide to slice up this type into smaller ones. In this respect, no prin-
21
22
The Structure of Arguments
Operation
not targeting a previous operation Presentation
targeting a previous operation
not adding new information Interpretation
adding new information …
…. to an outcome Elaboration Cause Inference Nescience
… to an operator Adjudgment * JustiWcation
Figure 2.1. Eight classes of operations
cipled decision has been made (and probably none is possible); instead, our categorization into types of operations has been arrived at by considerations of expediency, on the basis of analysis of numerous texts of various kinds — legal, discursive, expository, etc. Operations can be compounded by so-called functors, which include conjunction, disjunction and implication (if … then …). These are discussed in Chapter 4. Besides operations, there may be relations of a diVerent kind in an argument, which we call connections; these will be dealt with in Chapter 8.
5.
Basic concepts — a summary
In this chapter the central concepts of our analytic system have been illustrated. An argument is conceived of as a set of (one or more) operations. Each operation is constituted of an operator, a target, and an outcome. There is a speciWc operator for every type of operation, and both the operation and the corresponding operator are symbolized by the same capital letter. The outcome of operation X is symbolized by the lower-case letter x. * As will become clear in the next chapter, this is not quite precise: some types of Adjudgment operations may apply to outcomes.
Arguments as operations
The target of the operation is symbolized by a parenthesized lower-case letter, when an outcome is targeted, and by a parenthesized capital letter, when an operator is targeted. A subscript serves as index to the speciWc outcome or operator that is targeted.
23
Chapter 3
Operators, targets, outcomes
In the preceding chapter, the principles of our system have been presented in outline. We discussed the main facets of an operation: an operator, its target, and its outcome. It remains now to give a detailed account of these notions. The treatment here will perforce be rather schematic, only few examples being given. More examples will be met with in later chapters, where the technical apparatus of our analyses will be further developed. The reader should be aware that the names we use for operations are technical terms and our use of them often deviates somewhat from the way the same names are commonly used. This seemed preferable to introducing new coinages. In Section 1 various types of operators will be listed. Sections 2 deals with targets and Section 3 — with outcomes.
1. Operators It will be recalled that each operation has its speciWc operator:1 The Eduction operation has an Eduction operator, and both are symbolized by E, the Truth value operation has a Truth value operator, T, and so on. A list of operators is therefore at the same time a list of operations. In compiling a list of operations, one is faced with the question of how these should be individuated. Our objective is to achieve a maximally revealing account of arguments with the minimum of conceptual apparatus, and the problem is therefore not which distinctions can be made but which ones it is important to make. There is nothing Wnal about the list of operations proposed here; what commended it to us is that these operations served us well in the analysis of many arguments. It may turn out that, for some purposes, additional operations will be useful. Wner distinctions within each operation can be made by means of superscripts. The question what is and what is not a separate operation has no single answer and the decision will often depend on the purposes the analytical framework is used for.
26
The Structure of Arguments
1.1
Classes of operations
Some operations have so much in common that they are grouped together as a class of operations (more precisely: operation types; but we will often use ‘operations’ as a shortcut). They not only have a common semantic denominator but are also syntactically similar: as will become clear further on, they have certain rules of notation in common, speciWcally, the kinds of targets and outcomes of these operations, and — as shown in Chapter 6 — the possibility of conXating with other operations. We distinguish eight classes of operations. Four of these classes consist of one operation type each, and the remaining four have a more numerous membership. Class 1: Presentation This class comprises a single operation type, Presentation (P). Presentation introduces a new text and provides a starting point for the argument. This is the only operation that does not refer to any previous operation; properly speaking, a Presentation has no target. But for the purpose of uniformity, each Presentation is assigned a “dummy” target, p; see Line 1 of Example 1, below. Class 2: Interpretation This class also comprises a single operation, Interpretation (I). The outcome of this operation consists of two parts: iP and iI. Here is an example of a written text. The Wrst author presents an ‘argument’, in the wider sense as used in our system (see Introduction; this example is from Shakespeare’s Hamlet, Act 2, Scene 2). This is interpreted in another argument, made by Author 2. Example 1 Author 1 1. P(p) p
Let her not walk in the sun.
Author 2 2. I(p1 ) iP iI
Keep her from the contamination of the world. This is the meaning of p1.
The verbal description pertains, as usual, to the underlying structure (Author 2 perhaps said “This means you should …” or the like). Author 2 commits himself only to iI , namely that iP is the correct Interpretation of Author 1’s admonition; as far as Author 2 is concerned, this admonition may be appropriate (acceptable) or not.2 (The superscript P serves as a reminder of ‘Presenta-
Operators, targets, outcomes
tion’, and the superscript I — of ‘Interpretation’.) ‘Interpretation’ is a technical term, and care should be taken to distinguish between its use within our system and the everyday use of this word. An Interpretation, in our usage, pertains to statements and texts. In everyday parlance one may discuss the “interpretation” of an event, but this will not be analyzed as an Interpretation. An Interpretation may take various forms, inter alia, translation into another language and a paraphrase for the purpose of explanation (but note that paraphrases may serve other purposes: e. g., to summarize, in which case it is what we call a connection; see Chapter 8, Section 2, under “Summarizing”; or for a non-verbatim report of what somebody said; see Chapter 10, Section 4.4). Misinterpretations and their formalization will be discussed in Chapter 10, Section 4.2. Class 3: Elaboration An Elaboration (O) adds information to a previously presented text, providing details that may serve to establish the identity of a participant or to add precision to something in the text. An Elaboration of “John sent a message to his neighbor”, for instance, may answer any one of the following questions: Which John (John Smith or John Carey)? How did he send it (by mail, by a messenger)? To which neighbor? Moreover, an Elaboration may pertain to the time or location of the event or situation referred to (John sent the message in the afternoon, from his oYce) even though no time or location is mentioned in the sentence (because they are usually ‘latent’ in the sentence: each event or situation occurs sometime and somewhere). (For some purposes, it may be expedient to diVerentiate between these diVerent kinds of Elaborations by means of superscripts, but this will not be done here.) Here is an example of an Elaboration: Example 2 Author 1 1. P(p) p Author 2 2. O(p1 ) o
Rudolph Hess, a high-ranking Nazi leader, deserted. Rudolph Hess, a high-ranking Nazi leader, deserted to England in 1941.
Suppose now that Author 2 states that following his desertion, Hess was imprisoned. As stated, Elaborations serve to identify or to add precision. What happened to Hess subsequently refers to a diVerent event. This information
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The Structure of Arguments
does not supply any details about the desertion; it does not help us in identifying a participant in Author 1’s statement or to specify anything said therein. This, then, would not be an Elaboration but rather an additional Presentation, albeit one that is connected in some way to the statement about the desertion. This type of connection will be discussed in Chapter 8, Section 2. ‘Elaboration’, then, is one of the technical terms in our system: not everything that is commonly called ‘elaboration’ falls under this term. Class 4: Cause This class consists of two operations: Accounting (A) and Result (R). Accounting contains several distinct notions: causes as well as reasons, motives for actions as well as purposes for carrying them out, and also excuses, which are reasons or motives that are given to justify someone’s behavior.3 Result includes consequences of an action or state of aVairs. Result and Accounting are converse operations; that is, when x is the cause of y, one can either have an Accounting operation targeting y — A(y) — or a Result operation targeting x: R(x); similarly, when x is the motive for action y, this can be symbolized either as an Accounting operation targeting y or as a Result operation targeting x. Take, for example, the statement “Because unemployment was on the increase, there was widespread discontent among the working classes”. This can be analyzed with either a Result operation or with an Accounting operation. The outcome of Result consists of two parts, and so does the outcome of Accounting, as illustrated in Examples 3–4. Example 3 1. P(p) 2. R(p1 )
p rP rR
Unemployment was on the increase. There was widespread discontent among the working classes in Serbia. This was the result of p1.
The author of this argument commits himself to two statements, rP and rR (the superscript P serves as a reminder of Presentation, and the superscript R — of Result). Note that rP may be true (there was discontent) and yet rR may be false (this was not the result of unemployment); whereas the reverse is impossible. More about this in Section 3.1 in this chapter. Example 4 1. P(p)
p
There was widespread discontent among the working classes in Serbia.
Operators, targets, outcomes
2. A(p1 )
aP aA
Unemployment was on the increase. This was the reason for p1.
Here, too, the author commits himself to two statements, aP (P for Presentation) and aA (A for Accounting). Again, aP may be true and aA false, but the reverse is impossible. Result is a progressive operation: the sequence of operations conforms to the sequence of events (Wrst x, then its consequence y). Accounting is the corresponding regressive operation; see Chapter 5, Section 1, for further discussion. Class 5: Inference There have been quite a few proposals for the classiWcation of inferences, from the Aristotelian list of topoi, through medieval adumbrations of these, to recent proposals by Perelman and Olbrechts-Tyteca (1969), Toulmin, Rieke and Janik (1984), and Kienpointer (1992), among others. We have not attempted to improve on these in any way; nor did we opt for any one of these; our objective was the more modest one of presenting a short, not exhaustive, list of Inferences that were found to be useful in our analyses. In our system the Inference class comprises three subclasses. One subclass contains operations involving deductions (or modeled after deductions), and one — operations involving inferences which, while not sanctioned by deductive logic, frequently appear in argumentation. The third subclass includes the operation of restoring the presupposition of a previous operation. Subclass 1: Deductive inferences. First, a general comment is in order. The operations in this subclass include those that are modeled on true deductive inferences, but are not strictly analytic (see, for instance, Chapter 6, Example 15). There are, for instance, “… bad deductions that cannot be classiWed as inductions” (Wachbritt 1996: 177). Toulmin (1958) even claims that inferences used in everyday arguments — which he calls “substantial” arguments — are not and cannot be truly analytic (see also Perelman 1982: 53, on “quasilogical” arguments that have a “logical appearance”). Keeping this in mind, the following operations belong under Subclass 1: Modus Ponens (N): Given two premises “if a then b” and “a”, one may infer “therefore b”. We also include in this category syllogisms (as, for instance, inferring “x is a B” from “All As are B” and “x is an A”).
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The Structure of Arguments
Modus Tollens (M): Denying the consequent: Given that “if a then b”, when the consequent is false (not b), it may be concluded that the antecedent is also false (not a). Deduction (L): This is the default category of Subclass 1: it includes all deductions that do not fall under the head of syllogism, Modus Ponens, or Modus Tollens. An instance of L would be inferring “A is bigger than C” from “A is bigger than B” and “B is bigger than C”. It seems appropriate to single out M and N as separate categories because of their importance and frequency. Should there be a need to distinguish additional types of deduction, this can be done by superscripts on L. Subclass 2: Non-deductive inferences. Operations in this subclass are neither logically compelling nor modeled after a deduction. They are, however, very commonly deployed, and often are quite convincing, as will be seen presently. The subclass includes the following operations: Backward Modus Ponens (B): When the consequence of a conditional is aYrmed, one often concludes that its antecedent is true: If a then b; b; therefore a. In contrast to Modus Ponens and Modus Tollens, this operation does not result in a logically valid conclusion; an unwarranted application of it constitutes the Fallacy of AYrming the Consequent. Such a conclusion may be justiWed, however, when there is no likely alternative antecedent of b. Suppose we know that “If it rains, the pavement gets wet” and that “The pavement is wet”; then one may tend to conclude that it has rained, although this is not logically valid. Similarly, a physician may infer (with a certain probability) the nature of the disease from certain symptoms, sometimes even from a single one. Peirce discusses, under the term abduction, hypothesized explanations of new facts as a legitimate form of inference: “The surprising fact, C, is observed; But if A were true, C would be a matter of course, Hence there is reason to suspect that A is true.” (Buchler 1940: 151; see also the treatments of abduction by Novak 1995, Bybee 1996, and Walton 1996, Chapter 8). Generalization (G): Although Generalizations are not logically compelling, they are often resorted to, and sometimes with good reason. When you go to a new country and are served by a red-headed waiter, it is hardly appropriate to conclude that all waiters in that country are red-headed, but when you buy, say, a Peugeot 306 and enjoy the smooth driving, you may conclude with good reason that all cars of this make drive smoothly. And the child who gets badly
Operators, targets, outcomes
burned when touching a lighted candle had better conclude that all burning candles can hurt. Perelman (1982: 106) treats this under “argument by example”. See also Klein (1980: 28). Analogy (W): Much of our reasoning is based on analogies: when two cases are similar in some relevant respects we may conclude that they are similar in certain other respects (see Perelman 1982: 114f, on analogy in argumentation, and Klug 1966: 97–123, on the problem of the validity of analogies). Care should be taken not to let oneself be misled by the everyday use of the term “analogy”. This term is used here only for inferences from other statements. It does not include analogies deployed in explanations (see Govier 1988: 216), which would be analyzed in our system as Comparisons (Class 7, subclass 2). Also, if I compare thee to a summer day, this is not an analogy, in our sense. But from the fact that on a summer day food spoils when left outside one might infer by analogy that food will spoil when left in a very warm room. The term ‘Analogy’ is used here only for a conclusion drawn from a proposition on the basis of some similarity; it does not pertain to parallelisms such as those deployed in test items (e.g., “foot is to shoe like hand to ….?”). A possible objection here would be that an Analogy is really a Generalization from an instance to a rule, followed by a deduction from this rule to a new instance, and that it is therefore unparsimonious to introduce an additional category, Analogy. However, it is often impossible for the analyst to carry out such a reduction. The nature of the general rule that underlies the Analogy may be unclear even to the author of the argument, who may merely have felt that the instances are suYciently similar to warrant drawing the Analogy. It would be futile, therefore, for the analyst to exercise his ingenuity in constructing a general statement from which the outcome of the analogy might then be deduced. However, when it is clear in what the similarity lies, it may be preferable to analyze the Analogy as a Generalization followed by a syllogism. Take, for instance, the following argument (Walton 1989: 258, quoting Copi’s introductory text): I infer that a new pair of shoes will wear well on the grounds that I got good wear from other shoes previously purchased from the same store.
Example 5 1. P(p)
p
I got good wear from other shoes purchased from store X.
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The Structure of Arguments
2. G(p1 )
g
3. N(g2 )
n
〈 It may be inferred by Generalization that 〉 all shoes, bought at store X, will wear well. 〈 It may be inferred by a syllogism that 〉 these shoes will wear well.
(A more detailed analysis of syllogisms will be presented in Chapter 5, Section 3.1.) Eduction (E): This operation comprises all other non-deductive Inferences (unless they are modeled after deductive ones; see above); it is the default category of Subclass 2. For instance, Abe has a haggard look today. One can infer from this that he has been at Ben’s wild party last night.
It is important to distinguish between an inference from a given statement and an operation that has the outward appearance of such an inference. Thus, when one says that the reason Abe has a haggard look is that he attended Ben’s party, one assumes both Abe’s looks and his attendance at the party to be “given”, and sets out to establish a causal relation between them; one does not infer anything. Hence this is a Presentation followed by Accounting (see above, Class 4), rather than by an Eduction. Eduction includes, among others, inferences by a fortiori reasoning and reasoning that is “justiWed … by the way things habitually happen in the world” (Strawson 1952: 37). It would have been possible to provide for several types of operations instead of an overall type, Eduction, but for our purposes there seemed to be no need for such a Wner subdivision. Subclass 3: Presupposition restoring. In a discussion, one frequently claims that a preceding argument is based on a certain presupposition and responds to the latter; hence we introduce the following operation type: Presupposition restoring (H): Assertions (and questions) have presuppositions underlying them. “The present king of France is bald” presupposes (incorrectly) that there is a person who is now king of France. Behind the statement that Jones has stopped using drugs, there lurks the presupposition that Jones had been using drugs. When another person responds to this, she may explicate: “So he had been using drugs”, or she may base an argument (e.g., “He always had a weak character”) on the assumption that Jones had been using drugs. In other words, she ‘restores’ the presupposition from the
Operators, targets, outcomes
speaker’s assertion (without there necessarily being any conscious retrieval process: ‘restore’ is being used Wguratively here). Restoring a presupposition diVers from other Inferences in our system: the same presupposition could have been restored also from the negation of the statement, “Jones has not stopped using drugs” (see Levinson 1983, Section 4.3 for further discussion of the diVerence). But, like other Inferences, Presupposition restoring creates a new statement from a given one. The presuppositions of a statement made by Author A will often not be included in the formalization of Author A’s argument (the analyst avails herself of the Formalization principle; see Chapter 2, Section 2.2). But when a participant states explicitly what is presupposed by a previous statement, this will of course have to be included in the formalization of her argument. Also, when she infers something from a presupposition of a previous statement, refutes it, or otherwise targets it, she must Wrst have ‘restored’ it, and a Presupposition restoring operation will appear in the analysis of her argument. For example: Example 6 Author 1 1. P(p) p
I had forgotten that today is Dora’s birthday.
Author 2 h 2. H(p1 ) 3. T – (h2 ) t–
〈 This presupposes that 〉 today is Dora’s birthday. This is not true.
The Presupposition restoring operation may also target an outcome in the same argument, as when one makes a statement and then goes on to spell out its presuppositions (e.g., “John has stopped taking drugs. I take it for granted that he had been using them”). (On Presupposition restoring see also Chapter 10, Note 16.) Class 6: JustiWcation This class comprises a single operation, JustiWcation (J) (akin to Chittleborough and Newman’s 1993, ‘supportive’). A detailed discussion of various kinds of JustiWcations is presented in Chapter 5. There is some similarity between this operation and Accounting, but it is important to distinguish between them. An Accounting operation is an answer to the question “Why is that so?”, whereas a JustiWcation answers the question “What justiWes this assertion?”. The diVerence between these two operations is discussed more fully in Chapter 5, Section 1.2.
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The Structure of Arguments
JustiWcation is a regressive operation whereas Eduction is a progressive one (see Chapter 1, Section 2). Corresponding to the Eduction argument given in the preceding, there is an argument with a JustiWcation, which reverses the sequence of operations: Abe has been at Ben’s wild party last night. What justiWes my saying so is that he has a haggard look today.
The distinction between Inference operations and JustiWcation is discussed at length in Chapter 5, Section 1. Class 7: Adjudgment Within this class there are four sub-classes: Subclass 1. Adjudgments bearing on the truth or falsity, or validity / nonvalidity of propositions. Subclass 2. Adudgments pertaining to other norms or values (e.g., ethical, legal or esthetic values). Subclass 3. Adjudgments identifying the author of a claim or bearing on the circumstances in which an operation was made, the propositional attitude expressed by it and its illocutionary force. Subclass 4: Adjudgments bearing on the relationship between a category or class and its members. What all these have in common is that they make statements about other propositions. Aside from this “aboutness”, the Adjudgment class is semantically heterogeneous. There are, however, similar rules of well-formedness which the operations of this class are subject to, as will become clear further on (Section 2, below; see also Chapter 6, Section 3.2). Subclass 1. Adjudgments bearing on truth / falsity, or validity / non-validity. Truth Value (T): This operation pertains to statements about truth or falsity. For example: Your claim that Abe was at Ben’s party is false.
The outcome of an operation may be claimed to be true, false, incorrect, or correct, in a certain sense only, or “in the main”. Expressions like “analytically true (or false)” are among the possible meanings of T. Hedges (e.g., “Is a whale a Wsh?” “No, technically, the whale is a mammal”) are also formalized as a
Operators, targets, outcomes
special kind of Truth values. This operator thus may have a diVerent interpretation in each case (but one can, of course, always resort to superscripts to identify certain meanings). To indicate the two values ‘true’ and ‘false’ we use superscripts: T+ and T–.4 Validation (V): This pertains to a statement about the extent to which another operation is valid, justiWed or well-founded. To indicate ‘valid’(‘well-founded’) and ‘invalid’ (‘unfounded’) we use superscripts: V+ and V– , respectively. On the diVerence between Validation and Truth value see Section 2.2, below. Confrontation (C): Confrontation is a comparison between statements in respect to their truth value. It applies to at least two terms, whereas T applies to only one (see Section 2.1 of this chapter, on the target of C). This operator is deployed to indicate that statements are compatible or incompatible with each other, that they diVer in the degree of conWdence assigned to them (see below, Section 1.3), or that they are logically equivalent. Subclass 2. Adjudgments pertaining to other norms or values. Evaluation (Q): An Evaluation (‘Q’ stands for ‘quality’) is a judgment in regard to any norm or value other than Truth value, T, or validity, V. It includes esthetic judgments as well as deontic statements (e.g., judgments vis à vis a social or legal norm), as when an action or state of aVairs referred to in a statement is claimed to be immoral, permitted, obligatory, or requested. (While it would be possible to introduce further diVerentiations by means of superscripts, we will not do so in this work.) Status (S): While Evaluation, Q, applies to actions, events, or situations, Status applies to operations or arguments; it refers to any property of an operation or argument other than its validity. Examples are: “This argument is redundant (tautologous, etc.)”, “This is a brilliant argument”, “This is a syllogism”. Status may refer also to the function of an operation in an argument or in the discussion, and to any claim about the verbal form of the operation (“This is Wgurative/ archaic language”, etc.). It can also apply to a whole sequence of arguments, as in “This discussion is getting out of hand”. Comparison (K): Confrontations (see Subclass 1, above) apply to truth values and probabilities, whereas Comparisons apply to all other values. To illustrate, take an a fortiori argument such as: “Even Tim, who is much stronger than you, couldn’t force the door, so it follows that you won’t be able to force it”. This
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The Structure of Arguments
argument rests, among others, on a Comparison of the strength of two people. Similarly, when an Analogy is drawn, a Comparison, K may state what the compared entities have in common; see Chapter 5, Section 3.2. Not only similarity, but also identity of two items referred to in previous statements may be analyzed as a Comparison (e.g., “The consul-general turned out to be the spy who sold the plans to the enemy”). A special type of Comparison pertains to correlations: x increases (or decreases) with y. A Comparison may hold between entities (see Section 3.3, below, for the notation of these) or between statements (e.g., “Statement x is more authoritative than statement y”). Subclass 3. Adjudgments identifying the author of a statement or bearing on the circumstances in which it was made, and the type of statement made. Designation (D): There are three sub-types of Designation: Sub-type A. Sub-type B.
Sub-type C.
Designations of the author of an operation. Designations of the circumstances in which the operation was made, viz. the time, the place, or the (linguistic or extralinguistic) context of the operation. Designations characterizing statements or sentences
As will be shown presently, within each sub-type there are several kinds of Designations, distinguished by superscripts. In principle, every operation may have several Designations. The conventions for symbolizing Designations are discussed in Section 2.2, below, and in Section 4 of Chapter 6. Sub-type A. Designations of the author. This sub-type includes: DA – author; DI – indeWnite author, i.e., when the author is “someone”, “anyone”, and the like; DR – when the “author” is a law, regulation or rule; It is important to keep in mind that these Designations are not used to indicate what the analyst knows about the identity of the author, but only what is implicit in the text. The identity of the author of an argument may be indicated by the analyst as “Author 1”, or the like — see Example 6, above — but not by a Designation operator. The formalization will include a Designation only when the author of the argument ascribes a statement to someone else (“X said that …”).
Operators, targets, outcomes
Since the most frequent Designations are of authors, we will introduce the convention that the superscript in DA may be omitted — D will stand for DA — unless there are additional superscripts (because in that case, omitting the superscript A might seem to indicate that there is no author Designation). Sub-type made: DT DL DC
B. Designations of the circumstances in which the operation was – – –
time; location, place; other information about context: situation, circumstances, addressee, etc..
These Designations are used when an author reports what someone else said at a certain time or place, etc. (e.g., “Yesterday Jim claimed that …” or “This has also been claimed by Jim yesterday”). Therefore the superscripts T, L, or C will appear always in conjunction with a superscript of sub-type A; e.g., DA, T (“This has been said by Jim yesterday”), DI, L (“This has been said by somebody at the pub”), or DA, C, T (“This has been asserted by Mr. Smith in the presence of witnesses last Monday”). Sub-type-B Designations (like those of sub-type A) do not apply to what the analyst knows about the time and place at which the operation was performed, but only to what an author reports about the time, place or circumstances of someone else’s operation. Designations of sub-type B must be distinguished from Elaborations. The former pertain to the time, place, or circumstances in which a previous operation was performed. When an author speciWes the time or place of an event or a situation described by a previous operation, this will not be a Designation, but an Elaboration; cf. Example 2, above. Sub-type include: DP DD DF DO
C. Designations characterizing statements or sentences. – – – –
These
propositional attitude intention to act performative (other than assertives, questions, and imperatives) imperative
Propositional attitude. An author may state that he fears, hopes, wishes, etc. that x; in other words, he has a certain propositional attitude toward x. In a sentence referring to such a propositional attitude — e.g., “I fear that hobgoblins will invade our home” — one can distinguish between a “core” clause indicating the state of aVairs that is feared (hoped for, etc.) — hobgoblins will invade our
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The Structure of Arguments
home — and a statement that this state of aVairs is feared (hoped for, …). Each of these can be targeted by itself (cf. “You should not be afraid because of this” versus “No hobgoblins will ever invade your home”). The expression of a propositional attitude — “I fear”, “I hope”, etc. — will be symbolized by DP (P for ‘propositional attitude’). This symbol will be used for any propositional attitude — fearing, hoping, and so on — and only the verbal description will reveal which one has been so symbolized.5 Details of the analysis (how DP targets the outcome of another operation and how it pertains to an operation that has not appeared previously in the analysis) will be given in Section 4.4 of Chapter 6. Intention to act. Suppose an author expresses his intention to perform (or not to perform) a certain activity; for instance: “I am going to revenge myself on him” (note that this diVers from an assertion like “I have taken revenge on him”, which is not a statement of intention). To indicate that the author’s assertion concerns his own intended activity, we use D with the superscript D (for ‘design’): DD.6 Performative. By DF we symbolize performatives other than imperatives (requests, commands, etc.; see below) and questions (see Class 8 of our operation types, further on). Assertives, which some authors treat as performatives, are also excluded. DF, then, serves to indicate speech acts fulWlling such functions as promising, apologizing, thanking, declaring (e.g., declaring war). Our formalization does not distinguish between various performatives — e.g., between promising and declaring; only the verbal description will make it clear which of these applies. It should be noted that DF diVers from other types of operations in that it deals with the speech acts performed by utterances (rather than with their propositional content). While our system is not primarily concerned with the pragmatic functions of arguments (see Introduction), it was decided that the analysis should reXect the fact that a sentence does not function as an assertion. Our system focuses on propositions, and accordingly our analysis of performatives isolates the propositions contained, but not asserted, in them (see Lyons 1981: 141). How DF may target the outcome of another operations will be shown in Chapter 6, Section 4.4. Imperative. Commands, advices, invitations, and all sorts of imperatives (see Hamblin 1987, for discussion) will all be symbolized by DO (O for ‘order’).7 In the foregoing we have seen that the Evaluation operator, Q, is used,
Operators, targets, outcomes
among others, to indicate that an action or state of aVairs is permitted, obligatory, or requested. It should be appreciated that such statements diVer from imperatives: telling someone that an action is prohibited does not necessarily constitute an order (command, advice) to abstain from it (the prohibition may apply to a diVerent class of people, or one may exhort someone to disregard it). When a statement like “X is obligatory (prohibited)” is construed as both an assertion that X is obligatory (prohibited) and an injunction to do (or not to do) X, it will be formalized as two operations, Q and DO, with the latter following from Q by an Inference; see Chapter 6, Section 4.4 for an analyzed example. The superscripts of this sub-type may appear in combination with other superscripts of D. To illustrate, suppose one asserts that statement x (appearing in a previous outcome) was made by John at the train station, and that this statement referred to what John feared would happen. This will be symbolized by DA, L, P (x) — A, L, and P, for author, location and propositional attitude, respectively (there will be no superscripts for time, T, and other circumstances, C, because these are not provided by the author of the argument). When it is asserted that a week ago John intended x, we write DA, T, D (x), and so on. This completes our discussion of Designations, that is, of Subclass 3 of Adjudgments. We now turn to the next subclass. Subclass 4: Adjudgments bearing on the relationship between a category or class and its members. Subsumption (U): A Subsumption is a claim that a certain term is included in some category. For example, the syllogistic inference that Socrates is mortal from the general statement that all men are mortal is made via the Subsumption that Socrates is included in the category of “men”. Examples that serve to illustrate a general statement are also Subsumptions. Suppose someone says: “Animals that eat Xesh have shorter intestines than those who eat only plants; lions, for instance…”. The last clause is a Subsumption of ‘lions’ under ‘animals that eat Xesh’.8 Subsumption may be partial. One may state that some teachers are member of the teachers’ union (and such statements may also Wgure in syllogisms). The U operator will then be supplied with a superscript: US. There are additional relations between classes; for instance, classes may overlap or may be coextensive. These could be added to our list of operations; but since they seem to occur infrequently, we will not go into this further here.
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The Structure of Arguments
Class 8: Nescience This class (the word ‘Nescience’ means ‘non-knowledge’) comprises two operations, which will be dealt with in Chapter 7: Question: The symbol for the Question operator is ? (with a superscript). “I don’t know”: The symbol for this is /?/ (with a superscript). The table below lists the classes of operations and the operations belonging to them. The examples are designed to serve as reminders and are not introduced Table 3.1 Eight classes of operations Examples 1. 2. 3. 4.
Presentation Interpretation Elaboration Cause Result Accounting 5. Inference Modus Ponens Modus Tollens Deduction
(P) (I) (O)
[A new statement] This means that … . This event took place at … .
(R) (A)
The result of this was that … . The reason (motive) of this was … .
(N) (M) (L)
Generalization
(G)
Analogy
(W)
Backw. Mod. Pon. Eduction
(B) (E)
[ ‘if a then b’ and ‘a is the case’], hence ‘b’ [‘if a then b’ and ‘not b’], hence ‘not a’. [‘a is bigger than b’ and ‘b is bigger than c’], hence ‘a is bigger than c’ [In Nice we met an English-speaking oYcial.] So apparently all Nicean oYcials speak English. [In summer food spoils when left outside.] So food will spoil when left in a very warm room. [‘if a then b’ and ‘b is the case’], hence ‘a’. [He gambles for high stakes.] So he must be irresponsible. [J. has stopped smoking.] So J. had been smoking. What justiWes this operation is … .
Presupposition restoring (H) 6. JustiWcation (J) 7. Adjudgment Truth value (T) Validation (V) Evaluation Status Confrontation Comparison Designation Subsumption 8. Nescience Question “I don’t know”
(Q) (S) (C) (K) (D) (U)
This [statement] is true/false (correct/incorrect). This [operation] is valid (well-founded)/ invalid (unfounded). This is not permitted. This [operation] is ingenious. These claims are contradictory. a is bigger than b. The author of this claim is N. a is a member of category b.
(?) (/?/)
What does this mean? I do not know what this means.
Operators, targets, outcomes
in lieu of deWnitions. The square brackets in the examples for the Inference class enclose the premises of the respective Inferences. In this book we will use the last three letters of the alphabet, X, Y, and Z (italicized) as variables for operators, and the italicized letters in lower case, x, y, and z — as variables for outcomes. 1.2
Scope of meaning of operations
As pointed out at the beginning of this chapter, the categorization of operations proposed here necessarily entails a decision as to the scope of each category. In fact, some of our operations cover a rather wide range of meanings. Take Eduction; this operation will be deployed in common-sense arguments (like “he looks haggard; this shows that he was at the party last night”), in a fortiori arguments (“thieves get prison sentences, so robbers should certainly be imprisoned”), and in fact, in all arguments that do not fall under one of the other Inference categories N, M, L, G, W, B, or H. The meaning of E thus has a rather wide scope. Compare this operation to N, Modus Ponens, which applies to a closely circumscribed range of Inferences, and which thus has a narrow range of meanings. Scope of meaning forms a continuum on which the various operations can be placed (though in practice such placing is vitiated by the incommensurability of most operations in regard to this variable). It is always possible, as has often been done in the preceding, to restrict the meaning of an operation by means of superscripts. Thus, the Designation operator with the superscript A means “The author of … is …”; with the superscript T it means “The time the statement was made is…”, and so on. 1.3
Degree of conWdence
An author may have complete conWdence in the operation he performs, or else, he may express a lower degree of conWdence. For instance, he may begin an argument by stating a proposition (a Presentation operation) and indicate that it is only plausible; he may state that from this proposition such-and-such can be inferred with some probability (an Inference operation), or he may state that so-and-so probably is the author of some statement (a Designation operation). Apart from Questions, where the concept degree of conWdence does not apply (there is no sense in asking something with a certain degree of conW-
41
42
The Structure of Arguments
dence), all operations may be carried out with less than complete conWdence on part of the author. To indicate this, the operator is preceded by a superscript %: %P, %E, %D, and so on. The % superscript is not of the same kind as the superscripts that provide subclassiWcations of operators (Section 1.1); unlike the latter, % does not classify the operator it is appended to but, rather, modiWes it. The % superscript may also be used with the Truth value operator, T. When a previous outcome, x, is said to be probable, we cannot append % directly to a target x (% is not an operator); instead, this will be symbolized by %T(x).9 The degree-of-conWdence superscript, then, typically serves to indicate less than perfect certainty; operations carried out with complete certainty require no such superscript. However, when the author expressly states that he is completely certain of a given operation, this has to be taken care of by the formalization. Thus, when the author states concerning a previous outcome, x, that it is “quite certainly so”, this will be indicated by %T+ (x). The diVerence between quite certainly and probably will become apparent only in the verbal description. For most classes of operations, the degree-of-conWdence superscript is either appended both to the operator and to the outcome of the operation (as in Line 1 of the following example) or to neither (as in Line 2 of the following example). This rule does not hold for Inference operations: in some arguments, the Inference operator, but not the outcome, has a degree-of-conWdence superscript, and in others — only the outcome of the Inference and not the operator has this superscript. In Line 3 of the following example, the Inference, E, has an outcome that “inherits” the degree of conWdence attached to the targeted outcome p1. Example 7 1.
Author 1 %P(p)
%p
Author 2 2. D(%p1) d Author 3 3. E(%p1)
%e
It is probably going to rain much this season. This is what the Weather Bureau predicts. 〈 One may infer from this that 〉 the prices of vegetables will probably go down.
However, outcomes of Inferences do not invariably inherit the degree-ofconWdence of the target. Consider: “It will probably rain. It follows that they
Operators, targets, outcomes
will all take their umbrellas when going out”: This will be analyzed as: %P(p) with outcome %p; E(%p) with outcome e (and not %e). Likewise, Presupposition restoring sometimes does not inherit %. Thus, that Donald probably stopped smoking — %P(p) %p — presupposes that he had been smoking: H(%p) h. Inferences from probable outcomes, then, can have either one of these forms: E(%x) E(%x)
%e
e
(where E serves as an example of an Inference). Now, the situation is similar in regard to Inferences from statements made without any reservation, i.e., those targeting outcomes not marked with %. From the fact that there is going to be a lunar eclipse one may infer that Jill, an amateur astronomer, will probably be out with a telescope to watch it, or else that she will certainly do so: %e
E(x) E(x)
e
In some arguments, the Inference operator will itself be marked by %. As discussed by Allen (1994) there is a distinction between ‘probably P, so [probably Q]’ (the normal reading of ‘probably P, so probably Q’) and ‘probably P, [so probably] Q’ (for instance, from “Our new type of blood test showed that ….” one can probably infer that the patient will reject the transplant). This means that, at least in principle, the above four operation schemes have four parallel schemes with %E instead of E. What all this amounts to is that whether the outcome is or is not marked by % does not depend entirely on the marking of either the operator E or the target. As stated, it is only operations of the Inference class that oVer such a diversity in the use of %. In most other types of operations the presence of % in the outcome depends on its presence in the operator; that is, there are only four possibilities. For example, for Designations there are only the following alternatives: D(x) %D(x) D(%x) %D(%x)
d %d
d %d
(e.g., ‘d is the one who wrote “x”.) (e.g., d is probably the one who wrote “x”.) (e.g., d is the one who wrote “%x”.) (e.g., d is probably the one who wrote “%x.”)
43
44
The Structure of Arguments
As we have seen in Examples 1, 3, and 4, above, Interpretations, Accounting, and Result have outcomes consisting of two parts; for instance A(x)
aP aA
In regard to presence or absence of the % superscript, aA is dependent on A (just as the outcome d is dependent on D in the preceding), whereas there is no such dependence of the % superscript of aP on A; for instance, we may have A(x) %A(x)
%aP
aA
Probably … [aP]. This is the reason that x.
aP %aA
….. [aP]. This is probably the reason that x.
(and likewise with %x as target). The same holds for Result and Interpretation operations.
2.
Targets
2.1 Multiplex and simplex targets Three operators of the Adjudgment class, Comparison, Confrontation and Subsumption, have multiplex targets, that is, they apply to more than one term. Multiplex targets are divided by commas. A Comparison, for instance, holds between two or more terms; when x is compared to y, we write accordingly: K(x, y). What determines the sequence of the two terms in the target, x and y, is the meaning assigned to the operator. Suppose that it is claimed that statement x is formulated more clearly than statement y. We have now two options: K may be assigned either the meaning ‘is formulated more clearly than’, and then we write K(x, y); or we assign to K the meaning ‘is formulated less clearly than’, and write K( y, x). Of course, when the Comparison involves a symmetrical relation (like ‘is diVerent’ or ‘is similar’), the sequence of x and y is indiVerent. Similarly, “x and y are contradictory”, which states something about the Truth value of x and y, may be symbolized either as C(x, y) or as C( y, x): ‘contradictory’ is a symmetrical relation. In Subsumption, U, the sequence is: subsumed term, term under which the latter is subsumed. Thus, the assertion that x is a member of the category y, is symbolized: U(x, y).
Operators, targets, outcomes
K and C may have multiplex targets of more than two terms. For instance, if x is bigger than y and y is bigger than z, one may write K(x, y, z). Comparison, Confrontation and Subsumption are operations that inherently require more than one term (a may contradict b, but “a contradicts”, tout court, does not make sense).10 Other operators do not have multiplex targets; their targets are simplex. Thus, Truth value has a simplex target. The operator that compares two outcomes in respect to Truth value is not T, but rather C, a Confrontation. C(x, y) applies even where no claim is made concerning the Truth value of x by itself or of y by itself, but only about their value relative to each other. Similarly, when an author says in which circumstances a text was presented, this will be symbolized by a Designation of circumstance, DC; but when he states that text x was presented immediately after text y, then x and y will be targets of a Comparison, K. 2.2
Operations and outcomes as targets
An operation may apply either to another operation or to its outcome (a third possibility will be discussed in Chapter 10, Section 4). When the target is an outcome, it will be symbolized by a parenthesized lower-case letter: X (y), with the outcome x
By contrast, when the operation applies to a previous operation, the target of the operation will be an operator symbolized by a parenthesized capital letter: X (Y ), with the outcome x.
Since there is a one-to-one relationship between operations and operators, we will speak indiscriminately about operations and operators in this context. The distinction between these two types of targets can be elucidated by comparing Truth value, which targets outcomes, with Validation, which targets operations (or, what amounts to the same, operators). As shown in the next example, one can claim that there are no grounds for drawing a certain Inference, while agreeing with the outcome of that Inference. Example 8 Author 1 1. P(p) p e 2. E(p1 )
Jane does not like rock music. 〈 This shows that 〉 she is a sensitive person.
45
46
The Structure of Arguments
Author 2 3. T+ (e2 ) t+ – v– 4. V (E2 )
It is true that Jane is a sensitive person. 〈 But 〉 this cannot be concluded from her dislike of rock music.
Explanation: Line 4: The word “but” in the verbal description is not represented in the formalization. The outcomes in Lines 3 and 4 are obviously somehow related, but this is not a targeting relation. Chapter 8, Section 2 deals with the notation for this type of relation.
The distinction made here parallels the one made by Shaw (1996) between ‘assertion based’ and ‘argument-based’ objections, and that by Rips (1998) between ‘rebutting’ and ‘undercutting defeaters’. The following table compares the use of Validation and Truth value operators with various operators and outcomes as targets. Table 3.2. Operators and outcomes as targets: V versus T Validation Presentation
T–
V– (O): Making this Elaboration is unfounded. V– (A): Giving this reason is unfounded. V– (X): Making this Inference is unfounded. V– (X): Making this Adjudgment is unfounded.
T– (iI ): This is not the correct Interpretation. T– (iP ): The statement iP is false. T– (o): The outcome of this Elaboration is false. T– (aA ): This is not the reason. T– (aP ): aP (the reason) is false. T– (x): The inferred statement is false. T– (x): The outcome of this Adjudgment is incorrect.
(P): This Presentation is unfounded / insuYciently supported. Interpretation V– (I): Making this Interpretation is unfounded.
Elaboration Cause Inference Adjudgment
Truth value
V–
(p):
The assertion p is false.
There will be arguments that can be analyzed with either the Validation or the Truth value operator, the choice between them being immaterial. Some operations are like V in that they can target only operators; others, like T, can target only outcomes; and still others can target either operators or outcomes. This is summarized in the following table. The table does not include Presentation, because this operation, by deWnition, does not apply to a previous operation.
Operators, targets, outcomes
Table 3.3. Possible targets of operations Operations that can target only operators
Adjudgments: V, S JustiWcation Note:
only outcomes Interpretation Elaboration Cause (A, R) Inference (all operations) Adjudgments: T, C, Q
operators or outcomes
Adjudgments: D, K, U Nescience (?, /?/ )
On the targets of JustiWcations see Chapter 5, Section 2.1, and on the targets of Nescience — Chapter 7, Sections 1 and 6).
The following comments explain this table. 1. Operations that can target only operators Validation, V, assesses the validity of an operation, whereas Status, S, assesses any other characteristic of an operation. When an operation is judged as being trivial, redundant, esthetically pleasing (“What a brilliant argument!”), or an instance of ‘male reasoning’, the symbolization will be S(X). The targets of JustiWcations will be dealt with in Chapter 5, Section 2.1. 2. Operations that can target only outcomes Interpretation, Elaboration, and the operations of the Cause, and Inference classes can target only outcomes: One does not interpret the operator I or elaborate on the operator O, but rather outcomes, and likewise, reasons, motives, or results can be ascribed only to activities, events, or situations referred to in outcomes. The same holds true for Inferences. These can have only outcomes, not operators, as targets. It is often possible to infer something from the fact that a certain operation has been made, but the target of such an Inference is not the operation (or operator) in question but rather the fact of its having been made by somebody, and then DA (or DI ) will be included in the formalization (details of the notation will be given in Chapter 6, Section 4.1). Three operators of the Adjudgment class can target only outcomes: Truth value (T) is, by deWnition, an operation applying to propositions, and these appear as outcomes. Confrontation (C) compares the Truth values of two or more statements or
47
48
The Structure of Arguments
their degrees of conWdence and, like T, targets only outcomes (comparisons of degree of validity involve K, Comparison). Evaluation (Q) does not refer to truth or correctness, but to other values or norms. It applies to actions, events, or situations that appear in outcomes. When another operation is judged in respect to some norm, this is not symbolized by Q, but by S (the Status operation). Operations of the types that target outcomes can also target constituent elements of outcomes; this concept is explained in Section 3.3, below. 3. Operations that can target either an operator or an outcome Designation, Comparison, Subsumption and Nescience may target either operators or outcomes. Designation. Consider Designations of author, DA. An author may cite someone else or ascribe to someone else an operation (say, an Inference). Suppose there are certain rumors about an heiress, and an author (Author 4, in the following example) reports that someone else inferred something from these rumors. Here is the analysis: Example 9 Author 1 1. P(p) p Author 2 o 2. O(p1 ) 3. E(o2 )
e
Author 3 4. DA (e3 ) d Author 4 5. DA (E3 ) d
There are rumors about the heiress of the N estate. There are rumors that the heiress of the N estate is going to marry a gypsy. 〈 One may infer from this that 〉 there will be quite a ¼ght in the family. Mr. Smith, too, thinks that there will be a ¼ght in the family. Mr. Jones, too, drew this conclusion from the rumors.
Note the distinction between DA targeting the outcome e3 and DA targeting the operator E3.11 Author 3 claims that Mr. Smith assents to the outcome of a previously made Eduction; i.e. he assents to the statement that there will be a Wght, but does not necessarily infer this from the rumors (as Author 2 did). By
Operators, targets, outcomes
contrast, Author 4 claims that Mr. Jones made the same operation that Author 2 made, E3. Similarly, DA (I) is a Designation of an Interpretation, and DA (iP) — of its outcome, that is, of the statement as interpreted; DA (A) is a Designation of the operation of giving a reason (cause, motive, etc.), whereas DA (ap) is a Designation of the statement that serves as reason (cf. Example 4 for the diVerence between aP and aA). (DA (aA) would mean the same as DA (A)). In the case of some operations, the diVerence between a Designation targeting an operator and one targeting an outcome is very subtle. Thus, DA(o) means that some author asserts the outcome of the Elaboration (in the previous example it might mean: “Jim also says that the rumors are about the heiress marrying a gypsy”), whereas DA(O) means that a certain author made the Elaboration (“Jack, too, made this Elaboration”). For certain arguments, either one of these formalizations may be appropriate. Turning to Designations targeting Adjudgments, a Designation may target indiVerently either the operator or the outcome of an Adjudgment operation. This is because the outcome of an Adjudgment comprises both its target and a statement about the target. Take T –(x)
x
DA (t– ) then means that so-and-so said that outcome x is not true, and DA(T–) means that so-and-so performed the operation of asserting the falseness of x , which in eVect amounts to the same. The same holds, mutatis mutandis, for Designations of other Adjudgments. Likewise, there is no diVerence between DA(P) and DA(p): stating who is, say, the Author of the Presentation is the same as stating who is the Author of the statement that is the outcome of this Presentation. In principle, the observations made here about author Designations are true also for other types of Designations, but it is hard to Wnd true-to-life examples to illustrate this. Comparison. K applies to comparisons of all kinds, except those of Truth value or degrees of conWdence, which are symbolized by C. When two statements that are outcomes of previous operations are compared in respect to, say, comprehensibility, the multiplex target of K is a pair of outcomes: K(x, y). K may also compare operations. For instance, Status, an operation with a simplex target, describes a characteristic of a single operation; S(X) may mean that operation X is, say, trivial. When two or more operations are compared in
49
50
The Structure of Arguments
respect to this characteristic, we have a Comparison: K(X, Y ) may mean “Operation X is more trivial than operation Y”. K(X, Y) may also compare the degree to which each of two operations were justiWed, i.e., it may be the multiplex counterpart of Validation. Subsumption, U, has a multiplex target. The latter may consist of outcomes (or more commonly — constituent elements of outcomes; see below, Section 3.3), operators (as when a given Inference is said to be a syllogism), or both. Nescience. Targets of Nescience are discussed in Chapter 7, Sections 1 and 6. 2.3
Superscripts to outcomes and targets
Any superscript appended to the operator of an operation is appended also to its outcome. Moreover, when an operator or outcome bearing a superscript is targeted, this superscript will also appear with the target. This is illustrated in Table 3.4 (where subscripts indicating line numbers have been omitted). In each line, the expression in the right-hand column is an operation that targets the operation appearing in the left column or its outcome. Table 3.4. Examples of outcomes and targets Operation T+ (e) DA, L, P (v+ ) A(p) %O(p)
Outcome or operator as target t+ dA, L, P aP aA %o
D(t+) S (DA, L, P ) O(aP ) E(% o) a
Note a. In some arguments, the target will not be marked %; see note 9.
2.4
Operations pertaining to the same argument
Most operations can target outcomes or operators that occur either in the same argument or in a previous argument. Thus, one can make an Inference from a statement one has just made oneself or from a statement someone made in a previous argument. A problem arises in regard to two types of operations: Interpretation and Elaboration. An Interpretation pertains typically to a previous argument. It is possible, however, for an author to interpret his own words. Look again at Example 1, and suppose Hamlet had explained his cryptic advice: “Let her not walk in the
Operators, targets, outcomes
sun; I mean: keep her from the contamination of the world”. In analyzing this, there are two approaches that one might take: 1. One might hold that the explanation “I mean…” appears only in the expressed argument and not in its underlying structure; the latter contains just one statement, ‘Keep her from the contamination of the world’. 2. Alternatively, one might argue that the fact that the author made a statement and then went on to interpret it, reXects his reasoning process and should therefore be expressed by the formalization (see Chapter 2, Section 2), which ought to contain both the statement and its Interpretation. The same holds for Elaborations. If the Presentation and its Elaboration in Example 2, above had been made by a single author — e.g., “Rudolph Hess, a high-ranking Nazi leader, deserted. That was in 1941” — this might be considered to be a single operation in the underlying structure, or alternatively a Presentation and its Elaboration. Rather than decide this question by Wat, we propose that it should be left to the analyst which approach to choose. Perhaps the decision should be made for each argument separately according to factors like type of Interpretation or Elaboration, or its distance from the interpreted or elaborated statement. The foregoing does not apply to Interpretations and Elaborations that pertain to a previous argument (made by the same author or another one): Whenever one interprets or elaborates on something one has said previously, this will have to appear in the analysis. (A special symbol is needed to formalize such reports of what someone else said; see Chapter 6, Section 4.1.)
3.
Outcomes
The notation of outcomes has already been discussed in the last section. In Sections 3.1 and 3.2, several special problems pertaining to outcomes will be dealt with, and in Sections 3.3–3.5 we discuss more complex outcomes. 3.1
Parts of outcomes
We have already noted that the outcomes of some operations fall into two parts. The outcome of Interpretation is partitioned into iP and iI , that of Result into rP and rR, and that of Accounting — into aP and aA.12 Each of these parts can be targeted separately. Let us see now why it is just these three operations, and no others, that have such bipartite outcomes.
51
52
The Structure of Arguments
Take Accounting. An Accounting operation aVords three diVerent ways of targeting: not only any one of the two parts of the outcome may be targeted but also the operation itself, as shown in the next example. Example 10 a Author 1 1. P(p) p 2. A(p1) aP aA
John is late at the o~ce. He overslept. This is the reason for p1.
Author 2 — ¼rst alternative 3. T– (aP2) t– It is not true that he overslept. Author 2 — second alternative 3'. T– (aA2) t– It is not true that oversleeping is the reason for his coming late. Author 2 — third alternative 3”. V– (A2 ) v– Attributing his being late to oversleeping is unfounded. Explanation: Lines 3–3′: Note that T– (aP) always implies T– (aA) — when these are parts of outcomes of the same operation — but not vice versa. For positive Truth values, the reverse holds: T+ (aA) implies T+ (aP), but not vice versa. Likewise, a Result operation has two partial outcomes, rP and rR. T– (rP) always implies T– (rR), but not vice versa, and T+ (rR) implies T+ (rP), but not vice versa.
According to the third alternative — unlike the second one — Author 2 does not commit himself as to the truth or falsity of the reason given by Author 1; he merely claims that there are insuYcient grounds for giving this reason.13 The same holds for the Result operation. When it is claimed that as a Result of his being late John was Wred, one can target either rP (e.g., it is false that he was Wred) or rR (it is false that this was the result of his being late) or the operation R (e.g., the claim that the one resulted in the other is unfounded). Similar observations apply to Interpretation. If one says that “Let her not walk in the sun” means “Keep her from the contamination of the world.” (Example 1), one can target iP (the admonition to keep her from contamination), or iI (the claim that this is what “Let her not…” means), or the operation I (e.g., the Interpretation is well-founded). As for the outcomes of other operations, there is no reason for breaking
Operators, targets, outcomes
them up into two parts, as will now be shown. Consider the following example: Example 11 Author 1 1. P(p) p Author 2 e 2. E(p1 ) Author 1 3. V– (E2 ) v– Author 3 4. T– (e2 ) t–
The Labor candidate went on vacation. 〈 One may infer from this that 〉 he expects to win the elections anyhow. It is not justi¼ed to infer from p1 that he expects to win the elections anyhow. I am sure he does not expect to win the elections anyhow.
Explanation: Line 2: As formulated here, this is not an Accounting operation. It does not explain a given fact as being the motive for p1 ; instead, it infers this fact from p1 .
Suppose now that the outcome in Line 2 were broken up into two parts: eP: He expects to win the elections anyhow. eE : This may be inferred from the fact that he went on a vacation.
A comparison with Example 10a shows that no purpose would be served by such a partition. In the case of Inferences, no provision need be made for a third possibility of targeting (in addition to those in Lines 3 and 4). If there were an operation T– (eE ) it could mean “it is not true that this may be inferred from the fact that he went on a vacation”; but this is hardly distinguishable from the meaning of V– (E2) in Line 3. There is thus no need to partition e into eP and eE. It can easily be seen that other operations, too, do not require more than two ways of targeting. This is due to the meanings of their respective outcomes, an issue that will be dealt with presently. 3.2
Meanings of outcomes and targets
Operations diVer in respect to the relationship between the meanings of their targets and those of the corresponding outcomes. As will now be shown, some
53
54
The Structure of Arguments
operations have outcomes that contain new statements, not included in their targets, whereas the outcomes of others contain statements that include those made in the respective targets. Furthermore, we will see that operations diVer in respect to the commitments of the author entailed by the respective outcomes. Interpretations The outcome of an Interpretation has two parts (see Example 1): ip, which is a recast of the target; it states the targeted outcome in a diVerent form, I i , which states that iP interprets or explains the statement targeted by the Interpretation operator. The author of the Interpretation commits himself only to iI; as far as he is concerned, iP may be correct or not. Elaborations The outcome of an Elaboration includes the target and adds something to it (see, for instance, Example 9, above). The author of an Elaboration, O(x), then, commits himself to the outcome o and to the statement x included in o. Cause In a Result operation, R(x), the outcome rP is a statement describing the result or consequence of x. This new statement is then connected to x by rR (‘rP is the result of x’). Similarly, in an Accounting operation, A(x), the outcome aP is a new statement of the reason of or motive for x, and aA connects aP to the operation x which A accounts for. Note that the author here commits himself to both parts of the outcome; in this respect the outcomes of a Cause operation diVer from the outcome of Interpretation, which as we have seen above, also has two parts. Inferences The meaning of the outcome of an Inference operation has nothing in common with the meaning of the target, that is, the meanings are independent. In Example 11, above, “One may infer from this that“ is not part of the outcome; this phrase is added only for the sake of clarity, which is why it is enclosed in angular brackets. Inferences diVer from most other classes in that the author is not commit-
Operators, targets, outcomes
ted to the outcome. Author 2 in Example 11, above, does not necessarily concur with the claim that the candidate expects to win the elections; he merely states that “The Labor candidate went on vacation” (whether true or not) leads to the conclusion that he expects to win the elections. JustiWcation The outcomes of JustiWcations involve certain complexities and will be discussed in Chapter 5. An author of a JustiWcation does not necessarily commit himself to its outcome. Adjudgment The outcome of an Adjudgment operation represents a fusion of its target with new material, as shown in Example 12: Example 12 Author 1 1. P(p) p Author 2 2. D(p1 ) d
Rudolph Hess, a high-ranking Nazi leader, deserted to England in 1941. This is what the history book says.
“This”, in Line 2 refers to the target of the Designation — i.e., the whole of the outcome of Line 1 — and “is what the history book says” is the new material introduced by the Designation operation. Similarly, the outcome of a Truth value operation is a fusion of the truth value with the information in the target; the outcome of U(x, y), the Subsumption operation, contains a fusion of the information in x and y and the claim that x is contained in y; and so on. The author of an Adjudgment operation commits himself to its outcome. In Chapter 7, Sections 1 and 6, it will be seen that outcomes of Nescience operations are also fused. Obviously, since a Presentation does not have a real target, the question of the meaning of its outcome in relation to that of its target does not arise. The author, of course, commits himself to the outcome. 3.3
Constituent elements of outcomes
In our system, outcomes are whole propositions. An operation may refer not to a whole outcome but to one of the clauses, phrases, or words included in it. To enable targeting such parts of an outcome, the latter is broken down into
55
56
The Structure of Arguments
constituent elements. As shown in the following example, a constituent element is indicated by a digit or a lower-case letter as superscript. Example 13 Author 1 1. P(p)
p: … pq
Author 2 2. P(p)
p: … pr r q 3. K(p 2 , p 1 ) k
Jones drives a Jaguar. Smith drives a Porsche. A Porsche is a much nicer car than a Jaguar.
As stated, the purpose of breaking down an outcome into constituents is to permit targeting part of the outcome rather than all of it. When the whole of the outcome is targeted (or when it is not targeted at all), no constituents will appear in the analysis. However, the bipartite outcomes — iP and iI, rP and rR, aP and aA invariably appear alongside Interpretation, Result and Accounting, respectively (but see note 12); unlike constituent elements, they have capital letters as superscripts. Constituent elements will be used as targets mainly in Comparison (K), Subsumption (U), and Evaluation (Q) operations. Take, for example, an esthetic judgment of an object that has been referred to in the outcome of a previous operation; this object will then Wgure as a constituent element in that outcome and be targeted by Q. In some cases, a reformulation of the outcome will be necessary. Thus, when one judges an activity — say, the way Sam is dancing — referred to in the outcome of a previous operation “I saw Sam dancing”, the constituent will be formulated as “Sam was dancing” (a proposition) which is then targeted by Q. Suppose now that some constituents of an outcome are subsequently targeted while others are not. Then the latter need not be symbolized: it will be suYcient to represent them by a sequence of dots, as in the following example. Example 14 Author 1 1 P(p)
p: pq pr ps …
They raise in their farm stallions, horses, and chickens.
Operators, targets, outcomes
Author 2 2. U(pr1 , ps1 ) u
A stallion is really a kind of horse.
Author 3 3. T – (pq r1 )
They do not raise stallions.
t–
Explanations: Line 1: Each of the constituents is targeted by a subsequent operation, except ‘and chickens’, which is therefore not accorded a symbol, but indicated by three dots. Line 2: U is the Subsumption operator, which has a multiplex target (Section 2.1, above)
This example also illustrates that constituent elements can be deployed to show what it is in a statement that is claimed to be incorrect. When a T – operator targets an outcome, it states that a certain proposition is false, and in order to specify what makes it so, constituent elements Wgure in the target. If Author 3 had argued simply that p1 is false, this would have been symbolized as T – (p1 ) t –. But in the present example we construe what Author 3 says as: what makes p1 false is that they do not raise stallions (not that they do not raise horses or raise neither horses nor stallions), and this is symbolized by the two constituent elements pq and pr — contracted here into pq r — in the target of T –. 3.4
Annotations
Often there is a partial identity between the outcomes of two operations; that is, they share a constituent element. This can be indicated by an annotation, as illustrated here: Example 15 Author 1 1. P(p) Author 2 2. T –(p1 ) 3. P(p)
p: pk …
Cecilia was born in Summer 1945.
tThis is wrong; p: pl (= pk1 ) she was born … in Spring 1946.
The Presentation in Line 3 is related to that of Line 1 — both concern Cecilia’s date of birth — but this fact is not captured by targeting. Instead, it is indicated
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The Structure of Arguments
by the annotation in Line 3: the expression (= pk1) is an annotation of pl3 and an annotation to the expression pk in Line 1. Note that the annotation is appended always to the later occurrence of the element (Line 3, in the present example). A caveat is in order here. Annotations are not to be used in lieu of the operation of identifying two entities. By an annotation, the analyst indicates the identity of two elements. When an author claims that, say, Leonardo was the artist who painted the Mona Lisa, this is a Comparison operation targeting two constituent elements: ‘Leonardo’ and ‘the artist who painted the Mona Lisa’ (remember that the Comparison operation also applies to statements of identity). Further, annotations do not indicate the equivalence of complete outcomes; such an equivalence may be expressed by T+ as a collateral operation, a concept that will be discussed presently. 3.5
Collateral operations
A single step of an argument may involve two diVerent operations. For instance, one may infer from the outcome of a previous operation that the statement in another previous outcome is false; we then have an Inference, the outcome of which is equivalent to the outcome of a Truth value operation. Here is an example. Example 16 Author 1 1. P(p) p
All men are male chauvinists.
Author 2 2. P(p) p I know some men who are feminists. – l: T (p1 ) 〈 It follows logically that 〉 it is not true that all men 3. L(p2 ) are chauvinists. Explanation: Lines 1 and 2: The expressions “all” and “some” have a special status in logic. Our concern, however, is with a general description of operations, which neglects some diVerentiations that might have been made.
The outcome “it is not true that all men are chauvinists” in Line 3 is inferred from p2 , and at the same time it is also the outcome of a Truth value operation:
Operators, targets, outcomes
p1 is false (recall that the expression in angular brackets is not part of the outcome). The operation which appears after the outcome of the main operation — here T– — will be called a collateral operation. A collateral operation has an outcome of its own; here the outcome of the collateral operation is t –. Usually one will not write down this outcome (which, after all, is easily recoverable) so as to avoid cluttering up the analysis. The Inference in Example 2 of the previous chapter was formalized as two separate operations: an Inference (‘One can infer from this that Abe was not at Ben’s party) and a Truth value operation (Your claim that Abe was at Ben’s party is false). A more precise way of formalizing that argument would be to append the Truth value operation as a collateral operation: E(p4 ) e: T– (e2 ). The outcome of a collateral operation has to be equivalent to the outcome of the main operation. In the above example, the outcome of T– (p1 ) is “it is not true that all men are chauvinists”, which is also the outcome of L(p2 ). A subsequent operation thus may have one of the following forms: X(L3), X(T–3), X(l3), and X(t–3 ), the latter two expressions being equivalent. When an outcome x is identical to a previous outcome y, this will also be indicated by a collateral operation: X(…) x: T+ (y) A collateral operation may be associated with a part of an outcome iP, rP, or P a . For instance: Example 17 1. P(p)
2. A(p1 )
p: … pk … pl P a : K(pk1 , pl1 ) aA
Cecil and Sheila will go to Spain instead of to Switzerland. Spain is cheaper for tourists than Switzerland. aP is the reason for p1.
Here the collateral operation, K, has an outcome that is equivalent to part of the outcome of the main operation, namely, to aP (not to aA).14 To return to Example 16, the main operation there is a Deduction (L) and the collateral operation is Truth value (T–). An alternative that suggests itself is to reverse the roles of L and T– in Line 3: (*) 3'. T– (p1 )
t– : L (p2 )
It is not true that all men are chauvinists.
The asterisk is used here to indicate that this analysis is faulty. This is because the collateral operation in Example 16, T– (p1 ) says only that p1 is false, whereas
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The Structure of Arguments
the main operation, L(p2 ), shows, in addition, how this judgment is derived. In general, when an argument can be analyzed in terms of an Adjudgment operation (with an Inference operation as collateral operation) or with an Inference operation (with an Adjudgment operation as collateral operation), the latter is to be preferred. A rule similar to that applying to Inferences and Adjudgments applies to Cause operations and Adjudgments: the correct analysis is Cause as main operation and Adjudgment as collateral operation (rather than an Adjudgment operation with a collateral Cause operation). Thus, in Example 17, the main operation is A, which contains more information than the collateral Adjudgment operation, K. For reasons that will become clear in Chapter 5, JustiWcations take precedence over any other operation. Another restriction on collateral operations may be illustrated by means of Example 11, above, which included the following operations: 1. P(p) 2. E(p1 )
p e
The Labor candidate went on vacation. 〈 One may infer from this that 〉 he expects to win the elections anyhow.
Consider now the following alternative to that analysis: (*) 1. P(p) 2'. P(p)
p p: E(p1 )
The Labor candidate went on vacation. He expects to win the elections anyhow.
This will not do. The purpose of an analysis is to show how the various operations relate to each other, and this is achieved by, e.g., an Inference operation, which targets a previous operation. A Presentation, by contrast, does not target any other operation, and thus does not contribute to binding the operations together. Therefore it is not an appropriate main operation. To summarize, the choice between analyses is governed by the following Precedence principle: If faced with the choice between two analyses, viz.: (i) an operation X (w) with collateral operation Y (z) and (ii) an operation Y (z) with collateral operation X (w), then (a) if X is an Inference or a Cause operation and Y is an Adjudgment, (i) takes precedence over (ii); (b) if X is a JustiWcation and Y is any other operation, (i) takes precedence over (ii).
Operators, targets, outcomes
A Presentation cannot have a collateral operation (that is, (i) is inappropriate when X is a Presentation). Further, a Presentation will usually not be a collateral operation. The last line of the preceding example cannot be replaced by (*) 2'’. E(p1 )
e: P(p)
〈 One may infer from this that 〉 he expects to win the elections anyhow.
Here P(p) would be completely redundant: the outcome of the main operation, e, says all there is to be said. There are cases, however, where a collateral operation P is required, because it is subsequently targeted. This can be illustrated by Example 10a, part of which is repeated here: Example 10 b 1. P(p) 2. A(p1)
p aP aA
John is late at the o~ce. He overslept. This is the reason for p1.
In Example 10a, three ways of refuting the explanation in Line 2 were illustrated: V– (A), T– (aA ), and T– (aP ). Of these, V– (A) and T– (aA ) pertain to the imputed causal link between oversleeping and being late, whereas T– (aP ) pertains to the fact of John’s oversleeping; see the following table. A fourth possibility of refuting — not included in Example 10a — would be: “The claim that he overslept is unfounded”; this would Wll the lower left-hand cell in the table. Table 3.5. Refutations of Accounting V– (A) Attributing his being late to oversleeping is unfounded:
T– (aA ) It is not true that this is the reason of his being late. T– (aP ) It is not true that he overslept.
Now, V always targets an operator (an operation); that is, it cannot target aP. When it is asserted that the claim that he overslept is unfounded, we therefore append in Line 2 a Presentation as collateral operation to aP , and this collateral operation is then targeted by a Validation: V– (P). This is illustrated in Example 10c.
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The Structure of Arguments
Example 10 c Author 1 1. P(p) p 2. A(p1 ) aP : P(p) aA
John is late at the o~ce. He overslept. This is the reason for p1.
Author 2 v– 3. V– (P2 )
The claim that he overslept is unfounded.
An example of a more complex kind of collateral operation is analyzed in Appendix C.
4.
The symbols of the notation — a summary
In concluding this chapter, let us summarize the use of various types of symbols. Capitals stand for operations, e.g., P, I, E, T. Lower case letters stand for outcomes; the outcomes of the above operations are symbolized by p, i, e, and t, respectively. Parenthesized capital letters stand for targets which are operations; e.g., V+(P), S(I), D(Q), K(Ei , Ej ). Parenthesized lower case letters stand for targets which are outcomes; e.g., T+ (p), E(i), D(q), K(ei , ej ). Superscript capitals serve to distinguish between diVerent sub-types of operations and their outcomes; e.g., DA vs. DT and dA vs. dT. Further, the two parts of outcomes of Interpretations and Cause operations are distinguished by superscript capitals: For Interpretations we use the capital letters P and I as superscripts (iP, iI ); for Result we distinguish between rP and rR, and for Accounting — between aP and aA. Superscript lower-case letters or superscript digits indicate constituent elements of outcomes, as in: P(p)
pm pn
As will be seen in Chapter 4, Section 2, these also serve to distinguish between repeated occurrences of a given letter in the same line; e.g., P1 / P2 with the outcome p1 / p2.
Operators, targets, outcomes
The symbols + and – are deployed as superscripts of the operators T and V and serve to indicate values of their outcomes. The symbol % as superscript preceding the operator stands for the degree of conWdence expressed by the author in respect to the operation. This symbol may be carried over to the outcome, as in: %E(p)
%e
In some cases it will appear only in the outcome. Subscripts appended to targets refer to preceding lines and are always digits.
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Chapter 4
Compounds
Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of human misunderstanding. – Ambrose Bierce, The Devil’s Dictionary.
In this chapter we deal with ways of combining two expressions into one compound expression. Compounding can be eVected by three types of functors: functors for conjunctions, disjunctions, and implications.1 It is important to make clear from the outset that the functors in our system diVer from the symbols used in logic. In modern logic, these connectives play a precisely deWned role, which diVers in some respects from that played by the corresponding everyday terms, “and”, “or”, and “if … then …” in everyday use (see Strawson 1952: 35–36, 77–93; Kienpointer 1992: 55V ). To give but one example, the horseshoe is used in logic for material implication, so that any consequent follows from a false antecedent (Copi 1954: 18). This is clearly not the way we use expressions like “if… then…” in conversation, and neither will our functors be used in that way.2 Our system has not been constructed for the purpose of evaluating the validity of arguments, but rather to describe them, and perspicuity of description is what guided the introduction of functors. In the following three sections, we deal with compounds — a term that will be used here for two or more operations joined by a functor — and their outcomes. Section 4 deals with compound targets.
1.
Implications
There are several kinds of implicational functors. One of these is “if ___ then ___”; in the two blanks appear operations between which the implication holds. For example:
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The Structure of Arguments
Example 1 1. if P(p) 2. then P(p) 3. T– (p1)
if p then p t-
4. E(t–3 & if p1 then p2 )
e: %T (p2 )
If Jessica gets a promotion, then she will get a raise in salary. It is not true that Jessica will get a promotion. 〈 One can infer from this that 〉 it is doubtful whether she will get a raise in salary.
Explanations: Lines 1–2: The outcome contains both the functor and the lower case letter corresponding to the operator. Line 3: In the outcome of Line 1, p (“Jessica gets a promotion”) is the sentence radical (Clarke, 1985). It is only this sentence radical — not the whole outcome “if p” — which is targeted by the Truth value operator in Line 3. Line 4: The conjunction functor & is discussed in Section 3, below. Degree of conWdence is indicated by % (Chapter 3, Section 1.3) .
The two Presentations in Lines 1–2 are linked by a functor to form one compound, but for convenience we adopt the convention of apportioning an implication to two separate lines. Either one of the two Presentations or its outcome may then be targeted by itself; in Line 3, for instance, only p1 is targeted.3 The implicational functor “if___ then ___”, like all functors, applies primarily to operations. When the antecedent of an implication is, say, an outcome p of a previous Presentation operation, we therefore cannot write ‘if px’. Instead we write: if T+ (px ), i.e., if px is true (see also Example 4, below). One frequently draws a conclusion subject to a certain proviso: A follows from B, unless C is the case. Toulmin (1958) calls these provisos “rebuttals”. The proviso will be the antecedent and the Inference — the consequent of a conditional, as in Example 2 1. P(p)
p
2. if P(p)
if p
3. then E(p1 )
then e
Harry is an octogenarian and the sole owner of United Coal Mines. If he does not make a will in someone else’s favor, then 〈 it can be inferred that 〉 his children will inherit a large fortune.
Compounds
Explanation: Lines 1–2: Here, again, the implication is written in two lines, although it is one compound.
Another functor is the biconditional “iV ___ then ___” (that is, “if and only if …, then…”). An implication with this functor — unlike one with the “if ___ then ___” functor — licenses a conclusion from the truth of the consequent to the truth of the antecedent, as in Line 4: Example 3 1. i¬ P(p)
i¬ p
2. then P(p) 3. T+(p2 ) 4. L(t+3 & i¬ p1 then p2 )
then p t+ l: T+(p1 )
If and only if Jessica gets a promotion, she will get a raise in salary. Jessica will get a raise in her salary. 〈 It is to be concluded therefore that 〉 she got a promotion.
Explanation: Line 4: L stands for Deduction (Chapter 3, Section 1.1, sub Inference). The ampersand indicates a conjunction; see Section 3, below. T+ (p1 ) in this line is a collateral operation (see Chapter 3, Section 3.5).
The “iV ___ then ___” functor is also deployed to indicate that a previous claim is correct only under certain conditions. Thus, in response to the claim that “every citizen has a right to vote” — P(p) — one may state that this is so only in case that citizen has not been convicted of a criminal act of a certain category: iV P(p) then T+ (p). The “iV ___ then ___” functor is included in our framework as a matter of convenience, Obviously, we could do without it, deploying instead two implications, ‘if X then Y’ and ‘if not X then not Y ’ (alternatively: ‘if Y then X’). This is actually mandatory when a subsequent operation targets only one of the “if ___ then ___” implications. Suppose a reason is given why Jessica will not get a raise in salary unless she gets a promotion: say, the Wrm does not raise salaries on the basis of seniority only. The analysis will be: Example 4 1. 2. 3. 4.
if P(p) then P(p) if T– (p1 ) then T– (p2 )
if p then p if t– then t–
If Jessica gets a promotion, then she will get a raise in salary. If she does not get a promotion, then she will not get a raise in salary.
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The Structure of Arguments
5. A (if t–3 then t–4 )
aP aA
The ¼rm she works for does not raise salaries on the basis of seniority. This is the reason why, if she does not get a promotion, then she will not get a raise in salary.
Explanation: Line 5: The operation of giving a reason is A, Accounting, which has a bipartite outcome (Chapter 3, Section 3.1). The target of A is the outcome of Lines 3 and 4 (aP is not the reason of the outcome in Lines 1–2, “if Jessica will get a promotion, then she will get a raise in salary”).
DeWnitions deploy the “iV ___ then ___” functor. A parallelogram may be deWned as “a quadrilateral with opposite sides parallel and equal” (Webster’s Seventh New Collegiate Dictionary 1970). This deWnition can be rephrased as “if and only if a Wgure is quadrilateral and has opposite sides parallel and equal, then it is a parallelogram”. In everyday discourse, sentences with an “if”-phrase are often construed as involving a biconditional (see Cummins 1995, for research on some determinants of people’s understanding of conditional sentences). Arguments that are verbally expressed as “if… then …” may therefore have an underlying structure with the “iV___ then___” functor.4 A third kind of functor is used for counterfactual implication. Suppose someone says: “If she would have got a promotion she would have got a raise in salary”. This assumes that she got neither a promotion nor a raise in salary. The symbolization is “if C___ thenC ___” (the superscript C stands for ‘counterfactual’): Example 5 1. if C P(p) 2. thenC P(p)
if C p thenC p
If Jessica had got a promotion, then she would have got a raise in her salary.
There are also counterfactual “if-and-only-if” implications: Example 6 1. i¬ C P(p) 2. thenC P(p)
i¬ C p thenC p
If and only if Jessica had got a promotion, she would have got a raise in her salary.
An implication may be a collateral operation (Chapter 3, Section 3.5); for example:
Compounds
Example 7 1. P(p)
p
2. E(p1 )
e: if P(p) then P(p)
Norman is a very determined and stubborn person. 〈 It can be inferred from this that 〉 if he does not like our plan, he will not give in to persuasion.
Wnally, there is a type of implication which may be called supposition. One may state something not as a fact, but as a supposition on which the remainder of the argument is based (“Suppose that …”, and the like). Making a supposition does not commit one to its truth; one posits conditions that one does not know whether or not they exist or that are known not to exist. We use ‘if S’ and ‘thenS’ for such suppositions. Take, for example, an argument that might be made in a discussion on the causes of the disappearance of dinosaurs: Example 8 1. if S P(p)
if S p
Suppose that a large meteor collided with the earth in the Cretaceous period, 2. then S [R′ (p1) & R′′p1)] then Srp′ & rp′′ then dinosaurs would have become extinct and craters would have formed in Central America. rR This would be the result of p1. Explanations: Line 2: The scope of ‘then S’ is indicated by square brackets: the consequent (‘then S’) includes two events resulting from p1. To distinguish between the two occurrences of R we use superscripts (here: ′ and ′′). R, Result, has a bipartite outcome (Chapter 3, Section 3.1): rP and rR. Since there are two resulting events, there are two conjoined rP ’s. These, too, must have superscripts, namely, those of the corresponding operators.
Suppositions are involved, among others, in reductio ad absurdum arguments (Pollock 1989: 130–131, 143–144). It might be argued that any supposition can be analyzed in terms of implications: either “if … then …” (which assumes that the antecedent may be true) or “if C … thenC ” (which implies that it is not true).5 We claim that suppositions diVer from implications in the way that pretend play diVers from behaving “seriously” (which of course is not to deny that suppositions are
69
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The Structure of Arguments
typically used in order to justify claims). The antecedent of an implication may be open to confutation, but a supposition is based on a decision — it is a sort of announcement of the rules of the game one plays — and confuting it would be absurd.6
2.
Disjunctions
The functor for a disjunction is symbolized by a slash, /. The outcome is also a compound expression, and a subsequent operation may target only one of the disjunct outcomes: Example 9 1. P1(p) / P2(p)
p 1 / p2
2. E( p21 )
e
In his free evenings, James plays cards or reads the ¼nancial section of the Times. 〈 From his reading the Times one may infer that 〉 he must be quite an expert in Economics.
Explanations: Line 1: The implication functor consists of two symbols, ‘if ‘ and ‘then ‘, and can therefore be written in two lines. Disjunct operations, by contrast, make do with a single symbol, the slash, and therefore they cannot be written in two lines. Superscripts are needed to distinguish between two or more occurrences of the same letter (in the operator or outcome), so that a subsequent target can refer to only one of them. Thus, in Line 2, only p2 (not p1 ) is targeted.
The antecedent (or the consequent) of an implication may be a disjunction, as in Example 10 1. if [P1 (p) / P2 (p)]
if [p1 / p2]
2. then P(p)
then p
If you buy me a drink or take me to a movie, then I will show you the present I got from him.
Explanation: Line 1: The scope of ‘if ’ is indicated by square brackets. 7 The superscripts distinguish between occurrences of the same operators and the same outcomes, thus permitting subsequent targeting of any one of them; cf. Explanation to Example 9.
Compounds
The functor / stands for inclusive disjunction, that is, it does not exclude the possibility that both disjuncts are the case. The foregoing analysis does not rule out the possibility that the addressee will be shown the present also when he fulWlls both conditions in the antecedent: buy a drink and take to movies. For exclusive disjunction we use the double slash, //, as in:8 Example 11 1. P1(p) // P2(p)
3.
p1 // p2
You are entitled to either a free week-end for two at a deluxe hotel or to a new set of skis (but not to both).
Conjunctions
The conjunction functor is symbolized by an ampersand, &. Ordinarily, two or more operations will not be conjoined by &; instead, they will be written in two separate lines. Consider: Her daughter is a good cook and her son is good at cleaning up. They therefore always eat well and their home is very clean.
The analysis involves two Presentations in separate lines:9 Example 12 1. P(p) 2. P(p) 3. R(p1 ) 4. R (p2 )
p p rP rR rP rR
Her daughter is a good cook. Her son is good at cleaning up. They always eat well. This is the result of p1. Their home is very clean. This is the result of p2.
Explanations: Although there is no targeting between the two Presentations, they are obviously somehow related; and so are the two Result operations. Chapter 8 deals with the way such relationships may be expressed. Note that in this example a diVerent sequence of operations would be permissible, e.g., the sequence of Lines 2 and 3 could have been reversed. In determining the sequence, the analyst may be guided by the sequence in the expressed argument; but since the object of the formalization is the underlying structure (Chapter 1, Section 1), mirroring the sequence in the expressed argument is not mandatory.
71
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The Structure of Arguments
There are two cases, however, in which two (or more) operations will be written in one line, conjoined by an ampersand: 1. When the two conjoined operations are a part of another compound, it will be impractical to write them in separate lines. Compare the following two examples to Example 10: Example 13 1. if P(p) if p If you do the dishes now, 2. then [P1 (p) & P2 (p)] then [p1 & p2] then you don’t have to do them on Monday, and you can take the car tonight.
This is similar to Example 8, which also deploys an ampersand. Example 14 1. if [P1 (p) & P2 (p)]
if [p1 & p2]
2. then P(p)
then p
If you buy me a drink and take me to the movies, then I will show you the present I got from him.
Conjoint operations have conjoint outcomes, as indicated here by the symbol for conjunction. It will be recalled that the target of P is not a “real” target (Chapter 2, Section 1). A Presentation operator therefore cannot have a compound target; that is, P(p1 & p2 ) is not well-formed. 2. Two or more operations may be conjoined by an ampersand in a collateral operation, as illustrated in Example 15: Example 15 Author 1 1. P(p) p 2. P(p)
p
Author 2 3. P(p) p 4. E(p3)
Arnold J. killed the old woman in Paris last evening, and he killed the teenager in Paris after midnight.
Arnold J. was in London all through last night. e: T – (p1) & T – (p2) 〈 One may infer from this that 〉 he murdered neither the old woman last evening nor the teenager after midnight in Paris.
Compounds
Explanation: Line 4: Recall that the outcome of the main operation (here: e) is equivalent to that of the collateral operation (Chapter3, Section 3.5), which is a conjunction in this example. An alternative would be to have two separate Eductions, the one with T– (p1) as collateral operation and the other with T – (p2) as collateral operation.
The functor & is commutative — X & Y is equivalent to Y & X . In the foregoing example we have assumed that the sequence of activities — buying a drink and taking to the movies — is immaterial. Cases where this is not so are discussed in Chapter 8, Section 2. A bracketed conjunction is not distributive. Look again at Example 14. From “if you buy me a drink” by itself it does not follow that “then I will show you …”, nor does it follow from “if you take me to the movies”. In some instances, one of the conjoined operations will target the other. Suppose that in Example 14 the antecedent would be, say, “If you buy me a drink because you like me”, the analysis would begin: 1. if [P (p) & A (p1)]. A Wnal comment: The analyst may decide (availing herself of the Formalization principle — Chapter 2, Section 2.2) to collapse the compound into a single non-compound operation. This is illustrated in the following two examples, which should be compared to Examples 3 and 9, respectively. Analyzing a given operation as compound is mandatory only when this is needed in the analysis of subsequent operations in the argument, that is, when a constituent operation or its outcome is targeted. Example 16 1. P(p)
p
2. A(p1 )
aP aA
If and only if Jessica gets a promotion, she will get a raise in her salary. Jessica is not pushy. This is the reason she will get a raise only if she gets a promotion.
Example 17 1. P(p)
p
2. E(p1 )
e
In his free evenings, James plays cards or reads the ¼nancial section of the Times. 〈 One can infer from this that 〉 he won’t be bored.
This completes our inventory of compounds and their outcomes. In the following sections, compound targets will be dealt with.
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The Structure of Arguments
4.
Compound targets
Targets, like operations and outcomes, can be compound expressions.10 For instance, Example 18 Author 1 1. if P(p) 2. then P(p)
if p If Jessica gets a promotion, then p then she will get a raise in salary.
Author 2 3. T– (if p1 then p2)
t–
It is not true that if Jessica gets a promotion, then she’ll get a raise in salary.
The target in Line 3 is the compound outcome of a previous operation (Lines 1–2). An example of a disjunct target is Example 19 1. P1(p) / P2 (p)
p 1 / p2
2. E(p11 / p21)
e
Tom either abandoned his wife or he just forgot to let her know his whereabouts. 〈 In either case, one can infer from this that〉 he is quite irresponsible.
In the above examples, outcomes of compound operations Wgure subsequently in targets. It is also possible for outcomes of simple, uncompounded, operations to be conjoined or otherwise compounded in a subsequent target. This is shown in the last lines of Examples 1 and 3. Another example is: Example 20 a 1. 2. 3. 4.
Author 1 P(p) P(p) P(p) E(p1 & p2 & p3)
5. E(p3)
p p p e e
John and Mary married when they were very young They are very much in love with each other. They have ¼ve children. 〈 It may be inferred from this that 〉 they are very happy. 〈 And it can be inferred from p3 that 〉 they are very busy.
Explanation: Lines 1–3: There is no targeting relation between the three Presentations; the
Compounds
intuition that they are somehow related should be reXected in the formalization by a connection, a notion that will be introduced in Chapter 8.
A target can also be a compound operator. This is illustrated in the following example, which also shows how an operation can target an argument as a whole, rather than only one (or part of) its operations. Example 20 b Author 2 6. S(P1 & P2 & P3 & E4 & E5)
s
This is a completely trivial account (argument).
An argument is a partially ordered set of operations. The operation in Line 6 (a Status operation), refers to the whole of the preceding argument. Its target, however, consists of an unordered set of operators (recall that the conjunction functor is commutative). But this does not present a problem, because this target refers us to the speciWc operations in that argument — P1 , P2 , etc. — and these operations contain all the information of the partial order: E4 must succeed P1, P2 , and P3 (since the latter are its targets), and E5 must succeed P3 .11
5.
Dependent and independent eVects
In this section we discuss two types of Inferences: those involving a dependent and those involving an independent eVect. 5.1
Dependent eVects
Some Inferences are based on two or more outcomes which jointly lead to a conclusion or have a certain eVect. In the two following examples, the conclusion is based on two statements, and would not have followed from any one of these taken by itself. Example 21 1. P(p) 2. P(p) 3. L (p1 & p2)
p p l
Jane is taller than Susan. Susan is taller than Doris. 〈 From p1 and p2 jointly it follows logically that 〉 Jane is taller than Doris.
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The Structure of Arguments
Example 22 1. P(p) 2. P(p)
p p
3. E(p1 & p2)
e
Egypt has over 60 million inhabitants. Only a small strip of land near the Nile is inhabited. 〈 From p1 and p1 jointly it follows that 〉 Egypt’s population density is very high.
Not only Inferences, but also consequences of actions or events may involve dependent eVects. The formalization then may resort to conjoined collateral operations (Chapter 3, Section 3.5), as in Example 23 Author 1 1. P(p)
p
Author 2 2. P(p)
p
3. A(p2)
Bert has not had any alcoholic drinks for the past few hours.
Bert su¬ers from hallucinations and dizziness right now. aP: T – (p1 ) & P(p) Bert has had an alcoholic drink some time ago and he has taken two aspirins at the same time. aA ap is the reason for p2 .
Explanation: Line 3: In the collateral operation, p1 is said to be false, and another Presentation that has not appeared before (“he has taken two…”) is introduced.
We are dealing here with dependent eVects: it is being assumed that neither alcohol nor aspirin by itself causes hallucinations. The two dependent causes appear therefore as a conjoint collateral operation. Similarly, Result operations will have conjoint targets when dependent eVects are involved. An alternative analysis of Accounting and Result operations with dependent eVects is discussed in the next chapter (Section 5.2). 5.2
Independent eVects
An event or a situation may have two or more causes, each of which would have been independently eYcacious in bringing it about. For instance, certain types of blood tests should not be performed if the patient has eaten anything
Compounds
or has drunk anything but water within some ten hours before the test. Here is an argument involving such an independent eVect:12 Example 24 1. P(p) 2. P(p) 3. E(p1)
p p e
4. E(p2)
e
Belinda has just had a sandwich. Belinda has just had some Cola. 〈 One can infer from p1 that 〉 she cannot have a blood test. 〈 One can infer from p2 that 〉 she cannot have a blood test.
Each of these culinary delights is suYcient for making a blood test unreliable; the eVects are independent, and therefore the analysis involves separate Inference operations, unlike dependent eVects (like those in Examples 21–22), which require compound targets.13 When a situation is explained as being due to two or more independent factors, the analysis has two or more separate Accounting or Result operations. An alternative analysis of Accounting and Result operations with independent eVects is discussed in the next chapter (Section 5.2).
77
Chapter 5
JustiWcations
The chain of reasons comes to an end. – Wittgenstein, Zettel (1967: 55, § 301)
The subject of this chapter is the JustiWcation operation, which has been dealt with only perfunctorily in Chapter 3. The syntax of this operation has some special features, as will become clear in the present chapter.
1.
The nature of JustiWcation
When people argue, they often make statements, draw inferences, and make judgments, which they then defend and support by other statements. These supporting statements are analyzed as JustiWcations. In the following example, the second line contains the JustiWcation of the operation in the Wrst line: Rosie is inquisitive. Even her best friends say so.
It is important to keep in mind that ‘JustiWcation’ is used here as a technical term, which should not be confused with some of the uses of the word ‘justiWcation’ in everyday language (cf. Feigl 1950: 122). To understand the concept of JustiWcation, it is important to distinguish it from Inference, on the one hand, and from Accounting, on the other. These distinctions will be elucidated presently. 1.1
JustiWcation versus Inference
Every argument with an Inference (except for the Presupposition restoring operation) could, in principle, also be analyzed as an argument with a JustiWcation. An argument deploying an Inference “progresses” from one proposition to
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The Structure of Arguments
another that follows from it. The preceding argument can be reformulated as: (a) Rosie’s best friends say that she is inquisitive. (b) One can infer from this that she really is inquisitive. This sequence of operations in the underlying structure has been called the progressive mode (Chapter 1, Section 2). The sequence of (a) and (b) is reversed in an argument with a JustiWcation; a sort of backtracking is involved: (b) Rosie is inquisitive. (a) What justiWes this statement is the fact that her best friends say so. We call this the regressive mode. In Section 6.1, below, we discuss some considerations concerning the choice between a progressive and a regressive analysis. Here is another illustration of an argument that can be formulated either in the progressive mode, as an Inference, or in the regressive mode, as a JustiWcation. The second line in each of the following examples is an Inference and a JustiWcation, respectively. Inference – Progressive mode: Prices in Sweden are higher than those in Norway, and prices in Switzerland are higher than those in Sweden. One can infer from this that prices in Switzerland are higher than those in Norway. JustiWcation – Regressive mode: Prices in Switzerland are higher than those in Norway. What justiWes saying so is that prices in Sweden are higher than those in Norway, and prices in Switzerland are higher than those in Sweden.
Our system comprises both Inferences and JustiWcations. It might be objected that this introduces redundancy into it. An argument that is formulated with a JustiWcation may also be analyzed with an Inference; but in some instances this would mean disregarding what we have called the “mode” of reasoning (Chapter 1, Section 2). In any case, the system would still have to provide for JustiWcations for arguments in which someone justiWes an operation made in a previous argument (for instance, when “What justiWes saying so…” in the foregoing is said by another author); it would be very cumbersome to analyze these as Inferences. Likewise, an Inference made from an outcome in a previous argument can only circuitously be analyzed as a JustiWcation. See also
JustiWcations
Chapter 7, Section 4.4 (on a JustiWcation — but not an Inference — targeting a Question). 1.2
JustiWcation versus Accounting
JustiWcation has to be distinguished clearly from Accounting, which is the operation of giving a reason for a given state of aVairs, stating what caused it or what was the motive for an action (see Wittgenstein 1958, Section 475 et passim). The distinction here is a subtle one. Both JustiWcation and Accounting involve a sort of “reason”; in fact, some writers apply the term ‘reason’ indiVerently to both these operations (e.g., Geach 1976, Chapter 1, but see ibid. p. 84; Wittgenstein 1966: 22 mentions this distinction; see also Chapter 9, Section 4.1).1 However, while a JustiWcation is the operation of supporting an assertion and defending it, Accounting is the operation of explaining: giving a reason for a state of aVairs or stating what is its cause (see also Hamblin 1986: 228; Hoaglund 1986; Govier 1987, Walton 1996: 31–33, 63–67). An example will clarify this: JustiWcation: Prices in Switzerland are higher than those in Norway. What justiWes saying so is that prices in Sweden are higher than those in Norway, and prices in Switzerland are higher than those in Sweden. Accounting: Charlie is beside himself with joy. The reason is that he has just won the great prize.
The JustiWcation states why the author believes he is entitled to make the claim, whereas an Accounting operation states what is the reason for a certain state or event. Now, in these examples the distinction is quite obvious. It becomes more subtle when the cause of Charlie’s state of mind serves as JustiWcation (instead of an Accounting operation, as in the foregoing):2 JustiWcation: Charlie must be beside himself with joy. What justiWes saying so is that he has just won the great prize.
JustiWcation, we have observed, involves “backtracking” and is a regressive operation. Accounting is also regressive; the time sequence of the two events is
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The Structure of Arguments
reversed: after stating the consequence (Charlie’s joy), the reason (winning the prize) is given. A JustiWcation may refer us to the cause, as it does in the last example. But it is also possible to justify a claim by referring to the known consequences, i.e., to reverse the statements in the above example, as in JustiWcation: Charlie has won the great prize. What justiWes saying so is that he is beside himself with joy.
Although the temporal sequence is preserved here — the cause is stated before the consequence — we call this operation regressive, because of the mode of reasoning, which does not proceed from a proposition to what follows from it (as is the case in an Inference). There is a kind of Accounting that has some aYnity with JustiWcation. One may ‘justify’ one’s behavior, as in: I did not come to your wedding because I was ill.
Illness was the reason the speaker did not come to the wedding, but it is also her excuse for not coming. In everyday language, an excuse is sometimes called justiWcation, but in our system, justiWcation of behavior is analyzed as Accounting; the term JustiWcation is used only for what justiWes an operation referring to this behavior. The choice between JustiWcation and Accounting often depends on the researcher’s interpretation of the argument. Here is a quotation from the report of the commission investigating arms shipment to Iran (“Irangate”): At another point, Mr. McFarlane said he distinctly remembered telling President Reagan in the hospital about the arms shipment ‘because the President was wearing pajamas’. (Quoted in Hilton 1990: 75).
The because-clause might be interpreted as stating what caused MacFarlane’s remembering that he informed the President — the episode made a great impression on him owing to the President’s outWt — and then it is an Accounting operation. Alternatively, one may view it as a JustiWcation: evidence for his contention that he correctly remembers informing the President is that he also remembers what the President was wearing.
JustiWcations
1.3
Inference versus Result
JustiWcation and Accounting are two regressive operations. The distinction between them parallels that between the Inference operation and the Result operation, which are both progressive. This distinction, too, is liable to be overlooked; in fact, both Inferences and Results may be verbally expressed by “therefore”. But “therefore” is ambiguous: it may stand for either one of the italicized expressions in the following: Inference: Prices in Sweden are higher than those in Norway, and prices in Switzerland are higher than those in Sweden. One can infer from this that prices in Switzerland are higher than those in Norway. Result: Charlie has just won the great prize. As a consequence he is beside himself with joy.
The distinction here is quite obvious; it becomes more subtle when a result is inferred from its cause, as in Inference: Charlie has just won the great prize. One can infer from this that he must be beside himself with joy.
When the causal connection between two events or situations is being established, we have a Result operation. When the result is inferred from its cause, we have an Inference.3 The observation made in Section 1.2, that either the cause (reason) or its consequence can serve as a JustiWcation, has a parallel here: an Inference can refer either to the consequence, as in the previous example, or to the cause, as in Inference: He is beside himself with joy. One can infer from this that he has won the great prize.
Here an event is inferred from a later-occurring event. But although the temporal sequence of events is reversed, this is a progressive operation: there is no “backtracking” of the kind we have in a JustiWcation. In sum, Result and Accounting reveal the direction of the causal relationship, whereas Inference and JustiWcation do not.
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The Structure of Arguments
Table 5.1. Inference, JustiWcation, Result, and Accounting Progressive
Regressive
Inference He has won the great prize. One can infer from this that he must be full of joy.
JustiWcation He must be full of joy. What justiWes saying so is that he has won the great prize.
Result He has won the great prize. As a consequence he is full of joy.
Accounting He is full of joy. The reason is that he has won the great prize.
The table above summarizes the distinctions between the four operations dealt with here.
2.
The formalization of JustiWcations
2.1 Targets of JustiWcations It will be recalled that a Validation operation is a claim about the validity (or lack of it) of another operation and targets the operator of that operation: V+ (X) or V– (X). A JustiWcation is an operation that intends to establish the validity of another operation, it supports it; its target is the operator of that other operation: J(X). Note that it is not the outcome of an operation that is being justiWed by J, but the operation itself. This can be illustrated by an example: Barbara: John is not going to get a raise in his salary.
(a) Presentation
Tom: His wife is going to get mad at him. What justiWes inferring (b) is that she is very ambitious.
(b) Inference (c) JustiWcation
What Tom justiWes is not the outcome of the inference in (b), that is, not the claim that John’s wife is going to get mad at him (in fact, Tom may doubt Barbara’s prophecy will come true). Instead, this is a JustiWcation of the operation of inferring that, if what Barbara predicts comes true, John’s wife will be angry.
JustiWcations
Example 1 Barbara 1. P(p)
p
John is not going to get a raise in his salary.
Tom 2. E(p1 )
e
3. J(E2 )
j
〈 One can infer from this that 〉 his wife is going to get mad at him. 〈 What justi¼es this Inference is that 〉 she is very ambitious.
The outcome of the JustiWcation operation in Line 3 is “she is very ambitious”. The phrase “what justiWes this Inference …” is added only for the sake of clarity and does not form part of the outcome, which is why it is put between angular brackets (like the phrase “one can infer from this that” in an Inference). It is instructive to compare Example 1 with an analysis of the argument in the progressive mode, i.e., with an Inference replacing the JustiWcation: Example 2 Barbara 1. P(p)
p
John is not going to get a raise in his salary.
Tom 2. P(p) 3. E(p1 &p2 )
p e
His wife is very ambitious. 〈 One can infer from these two facts that 〉 she is going to get mad at him.
Note that here the Inference is based on two statements: one that has been made by Barbara (and which is the target of the Inference in Example 1) and one — by Tom (the JustiWcation of the Inference in Example 1). That JustiWcations must target operations (rather than outcomes) is obvious in cases like the one discussed here — but not in all. Take Presentations, for example, “There is going to be rain tomorrow.” When this Presentation is justiWed by, say, “The weather forecaster said so”, one might view this as either a JustiWcation of the outcome or a JustiWcation of the operation. But for the sake of uniformity of the system we stipulate that all JustiWcations apply to (`target’, in our terminology) operations. We now turn to the outcomes of JustiWcations.
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The Structure of Arguments
2.2
Outcomes of JustiWcations
Before dealing with the outcomes of JustiWcations let us consider for a moment the outcomes of Cause operations — Accounting and Result. It will be recalled (Chapter 3, Section 3.1) that an Accounting operation has a bipartite outcome, aP and aA, and can be targeted in three ways, as illustrated in Example 3 (and the same holds, mutatis mutandis, for Result): Example 3 Author 1 1. P(p) p 2. A(p1 ) aP aA
He is full of joy. He has won the great prize. This is the reason for p1 .
Author 2 3. T– (ap2 ) t–
It is not true that he has won the great prize.
Author 3 4. T– (aA2 ) t–
It is not true that aP2 is the reason for p1 .
Author 4 v– 5. V– (A2 )
The explanation A2 is not well founded.
By contrast, there are only two ways of targeting a JustiWcation, as shown in Example 4 Author 1 1. P(p) p 2. J(P1 ) j
Charlie must be beside himself with joy. 〈 What justi¼es this Presentation is that 〉 he has won the great prize.
Author 2 3. T– (j2 ) t–
It is not true that he has won the great prize.
Author 3 4. V– (J2 ) v–
The Justi¼cation J2 is inadequate
Observe that the claim that “The JustiWcation J2 is inadequate” (Line 4) is practically identical to the claim “It is not true that j2 justiWes p1”. The distinction between the operations in Lines 4 and 5 of the Accounting example has no parallel in the JustiWcation example. The outcome of a JustiWcation, then, is not divided into two parts (unlike that of Accounting or Result).4
JustiWcations
Frequently, a JustiWcation has a collateral operation, i.e., the outcome j is equivalent to that of another operation (see Chapter 3, Section 3.5). Take, for instance, the following conversation: – –
Theodore Dreiser joined the Communist party. That was after he visited Russia in 1927; Macmillan’s Encyclopedia says so.
The formalization will be: Example 5 Author 1 1. P(p) p Author 2 2. O(p1 ) o 3. J(O2 )
j: D(o2 )
Theodore Dreiser joined the Communist party. Theodore Dreiser joined the party after he visited Russia in 1927. 〈 What justi¼es this Elaboration is that 〉 Macmillan’s Encyclopedia says so.
Explanations: Line 2: This is an Elaboration (O) of Author 1’s claim. The outcome of an Elaboration includes the targeted text as well as the material that has been added. Line 3: The collateral operation is D (short for DA ): a Designation of the author (of o2 ).
The collateral operation speciWes that the JustiWcation consists of a Designation of the author. In Example 4, by contrast, there is no collateral operation in Line 2: appending P(p) as a collateral operation to j would not have provided any additional information.5 2.3
Warrants and articulations
There are two kinds of JustiWcations. The JustiWcation in Example 4 is a warrant, and so is that in Example 5, which has a collateral operation.6 Another type of JustiWcation involves a chain of reasoning that ends in a conclusion. These two types may be illustrated by two alternative analyses of Modus Tollens. Here is the analysis with a warrant:
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The Structure of Arguments
Example 6 1. P(p) 2. M(p1 ) 3. J(M2 ) 4.
p m
There are no lights in the Smiths’ apartment. 〈 Hence, by Modus Tollens, 〉 the Smiths have not come home. j: if C T– (m2) 〈 What justi¼es this Inference is that 〉 if the Smiths had returned home, thenC T– (p1) then there would be light in their apartment.
Explanations: Lines 3–4: The collateral operation here is an implication, and implications, it will be remembered, are written in two lines. On counterfactual implications, “ifC __ thenC __”, see Chapter 4, Section 1. “If the Smiths had returned home” contains the negation of the outcome in Line 2, and “there would be light in their apartment” negates the outcome in Line 1; hence the collateral operation includes ‘if C T–’ (and for similar reasons it includes ‘then C T–’).
In Example 6 the JustiWcation is a warrant: it is not carried through to its conclusion, and we are left to complete the train of thought begun in Lines 3– 4 and conclude that the Smiths have not come home. An alternative analysis of this Modus Tollens involves a JustiWcation that does spell out the conclusion. Such a JustiWcation, which we call articulation, is given in Example 7. Here the JustiWcation comprises several operations; the fact that they are part of the same JustiWcation is indicated by a vertical line. These operations lead up to and include the conclusion: Operation 6, indicated by an arrow. Example 7 1. P(p) 2. J(P1 ) | | | | | → | |
3. 4. 5. 6.
p j
The Smiths have not come home. 〈 What justi¼es this Presentation is that 〉 if C T– (p1 ) if C t– if they had come home, thenC p then there would be light thenC P(p ) in their apartment. T– (p4 ) t– It is not the case that there are lights in their apartment. M(ifC t–3 thenC p4 & t–5 ) m 〈Hence, by Modus Tollens,〉 the Smiths have not come home.
JustiWcations
Explanations: Line 6: The target of M is compound, because a Modus Tollens rests on two premises (the one in Lines 3–4 and the one in Line 5 ). The target of M in Line 2 of Example 6, however, is not compound: “If the Smiths had returned home, then there would be light in their apartment” cannot be included in the target of M, because an operator can target only a preceding outcome. In the present example, the conclusion is the last operation in the articulation. This is not always so: when the conclusion itself has a JustiWcation, the latter will succeed it, as in Example 16a, below.
Observe that while the conclusion, M, in the foregoing example is an operation that diVers from the operation targeted by the JustiWcation (P), the outcomes of the two operations have equivalent meanings: “The Smiths have not come home”. The conclusion of an articulation has an outcome that is equivalent to the outcome of the operation targeted by J, and thus the JustiWcation comes full circle.7 The operations in an articulation are set oV by a vertical line. This is a convention adopted as a matter of convenience: it contributes to the clarity of the presentation. The set of outcomes in the articulation (without the conclusion) is equivalent to j (the outcome of J). The articulation is therefore a kind of collateral operation (Chapter 3, Section 3.5) of the JustiWcation.8 Articulations, then, diVer from warrants in that 1. An articulation contains a conclusion, the outcome of which is equivalent to the outcome of the operation targeted by the JustiWcation (compare Lines 1 and 6 in Example 7). Warrants, by contrast, do not include a conclusion; to wit, the outcome in Lines 3–4 of Example 6 diVers from that in Line 1. A warrant may thus be looked on as a JustiWcation that is not carried through to its conclusion. 2. An articulation always comprises more than one operation; a warrant may contain a single operation. (When a warrant contains two or more operations, the latter will be Xanked by a vertical line, like the “sub-operations” of an articulation, but since there is no conclusion, no arrow will appear; see Chapter 9, Example 1, Lines 23–25 and Example 2, Lines 3–5.) It would have been possible, technically, to append to each warrant an Inference that constitutes a conclusion, and this would turn it into an articulation. Why, then, do we make provision for warrants alongside articulations? A
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simple example shows that, in the case of many warrants, adding such a conclusion would be redundant and uninformative. Suppose we reanalyze Author 1’s argument in Example 4 as follows (the asterisk indicates that the analysis is not well formed): (*) 1. P(p) p Charlie must be beside himself with joy. 2. J(P1 ) j 〈What justiWes this is that〉 | 3. P(p) p Charlie has won the great prize. → | 4. E(p3) e 〈One can infer from this that〉 he must be beside himself with joy.
Instead of the two lines of Author 1’s argument in Example 4, a Presentation and its JustiWcation, we now have four. There are two reasons why we reject this analysis: 1. The JustiWcation is very short and comes immediately after the operation that is being justiWed. 2. The relation between the Presentation in Line 3 and the operation that is justiWed (Line 1) is quite transparent; the extra Eduction is entirely gratuitous; it does not clarify anything here. In this it is unlike the conclusion of the articulation in Example 7, which shows which type of Inference operation licenses the Presentation in Line 1 (“The Smiths have not come home”), namely, the Modus Tollens. The preceding argument should therefore be analyzed with a warrant, as in Example 4. JustiWcations may be hierarchically organized. This is illustrated in Example 16a, below, where an articulation includes a warrant, and in Example 19, where a warrant is justiWed by another warrant. To familiarize the reader with the notions of warrant and articulation and the diVerences between them, we analyze in the following sections some commonly occurring types of arguments.
3.
Some common JustiWcations
3.1 Syllogisms and Modus Ponens Syllogisms and Modus Ponens are closely related, and in our system they are therefore both symbolized by N. Their analyses diVer in important respects, however. Let us take syllogisms Wrst. A syllogism can be analyzed either with a
JustiWcations
warrant (Example 8) or with an articulation (Example 9). Example 8 1. P(p) 2. N(p1) 3. J(N2 )
p: pm pn n: nq n r (= p n1 ) j: U(n q 2 , p m1 )
All politicians are shrewd. 〈 Hence 〉 Carl Caldwell is shrewd. 〈 What justi¼es this Inference is that 〉 Carl Caldwell is a politician
Explanations: Line 1: Although “All politicians are shrewd” is a general (universal) statement, it is not formalized as a Generalization (G), because in our system, this term refers to a type of Inference (Chapter 3, Section 1.1). Lines 1–2: Superscripts indicate constituent elements of outcomes, which may be targeted (Chapter 3, Section 3.3). Two of these constituent elements (and not the outcomes as a whole) are targeted in Line 3. Line 3: Recall that in Subsumptions, U, the sequence of targets is: subsumed term, term under which the latter is subsumed. Example 9 1. P(p)
p: pq pr j
2. J(P1 ) | 3. P(p) | | 4. U(pq1, p m 3) → | 5. N(u 4 & p3)
Carl Caldwell is shrewd. 〈 What justi¼es this Presentation is that 〉 p: p m All politicians n r p (= p 1 ) are shrewd. u Carl Caldwell is a politician. n 〈 One can infer from this that 〉 Carl C. is shrewd.
Explanation: Line 5: The target is the conjunction of the two premises (Lines 3–4). Note that the premise in Line 4 Wgures as warrant in Example 8.
In the analysis with a warrant (Example 8), N is the operation targeted by the JustiWcation, whereas in the articulation (Example 9), N is the conclusion.9 In actual conversations, speakers typically omit mention of either the unconditional premise (“Carl Caldwell is a politician”), or of the conclusion (“Carl Caldwell is shrewd”) (Salmon and Zeitz 1995), and occasionally — the universal statement (“All politicians are shrewd”). Our analysis spells out premises in the underlying structure that may be missing in the expressed argument.
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The Structure of Arguments
Examples 8–9 are in the regressive mode. Here is a syllogism with all operations in the progressive mode: Example 10 Author 1 1. P(p)
p
2. G(p1)
g
Author 2 3. P(p) 4. U(G2, pk3) 5. N(p3 & u4)
In the streets of Messina people kept bumping into us without apologizing. 〈 This shows that 〉 Sicilians have no manners.
p: pk … u
Generalizations about ethnic groups are morally unacceptable. The conclusion you draw is based on a generalization about ethnic groups. n: S(G2) 〈 One can infer from this that 〉 drawing this conclusion is morally unacceptable.
Explanations: Line 4: This example shows that Subsumption can target an operator (G of Line 2) as well as a constituent element of an outcome. Line 5: The outcome of this syllogism is equivalent to that of a Status operation (i.e., an operation that states something about another operation; see Chapter 3, Section 1.1, sub Adjudgments); hence the collateral operation.
Returning to Examples 8–9, let us see whether these syllogisms, too, can be analyzed in the progressive mode (that is, without a JustiWcation). Suppose one were to attempt such an analysis. The sequence of outcomes would have to be: a. b. c.
All politicians are shrewd. Carl Caldwell is a politician. (One can infer from this that) Carl Caldwell is shrewd.
Step (b) is a Subsumption, U, which has to target the subject of (c), “Carl Caldwell”, as well as that of (a), “all politicians”. Now, according to our convention, only a preceding outcome can be targeted. To target “Carl Caldwell”, this term must therefore have been mentioned before (b). In Example 10, G, the target of U, has been introduced previously, by Author 1, and thus a progressive formalization is possible. But in Examples 8–9 there is no previous author. To formalize these examples in the progressive mode one would have to introduce “Carl Caldwell”, somewhat artiWcially, by having a presupposition precede (b), stating that there is a person called Carl Caldwell.
JustiWcations
A Modus Ponens, we have noted, is very much like a syllogism, and both involve the N operator.10 The following two examples illustrate that a Modus Ponens can be analyzed either in the progressive or in the regressive mode. Example 11 1. 2. 3. 4.
if P(p) then P(p) T+ (p1) N(if p1 then p2 & t+3 )
if p then p t+ n
If stocks rise on the market, then investors will buy more stocks. Stocks have risen on the market. 〈 Hence, by Modus Ponens, 〉 investors will buy more stocks.
Example 12 1. P(p) 2. N(p1 )
p n
3. J(N2 )
j: if T+ (p1 )
4.
then T+ (n2)
Stocks have risen on the market. 〈 Hence, by Modus Ponens, 〉 investors will buy more stocks. 〈 What justi¼es this Inference is that 〉 if stocks rise on the market, then investors buy more stocks.
Explanation: Lines 3–4: Functors apply to operators, not to outcomes (Chapter 4, Section 1), and therefore we cannot write here “if p1” or “then n 2”, but have to avail ourselves of the Truth value operator.
It is a commonplace that in everyday discussion people do not abide strictly by the rules of deductive logic. What our analysis is concerned with, however, is the argument that has been produced, and not whether this argument is formally valid. Take, for example the following paragraph: A woman has a right to decide what to do with her body, and since her unborn child is a part of her body, she can decide whether to have an abortion, at least when the fetus endangers her health.
From a logical point of view, this is not an impeccable argument. The syllogism, as it stands, entitles one to draw a stronger conclusion, namely, that a woman has a right to have an abortion in any case, even if there is no danger to her health. Why did the author add the reservation “at least when the fetus endangers her health”? Perhaps, he really did not intend the premise — “a woman has the right to decide what to do with her body” — to be true without qualiWcation and thus did not believe an abortion to be admissible under all
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The Structure of Arguments
circumstances and whatever its motivation. The author himself may not have taken into account all situations which, by his lights, merit an exception to the rule that a woman may decide what to do with her body; all he knows is that this rule should not apply to certain cases of abortion he would not condone. The analyst must take the argument as it stands; she should not conjecture which circumstances the author may have in mind. We propose the following analysis: Example 13 1. P(p) 2. N(p1 )
p: … ps n: …
3. J (N2 )
nr j: U(nr2, ps1)
4. if P (p) if p 5. then % T+ (n2 ) then % t+
A woman has a right to decide what to do with her body. 〈it follows that〉 she is morally entitled to have an abortion; i. e. to remove her fetus. 〈What justi¼es this is that 〉 the fetus is a part of her body. If the fetus endangers her health, then she is certainly morally entitled to have an abortion.
Explanation: Line 5: The symbol for degree of conWdence, %, is usually appended only when the author is less than certain concerning the operation or outcome (see Chapter 3, Section 1.3); but here it is needed, because the point of the operation (“if... then...”) is that he is quite certain. In general, % may be used for any degree of conWdence from low to high and “total”.
3.2
Analogies
An analogy is a claim that, to put it crudely, since two things are known to be similar in one respect, they should be held to be similar in another respect. Frequently, the similarity on which the analogy is based is not referred to in the expressed argument. But the underlying structure always includes a claim about the existence of some relevant similarity between the cases, and this claim must therefore appear in the formalization. For instance, Example 14 1. P(p)
p: pq pr
It is wrong to make su¬er people.
JustiWcations
2. W(p1 ) 3.
J(W2 )
w: ws (=pq1) wt j: K(wt2, pr1)
〈 By analogy, 〉 it is wrong to make su¬er animals. 〈 What justi¼es this Analogy is that 〉 animals are like people (in some relevant respect).
Explanations: Lines 1–2: The outlandish syntax has been adopted in the verbal description so as to enable a line-by-line rendering of the outcomes. Line 3: The JustiWcation of the Analogy (W) is that animals may be assumed to have some similarity to people. This assumed similarity is introduced by a Comparison (K), which serves as warrant of the conclusion. Even when the similarity in question is apprehended only vaguely, the Comparison is an integral part of the underlying structure of an analogical argument.
An analogy can also be formalized as an argument with an articulation: Example 15 1. P(p)
p: pq pr j
It is wrong to make su¬er animals. 〈 What justi¼es this Presentation is that 〉 s p: p (=pq1) it is wrong to make su¬er pt people. k Animals are like people (in some relevant respect). w 〈 By analogy, 〉 it is wrong to make animals su¬er
2. J(P1 ) | 3. P(p) | | 4. K (p r1 , p t 3 ) | → | 5. W(p3 & k4) | Explanation: Line 5: In this articulation, the Analogy operator, W, has a compound target, whereas in the corresponding analysis with a warrant (Example 14) it has a non-compound one. This parallels the two analyses of the Modus Tollens, M, in Examples 6–7.
An alternative analysis would reverse the sequence of operations in Lines 4–5: Example 16 a Author 1 1. P(p) p: pq pr
It is wrong to make su¬er animals.
95
96
The Structure of Arguments
2. J(P1 ) j | 3. P(p) | → | 4. W(p3 ) | | 5. J(W4 ) |
〈 What justi¼es this Presentation is that 〉 p: ps (=pq1) it is wrong to make su¬er t people. p w 〈 By analogy, 〉 it is wrong to make animals su¬er. j: K(p r1 , p t 3 ) 〈 What justi¼es this analogy is that 〉 animals are like people (in some relevant respect).
Both Example 15 and Example 16a contain articulations and are therefore regressive; but while in Example 15 the operations within the articulation are progressive, the articulation in Example 16a includes a regressive operation, J. One cannot speak, then, of progressive and regressive arguments, but rather of arguments consisting of more or fewer regressive or progressive operations. Both in Example 15 and in Example 16a, “animals”, a constituent element targeted by K appears in a line preceding K, viz. Line 1, which states the conclusion that it is wrong to make animals suVer. If we were to formalize the analogy exclusively with progressive operations, the Comparison K, which is part of the JustiWcation, would appear before the conclusion, that is, before the occurrence of a constituent element “animal”. This would preclude its targeting this constituent element. The situation here is like that discussed in Section 3.1 in regard to the Modus Ponens: an analogy is analyzable in the progressive mode only if preceded by an operation that includes the relevant constituent element (here: “animals”). A refutation of an analogy is usually based on a distinction between the relevant entities, that is, on an additional Comparison, K. Thus, to refute the argument in Example 16a, one might point out a crucial diVerence between animals and people: e.g., being less conscious, animals suVer less than people. This refutation would be analyzed as follows: Example 16 b Author 2 6. K(pr1, pt3) 7. K (k6, k5) 8. E(k6 & k7)
k
Animals di¬er from people, in that they are less conscious and su¬er less. k This di¬erence is more relevant here than the similarity pointed out in K5 . e: V (W4 ) 〈Therefore〉 the above analogy is not justi¼ed.
JustiWcations
Explanations: Line 6: The verbal description makes it clear that the meaning of K6 diVers from that of K5 in Example 16a. Line 7: This may not appear in the expressed argument, but it is part of the underlying structure, because it is essential in the refutation of the analogy.
3.3
A fortiori arguments
An a fortiori argument, like an Analogy, involves a Comparison and can be analyzed with a warrant, as in Example 17, or with an articulation, as in Example 18. Example 17 1. P(p) 2. E(p1 ) 3. J(E2 )
p: pj … e: e k … j: K(ek2, pj1)
Bikes are not allowed in the park. 〈 A fortiori,〉 motor scooters are not allowed in the park. 〈 What justi¼es this Inference is that 〉 motor scooters are more detrimental to parks than bikes.
Explanations: Line 1: Alternatively, one might include here the Evaluation operator Q, for “not allowed” (and in Chapter 6, Section 4.4 it will be shown how this can be done). But since Q is not targeted, it is permissible to write simply P (see Chapter 2, Section 2.2 on the Formalization principle). Line 2: An a fortiori argument is not deductive, and is therefore one of the many kinds of Inferences that are categorized as Eductions (E) in our system.
The same argument can be analyzed with an articulation as follows: Example 18 p: p m Motor scooters … are not allowed in the park. 2. J(P1 ) j 〈What justi¼es this Presentation is that〉 | 3. P(p) p: p n bikes | … are not allowed in the park; | 4. K(pm1, pn3) k motor scooters are more detrimental to parks | than bikes. → | 5. E(p3 & k 4) e 〈and so, a fortiori 〉 motor scooters are not | allowed in the park. 1. P(p)
97
98
The Structure of Arguments
The articulation includes the Presentation: “Bikes are not allowed in the park”. Could this Presentation be moved out of the articulation? Consider: (*) 1. P(p) 2. P(p) 3. J(P2 ) | 4. K(pm2, pn1) | → | 5. E(p1 & k4) |
p: pn … p: pm … j
Bikes are not allowed in the park. Motor scooters are not allowed in the park. 〈 What justiWes this Presentation is that 〉 k motor scooters are more detrimental to parks than bikes. e 〈 A fortiori, 〉motor scooters are not allowed in the park.
The sole function of the Presentation “Bikes are not allowed in the park” is to subserve the JustiWcation of the claim that motor scooters are not allowed in the park, and it should therefore not be separated from the rest of the articulation. We therefore introduce the convention that an operation that can be deployed in an articulation should be placed, if possible, within the articulation rather than before it. When the operation in question has to appear anyhow before the articulation, this constraint on articulations does not apply. The conditions for analyzing a fortiori arguments in the progressive mode are the same as those for syllogisms and analogies; see Sections 3.1 and 3.2 of the present chapter. This completes our survey of some common forms of JustiWcations. An example of a more complex type of warrant is analyzed in Appendix C.
4.
JustiWcations as targets
4.1 Targeting warrants In the following we discuss targeting of a warrant (i) by another JustiWcation, (ii) by T or V, and (iii) by other operators. As shown in the next example, a JustiWcation can target another JustiWcation: in Line 3, J targets the collateral operation of a JustiWcation and in Line 4, J targets the J operator of a warrant.
JustiWcations
Example 19 1. P(p) 2. J(P1 )
p j: P(p)
3. J(P2)
j: D(p2 )
4. J(J2)
j
Jeremy is angry with Jolanda. 〈 What justi¼es the claim that he is angry with her is that 〉 Jeremy did not come to her party. 〈 What justi¼es the Presentation that he did not come to her party is that 〉 Joe told me that he wasn’t there. 〈 What justi¼es the Justi¼cation (in Line 2) is that〉 all of Jolanda’s friends make a point of not o¬ending her by missing any one of her parties.
Explanations: Line 2: A collateral operation P(p) has to be included expressly (unlike in, e.g., Example 4, above), because this is the operation targeted in Line 3. Line 3: The target of this JustiWcation is the Presentation in the collateral operation of Line 2, stating that Jeremy was not at Jolanda’s party. In this JustiWcation, the collateral operation is D (short for DA ) a Designation of the author (of p2 ). Line 4: Unlike the JustiWcation in Line 3, this JustiWcation targets the JustiWcation (in Line 2) itself: it answers the question of how Jeremy’s absence from Jolanda’s party shows that he is angry with her.
A warrant can also be targeted by a Validation or a Truth value operator; in the above example, for instance: a. V– (J3) would mean that the JustiWcation is not acceptable (because, e.g., Joe is unreliable, or because he got his information from some gossip intent on spreading calumnies).11 b. V– (D3) would mean that the Designation oVered as a JustiWcation is unfounded, viz., there is no good reason to ascribe this claim to Joe. c. T– (j3) would mean that the outcome of the JustiWcation, namely, the assertion that Joe told him so, is false. (Note that V targets an operator, while T targets an outcome; see Chapter 3, Section 2.2.) d. T– (d3) would mean the same as T– (j3), because the outcome of a collateral operation is equivalent to the outcome of the main operation (d3 is equivalent to j3); see Chapter 3, Section 3.5. JustiWcations can be targeted not only by J, V or T, but also by other operators. For instance one can ascribe a characteristic to a JustiWcation — S(J) — or infer something from the outcome of a JustiWcation: E (j).
99
100 The Structure of Arguments
4.2 Targeting articulations We have seen that in a warrant either the J operator, or its outcome, or the collateral operation associated with it can be targeted. Likewise, in an articulation either the J operator or one of the operators or outcomes can be targeted. The targeting operator may be either J (as in Example 16a) or some other operator. To illustrate, in Example 18 one might confute the Comparison between motor scooters and bikes, which is one of the operations included in the articulation, and claim either T– (k4) (it is not true that motor scooters are more detrimental than bikes) or V– (K4) (the claim that they are more detrimental is not well-founded). In either case, the validity of the JustiWcation would be impugned, that is, V– (J2) would be entailed.
5.
Dependent and independent eVects
In Section 5 of the preceding chapter, dependent and independent eVects were discussed. Let us see now how arguments involving these eVects may be analyzed in the regressive mode, i.e., with JustiWcations and with Accounting operations. 5.1
Dependent and independent JustiWcations
It will be remembered that Inferences with dependent eVects have conjoint targets. The next example illustrates a dependent eVect: hallucinations are caused by taking aspirin and alcohol, not by any one of these substances by itself. Example 20 a 1. P(p) 2. P(p) 3. E(p1 & p2 )
p p %
e
Vincent has taken an aspirin. Vincent has had a lot of alcohol at the same time. 〈 One can infer from this that 〉 he is likely to have hallucinations.
Explanation: Line 3: The degree-of-conWdence marker, %, is needed here, because Vincent is said to be only likely to have hallucinations; cf. Chapter 3, Section 1.3.
The same argument can be analyzed with a JustiWcation:
JustiWcations 101
Example 21 %p 1. % P(p) Vincent is likely to have hallucinations. 2. J(%P1 ) j 〈 What justi¼es this Presentation is that 〉 | 3. P(p) p He has taken an aspirin. | 4. P(p) p He has had a lot of alcohol at the same time. 〈 One can infer from this that 〉 he is likely to → | 5. E(p3 & p4 ) %e | have hallucinations. Explanation: Line 1: See Explanation to previous example on %.
Independent eVects, unlike dependent ones, are analyzed as two operations (rather than with conjoint targets).12 The example of an independent eVect given in the preceding chapter was Example 22 a 1. P (p) 2. P (p) 3. E (p1 )
p p e
4. E (p2 )
e
Belinda has had a sandwich. Belinda has had some Cola. 〈 One can infer from p1 that 〉 she cannot have a blood test. 〈 One can infer from p2 that 〉 she cannot have a blood test.
This can also be analyzed in the regressive mode, with a JustiWcation: Example 23 1. P(p) p 2. J(P1 ) j | 3. P(p) | 4. P(p) → | 5. E (p3 ) | → | 6. E(p4 ) |
Belinda cannot have a blood test. 〈 What justi¼es this Presentation is that 〉 p She has had a sandwich. p She has had some Cola. e 〈 One can infer from p3 that 〉 she cannot have a blood test. e 〈 One can infer from p4 that 〉 she cannot have a blood test.
Explanation: Alternatively, one might analyze this argument with two separate articulations (one that includes Lines 3 and 5, and the other – Lines 4 and 6).
Dependent and independent JustiWcations can also be formalized as warrants. For the articulation in Example 21 one could substitute a single warrant:
102 The Structure of Arguments
J(P1 )
j
〈 What justiWes this Presentation is that 〉 he has taken an aspirin and has had a lot of alcohol at the same time.
Instead of the articulations in Example 23, one could have two separate warrants:
5.2
J(P1 )
j
J(P1 )
j
〈 What justiWes this Presentation is that 〉 she has had a sandwich. 〈 What justiWes this Presentation is that 〉 she has had some Cola.
Dependent and independent Cause operations
Dependent and independent eVects must be distinguished in Cause operations as well as in JustiWcations. Suppose that, rather than justifying the claim that Vincent is likely to have hallucinations, one explains why he does have them. One way of analyzing dependent eVects in Cause operations has been discussed in the previous chapter (Section 5.1), and here we will deal with an alternative analysis. When a dependent eVect is involved, the Accounting operation may be broken down into a sequence of “sub-operations”, and the convention here is like that adopted for articulations: the “sub-operations” are Xanked by a vertical line, and there is a conclusion, indicated by an arrow. Example 24 1. P(p) p a 2. A(p1 ) | 3. P(p) | 4. P(p) → | 5. R(p3 & p4 ) |
Vincent has hallucinations. 〈 The reason is that 〉 p He has taken an aspirin. p He has had a lot of alcohol at the same time. P r Vincent has hallucinations, rR and this is the result of p3 & p4 .
The similarity of this analysis to that with an articulation, in Example 21, is obvious.13 The outcome rP (of the conclusion) is identical to the outcome of the operation targeted by A, viz., p1 ; in this respect, too, the “suboperations” of Accounting are like articulations. The conclusion of the JustiWcation in Example 21 was its progressive counterpart — an Inference (Eduction). The conclusion of the Accounting operation (Line 5) is its progressive counterpart, Result.
JustiWcations 103
The analysis here diVers from that of the more usual type of Accounting operations in that the outcome of A is not broken up into aP and aA. The set of operations 3–4 fulWlls the role of aP, and the conclusion in Line 5, “Vincent has hallucinations, and this is the result of…”, fulWlls the role of aA ; cf. Chapter 4, Example 23. Since the eVects of aspirin and alcohol are dependent, the target of R in the foregoing example is conjoined. By contrast, when the eVects are independent, there will be two Result operations (which, again, parallels JustiWcations — see Example 23): Example 25 1. P(p p a 2. A(p1 ) | 3. P(p) | 4. P(p) → | 5. R (p3 ) | → | 6. R (p4 ) |
p p rP rR rP rR
Belinda cannot have a blood test. 〈 The reason is that 〉 She has had a sandwich. She has drunk some Cola. She cannot have a blood test. This is the result of her having had a sandwich. She cannot have a blood test. This is the result of her having drunk Cola.
Alternatively, this argument might be analyzed with two separate Accounting operations. “Sub-operations” of Accounting may also be deployed when there is a chain of causes; for example: Example 26 1. P(p)
p
2. A(p1 ) a | 3. P(p) | 4. R (p3 ) | → | 5. R(rP4 ) | | |
p rP rR rP rR
The Dicksons are temporarily staying at their in-laws. 〈 The reason is that 〉 There has been a forest ¼re. Their home burnt down. This was the result of the forest ¼re. The Dicksons are temporarily staying at their in-laws. This is the result of the burning down of their home.
This argument can also be analyzed as a sequence of Accounting operations: The Dicksons are temporarily staying at their in-laws; the reason is that their
104 The Structure of Arguments
home burnt down; the reason for that is that there has been a forest Wre. Result, like Eduction, is a progressive operation, and the analyses of dependent and independent eVects will be the same as in Examples 20a and 22a, respectively, except that a Result operation will take the place of the Eduction: Example 20 b 3'. R(p1 & p2 )
rp rR
Vincent has hallucinations, This is the result of his having had an aspirin and a lot of alcohol at the same time.
rP rR rP rR
Belinda cannot have a blood test. This is the result of her having had a sandwich. Belinda cannot have a blood test. This is the result of her having drunk Cola.
Example 22 b 3'. R (p1 ) 4'. R (p2 )
6.
Deciding on the appropriate analysis
In this chapter we have seen that there are often several alternative ways of formalizing an argument. In this Wnal section we consider the question of how the analyst decides between such alternatives. 6.1
Alternative formalization
It will be recalled (see Chapter 1) that progressive and regressive operations parallel two possible reasoning processes. One may Wrst think of a claim and then deliberate on the reasons for its being correct; or alternatively, one may proceed step by step to a conclusion. Likewise, one may move from the cause to its result, or alternatively, from the result to its cause. In analyzing an argument, it would be desirable to follow the author’s reasoning process. The only clue to the author’s internal processes is, of course, the expressed argument. The analyst may tend to follow the sequence of the author’s assertions. When the author Wrst makes a claim and then states what justiWes it, the analyst may opt for the regressive mode, whereas when he states the conclusion after the claim that justiWes it, the progressive mode may be preferred. Similarly, the sequence in which statements are expressed by the author may lead to preferring an analysis with an Accounting or a Result operation.
JustiWcations 105
Now, the verbal expression of the argument is no sure guide to the internal processes by which the argument was constructed. The author’s reasoning process may have been in the progressive mode, and he may have subsequently edited the argument for the purpose of communicating it and turned it into the regressive mode, or vice versa (or it may have been in neither; see Chapter 1, Section 3). The analyst, then, is under no obligation to honor the manner of expression. For some arguments she might do well to adopt whatever analysis is more perspicuous. Thus, in a complex argument containing various “interim” conclusions that are subsequently referred to, it may be preferable to set these oV by articulations, so that the conclusions (i.e., the operations targeted by JustiWcation operations) stand out as part of the skeleton of the argument. But a point in favor of following the sequence of the expressed argument is that, trivially, at some point before uttering the argument, the author must have constructed it internally in the way it is expressed, if only in the process of editing it for the purpose of verbalization. The same considerations apply to the choice between alternative sequences of operations. Take, for instance, the analysis of the syllogism in Example 8: All politicians are shrewd; 〈 hence 〉 Carl Caldwell is shrewd; 〈 what justiWes this Inference is that 〉 Carl Caldwell is a politician.
It is permissible to interchange the Wrst and the last clause (but still retain the P-N-J sequence): Carl Caldwell is a politician;〈 hence 〉 Carl Caldwell is shrewd; 〈 what justiWes this Inference is that 〉 all politicians are shrewd.
Again, the analyst may take her lead from the verbal expression of the argument, or else she may be led by considerations of perspicuity. Often the same argument can be analyzed either with a warrant or with an articulation (see, for instance, Examples 6–7, 8–9, 14–15, and 17–18). Here, too, the decision ought to be guided by considerations of the overall perspicuity of the formalization. 6.2
An end to JustiWcation
We have seen that a JustiWcation can be supported by another JustiWcation (see, e.g., Example 19). Now, almost every JustiWcation can, at least in prin-
106 The Structure of Arguments
ciple, have a JustiWcation in its turn, and we thus seem to be faced with an interminable chain of JustiWcations.14 However, in actual conversations and discussions the chain of JustiWcations exhausts itself, so to speak, after a very small number of steps. Take Example 17. The warrant there includes a Comparison: Proponent: Motor scooters are more detrimental to parks than bikes.
The Interlocutor may not be satisWed with this: Interlocutor: How do you know? Proponent: Motor scooters are faster than bikes. Because they are faster, they may cause more damage to gravel paths, lawns, etc. (JustiWcation of the claim that they are more detrimental.) Interlocutor: How come? Proponent: The greater the speed of an object, the greater the force of its impact on another object. (JustiWcation of previous JustiWcation) Interlocutor: How do you know? Proponent: Any Physics textbook will tell you that. (JustiWcation of previous JustiWcation) Interlocutor: Why should I trust those textbooks?
It is a rare Interlocutor who would press as far as that, and even the most angelic Proponent will soon be at the end of his tether. Often a proponent of a claim may be only intuitively aware of what justiWes it and be unable to formulate a JustiWcation. Thus, in advancing an analogy between animals and people (Example 14), the Proponent may have only a vague idea about the relevant respects in which animals are similar to people and why this justiWes his thesis, and when pressed for further JustiWcations, he may be unable to explicate his intuitions. At any rate, even the most articulate Proponent will have to stop after a few links in the chain of JustiWcations. JustiWcation has to end somewhere. This raises the question of how far in the chain of JustiWcations the analysis of the argument has to go. Is the analyst under an obligation to play the role of the most articulate of Proponents and take the chain of JustiWcations as far as it can possibly be stretched? If so, the above imaginary conversations between the Proponent and the Interlocutor would seem to entitle a critic to fault the analysis in Example 17 for being incomplete.
JustiWcations 107
It is by no means evident, however, that the author in that argument had these JustiWcations in mind. There are others that might have been at his disposal; for instance, that the speed of motor bikes is relevant because it implies a greater probability of people getting run over (rather than a greater probability of damaging gravel paths and lawns). Which JustiWcation, then, should the analyst decide on? The formalization of every argument is based on the analyst’s interpretation, but here the interpretation will be more like guessing. The analyst had therefore better stop early, and the analysis in Example 17 seems to reXect a reasonable decision as to where to stop. The moral of all this is that the question of how far the process of JustiWcation ought to be carried cannot have any deWnite answer. In line with the Formalization principle (Chapter 2, Section 2.2), it is for the researcher to decide how Wne-grained his analysis ought to be.
Chapter 6
ConXations
Life is the art of drawing suYcient conclusions from insuYcient reasons. – Samuel Butler
A conXation is a combination of two or more operations that are introduced simultaneously. In this chapter it will be shown how the need for such simultaneity arises and how conXations function.
1.
The concept of conXation
One can either assert something or one can ascribe this assertion to someone else. The formalization will diVer accordingly, as shown in Example 1 1. P(p) 2. D(P1 )
p d
Jessica will get a promotion. John says so, too.
This author commits himself to two statements. Suppose now that an author advances only the second part of this argument (Line 2): “John says that Jessica will get a promotion”; that is, he does not commit himself to “Jessica will get a promotion” (which he may well believe to be wrong) but only to the fact that John says so.1 Unlike Example 1, such a statement cannot be analyzed as two separate operations, because the author does not commit himself to both. Instead, we have to collapse the two operations into one, as shown in the next example. The two operations are introduced simultaneously as a conXation. The symbolization deploys a caret posed between the two operators: Example 2a 1. D∧P(p)
d∧p
John said that Jessica would get a promotion.
110 The Structure of Arguments
This author commits himself only to the fact formalized as d∧p, namely, that John said that Jessica would get a promotion (and not to her actually getting it). A conXation introduces two (and occasionally more than two) new operations, one of which becomes the ‘object’ of the other operation. In the present example, P is a newly introduced Presentation and is the ‘object’ of a Designation (also newly introduced). This characterization of conXations will suYce for the time being; in Section 3.1 we will take a closer look at the interpretation of conXations. The Designation in Example 2a will be called the conXating operation (and D is the conXating operator) and the Presentation — the conXated operation (and P — the conXated operator). A conXation may comprise more than two operations, as in Example 3 1. T– ∧D∧P(p)
t–∧d∧p
It is false that John said that Jessica would get a promotion.
Here D is both conXating and conXated (and T– is only conXating and P — only conXated). Comparing this example to the next one shows that the sequence of operators in a conXation makes a diVerence: Example 4 1. D∧T–∧P(p)
d∧t- ∧p
John said that Jessica will not get a promotion.
Here “Jessica will not get a promotion” might have been formalized as P(p) (where the negation is included in p) instead of by T–∧P(p) (see Geach 1980: 262–263, in this connection). A conXation can also be a collateral operation, e.g., X(…) x: Y ∧Z(…)
2.
Outcomes of conXations and conXations as targets
2.1 Outcomes as targets As the above examples show, the outcome of a conXation is symbolized by lower-case letters, corresponding to the conXating and conXated operators, with a caret between them. This distinguishes the outcomes of conXations
ConXations
from those of non-conXated operations, which are constituted of a single letter. In Example 1, for instance, the outcome of D(P) is simply d, whereas the outcome of D∧P(p) in Example 2a is d∧p. The next example shows that, when two operations are conXated, there are two possibilities of targeting the conXated outcome: Example 2b Author 1 1. D∧P(p)
d∧p
John said that Jessica will get a promotion.
Author 2 2. T– (d∧p1)
t–
It is not true that John said so.
Author 3 3. T– (p1 )
t–
It is not true that Jessica will get a promotion.
Explanation: Line 2: When the target is the outcome of a conXation, the subscript is appended only to the rightmost symbol, because this is an unambiguous identiWcation of the targeted outcome.
One can, then, target the outcome of the whole conXation, d∧p, or the second part of it, p. It makes no sense, of course, to say, e.g., “It is not true that John says”, and so one cannot target only d. Author 2 does not commit himself as to Jessica’s getting or not getting a promotion; he merely denies that John made this statement. Conversely, Author 3 does not commit himself to any claim about what John said; he only says that Jessica will not get a promotion (whether or not John said so). The same two kinds of reply can be made in response to the argument in Example 1: Example 5 Author 1 1. P(p)
p
Jessica will get a promotion.
Author 2 2. D(P1 )
d
John says so, too.
Author 3 3. T – (d2 )
t–
It is not true that John said so.
Author 4 4. T – (p1 )
t–
It is not true that Jessica will get a promotion.
111
112
The Structure of Arguments
Compare operation 3 in this example to operation 2 in the previous one. The target here is d, rather than d^p. This is so because in the present example the information ‘John said so’ is wholly contained in d. The target d includes both ‘John said’ and ‘Jessica will get a promotion’ (recall that outcomes of Adjudgment operators, like D, have meanings that are a fusion of the information in the operator and that in the target; see Chapter 3, Section 3.2). In the previous example, by contrast, this information is contained in d∧p, where the Wrst element, d, means just “John said…”, and “Jessica will get a promotion” is included in the second element, p. Let us look now at the following arguments: Example 6 Author 1 1. T – ∧D∧P(p)
t– ∧d∧p
It is not true that John said that Jessica would get a promotion.
t–
It is unlikely that it is not true that John said that Jessica would get a promotion.
Author 3 3. T+ (d∧p1)
t+
It is indeed the case that John said that Jessica would get a promotion.
Author 4 4. T+ (p1 )
t+
It is indeed the case that Jessica will get a promotion.
2.
Author 2 %T – (t – ∧ d∧p ) 1
Here there are only three ways of targeting the outcome of operation 1: targeting (t– ∧ d∧p1), (d∧p1), and (p1). Other combinations — like (t– ∧ d1), (t–1), and (d1) — just don’t make sense and are inadmissible as targets. 2.2
Bipartite outcomes in conXations
It will be remembered that the outcomes of Interpretation, Accounting, and Result, have two parts (Chapter 3, Section 3.2). Normally, the author of an Accounting operation commits himself to both outcomes, aP and aA, and the author of a Result operation — to both rP and rR. An exception to this are conXations with a negative Truth value operator; here the author does not commit himself to aP or to rP. Take Accounting. The claim that x is the reason for y is formalized as an
ConXations
operation A(y), with the outcomes aP (= x) and aA (= x is the reason for y), and the author of this operation commits himself to both aP and aA. Consider now the claim that x is not the reason for y. Suppose that someone tells an expert about a problem she has with a word processor. The expert assures her that the problem is not caused by a virus. This is analyzed as a conXation: T – ∧A(y). The expert does not commit himself to the outcome aP — there is a virus — nor to its negation: all he says is that this particular problem is not caused by a virus, without knowing whether or not some programs have in fact been infected by a virus. Example 7 a Author 1 1. P(p) p
I have this problem with my word processor: …
Author 2 2. T – ∧A(p1 ) aP
A virus got into one of the programs. [Author 2 not committed to this] It is not true that aP caused the problem. [Author 2 committed to this]
t– ∧aA
The conXation T – ∧ A(p1 ) pertains to the claim that the problem was caused by a virus; it leads to the outcome that aA is incorrect: t–∧aA . Nothing is asserted concerning aP : Author 2 takes no stand for or against “A virus got into one of the programs”. Suppose now that Author 2 has in fact examined the program and found that it is not infected by a virus; that is, he intends to commit himself to the falsity of aP. Then his claim that there is no virus has to be represented as an additional operation: Example 7 b Author 1 1. P(p)
p
I have this problem with my word processor: ….
Author 2 2. T – ∧A(p1 )
aP
A virus got into one of the programs. [Author 2 not committed to this] It is not true that aP caused the problem. [Author 2 committed to this] It is not true that a virus got into one of the programs. [Author 2 committed to this]
t– ∧aA 3. T– (aP2)
t–
113
114
The Structure of Arguments
Alternatively, the expert might have claimed that one of the programs was indeed infected, but this was not the cause of the particular problem. Author 2’s argument would then be Example 7 c Author 2 2'. T – ∧A(p1 )
aP t– ∧aA
3'. T+ (aP2)
t+
A virus got into one of the programs. [Author 2 not committed to this] It is not true that aP caused the problem. [Author 2 committed to this] It is true that a virus got into one of the programs.
The role played by aP in such a negative Accounting operation parallels that of iP in an Interpretation (see Chapter 3, Section 3.2). The outcome of an Interpretation is also bipartite, and the author of T– ∧ I(x) commits himself to t– ∧ii (= this is not the correct Interpretation). If he, in addition, denies iP, this will have to be indicated by an additional operation T– (iP ). The same goes for negative Result operations: in T– ∧R(x), the author commits himself only to t– ∧ rR. The following example illustrates the analysis of it is not that… constructions (discussed by Delahunty 1995); for instance: I am not going to quarrel with my boss about this. It is not that I am afraid to be without a job, but I like the work I am doing now.
Example 8 1. P(p)
p
2. ifC T- (p1 ) 3. thenC P (p) 4. R(p3)
ifC t– thenC p rP rR aP: …. aP’ (=rP4 ) – ∧ t aA t–
5. T – ∧A(p1 )
6. T – (aP5 ) 7. A(p1)
aP aA
I am not going to quarrel with my boss on this issue. If I would do so, then he would ¼re me, I would be without a job. This would be the result of rP. That I am afraid I would be without a job. is not the reason for p1. It is not true that I am afraid of being without a job. I like my work at the present job. This is the reason for p1.
ConXations
2.3
Outcomes of multiplex conXated operations
The operators C, K, and U have multiplex targets: C(x, y), K(x, y), and U(x, y) etc. Both x and y may be introduced for the Wrst time and hence require a conXation. For example: Example 9 1. C∧[P1 (p), P2 (p)]
c∧[p1 , p2]
The statement that all furry animals are mammals is more likely to be true than the statement that all animals that have ¼ns are ¼sh.
Explanation: Confrontation, C, is an operation with a multiplex target; it compares two outcomes in respect to their truth value (e.g., x contradicts y, x is more/less likely to be true than y); see Chapter 3, Section 2.1. Square brackets indicate scope (Chapter 4, Section 2); here both P1 and P2 are within the scope of C: they are being compared in respect to their truth value. Either p1 or p2 may subsequently be targeted, and therefore both must appear in the outcome.
Suppose now that only one of the above statements appears in the operation in question for the Wrst time whereas the other has been mentioned previously. The analysis then will be: Example 10 Author 1 1. P(p)
p
All animals that have ¼ns are ¼sh
Author 2 2. C∧[P1 (p), p1 ]
c∧ [p1, p]
That all furry animals are mammals [p1 ] is more likely to be true than that all animals that have ¼ns are ¼sh [p1 ].
Explanation: Line 2: To provide for the possibility of targeting one of the two p’s in the outcome but not the other, we distinguish between them: a superscript is appended to the Wrst p, i.e., to the one that is not contained in Line 1. The same superscript has to appear also in the operator; hence we have [P1 (p)…] .
A constituent element of a conXated outcome — for instance “furry animals” in p1 — is symbolized like one in a simple outcome, e. g.: c∧p1: … p1 k furry animals
115
116 The Structure of Arguments
2.4
ConXating and conXated operators as targets
In the preceding examples, targets were outcomes of conXations. But conXating and conXated operators, too, can be targets. Compare the following to Example 6 in Section 1: Example 11 Author 1 1. T – ∧D∧P(p)
t– ∧d∧p
Author 2 2. V– (T – ∧ D ∧ P1) v–
It is false that John said that Jessica would get a promotion. The claim that it is false that John said that Jessica would get a promotion is not wellfounded.
Author 3 3. V+ (D∧P1)
v+
The claim that John said that Jessica would get a promotion is well-founded.
Author 4 4. V+ (P1 )
v+
The claim that Jessica will get a promotion is well-founded.
Observe that the permissible combinations of operators as targets parallel those of outcomes as targets (Section 2.1), namely: T – ∧ D∧P1 , D∧P1 , and P1.
3.
ConXating operators
3.1 The interpretation of conXations A conXation, it will be recalled, “introduces two (and occasionally more than two) new operations, one of which becomes the ‘object’ of the other operation”. We now turn to the question of how the ‘object’ of the conXating operation should be interpreted. Take the conXation X ∧ Y. What is the ‘object’ of X, what does X operate on: the outcome y or the operation Y itself? The answer will depend on the type of the conXating operation. If the conXating operation X is of a type that takes an outcome as target, the conXated operator stands for the outcome of the conXated operation; if it is of a type that targets an operator, the conXated operator stands for the operation as a whole. This is illustrated in Table 6.1 by means of two operations, one that targets
ConXations
outcomes (T) and one that targets operators (V). (Normally, of course, the non-conXated operations — see the left-hand column — will not be performed by the same author but by two diVerent ones; this is irrelevant for the purpose of illustration, however). Table 6.1 ConXated and non-conXated operations compared Not conXated 1. X (y) 2. T – (x1 )
ConXated 1. T– ∧X(y) t– ∧x
x t–
It is not true that x.
It is not true that x1. The ‘object’ of the conXating operation is the outcome x.
1. X (y) 2. V– (X1 )
x v–
Operation X1 is not valid.
1. V– ∧ X(y) v – ∧ x Operation X is not valid. The ‘object’ of the conXating operation is the operator X
A problem seems to arise with operators that can target either an operator or an outcome. A Designation, for instance, can target either an operation, D(X ), or its outcome, D(x). Consider E(x)
e
〈 It follows that 〉 the neighbors will move soon.
When one then states that so-and-so made this Inference, we write D(E), but when one states that so-and-so agrees to the assertion that the neighbors will move soon, this is symbolized D(e). Turning to conXations, remember that these pertain to operations that did not occur previously. Therefore D∧E(x) can only mean that so-and-so made an Eduction operation. When someone agrees to the outcome of an Eduction, the latter must have appeared previously in the analysis, and in that case D will target the outcome e; no conXation will be in order. The situation is only slightly more complicated in the case of bipartite outcomes; i.e., those of A, R, and I (Chapter 3, Section 1.1). Take Interpretation; e. g., I(x)
iP iI
One should not aim too high. This is what x means.
117
118
The Structure of Arguments
Then D(I) indicates who made this Interpretation, D (iP) indicates who assents to “One should not aim too high”, and D (iI) — who assents to the claim that this is the Interpretation of x. Again, there will be no ambiguity in a conXation with D: D ∧ I(x) can only mean that such-and-such an author interpreted x in a certain manner. It cannot mean that this author stated that one should not aim too high (iP ), because there is no such Interpretation preceding D ∧ I(x). If there were, no conXation would be in order; instead, we would have to write D (iP). (See Chapter 10, Section 4.2 for a slightly diVerent notation of the target of an Interpretation.) As shown in Example 10, above, a multiplex target may include an operation. Take Subsumption, U, and suppose now that an operation X (that has not appeared before) is targeted by a Subsumption, U. This is symbolized by a conXation: U∧ [X(y), z]. Here, again, there is no ambiguity: The expression can only mean that the operation X is a member of the category z. So far, then, we have not come across any possible ambiguities in construing the notation of conXations. Should such cases be discovered, some convention would have to be introduced to ensure disambiguation. 3.2
Which operators can be conXating?
All operations of the Adjudgment class can be conXating. In previous sections, examples were given of Truth value, Designation, Confrontation, Validation, and Subsumption (T, D, C, V, and U) as conXating operators. Here a few additional comments will be made. Validation and Truth Value. Neither T+ nor V+ can be conXating operations. Consider what could possibly be meant by T+ ∧ X (…). Since this is a conXation, X must have appeared here for the Wrst time (otherwise T+ would target the outcome x). At Wrst blush T+ ∧ X (…) might be taken to mean that the outcome of the newly introduced operation X is true. Recall, however, that conXations apply, by deWnition, to operations that the author does not commit himself to, whereas the claim that outcome x is true commits its author to x. When this claim is made we therefore have to formalize it, simply: X (…). Likewise, V+ ^ X (…) is inadmissible, because the conXated X is, by deWnition, an operation the author does not commit himself to, and this contradicts V+ (the claim that X is valid). Here, too, one writes simply X(…). So much for T+ and V +, which denote truth and validity, respectively. By contrast, T– and V–,which denote falsity and invalidity, may be conXating operations, because the foregoing considerations do not apply to them. Ex-
ConXations
amples 6 and 11, above, contain conXating negative Truth value operations. A conXating negative Validation occurs, for example in: Bert and Barbara will probably not go to Europe this year, because they have small children. But Jerry and Judy will go, because they have no small children, and so this is not a reason for them not to go. Example 12 1.
%P(p)
2. J(%P1 )
%p
j
%p 3. %P(p) % 4. J( P3 ) j | 5. P(p) | 6. E(p5 )
Bert and Barbara will probably not go to Europe this year. 〈What justi¼es saying this is that〉 they have small children. Jerry and Judy will probably go to Europe. 〈What justi¼es saying this is that〉 p They have no small children. ∧ ∧ e: V J P 〈 It follows that 〉 to claim that they are not going to Europe [P] because they have small children [J] would be invalid [V-].
Explanation: The ‘because’-clause has been dealt with here as a JustiWcation. Alternatively, it may be conceive of as giving a reason, and then the analysis would involve an Accounting operation; cf. Chapter 5, Section 1.2. Intuitively, Lines 3–6 are somehow connected to Lines 1–2. This is not a targeting relation, however, and to capture it we introduce the notion of ‘connection’ in Chapter 8.
Status. S can also be conXating. One may characterize an operation or set of operations without committing oneself to them; e. g., Example 13 1. S∧P(p)
s∧p
That honesty is the best policy is a trite saying.
Suppose now that an author does commit himself to the truth of a statement, then applying a Status operation does not involve a conXation: Example 14 1. if P(p) 2. then P(p) 3. S(if P1 then P2)
if p then p s
If a man is a bachelor, then he is unmarried. This is a trivial statement.
119
120 The Structure of Arguments
Evaluation. An Evaluation of an action or situation that has not been referred to previously in the analysis will be formalized as a conXation: Q ∧ P(p) q∧p. For instance, the author of “For Jack to invite Jill to the party is a nice gesture” commits himself to the outcome of the Evaluation of Jack’s action (q∧p) but not to the fact that this action has occurred (p). Confrontation, Comparison, and Subsumption. These may be conXating operations. ConXating Confrontations, C∧[P1 (p), P2 (p)] and C∧[P1(p), pi ], appear in Examples 9 and 10, above. So much for Adjudgments as conXating operators. In Chapter 7 it will be shown hat Nescience operators may also be conXating. Now, what about operators of other classes? Operators belonging to the Presentation, Inference, Interpretation, Elaboration, Cause, and JustiWcation classes cannot be conXating. This may be illustrated by Example 17 of the previous chapter, repeated here: Example 15 1. P(p) 2. E(p1 ) 3. J(E2 )
p: pj … e: ek … K(ek2 , pj1 )
Bikes are not allowed in the park. 〈 A fortiori,〉 motor scooters are not allowed in the park. 〈What justi¼es this Inference is that〉 motor scooters are more detrimental to parks than bikes.
It’s inadmissible to collapse two of these operations into a conXation (for instance, E∧P(p) instead of Lines 1and 2 or J∧E(p1 ) instead of Lines 2 and 3). This is because conXations are designed to permit formalization of cases where an author refers to an operation that he does not commit himself to, and the author of this argument commits himself to each of the operations and outcomes. The operators E and J in this argument, then, cannot be conXating; instead, they have to target p1 and E2 ,respectively. ConXations are not meant to be shortcuts for sequences of operations. Suppose now that the operations 1 and 2 in this example were made by diVerent authors, and the author of operation 2 does not commit himself to p1 (he merely asserts that from the prohibition on bikes — if there indeed is one — it follows that motor scooters are also prohibited). Then there will be an outcome p of the Wrst author’s Presentation, which Author 2 then targets (as in Line 2), and there will still be no occasion for a conXation E∧P(p).
ConXations
In the following example, the Accounting operation is not conXating, because the author is committed to the outcome of Line 1. Example 16 1. D∧P(p) 2. A (d∧p1 )
d∧p aP aA
Ms. Smith said that all her neighbors neglect her. Ms. Smith is a great egoist. This is the reason why she claims that all her neighbors neglect her.
A similar analysis would be in order with a Result operation instead of the Accounting operation. The foregoing discussion boils down to the following generalization: In an argument made by Author A, an operation X that belongs neither to the Adjudgment or to the Nescience class cannot appear as a conXating operation X ∧Y (…), because either one of the following will be the case: a. Author A is committed to the outcome of Y . In this case, the analysis of A’s argument will contain an operation Y and a later operation targeting Y or y (as in the Inference and Accounting operations in Examples 15–16). b. Y has already appeared in the analysis of an argument by another author. In this case, A’s argument will contain an operation targeting Y or y of the previous author. c. Author A has already stated that another author concurs with Y (this is analyzed as D ∧Y (…) ). In this case — as in case (a) — A will target Y or y, which were introduced in his own argument. An Interpretation applies typically to an outcome y in an argument made by another author; that is, it is an instance of (b) or (c) and will be analyzed as targeting y, not as conXating. When an author interprets his own statement, he is committed to that statement, and so this falls under (a). Elaborations, too, are typically performed on an operation made by another author, and thus fall under (b) or (c). When an author elaborates his own statement, this is a case of (a): the author has committed himself to that statement. A JustiWcation typically applies to an operation the author has made previously; this falls under (a): the author is committed to the preceding operation.
121
122 The Structure of Arguments
When one justiWes a statement made by another author, this is an instance of (b) or (c). We conclude that only Adjudgment and Nescience operations can be conXating. There is no such constraint on conXated operations, however: all operators can be conXated.
4.
ConXating Designations
In Chapter 3, Section 1.1 we introduced several kinds of Designations, which are distinguished by superscripts. In this section some problems concerning Designations will be discussed. 4.1
DA
People often appeal to “arguments by authority”. The fact that an assertion was made by a certain trustworthy person is claimed to vouch for its correctness. This can be formalized with DA and may require a conXation. For instance: Example 17 1. DA∧P(p) 2. DA∧Q(dA ∧p1 ) 3. K (dA’1 , dA’’2 )
dA∧p: dA’ … dA∧q: dA” … k
4. E(k3 & dA ∧p1 ) e: T+ (p1 )
Aunt Jemima says that oak bark heals chicken pox. Dr. Jenkins says that this is mere superstition. Aunt Jemima is a better authority than Dr. Jenkins. 〈 It can be inferred from this that 〉 it is true that oak bark heals chicken pox.
Explanations: Lines 1–2: dA means Aunt Jemima says / Dr. Jenkins asserts, and since the Comparison in Line 3 is between Aunt Jemima (not ‘Aunt Jemima says’) and Dr. Jenkins, dA must be broken down into constituent elements (Chapter 3, Section 3.3), indicated here by apostrophes. Line 2: Q symbolizes an Evaluation; see Chapter 3, Section 1.1 (sub Adjudgment). What is being evaluated here is not the fact that oak bark heals chicken pox, but the assertion of it (by Aunt Jemima, in this case). Line 4: The Inference is based on both Aunt Jemima’s statement and the fact that she is a better authority than Dr. Jenkins.
ConXations 123
There may be more than one conXating DA . In the following example we take advantage of the convention that the superscript A, being the most frequently occurring one, may be omitted in Designations (Chapter 3, Section 1.1, sub Adjudgment): Example 18 1. D1 ∧D2 ∧P(p)
d1 ∧d2 ∧p
2. D1 ∧E(d2 ∧p1 )
d1 ∧e
Dr. Jenkins says that Aunt Jemima claims that oak bark heals chicken pox. Dr. Jenkins says that 〈it may be inferred from this that〉 Aunt Jemima is superstitious.
Explanation: Line 2: Dr. Jenkins makes the Inference from the fact that Aunt Jemima said this, and hence the target is d2 ∧p1 (and not just p1 ). The superscript in D1 serves to identify this author with Dr. Jenkins in Line 1, rather than with Aunt Jemima.
As stated repeatedly, an author does not commit himself to the conXated operation. Thus, the author of DA ∧ O (…) does not commit himself to the outcome of the Elaboration, the author of DA ∧E(…) does not commit himself to the outcome of the Eduction, and so on. Recall that the author of an Interpretation commits himself only to iI, not to iP. In the example given in Section 3.1, for instance, iP = One should not aim too high; iI = This is what x means. The author of this Interpretation is committed only to this being the correct Interpretation, not to “One should not aim too high”. Now, when another author is asserted to have interpreted a text x, we write DA ∧ I(…), and the author of this assertion does not commit himself even to iI: he just reports that someone else claimed that this is the correct Interpretation. 4.2
DR
When a legal text is cited, the “author” is the law and is indicated by D with the superscript R (for “rule”). Here is an argument involving a law concerning the administration of drugs that have not passed all tests to terminally ill patients. A lawyer argues that banning such drugs without exception may have undesirable results.
124 The Structure of Arguments
Example 19 1. DR∧DO ∧P(p)
dR ∧dO ∧p
2. R(dR ∧dO ∧ p1 ) rP
3.
Q(rP
2)
rR q
There is a law prohibiting administration of drugs that have not passed certain tests, even for the purpose of scienti¼c experiments. There will be almost no scienti¼c experimentation. This will be the result of the law. This is a highly undesirable situation.
Explanations: Line 1: The law consists of an imperative (it says ‘do not…’), which is symbolized by DO; see Section 4.4, below. The activity that is prohibited is introduced by P(p). Line 2: Recall that the outcome of a Result operation is bipartite, rP and rR. The target of R can not be p1 , because the latter stands for ‘administering drugs etc.’ (and not for not administering them).
4.3 DI DI stands for some indeWnite or unknown author. Thus, a proverb may be cited as DI ∧P(p). It is possible to give a reason for DI ^P(p), or infer something from it; e. g., Example 20 1. DI ∧ P(p) 2. A(dI ∧ p1 ) 3. % T(p1 ) 4. E(dI ∧ p1 )
dI∧p aP aA %t e
People say that he has embezzled money. People envy him. This is the reason that they say this. It is doubtful whether their report is true. 〈However, it may be inferred from the fact that people say so that 〉 he is very rich.
Explanations: Line 2: What is being accounted for is not the fact that he embezzled money — which would be symbolized as A(p) — but the fact that people say so. Hence the target is dI ∧ p (cf. Example 16, above). Line 3: Unlike the target in Line 2, this target is p: It is the content of what people say that is of questionable truth. On the degree-of-conWdence preWx (%) see Chapter 3, Section 1.3. Line 4: The target is again dI ∧p; see the foregoing comment on Line 2. This
ConXations
operation is related to the preceding one; in the expressed argument it would be introduced with an expression like “however” or “but”. In Chapter 8, Section 2, it will be shown how such relationships are formalized.
4.4
Other Designations
The Designations discussed in the foregoing belong to sub-type A, pertaining to the author. Sub-type B, pertaining to the circumstance of the operation, presents no special problems. Here we will discuss conXations with sub-type C Designations. The operator DO is used for imperatives (commands, prohibitions, advices, etc.). DO stands for “I ask/ command/ advise…”, and the conXated operation stands for the object of this imperative, i.e., what the addressee is asked to do or not to do. Example 21a 1.
DO ∧ P(p)
dO ∧ p
Do not smoke!
In our analysis, this command is treated like an explicit imperative, “I ask you not to smoke”. The underlying structure contains `I ask you’, symbolized as DO, and ‘you will not smoke’ — P(p). The latter, while not asserted here, is contained in the command (see Lyons 1981: 141). Similarly, DP ∧ P(p) may stand for a propositional attitude, e.g., “I hope she will not smoke”. DD ∧P(p) — for intention to act, e.g., “I am going to smoke”. DF ∧ P(p) — for a performative, e. g., “I promise not to smoke”. 2
In all these cases, the analysis is similar to that of imperatives: a proposition corresponding to the action or state of aVairs that is hoped for, intended, promised, etc., is isolated, and reXected in a conXated operation, P. This is in line with our general approach, which analyzes underlying structures in terms of propositions.3 As argued in our discussion of sub-type C Designations (Chapter 3, Section 1.1), there are instances where an utterance is intended as both an Evaluation and an imperative. These are analyzed as two operations: an Evaluation, from which an imperative follows by an Eduction. Take:
125
126 The Structure of Arguments
Waiter : Smoking in the restaurant is prohibited, Sir.
This will be analyzed as Example 21b Waiter 1. Q∧P(p) q∧p 2. E (q∧p1 ) e: DO ∧ P(p)
It is prohibited to smoke in this restaurant 〈Therefore〉 do not smoke in this restaurant
Explanations: Line 1: Q is the Evaluation operator (cf. Section 3.2, above): something is asserted of smoking in the restaurant, namely, that it is prohibited. (We assume here that no law is being invoked: the owner just does not want clients to smoke.) Line 2: Note that the Presentation in the collateral operation refers to the addressee (‘you will not smoke’), whereas that in Line 1 refers to smoking by people in general. Hence we cannot write DO(p1).
The Designations discussed here typically occur as conXating operations. Thus, in Line 2 of the last example, DO is a conXating operation. For DO to target an outcome p, a Presentation would have to precede it. For instance: Example 21 c Guest A (to waiter) 1. DP ∧ P(p) dP∧ p
I hope that shady character at the back is not going to smoke.
Waiter (to Guest B, the “shady character”) 2. Q∧P(p) q∧p It is prohibited to smoke in this restaurant 3. E (q∧p1 ) e: DO (p1 ) 〈Therefore〉 do not smoke in this restaurant Explanations: Line 1: DP stands for the Designation of propositional attitude (here: hope). Line 3: ‘Do not smoke…’ is predicated of the person referred to by Guest A: ‘that shady character…’. It does not refer to people in general, who are alluded to in Line 2 (cf. the Explanation given for Example 21b). 4
Here is a somewhat more complex example, also involving DP:
ConXations 127
Example 22 1. DA, P ∧ P(p)
dA, P ∧ p
2. i¬C P(p) 3. thenC T+ (p1 ) 4. E(dA, P∧ p1 & i¬C p2 thenC t+3 )
Ted wanted very much to pass the exam. i¬ C p If and only if he had studied hard enough, thenC t+ then he would have passed the exam. e: Q(p2 ) 〈It follows that〉 he ought to have studied hard enough.
Explanations: Line 1: The Designation operator has two superscripts: A (for author, here — ‘Ted’), and P (for propositional attitude, here — ‘want’). P(p) stands for Ted’s passing the exam. Line 4: p2 is “Ted has studied hard enough” (cf. Line 2). Q(p2 ) is an Evaluation of this: studying hard would have been the right thing for Ted to do.5
5.
ConXations with compounds and with sequences
When the conXated operation is compound, the scope of the conXating operation will be indicated by square brackets, as in the following example, where DF denotes a performative (here — a promise): Example 23 1. DF ∧ [i¬ P1 (p) then P2 (p)]
dF∧ [i¬ p1 then p2 ]
If you do the dishes I’ll lend you the car.
In this example it is the conXated operation that is compound. ConXating operation can be compound, too: Example 24 1. [D1 / D2 ] ∧ P(p)
[d1 / d2 ] ∧ p
Either John (d1 ) or Jack (d2 ) said p.
Explanation: Superscripts distinguish between the two Designations; see Chapter 4, Section 2.
But “Both John and Jack said p” will be formalized as two operations, D ∧ P(p), in accordance with the rule that, wherever possible, conjunctions be treated as two operations (Chapter 4, Section 3).
128 The Structure of Arguments
An operation may be conXated with a sequence of operations, rather than with a single one. The sequence will be set oV by a vertical line, like the sequence of operations in an articulation (Chapter 5, Section 2.3). The following argument should be compared to that in Example 19: Example 25 a 1. DR∧DO∧P(p)
dR ∧dO ∧p There is a law prohibiting administration of drugs that have not passed certain tests, even for the purpose of scienti¼c experiments. – ∧ R ∧ O ∧ – ∧ 2. T | R(d d p1 ) t | rP The following is not true: There will be | | almost no scienti¼c experimentation. | | rR This will be the result of the law. | 3. Q (rP2 ) | q This is a highly undesirable situation.
In arguing, one often forestalls a possible objection: “Such-and-such is the case, although…[possible objection]”. The possible objection will then be introduced by a Status operation: Example 25 b 2'. S ∧ | R(dR ∧dO ∧ p1 ) s ∧ | | | | 3. Q (rP2 )
| rP | | | rR |q
The following objection might be made: There will be almost no scienti¼c experimentation. This will be the result of the law. This is a highly undesirable situation.
ConXated sequences can be hierarchically ordered:6 Example 26 1. D ∧ | Q∧P(p) d∧ | q∧p | | 2. | J(Q∧P1 ) |j | | 3. | | D ∧ | if T+ (p1 ) | | d∧ | | | | | 4. | | | then P(p) | | | | | | | 5. | | | J (if T+3 then P4 ) | | | | | | | | | | | | | | | | | | | | | |
Alice says: it is foolish to drink water after eating fruit. 〈and that what justi¼es this is that〉 | if t+ Aunt Jemima says that | if you do, | then p then you will get | stomach trouble. |j 〈and what justi¼es | this is that〉 | poor Charlie did so and | got a terrible | stomach ache.
Chapter 7
Questions
“I have answered three questions and that is enough,” Said his father, “Don’t give yourself airs! Do you think I can listen all day to such stuV? Be oV or I’ll kick you down stairs!” – Lewis Caroll
This chapter deals with the Nescience class of operations. Questions will be the subject matter of the Wrst Wve sections, and “don’t-know” statements — of the Wnal section. Questions are not usually conceived of as arguments. However, when dealing with discussions (dialogues, debates), one cannot aVord to leave questions out of account, because they aVect the discussion and may be an integral part of it. From the fact that a certain question has been asked, conclusions may be drawn concerning the beliefs or assumptions of the discussant who asked it; the presuppositions of a question may be discussed; the relevance of an answer to a given question may be debated; and so on. By the term ‘Question’ we refer to “a kind of request, viz. a request to tell the original speaker something, to give him a piece of information that he wants.” (Jespersen 1924: 302). Such a request is usually formulated as an interrogative sentence, but one may also utter declarative or imperative sentences and intend to request information, e.g., “I wish I knew where he has gone.”, “Tell me where he has gone” (see the treatment of indirect questions in Macaulay 1996). Conversely, there are interrogative sentences not intended as requests for information: rhetorical questions, for instance, or interrogative sentences like “Could you pass the salt please?”, which are requests, but not requests for information. These will not be analyzed as Questions in our system. It is not the syntactic form of the utterance that determines the analysis, but its function, the speech act performed by it. The author of a Question, then, requests some information.1 But although a question is a kind of request, it cannot be formalized just like any other
130 The Structure of Arguments
request. A request concerning what should be said — e.g., “You should say that you are going to give Bill a present” — is not a Question, but will be analyzed, instead, like other requests with a Designation (Chapter 6, Section 4.4): DO ∧P(p). When one asks a question, one typically wants to obtain some information from the addressee and does not know what the addressee should say (or else there would be no need to ask him). Questions like “Why did you say that?”, “To whom are you going to give a present?” or “What are you going to give Bill?” do not specify fully what the addressee is requested to say.2 The information requested by the Question is not invariably information that the author lacks. In an examination question, for instance, the examiner does not lack the information asked for, but checks up on the examinee. Cases like this will also be regarded here as Questions. Conversely, an author may state that he lacks a certain piece of information without requesting this information; this is the “don’t- know” operation dealt with in Section 6, and not a Question operation.
1.
Question operators and outcomes
A Question is symbolized by an underlined question mark with a superscript, e.g., ?A. For instance: Example 1 Author 1 1. P(p) p
In World War II the Allies landed in France.
Author 2 2. ?A (p1) ?A
What motivated the landing?
Author 1 3. A(p1) aP aA
Landing in France seemed to be the best way to defeat the German army. This was the motivation for the landing.
The superscript of the Question operator is determined by the kind of information that is requested. Thus, when one asks about the reason or motive of what is stated in the outcome of a previous operation, as in the preceding example, the superscript will be A, for Accounting; when asking who is the author of the statement, the superscript will be D, for Designation, and so on. The target of a Question is the operator or the outcome about which
Questions
further information is requested. The outcome of a Question (like those of all other operations) is symbolized by the same letter as the operator; since there is no lower-case question mark, the outcome of a Question will be symbolized by an underlined question mark. Like the outcome of an Adjudgment, the outcome of a Question is fused (Chapter 3, Section 3.2). The answer to a question will typically be symbolized by the same letter as the superscript of the Question operator (A, in the present example; Section 5 discusses exceptions to this rule). The answer will typically target the operator or outcome targeted by the Question. It will be recalled that the various types of operations in our system (A, I, E, V, etc.) fall into eight classes (Chapter 3, Section 1.1). There are Question types corresponding to operation types belonging to six of the eight classes, as shown in the following table. Table 7.1 Examples of types of Questions Class Interpretation Questions Elaboration Questions Cause Questions
Inference Questions JustiWcation Questions Adjudgment Questions
Example of Question ?I
3
(x) ?O (x) ?A(x)
?R (x) ?E (x) ?W (x) ?J (X) ?D (X) ?V (X) ?T (x)
How is x to be interpreted? What are the details of x? What is the reason (motive, purpose) for x? What is the result of x? What follows from x? What follows from x by analogy? What justiWes operation X? Who is the author of operation X ? Is operation X valid? Is x true?
Note: Questions like where? and when? are Elaboration questions and will be dealt with in Section 2, below.
As the above table illustrates, the targets of Questions may be outcomes or operators, depending on the type of Question. When an operator requires an outcome as target (as do, e.g., I, O, A, and L), the corresponding type of Question also targets an outcome (or, as will be seen below, a constituent element of an outcome). By contrast, operators which target operators (like J and V) have corresponding Questions that also target operators. (D may target either an operator or an outcome; see Chapter 3, Section 2.2). Two classes of operations do not have corresponding Questions: Presentation and Nescience.4
131
132 The Structure of Arguments
Let us look now at some types of Questions. An example of an Elaboration Question is Example 2 Author 1 1. P(p) p
In World War II the Allies landed in France.
Author 2 2. ?O (p1 ) ?O
When did the landing take place?
Author 1 3. O(p1 ) o
In World War II, in June 1944, the Allies landed in France.
Elaboration Questions can ask about the place, time, etc. of the targeted outcome, but there is nothing in the superscript to the question operator that distinguishes between these.5 In the next example we have an Interpretation Question (but see note 3): Example 3 Author 1 1. D∧P(p) d∧p Author 2 2. ?I (p1) ?I
Yeats wrote: “Things fall apart, the centre does not hold”. What does this mean?
A question about the truth value of a statement requires the operator ? T : Example 4 Author 1. 1. D∧P(p) d∧p 2. ? T (p1)
?T
Author 2 3. T+ (p1) t+
Bob claims that the author of Hamlet is really Francis Bacon. Is it true that Bacon is the author of Hamlet? Yes, this is true.
Explanation: Line 2: The superscript of the Question operator is neither T+ nor T–, but simply T. The question is whether the Truth value is ‘true’ (+) or ‘false’ (–), and T+ (…) and T– (…) are both possible answers.
Note that the target of the Question operator in this example is not the whole
Questions
outcome of Line 1, (d∧p), but only p1 . The symbolization ?T (d∧p1 ) would have meant: ‘Did Bob really say this?’. The superscript for degree of conWdence (Chapter 3, Section 1.4) may have to be appended to the superscript of the Question, as in Example 5 Author 1 1. P(p)
p
The author of Hamlet is really Francis Bacon.
Author 2 2. ? % T (p1)
? %T
How certain are you?
Author 1 % T+ (p ) 1
% t+
That is quite certain.
3.
Explanation: Line 3: The author asserts expressly that he is quite certain, and this requires appending the symbol for degree of conWdence, % (see Chapter 3, Section 1.3).
Subsumption Questions, ?U, require a special convention. There are two kinds of such Questions: Which category is x a member of? (i.e., what includes x?) What is included in category x ?
The target of the Question includes a comma and a blank space, and the position of the latter varies according to whether it is the category or the member one asks about: ?U (x, ) Of which category is x a member? (i.e., what includes x?) ?U ( ,x) What is included in category x?
A question may be ambiguous in the sense that the author expects any one of two diVerent types of answers. For instance, the answer to a why-question might be either a JustiWcation, J, or an Accounting operation, A (cf. Chapter 5, Section 1.2). Often, the context will suggest one of these interpretations, but when it does not, the investigator should not decide arbitrarily how to interpret the question;6 rather, she should take into account both possibilities. We therefore introduce the convention of a disjunct superscript; thus, a Question that may ask for either a JustiWcation or an Accounting operation will be symbolized as ?A / J (x). J(x) as well as A(x) will then both be appropriate answers.
133
134 The Structure of Arguments
2.
Backdrops
Certain kinds of questions necessitate introducing a backdrop in the analysis. Backdrop is our term for an operation which the author commits himself to in asking a question and which is targeted by the Question. The backdrop is not expressed verbally; it is a kind of presupposition (on presuppositions see Chapter 3, Section 1.1, sub Inference). Suppose someone starts a conversation by asking “Why did the Allies land in France in World War II?”. The analysis will deploy a Question operator: ?A. But what is its target? No argument preceded this question, but the formalization cannot begin without an operation that is targeted. It is therefore mandatory to include an operation, the outcome of which says that “The Allies landed in France in World War II”.7 The same applies to an Elaboration Question like “When did the landing of the Allies in France take place?”. Example 6 should be compared to Example 2: Example 6 Author 1 1. P(p) p 2. ?A (p1)
?A
Author 2 3. ?O (p1) ?O
In World War II the Allies landed in France. [= backdrop] What motivated the landing? When did the landing take place?
Consider now the following dialogue: – In World War II the Allies landed in France. – By what name is the day of landing known? – The day is known as D-day.
Recall that not every case of supplying additional information is an Elaboration. An Elaboration establishes the identity of a participant or speciWes the time or location of an event or state of aVairs or otherwise adds precision to a previous statement (Chapter 3, Section 1.1). “The day is known as D-day” does not give such a speciWcation for “In World War II the Allies landed in France”; instead, it introduces a new ‘aspect’ of the topic under discussion. Therefore “The day is known as D-day” is not an Elaboration of “In World War II…”. To formalize the above Question we need another backdrop:
Questions
Example 7 Author 1 1. P(p) p Author 2 2. P(p) p 3. ?O (p2)
?O
Author 1 o 4. O(p2)
In World War II the Allies landed in France. The day the Allies landed in France has a special name. [= backdrop] What is this name? The day is known as D-day.
Explanation: Lines 1–2: These two operations are linked by what we call in the next chapter a ‘connection’ (namely ‘Comment’). Line 3: Both here and in Example 6 the Elaboration Question is about “In World War II…”, but in Example 6 the Question targets this outcome directly, whereas in the present example an additional backdrop has to be inserted.
A backdrop, like any other operation, can be refuted. If Author 1 would have replied to the Question “That day has no special name”, this would be formalized as T – (p2 ) t–. Even a very general Question, like “What happened?” has a backdrop. What this Question normally presupposes is that “Something extraordinary, or non-trivial, happened” (the questioner would presumably not be satisWed with the answer “The Xy walking on the ceiling just changed course.”). “Nothing” might be an acceptable reply. Likewise, an acceptable response to “What shall we do now?” (an ‘imperative question’; see Hamblin 1987: 78) might be “Nothing”, and this Question has the backdrop “We should [perhaps] do something now”. “Nothing” as an answer to such Questions is analyzed as a refutation of the backdrop. The backdrop of some very general Questions may strike one as highly artiWcial. Thus, the question “Do you have the time?”, far from being a yes-no question as its wording might suggest, really means “What is the time?” and is formalized as an Elaboration Question targeting the backdrop “It is now a certain hour of the day”, or something like it. The backdrop of “How is your aunt?” sounds even more inane (“You have an aunt …”; this, too, can be refuted; for instance, “My aunt passed away twenty years ago…”). But remember that there is no intimation that the backdrop will ever be verbalized: our formalization pertains to the underlying structure.
135
136 The Structure of Arguments
The backdrop of “What did Betty say?” is “Betty said something” (the questioner may know no more than that it was “something” that she said) and that of “What did Betty ask?” is “Betty asked something”. These are both Elaboration Questions: Example 8 1. P(p) 2. ?O (p1)
p ?O
Betty said something. [= backdrop] What did Betty say?
p ?O
Betty asked a question. [= backdrop] What did Betty ask?
Example 9 1. P(p) 2. ?O (p1)
Another type of Question requiring an ‘artiWcial’ backdrop is one targeting a constituent element. For instance (see Section 1 on the notation for Subsumption questions): Example 10 1. P(p) 2. ?U (p r1 , )
3.
p: pr … ?U
The tiger is an animal. [= backdrop] To which zoological genus does the tiger belong?
Questions in conXations
3.1 ConXating Questions The purpose of a conXation, it will be remembered, is to avoid ascribing to an author an operation he does not necessarily commit himself to (Chapter 6, Section 3.2). For instance, a conXation permits us to analyze the statement “Johnny said that three and two are four”, without ascribing to its author the belief that that three and two are four — P(p) — the outcome of which is then targeted: D(p). By symbolizing the report about Johnny’s assertion with a conXation, D∧P(p), we avoid ascribing such a commitment to the author. There are Questions that have to be formalized as conXations. When one asks, for instance, who is the poet who wrote a certain line, one does not intend to commit oneself to what is stated in it. Therefore this question cannot be formalized with the quoted line as a backdrop: a backdrop is an operation to which the author commits himself.
Questions 137
In Example 11, which includes a Designation Question and an Interpretation Question (but see note 3), the author does not commit himself to the conXated operation, i.e., to the claim that things fall apart, etc. Example 11 1. ?D∧P(p)
?D∧p
2. ?I ∧ P(p)
?I ∧p
Who wrote “Things fall apart, the centre does not hold”? What does “Things fall apart, the centre does not hold” mean?
Example 11 should be compared to the Interpretation Question in Example 3, which targets a previous outcome. Yes-no Questions may also be analyzed as conXations, with ?T as the conXating operator: Example 12 Author 1 1. ? T ∧P(p) Author 2 2. T – (p1) 3. A(t– 2) Author 1 4. ? T ∧ E(aP3)
?T∧p
Did you go to see Jane today?
t– aP aA
No, she was too tired. That’s the reason I didn’t go to see her.
?T∧e
Does this mean that she won’t come to the party tonight?
Explanation: Line 4: “She won’t come to the party tonight” might be inferred from aP (“she was too tired”) and in Line 4 the author asks about the truth of this conclusion.
Here is an example with a disjunctive Truth value Question : “Did you go to the theater or to the opera?”: Example 13 Author 1 1. ? T ∧ P1 (p )// ? T ∧ P2 (p)
?t∧p1 // ?t∧p2
Did you go to the theater or to the opera?
Author 2 2. T+ (p21)
t+
I went to the opera.
138 The Structure of Arguments
Explanations: Line 1: The symbol // stands for exclusive disjunction (Chapter 4, Section 2): the person asked is assumed not to have gone both to the theater and the opera. The superscripts 1 and 2 serve to distinguish between the two Presentations (note that only the second is referred to in Line 2).
In a disjunctive Question there may be more than two disjuncts; e.g., when one asks which of three brothers was at the scene of a crime: ? T ^ P1 (p)// ? T ^ P2 (p) // ? T ^ P3 (p). But when the number of disjuncts is not known (‘who [of an undetermined number of people] was at the scene of the crime?’), a backdrop (‘somebody was at the scene of the crime’) and an Elaboration Question will be in order. To summarize, there are two ways of dealing with Questions that, standing by themselves, do not target a preceding operation: introducing a backdrop and conXating the Question with another operation. The former is mandatory when the author of the Question does commit himself to the statement that becomes the backdrop, while the latter is resorted to when he does not so commit himself.8 Note now that not every presupposition of a Question will be formalized as a backdrop. When a presupposition that does not appear in the analysis of the Question is targeted in a subsequent argument (e.g., when it is refuted), the analysis of the latter includes the Presupposition restoring operation, H (Chapter 3, Section 1.1 sub Inferences). Consider the following dialogue: – Do gargoyles speak English? – Gargoyles are not human! Here is the analysis: Example 14 Author 1 1. ?T ∧P(p)
?T ∧ p
Do gargoyles speak English? 9
Author 2 2. H(?T ∧ p1)
h
3. T– (h2) 4. E(t–3)
t– e: T– (p1)
〈 This question presupposes that 〉 gargoyles are human. This is false. 〈 Therefore 〉 they do not speak English.
Questions 139
Here is another example involving an Interpretation Question (cf. Example 11): Example 15 Author 1 1. ?I ∧ P(p) ?I ∧ p Author 2 2. H(?I ∧ p1) h 3. T– (h2) 4. DI ∧P(p) 5. I (p4)
t– dI ∧p iP iI
What does “March is the cruelest of months” mean? 〈 This question presupposes that 〉 this is the correct quote. This is false. The line goes “April is the cruelest of months”. [an Interpretation] This is what “April is…” means.
Explanations: Line 1: See note 3. Alternatively, one may want to include in the analysis the presupposition “Somebody (some poet) wrote ‘March is the cruelest of months’ ”, which would be symbolized DI ∧P(p), where DI stands for an “indeWnite” author. The Question would then be ?I (p), and the Truth value operation would target dI ∧ p. Line 4: The author is not mentioned. DI stands for an indeWnite author.
3.2
ConXated Questions
In the preceding we have dealt with Question as the conXating operator; that Question may also be the conXated operator is shown in the following example: Example 16 Author 1 1. P(p)
p
The Chinese have suspended diplomatic relations with Manchuria.
Author 2 2. D∧ ?A (p1)
d ∧?A
Smith asked, what is the reason for their doing so.
Explanation: Line 2: One may conceive of D as applying either to the Question operator or to the outcome of the Question: no diVerence in meaning is involved here.
140 The Structure of Arguments
4.
Questions as targets
Questions may be targeted by other operations in the discussion (including Question operations). When the outcome of a Question is targeted, the target is symbolized as ? X (recall that the question mark is italicized when it stands for an outcome); but when the Question operator itself is targeted, the symbolization is ?X (and the question mark is not italicized). 4.1
Comments and questions concerning Questions
A Question may target another Question; for example: Example 17 Author 1 1. P(p) p
The Chinese have suspended diplomatic relations with Manchuria.
Author 2 2. ?A(p1) ?A
What is the reason for their doing so?
Author 3 s 3. S(?A2)
This is a tricky question.
Author 4 4. ?D ( ?A2) ?D
Who asked it?
Explanations: Line 3: The target of Status is an operator (Chapter 3, Section 2.2). Line 4: The target of a Designation may be either an outcome or an operator (Chapter 3, Section 2.2), and likewise, a Designation Question may target an operator or an outcome. Here there is therefore the alternative ?D ( ?A2 ), with the operator as target. Again, as in Example 16, no diVerence of meaning is involved.
Here is another example: – Are you coming? – When? The second question should be glossed: ‘About which time are you asking whether I am coming?’ (after Ginzburg, in preparation; for a brief description of Ginzburg’s approach see Ginzburg 1997), and the analysis will be:
Questions
Example 18
4.2
Author 1 1. ? T ∧ P(p)
?T ∧ p
Are you coming?
Author 2 2. ?O (?T ∧p1)
?O
About which time are you asking whether I am coming?
Inferences from Questions
A Question operation cannot be inferred from.10 However, one might infer something from the fact that somebody asked a certain Question. The next example shows that the formalization requires introducing an extra operation so as to permit targeting the preceding Question. Example 19 Author 1 1. P(p) p Author 2 ?A 2. ?A(p1) Author 3 3. DA (?A2) dA 4. E (dA3) e
The Chinese have suspended diplomatic relations with Manchuria. What is the reason for their doing so? You asked this question. 〈 Your asking this question shows that 〉 you are not well-versed in current a¬airs.
Explanation: Lines 3–4: The Eduction is not made from the Question in Line 2, but from the fact that Author 2 asked the Question. Line 3 is therefore needed so as to permit referring to this author in the target of E.
4.3
JustiWcations of Questions
One may give a JustiWcation for asking a Question. Thus, when one expresses doubts about the veracity of someone else’s assertion, one may give reasons for not believing it. For instance, Example 20 1. D∧P(p) 2. ?T (p1)
d∧p ?T
Smith says that Jones is a swindler. Is this really so?
141
142 The Structure of Arguments
3. J(?T2 ) j | 4. P(p) | 5. E(p4)
〈What justi¼es this question is that〉 p Smith is quite unreliable. % e: T(p1) 〈 It can be inferred from this that 〉 what he says may be false.
Explanation: Lines 4–5 are a warrant comprising more than one operation. 11
In general, one may provide a JustiWcation for the operation of asking a question. This is of course diVerent from providing an Accounting operation, stating the reason for asking a question; but there will be boundary cases between the two (cf. Chapter 5, Section 1.2). That Questions may have JustiWcations raises an interesting problem, which will be examined presently. 4.4
Concerning the logic of questions
One can infer something only from a proposition, and a Question is not a proposition. An Inference cannot be drawn from a Question, but only from the fact that somebody asked a Question. The target of an Inference can therefore be d∧?, but never ?. Likewise, a Cause operation — Accounting or Result — may target d∧?, but never ?: One may propose a reason or motive for asking a Question12 (or about the result of asking it), but it makes no sense to talk about the reason or motive (or result) of the Question itself. In this respect, JustiWcations are unlike Inference and Cause operations: a Question operation can be justiWed, as illustrated in Example 20, where the Question operation has a JustiWcation. This JustiWcation serves to support the Question itself, and not the fact that somebody asked it (think of a lecturer saying that the question from the audience is a “good question” and going on to explain what justiWes it — e.g., something else said in the lecture or something reported by another scholar); hence the target, ?, does not allude to the author of the Question. 13 This diVerence is illustrated in the upper part of Table 7.2, which shows that there can be no Inference from a Question. Turning to the lower part of the table, we note that there is no Inference that results in a question; one can only infer the fact that someone asked a Question. This amounts to a qualiWcation of the claim, made in Chapter 5, Section 1, namely, that JustiWcation (a regressive operation) and Inference (a progressive one) form a pair, such that each argument with a JustiWcation can be reformu-
Questions 143
Table 7.2 Inferences vs. JustiWcations Possible Target Operation Outcome
Ruled Out
? JustiWcation [assertion]
Target Operation Outcome
? Inference [assertion] [assertion] Inference [question]
[assertion] JustiWcation [question]
lated as one with an Inference. We now note an exception to this rule: a JustiWcation targeting a Question has no parallel Inference resulting in a question. Thus, in Example 20, the assertion ‘Smith is quite unreliable’ is part of the JustiWcation of the Question in Line 2 , but it makes no sense to say that this Question can be inferred from ‘Smith is quite unreliable’. No chain of reasoning leads to a question.14
5.
Answers
The examples given in this chapter show that an answer to a Question will typically involve the same type of operation as that indicated by the superscript to that Question. Thus, the answer to an Accounting Question, ?A (x), will be A(x), that to an Elaboration Question, ?O (x), will be O(x), and that to a Truth value Question, ?T (x), will be T+ (x) or T– (x) (Examples 1, 2, and 4, respectively). Occasionally, however, an answer may involve a diVerent type of operation, as shown in Example 21 Author 1 1. P(p) 2. ?O (p1)
p ?O
Somebody sent Beatrice ½owers. [= backdrop] Who sent her ½owers?
Author 2 3. O(p1)
o
One of her admirers.
Author 3 4. P(p)
p
Norman certainly did not.
144 The Structure of Arguments
Author 2 commits himself to “Somebody sent Beatrice Xowers”. Author 3, by contrast, does not necessarily commit himself to this proposition (he may doubt whether Beatrice was sent any Xowers at all), and his response is therefore not an Elaboration of p1 but a Presentation that adds some relevant information.15 There is nothing in the symbolization of Author 3’s argument, which shows that it is an answer to the Question in Line 2. It is, however, a response to the question, and in the next chapter we will see how the formalization takes this into account. Further, answers that refute the presupposition of a Question — as those in Examples 14 and 15 — may also involve an operation of a type that diVers from that of the Question. As another example of a ‘response’ that is not, formally, an answer, take the following dialogue discussed by Harrah (1963: 51): – Is Throop a Democrat? – Throop isn’t the sort who really commits himself. – But does he usually vote Democratic? Example 22 Author 1 1. ? T ∧ P(p)
?T∧p
Is Throop a Democrat?
Author 2 2. H(?T ∧ p1)
h
3. T– (h2)
t–
〈 This question presupposes that 〉 Throop is the sort who really commits himself. This is false.
Author 1 4. ? T ∧ P(p)
?T∧p
But does Throop usually vote Democratic?
Here Author 2’s response provides a cue to the questioner as to a Question that might be more appropriate under the circumstances. The next section deals with “don’t know” operations. Admission of ignorance is a perfectly sensible response to a question, although no relevant information is imparted. Whether such responses deserve to be classiWed as ‘answers’ is a terminological issue which need not concern us here (but see Chapter 8, Section 3).
Questions 145
6.
“Don’t know”
The Nescience class of operations contains, besides Questions, “don’t know” statements. To ask a question is to (i) ask for information that, in the standard case, (ii) the questioner professes not to know. (The questioner may know the answer and ask the question in order to examine the person asked; but this is not a typical case of questioning.) In a “don’t know” operation, by contrast, only (ii) is the case: a person states that he or she does not know something. The symbol for the “don’t know” operation is similar to that for a Question, namely, /?/. Like the Question operator, this operator has a superscript, which is subject to conventions parallel to those applying to the Question operator. Here is an example, which should be compared to the Question in Example 22, Line 1.16 Example 23 1. /?/ T ∧ P(p)
/?/ T ∧ p
I don’t know whether Throop is a Democrat.
The outcome of a “don’t know” operation is fused, like that of an Adjudgment operation (Chapter 3, Section 3.2). Like Questions, some “don’t know” statements (e.g., those pertaining to Accounting, Inference, and Elaboration) may require a backdrop.17 Compare the following to Example 6. Example 24 Author 1 1. P(p) p In World War II the Allies landed in France. [= backdrop] 2. /?/A (p1) /?/A I don’t know what motivated the landing. Author 2 3. /?/O (p1) /?/O I don’t know when the landing took place.
As shown in this example, the target of a “don’t know” statement can be the outcome about which the author lacks information. Alternatively, it can be the operator, as in /?/ J (X): “I don’t know what justiWes operation X” (cf. Table 7.1 in Section 1). When “don’t know” is said in response to a Question, the analysis is similar:
146 The Structure of Arguments
Example 25 Author 1 1. P(p) p A 2. ? (p1) ?A Author 3. /?/A (p1)
In World War II the Allies landed in France. [= backdrop] What motivated the landing?
/?/A I don’t know what motivated the landing.
Unlike a Question operation, a “don’t know” operation can have a JustiWcation that is an articulation (cf. note 13): there is a chain of reasoning that leads up to the claim that one does not know something (think of someone trying to convince an investigator that he does not know who entered the house of the murdered man). Again unlike a Question, a “don’t know” operation can be inferred from (the fact that I don’t know … shows that you have been keeping a secret from me).
Chapter 8
Connections
Anyone who cannot speak simply and clearly should say nothing. – Karl Popper
His name is Nikolai Petrovich Kirsanov. He owns a Wne estate, located twelve miles or so from the carriage inn, with two hundred serfs … an estate with about Wve thousand acres of land. His father, a general who fought … .
This passage, excerpted from the Wrst page of Turgenev’s Fathers and Sons, contains several items of information. Consider now how one might go about analyzing it. Breaking it down into operations would be easy, but what kind of targeting relations can be detected between these operations? There are no Inferences, no Designations, no Validations — the passage seems to contain just a series of Presentations. And yet, these are obviously not isolated bits and pieces; rather, they somehow hang together: ‘A and B and…’. The same is true of any two statements, A and B, that are linked as in ‘A but B’, ‘although A, B’ ‘not only A but even B’, and the like. One way to deal with such links would be to enlarge our list of types of operations so that each of the above Bs falls under some type of operation that can then target the corresponding A. We suggest, however, that the links between the foregoing As and Bs are much more tenuous than the links between operations that target each other: A and B are relatively more independent than such operations. It seems preferable therefore to introduce into our system, in addition to targeting, a category of relationships, which we will call connection. B, in the above cases, will be said to be connected to A, not to target A. The concept of connection will become clearer by perusing the list of connections given in this chapter (for which no claim of exhaustiveness is being made, however).
148 The Structure of Arguments
1.
A notation for connections
Consider the following sequence: Bill and his wife are going to Paris next week. His wife will be visiting her cousin.
The operation corresponding to the second sentence is neither an Inference nor an Adjudgment of that in the Wrst; instead, it connects to it and the Wrst operation is connected to it. How are connections to be symbolized? It is proposed that they be dealt with as an additional tier of analysis, separate from the one that is constituted of operations and targeting relations. This means that an operation may both target another one and be connected to it. In the foregoing example, the second sentence adds something to the Wrst sentence; the connection between the two outcomes will be called Accrual, the symbol for which will be: Acc. For instance: Example 1 1. P(p) 2. P(p)
p p
Bill and his wife are going to Paris next week. His wife will be visiting her cousin. Acc{p, p1}
The fact that an outcome x is connected to a previously occurring one, y, as an Accrual, is indicated under the line that contains X. Two terms occur in the curly brackets after Acc, the symbol for Accrual. The Wrst term (here: p) refers to the line the formula appears under and thus does not need a subscript specifying the line number; the other term (p1 ) has such a subscript. Occasionally, an outcome of an operation connects to outcomes of more than one operation, and the second term will then be constituted of a conjunction of outcomes, e.g., Acc {x , yi & zj …} . Conversely, outcomes of more than one operation may connect to an outcome of a given operation. As stated, targeting and connecting are two independent tiers of analysis: the operations, their targets, and their outcomes provide the “scaVolding”, as it were, of the argument, and the tier of connections is superimposed on it. An operation X may have an outcome connected to another outcome, and at the same time X may target the outcome of (the same or another) operation, as shown in Example 6, below. It should be emphasized that the distinction between targeting relations
Connections 149
and connections is not a sharp one. It is important, though, that the two tiers are formally independent, in the sense that a connection cannot be targeted by another operation; that is, there is no operation X (Acc), or the like. Operations between which a connection holds may sometimes be collapsed into a single one. Thus, the two sentences in Example 1 might be viewed as a single Presentation. However, when a subsequent operation or connection refers to only one of these sentences — say, someone confutes only the claim that Bill’s wife will visit her cousin — the confuted statement will be analyzed as a separate operation, connected to the preceding one.1 In the following sections, several kinds of connections will be dealt with. Our list should not be regarded as Wnal: it may turn out that there are additional kinds of connections. It will be noticed that the list contains many of the categories deployed in various other systems proposed for the analysis of discussions. These systems, though, do not make our distinction between connections and operations. Furthermore, they deal with texts, i.e., with the verbal expression of arguments rather than with their underlying structures, as we do. No attempt will therefore be made to compare this list with those proposed by other authors.
2.
“Unrestricted” connections
In this section we deal with types of connections which (unlike those discussed in Section 3) may link either operations within a single argument or operations in two separate arguments. In this respect they are ‘unrestricted’. They include: Accrual (Acc). Example 1, above, and the passage from Turgenev at the beginning of this chapter contain Accruals: they contain statements that add something to previous ones, but there is no targeting relation between the operations corresponding to these statements. Linguistically, an Accrual may be expressed by “also”, “furthermore”, or the like; for example, John bought a new car. He also bought a video set.
An Accrual may link outcomes in a single argument, as in Example 1, above, or it may link outcomes appearing in two diVerent arguments: imagine that Lines 1 and 2 of Example 1 are due to two authors.
150 The Structure of Arguments
Comment (Cmm). When an operation adds some information to a preceding one without targeting it, it may be either an Accrual (as shown in the foregoing) or a Comment. For instance, King George fought in the battle of Dettingen. He was the last British king to appear in battle. (Comment)
Comments diVer from Elaborations. The latter serve to identify a participant in the elaborated outcome or to specify the time or location of an event or situation, or otherwise to add precision to a previous outcome (Chapter 3, Section 1.1); for instance: King George fought in the battle of Dettingen. That was in the year 1743. (temporal Elaboration) King George fought in the battle of Dettingen. That was King George the Second. (Elaboration of participant)
From the vantage point of the Wrst operation (‘King George fought…’), the information contained in the comment appears to be, in some respects, more peripheral than that contained in the Elaborations. Whether King George was the last British king to appear in battle or not, whether Dettingen is a major town or not, as important or piquant as such items of information may be, they appear to be less relevant to the event described in the sentence “King George fought in the battle of Dettingen”. The distinction between Comments and Elaboration corresponds to that between non-restrictive and restrictive relative clauses, respectively: “King George, who was the last British king to appear in battle, fought in the battle of Dettingen” contains a non-restrictive relative clause, separated by commas, whereas “The king who fought in the battle of Dettingen was King George the Second” contains a restrictive relative clause (“who fought… Dettingen”). There will be borderline cases, though, for which it will be hard to decide whether they ought to be analyzed as Comments or as Elaborations.2 Comments also diVer from Accruals. The latter, unlike Comments, connect statements that are felt to be somehow on the same level; cf. Example 1. Progression (Pro). When two statements can be placed on a kind of scale, such that the author regards the second as being more far-reaching than the Wrst, we have a Progression. Progressions are often linguistically marked by “even”, “and not only that, but”, etc. For instance:
Connections
John had his home renovated. He even planted a new garden.
In a Progression there is a sequence from less (in some sense) to more. Degression (Deg). This is the converse of a Progression: the second statement is less far-reaching than the Wrst; the sequence is from more to less: John had his home renovated. His neighbor made only some necessary repairs of his house.
Degressions are often marked by phrases like “only”, “at least”, etc. Progression and Degression are not just two diVerent linguistic expressions of the same underlying structure; to reformulate a Progressions as a Degressions or vice versa will often be extremely awkward. We therefore regard these as two diVerent types of connections. In this respect, Progressions and Degressions diVer from the connection to be considered next. Seriation (Ser). Two or more situations or events referred to in an argument may represent a temporal or spatial sequence. Such a Seriation does not involve any ‘more-to-less’ or ‘less-to-more’ order like Progressions and Degressions; but it diVers from Accrual, which does not impose any order. Here is an example of a Seriation; the outcome corresponding to the second statement (“then he broke it”) is connected to that corresponding to the Wrst: John bought a video set a month ago. Then he broke it.
This will be analyzed just like the following argument, in which the temporal sequence is reversed: John broke his new video set. He bought it only a month ago.
Only the verbal description will make it clear which temporal sequence is intended: Example 2 1. P(p) 2. P(p)
p p
John broke his new video set. He bought it only a month ago. Ser {p, p1 }
There are also Seriations with three or more terms, as when a sequence of
151
152 The Structure of Arguments
several events is referred to. The line indicating that there is such a sequence will then read: Ser {x, y, z, …}. A set of events may also be analyzed as a conjunction. However, conjunctions are commutative: X & Y is equivalent to Y & X (Chapter 4, Section 3). Thus, the formalization of “If you buy me a drink and take me to the movies” will be the same as that of “If you take me to the movies and buy me a drink” (Example 14 in Chapter 4). There are cases where the sequence of events is not immaterial. For instance: “He will either settle down now, or go to Canada and make some money” diVers in meaning from “He will either settle down now, or make some money and go to Canada”. A Seriation connection (holding between going to Canada and making money) indicates that a speciWc sequence of events is intended. However, as in the previous example, the symbol ‘Ser’ does not indicate which sequence is intended, and this will emerge only in the verbal description. Example 3 1. P(p)a / [P(p)b & P(p)c]
pa / [pb & pc]
He will either settle down (pa), or go to Canada (pb) and then make some money (pc).
Ser {pb , pc} Explanations: The slash, /, is our symbol for, disjunction (Chapter 4, Section 2). On the use of square brackets see Chapter 4, Section 2. Here the conjunction of P(p)b and P(p)c is the alternative to P(p)a . This Seriation links two outcomes of the same operation, viz. the one preceding the symbol Ser, and therefore no subscripts referring to line numbers are required.
Concession (Cnc). This connection is typically expressed by conjuncts that “… signal the unexpected, surprising nature of what is being said in view of what has been said before” (Quirk et al. 1972), like “however”, “although”, and by phrases like “that’s true, but …”, “yes, but …”. For instance: Sue has been out in the sun for hours; nevertheless she is not going to get sunburned. This comprises the following: a. Sue has been out in the sun for hours. b. Sue is going to get sunburned. c. Sue is not going to get sunburned
This may lead to an expectation: This expectation is countered:
Connections
In the formalization (as in the verbal expression of this argument) only (a) and (c) appear explicitly; (b) does not, but is alluded to, instead, by a Concession marker: Example 4 a 1. P(p) 2. P(p)
p p
Sue has been out in the sun for hours. 〈 Nevertheless 〉 she is not going to get sunburned. Cnc {p, p1 }
Observe that the Wrst term in the curly brackets, p , is underlined. The purpose of this is to indicate that p, “she is not going to get sunburned”, is what counters the engendered expectation. This convention facilitates comprehending the formalization when the two Presentations appear in a diVerent sequence, namely: Example 4 b 1. P(p) 2. P(p)
p p
Sue is not going to get sunburned, 〈 although 〉 she has been out in the sun for hours. Cnc {p, p1 }
“She is not going to get sunburned” is the statement that runs counter to the expectation, and hence in this example it is the second term in curly brackets, p1, that is underlined.3 In the preceding examples, the expectation is raised by our knowledge of the world: we know that prolonged exposure to the sun causes sunburn. There are arguments in which an expectation results only from what the author says. Consider: Maggie’s son is not really a genius; however, he is very bright.
The statement in the second line counters what might be expected from that in the Wrst line. “Expectation” is perhaps too strong a term here, but at any rate, as in our no-sunburn example, there is a reversal of direction. By saying that someone is not a genius, one detracts from his intelligence, and the second statement then reverses this: his intelligence is not so low after all. Here is the analysis:
153
154 The Structure of Arguments
Example 5 1. P(p) 2. P(p)
p p
It is not the case that Maggie’s son is a genius. 〈 However 〉 Maggie’s son is very bright. Cnc {p, p1}
Here, again, the statement that counters the “expectation”, p, is underlined.4 Another type of Concession is what Freeman (1991: 172–174) calls “counter-considerations”, namely, a consideration included in an argument that might appear to invalidate the conclusion and which is then shown not to do so. Still another case involving a Concession is illustrated in Example 8 in Chapter 3. “Yielding a point made in an argument” (Salmon and Zeitz 1995: 6) is also a Concession: a participant agrees with one of the assumptions of his opponent, but argues that the conclusion drawn by the opponent does not follow. Consider the following interchange (adapted from van Eemeren 1995: 148): – Human life is sacred. It follows that abortion should not be legalized. – But the sanctity of human life does not include a fetus. So this does not argue against legalizing abortion.
The second author claims that although it is true that human life is sacred (statement leading to an expectation), this does not imply that abortion should not be legalized (statement countering this expectation). He admits that Author 1 is right (T+ ) in respect to one point, but claims that he is wrong (T– ) in respect to another. The latter is connected to the former by a Concession: Example 6 Author 1 1. P(p)
p: ps pt j
2. J(P1) | 3. P(p) | | 4. U( ps1, pq3) → | 5. N(p3 & u4) 6. E(p1) e
p: pq pr u n
A fetus may not be killed. 〈 What justi¼es this Presentation is that 〉 Human life is sacred and should not be taken. A fetus is an instance of human life. 〈 It follows that 〉 a fetus may not be killed. 〈 One may infer from this that 〉 abortion should not be legalized.
Connections
Author 2 7. T+ (p3) 8. T – (p1)
9. J(T –8 ) 10. E(t –8 )
t+ t–
It is true that human life is sacred. 〈 However 〉 it is false that a fetus may not be killed. Cnc {t–, t+7 } j: T – (u4) 〈 What justi¼es saying so is that 〉 it is not true that a fetus is an instance of human life. e: T – (e6) 〈 It follows from Line 8 that 〉 your claim that abortion should not be legalized is false.
Correction (Cor). A speaker may correct himself, as in: The weather was depressing this week. Actually we did have one or two Wne days, but…
At times such a correction is oVered by another speaker, who, without disagreeing completely, corrects or modiWes a preceding statement.5 Summarizing (Sum). When one summarizes a train of thought, this is analyzed as a connection called Summarizing. Common expressions used in summarizing are “to conclude”, “in sum”, “in short”, etc. The material that is summarized will usually be formalized as a set of operations, and these will appear in the second term as a conjunction: Sum {…, x & y & z}. When the summary is itself constituted of several operations, the Wrst term will also be a conjunction: Sum {x & y & z, …). Solution (Sol). When an operation states a problem and another one speciWes ways in which it might be dealt with, the latter is connected to the former as a Solution. For instance, – Salt is not good for Carl, because his blood pressure is high. – He should try a salt-free diet.
The relationship between these statements is analyzed in terms of targeting, as in the example below. The connection, Sol, supplements this analysis by stating that a salt-free diet serves as a solution to the problem alluded to by the Wrst author. Example 7 Author 1 1. P(p) p 2. A(p1) ap aA
Salt is not good for Carl. His blood pressure is high. This is the reason that salt is not good for him.
155
156 The Structure of Arguments
Author 2 3. E(p1) e: Q∧P(p)
〈 It follows from p1 that 〉 he should try a saltfree diet. Sol {q∧p, p1 }
The Solution connection does not always go with an Eduction, as in this example; it may supplement some other kind of Inference operation. But of course not all Inferences are Solutions. An outcome may be connected by Solution to an outcome in a previous argument, as in this example, or to one in the same argument (“Salt is not good for Carl, and therefore he should try a salt-free diet”). Impediment (Imp). This is, in a way, the converse of Solution. Take We would like to take you out to dine, but we have no car.
The second clause is connected to the Wrst as an Impediment. It states what the problem is, but does not suggest a solution. (Subsequently such a Solution may be suggested, e.g., let’s take a cab; let’s walk). An Impediment may also connect outcomes appearing in two diVerent arguments: – Let’s go out to dine. – But we don’t have the car tonight.
The counterargument contains an implicit operation (‘we cannot go out’) and an expressed Accounting (‘we don’t have the car tonight’). Just as the Inference operation in the previous example does not make it apparent that a solution is involved, so the Accounting operation does not make it apparent that an impediment to going out is involved (not every reason refers to an impediment); the connection, Imp, is therefore needed here. Example 8 Author 1 1. P(p) p Author 2 2. P(p) p 3. A(p2) ap aA
Let’s go out to dine. We cannot go out tonight. We do not have the car. This is the reason that we cannot go out tonight. Imp {aP, p1 }
Connections
3.
Between-argument connections
In contrast to the “unrestricted” connections considered in the previous section, the two types of connections listed in the present section hold mainly between operations belonging to diVerent arguments. Response (Rsp). This is the connection between (i) a Question and an answer, and (ii) a request and the response made to it (e.g., the reply that one will or will not comply with the request), which includes the second parts of various so-called adjacency pairs, like invitation and acceptance (or rejection); see Clark (1992: 157–158).6 In Example 21 of the previous chapter, repeated here as Example 9, Line 2 contains an Elaboration question. Author 2’s reply is an Elaboration of p1, the outcome targeted by the Question. His reply does not target the question ?O, and the relation between it and the question is indicated by Rsp (Response). Author 3’s reply is not an Elaboration of p1, because he does not necessarily commit himself to “Somebody sent Beatrice Xowers” (Line 1). His response is formalized as a Presentation, and thus does not indicate any relationship with the question. The connection marker Rsp indicates that it is nevertheless a response to the question. Example 9 Author 1 1. P(p) p 2. ?O (p1) ?O Author 2 3. O(p1) o Author 3 4. P(p) p
Somebody sent Beatrice ½owers. Who sent her ½owers?
[= backdrop]
One of her admirers did. Rsp {o, ?O2 } Norman certainly did not. Rsp {p, ?O2 }
In making Responses like those in Example 9, one complies with the request for information. But even when the person addressed by the questioner does not supply the information asked for, her argument will be analyzed as a Response if she reacts in one of the following ways: 1. “I don’t know”; see Example 24 of the previous chapter. 2. Refusal to answer the Question (e.g., “I won’t tell you”).
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158 The Structure of Arguments
3. “Delaying tactics” (Ginzburg, in preparation, p. 25), like the response in this dialogue: – Where have you been? – Where have you been? 4. Questions preparatory to an answer, as in this dialogue: – What do you want to do tonight? – Which shows are on? 5. Requests for clariWcation of the Question (“What do you mean?” i.e., an Interpretation Question). 6. Remarks on the assumption on which the Question is based, as in Harrah’s (1963: 51) example discussed in the previous chapter, Section 5: – Is Throop a Democrat? – Throop isn’t the sort who really commits himself. 7. Remarks on the nature of the Question (e. g., “What a stupid question!”); see Example 17 of the previous chapter. A comment is in order here regarding the place of pragmatic aspects in our analyses. Responses are pragmatically relevant and are the kinds of relationships dealt with in current work in discourse analysis. There are, however, many other pragmatic relationships between moves in the discussion that will not be analyzed as connections. As a rule, only cognitively relevant relationships come within the purview of our analyses. Thus, when I say to someone in a conversation about basket ball “Your brother is an outstanding player”, this is cognitively relevant to the conversation (and may or may not be connected to a previously occurring outcome). However, the fact that my comment was intended to Xatter this participant or to rile him will not be reXected in the analysis of this comment. A Response (to a question or to a request) is not only pragmatically relevant but is felt to have also, in some sense, cognitive relevance. (There is no sharply deWned boundary, though, between these kinds of relevance.) This is why it has to be provided for in our framework. By contrast, the fact that an argument serves to threaten, cajole, appease, or ridicule someone, important as it may be, is not taken care of in our system. Hence we do not introduce connections like ‘provocation’, ‘threat’, or the like. Alternate (Alt). When two consecutive sentences form a disjunction, we use the functor / (Chapter 4, Section 2). When the two sentences appear in diVerent arguments, however, this functor cannot apply (recall that in our system functors create compound operations; see Chapter 4). Instead, we have a connection called Alternate. E.g.,
Connections 159
Example 10 1.
Author 1 % P(p)
2.
Author 2 % P(p)
%
p
%
p Or else, he may have gone into hiding. Alt {p, p1 }
He may have left the country.
Explanation: Line 2: Author 2 indicates that it is not certain that he will go into hiding (he may do so); hence the degree-of-conWdence marker, % (Chapter 3, Section 1.3).
4.
Connections as toned-down operations
In some arguments the analyst will have to decide whether the relation between two operations is a connection or a targeting relation. This is so because some connections in our system are closely related to certain types of operations. The distinction between such connections and the related operations is a subtle one, and occasionally two analyses will be possible: as an operation that targets an outcome or as an outcome that connects to another one. Similarity (Sim). When it is claimed that two events or situations are similar to each other, this may be analyzed as a Comparison operation, K. Consider now: John bought a video set. Jane bought a new hat.
These two sentences are merely juxtaposed; no special claim about similarity is being made expressly — such a claim is merely hinted at. Instead of a Comparison operation, the analyst will therefore opt for a connection, Sim. However, when the similarity is resorted to as a link in the chain of reasoning (as e.g., in Examples 14–16a in Chapter 5), this implies that it is more ‘central’ in the argument and will be analyzed as a Comparison operation the outcome of which can be targeted. Contrast (Cnt). When there is a contrast between two statements, this might be analyzed in terms of a Comparison operation (K). But when the contrast is not the focus of the argument, one may do well to opt for a connection. For example,
160 The Structure of Arguments
David has become a much-appreciated politician. But his brother has attained self-fulWllment through his vocation.7
If the author’s main intention (in the analyst’s view) had been to make the point that these two statements contrast each other, a special Comparison operation would have been in order. But here it seems preferable to analyze the contrast as a connection. A Contrast connection is typically expressed by words like “but”, “on the other hand”, and “however”.8 Sequel (Seq). This type of connection is similar to Seriation (Section 2), except that it implies also a causal relationship, which, however, does not merit analysis as a special operation. Here is an example from a collection of students’ bloopers (Richard Lederer, St. Paul’s School, unpublished): Milton wrote ‘Paradise Lost’. Then his wife died and he wrote ‘Paradise Regained’.
In addition to a temporal sequence, a causal connection is being suggested here (if we take the wording seriously) between his wife’s death and the subsequent literary achievement. If the student’s main point would have been to provide a reason for Milton’s writing ‘Paradise Regained’, this would have to be analyzed with an Accounting operation. As it is, we analyze this with the connection marker Seq. As stated, the boundary line between a ‘toned-down’ connection and the corresponding operation is a fuzzy one, and for some arguments either one may seem appropriate. However, there is an important diVerence between the two: connections, unlike operations, cannot be targeted. Suppose now that any one of the notions represented by a connection is subsequently referred to; for example, the implied causal link between the death of Milton’s wife and his subsequent literary achievement is debated by a second author. The analyst will then have two options: (i) she may decide to analyze the argument as containing an Accounting operation, instead of a Sequel connection, or (ii) she may include such an analysis as an Interpretation of the above argument by the second author. If she opts for the latter, the analysis will be: Example 11 Author 1 1. P(p) 2. P(p)
p p
Milton wrote ‘Paradise Lost’. Then his wife died, Ser {p, p1)
Connections
3. P(p)
p
and he wrote ‘Paradise Regained’. Seq {p, p2 }
Author 2 4. I(p2 & p3) | 5. P(p) | 6. A(p5) | | 7. T – (aA 6)
iP p aP aA iI t–
He wrote ‘Paradise Regained’. His wife died. This was the reason he wrote ‘Paradise Regained’. This is what Lines 2–3 mean. It is not true that this was the reason.
Explanations: Line 2: The connection ‘Ser’ (Seriation; Section 2) indicates that writing “Paradise Lost” and his wife’s death were temporally ordered; the verbal description shows which event came Wrst. Line 3: His wife’s death and writing “Paradise Regained” are connected by a Sequel connection: the former is said to have occurred prior to the latter and to have caused it. Line 4: In Chapter 10, Section 4.2, a somewhat diVerent notation for Interpretations will be introduced.
The same applies to other connections as well. Consider, for instance, Example 4b and suppose that someone claims that Sue is the type who never gets sunburned, and that the expression “although” is not warranted here. One may then choose to analyze the original argument as an explicit operation — stating that Sue’s getting sunburned might have been expected (and things turned out diVerently) — which is then refuted: one should not have expected Sue to get a sunburn. Alternatively, if this appears to be inappropriate, one may resort to an Interpretation in the analysis.
5.
Summary
Connections pertain to a separate tier of analysis. They include:9 “Unrestricted” connections Accrual (Acc) Comment (Cmm) Progression (Pro)
(Section 2)
161
162 The Structure of Arguments
Degression (Deg) Seriation (Ser) Concession (Cnc) Correction (Cor) Summarizing (Sum) Solution (Sol) Impediment (Imp) Between-argument connections Response (Rsp) Alternate (Alt)
(Section 3)
Toned-down operations Similarity (Sim) Contrast (Cnt) Sequel (Seq)
(Section 4)
Chapter 9
Relations within and between arguments
Sir, I have found you an argument; but I am not obliged to Wnd you an understanding – Samuel Johnson
The concepts in our system that were introduced in the preceding chapters deWne various kinds of relations between operations, the basic units of arguments. The question to be broached now is how arguments are to be individuated: What is an argument? As stated in the introductory chapter, we diverge from the usage of other writers in that we do not limit the term ‘argument’ to sets of statements that are made to convince or persuade, but use it to refer also to various statements that set out to provide new information, or explain or elaborate such information. Further, a statement does not have to be sound, plausible, or even acceptable to be counted as an argument. An argument is typically part of a larger stretch of discourse, like a discussion. In the present chapter we deWne both ‘argument’ and ‘discussion’ in terms of the concepts of our system. It will be seen that arguments and discussions are not only related as parts to wholes but also have certain structural similarities.
1.
‘Argument’ deWned
1.1 Turns and arguments Roughly speaking, an argument, in our system, comprises what is said in a single turn in the discussion or conversation. The correspondence between a turn in the discourse and an argument is far from perfect, however. An author may make some remark that does not bear at all on the topic of the argument he wishes to make; for instance, he may ask whether he may open the window to let some fresh air in, or he may ask the listener not to interrupt him. Such utterances are extraneous to the discourse, and do not belong to any argument.
164 The Structure of Arguments
Moreover, an author may tackle two unrelated topics in the same turn. In a Wnancial discussion, a participant may tack on to his contribution a quite unrelated remark about the political situation or some gossip. One would hardly want to regard these as belonging to one and the same argument (further on we will propose that such cases be regarded as two arguments in the same turn).1 In fact, the whole discussion may then wander oV to a completely diVerent topic, and it will be argued further on that it can no longer be regarded as a single discussion. It thus appears that an argument cannot be deWned solely in terms of social interaction, as a turn. An additional deWning criterion is needed. According to the pre-theoretical notion of argument, the various steps — operations, in our system — of an argument somehow hang together; they are connected by targeting or are otherwise related to each other, in a sense of ‘related’ that has to be speciWed. If we conceive of these relations as lines and of the steps (operations) between which they hold as points, we can describe an argument as a connected graph (Harary 1969), that is, the network of lines is connected and includes all the points. When a turn contains two or more arguments, by contrast, the network is disconnected: there are two or more such networks without any lines leading from one to the other. 1.2
Two types of relations
What are the relations that may serve to unite various operations in a turn into a single argument? One obvious relation is targeting: When one operation targets another, both belong to the same argument (if they are included in a single turn). But there are also operations which one would have to regard as belonging to the same argument although they do not stand in a targeting relation. For instance, the two operations in a conXation belong together, although one does not target the other. We distinguish between strong and weak relations: A strong relation holds between two operations X and Y if one of the following is the case: a. X targets the operator Y or the outcome of Y or one of its constituent elements. b. X forms a conXation with Y; c. X is a collateral operation of Y; d. X is a JustiWcation operation, J, and Y is an operation within its
Relations within and between arguments 165
articulation or warrant; e. X is a Cause operation, and Y is one of its sub-operations; cf. Chapter 5, Section 5.2 f. X is compounded with Y.2 When there is a strong relation between X and Y, we will say that they are strongly related. Operations between which there is only a connection (in the sense explicated in Chapter 8 — similarity, contrast, etc.) are intuitively knit together less strongly than operations between which targeting or one of the above strong relations hold. They nevertheless ought to be regarded as belonging to the same argument. “Your children are great eaters; mine aren’t” contains two Presentations that do not target each other, but one would hardly want to assign these to two separate arguments. We therefore stipulate that a weak relation holds between operations X and Y, if g. X is connected to Y Operations between which there is only a weak relation will be called weakly related. Note that ‘strongly related’ is symmetrical: when X is strongly related to Y, Y is strongly related to X, and vice versa. Likewise, ‘weakly related’ is symmetrical. Two operations X and Y are unrelated if no strong or weak relation holds between them, even if X has an annotation to Y (on annotations see Chapter 3, Section 3.4). An explanation is in order concerning Criterion (d). Without this criterion there would be cases where there would be no relation between an articulation and the rest of the argument, namely, when none of the operations within an articulation is related to any operation outside it. The articulation would consequently be considered to be disconnected from the rest of the argument. Recall now that an articulation is really a set of operations (Chapter 5, Section 2.3). Criterion (d) regards all operations within the articulation as strongly related to the JustiWcation, J. Since J always targets the operation that is being justiWed, Criterion (d) ensures that the whole articulation will be linked to the argument. Similar considerations apply to Criterion (e). In the next chapter (Section 4.6) it will be seen that some slight revisions are required of the foregoing deWnitions of strong and weak relations. As mentioned, a turn may contain material that is extraneous to the argument and the discussion (such as asking for the window to be opened).
166 The Structure of Arguments
Furthermore, there may be comments that do indeed pertain to the discussion at hand in that they direct the conversation, but do not directly aVect the content of the topic(s) discussed, or, as Hamblin (1986: 283) puts it, “… locutions [that] contribute not to the subject or topic of the dialogue but to its shape” (see also Rips 1998). We call them orienters. Examples are: Listen to him now! Let’s see whether we can agree on …. I’m going to give you the inside story.
Orienters like those in the preceding examples can appear as separate turns. So do orienters like “ah”, “mhm”, “yeah”, or “okay”, interspersed by a participant to indicate that she is listening or understanding. Alternatively, an orienter can be part of a turn that includes also an argument. Some orienters appear only alongside other operations that are part of an argument, e.g., By the way, …. (indicating a connection between the following operation and those that went before).
In neither case will the orienter be analyzed as an operation or an argument. The distinction between orienters and operations, however, is not a sharp one. “I’m going to give you the inside story” may be an orienter, but in a slightly diVerent guise — for instance, “This (the preceding) is the inside story (the oYcial version is quite diVerent…)” — it is an operation characterizing a previous operation, i.e., a Status operation. Furthermore, when one of the orienters is subsequently referred to, it must be analyzed as an operation so that it can be targeted. 1.3
A deWnition of ‘argument’
As stated (Section 1.1), an argument spans a single turn; two operations in two diVerent turns normally do not belong to the same argument. Two operations, X and Y, in the same turn will be regarded as belonging to the same argument if they are either strongly or weakly related. “Belong to the same argument” is a transitive relation: if X belongs to the same argument as Y, and Y as Z, then X belongs to the same argument as Z. We now deWne ‘argument’ by referring to the notion of connected graph (to be illustrated in Wgures 9.1 and 9.2, below): An argument is (i) a set of one or more operations (ii) within a single turn, such that (iii) the strong or weak relations between these operations form a connected graph.
Relations within and between arguments 167
According to condition (i), single operations can also be arguments. Thus, an argument may consist of a single Presentation, a Question, or some other type of operation. Condition (ii) speciWes that an argument cannot span more than one turn (but see note 1). When an author continues, in a subsequent turn, to state something about what he has said in the previous turn, the latter will be counted as a separate argument, even though the two arguments may be linked by targeting or a connection. An argument may consist of subsets of operations. This notion of subset can be introduced via the distinction between strong and weak relations (not distinguished in the foregoing deWnition). We call S a sub-argument of A, if A includes a set S of operations such that: (i) the strong relations between them form a connected graph, (ii) there is no operation in S that is strongly related to any operation in A that is not included in S, and (iii) there is at least one operation in S that is weakly related to another operation in A that is not included in S ((iii) is needed to ensure that S is not a separate argument). Figure 9.1 gives a schematic example of sub-arguments. 3 1
2 3 4
5 6
7
9 Figure 9.1
8
Two sub-arguments in a (Wctitious) argument: Operations 1–5 and 6–9. Strong relations are indicated by lines and the weak relation by a dotted line.
168 The Structure of Arguments
1.4
An illustrative example
As an illustration to the foregoing, let us look at Hamlet’s soliloquy, part of which has been quoted in Chapter 1. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Now might I do it pat, now he is praying; And now I’ll do’t. And so he goes to heaven; And so I am revenged. That would be scann’d: A villain kills my father; and for that, I, his sole son, do this same villain send To heaven. O, this is hire and salary, not revenge. He took my father grossly, full of bread; With all his crimes broad Xown, as Xush as May; And how his audit stands who knows save heaven? But in our circumstance and course of thought, ‘Tis heavy with him: and am I then revenged, To take him in the purging of his soul, When he is Wt and seasoned for his passage? No! Up sword; and know thou a more horrid bent: When he is drunk asleep or in his rage, Or in the incestuous pleasure of his bed; At gaming, swearing, or about some act That has no relish of salvation in’t; Then trip him, that his heels may kick at heaven, And that his soul may be as damn’d and black As hell, whereto it goes.
This soliloquy appears to contain four parts: The Wrst part spans Lines 1–3 (up to “and so I am revenged”) and contains Hamlet’s Wrst reaction on seeing the King at his prayers: This might be a good opportunity to take his revenge. The sentence “That would be scanned” is an orienter, in which Hamlet instructs himself, so to speak, to examine the proposition “And now I’ll do’t.” (Line 2). The second part begins with Line 4 and continues to Line 7 and contains Hamlet’s second thoughts: it would not be right to kill him now, and the JustiWcation for this conclusion is that doing so would send the King to heaven. The third part spans Lines 8–14, and in it Hamlet gives an additional JustiWcation for the claim that killing the king now is inappropriate: as a result of killing him now the fate of the murderer would be better than that of his victim. (“No!” in Line 15 may be viewed as belonging either to this part or to
Relations within and between arguments 169
the following one.) The fourth and Wnal part spans Lines 15 (or 16) to the end of the soliloquy, in which Hamlet decides to defer his revenge to a more appropriate time. Presumably, Shakespeare would not have been all too happy with the looks of the following analysis; possibly, he would have thought that we have misunderstood him. Perhaps we have; so do, occasionally, literary critics, who after all do not always agree on the reading of a given text. As pointed out in Chapter 2, Section 1, our analyses are valid only under a given interpretation, and our conceptual framework does not provide an algorithm for interpreting an (expressed) argument. It is one of the advantages of our method of analysis, however, that it compels the analyst to articulate the cognitive content and structure of the argument, and thus makes her recognize the possibility of alternative interpretations. Formal analyses of arguments, then, may be a useful tool for the literary analysis. In analyzing this monologue we were faced with two options. A progressive analysis would include two Inferences involving considerations (Lines 4–7 and 8–14) leading to the conclusion that the King should not be killed now. Alternatively, one might adopt a predominantly regressive analysis, in which these considerations function as JustiWcations. We opted for the latter alternative, because, on our reading of the monologue, Hamlet knows that he will not kill the king already in Line 3 of the text, at the latest, that is, before he gives the two JustiWcations. The regressive analysis has the additional advantage of making the structure more perspicuous; see discussion in Chapter 5, Section 6.1 on deciding between progressive and regressive analyses. Our analysis is presented in Example 1. Lines 17–19 of the text contain examples of “some act that has no relish of salvation in’t” that have been omitted here so as not to encumber our analysis too much. They would have been analyzed as Subsumptions (Chapter 3, Section 1.1) of the general statement “I should kill him when he is sinning” in Line 20 of the analysis below (note that the Line numbers in the analysis do not correspond to those in the text!). Example 1 1. Q∧P(p) 2. A(q∧p1)
q ∧ p: … pj aP aA
It would be right (q) that I kill the King now (p). killing the King now To kill him now would be appropriate revenge. This is the reason why it would be right to kill him now.
170 The Structure of Arguments
q: T– (q∧p1 ) 〈However,〉 it would not be right to kill him now. 4. J(Q3 ) j 〈 What justi¼es this is that 〉 | 5. P(p) p he is a villain, | 6. E(p5) e: Q∧P(p) q∧p: … 〈and therefore〉 should receive | pm severe punishment. C + C + | 7. if T (p1) if t If I were to kill him now, | 8. thenC P(p) thenC p: … then he would | pn go to heaven. | 9. A(ifC t+7 thenC p8) aP He is praying, and his sins will be | be atoned. | aA This is why he will go to heaven if | I kill him now. k There is a contradiction between | 10. K(pn8 , pm6) | going to heaven and the severe | punishment [which he merits]. | 11. J(K10) j: jm (= pn8) 〈What justi¼es this is that 〉 | going to heaven | … is a prize → |12. E (ifC t+7 thenC p8 &k10&q∧p6) e 〈From Lines 7–8, 10 and 6 it | follows that〉 it is not right to | kill him now. 13. J(Q3 ) j 〈It is also not right to kill him now because〉 | 14. Q∧P(p) q∧p: … revenge should b e fair and | equitable. | pk fair and equitable revenge | 15. P(p) p He killed my father, who had no | chance to repent. %rP | 16. %R(p15) My father may have gone to hell. | rR This is the result of p15 . % C + C | 17. E( r16 &if t 7 then p8) 〈Hence〉 there is a contradiction | e: K(pk14, pj1) | between fair and equitable | revenge and killing the King now ∧ – P | 18. E(k17 & q p14) e: T (a 2) 〈It may be inferred from this | that〉 it is not true that to kill him | now would be appropriate | revenge. 3.
Q(p1)
Relations within and between arguments
→ | 19. E(e18) e 〈 It may be inferred from this | that〉 it is not right to kill him | now. 20. E(q∧p14) e: Q∧P(p): … 〈From Line 14 it follows that〉 it would be right for me to pq kill him when he is sinning. 21. J(E20) j: U(pq20, pk14) 〈 What justi¼es this is that 〉 to do so would be fair and equitable revenge, 22. J(U21 ) j 〈 because 〉 | 23. if T+ (p20) if t+ if I kill the king when he is sinning, | 24. then P(p) then p then the king will go to hell. | 25. K(rP16 , p24) k There is a similarity between my | father’s going to hell (rP16 ) and the | king’s going to hell (p24 ). Explanations: Line 1: Both p and pj are needed here: p because it has to be conXated (as a whole clause) with q, and pj so as to enable targeting in Line 17; see comment to Line 17, below and Chapter 3, Section 3.3. Line 6: Here the outcome of the collateral operation has been spelled out in order to isolate the constituent element pm , which is targeted in Line 10. (See Chapter 5, Section 2.3 on the notation for constituent elements of conXated outcomes.) Line 7: This conditional statement has been analyzed as a counterfactual (Chapter 4, Section 1, because, on our reading, Hamlet is already certain that he will not kill the King, and justiWes his decision. On a diVerent interpretation, the if___ then ___ functor might be appropriate. T+ has to be inserted here, because functors — like ‘if… then…’ — apply to operations and not to outcomes; that is, the expression ‘if p1’ is well-formed only when it Wgures as an outcome . Line 8: The constituent element pn is targeted in Line 10. Line 9: What is accounted for here is not “he will go to heaven” but rather “if I kill him now, he will go to heaven”. In a fuller analysis, the Accounting operation would be broken down into a chain of reasons. These can be formalized as a sequence of suboperations of A (cf. Chapter 5, Section 5.2): 9'. A(if C t+7 thenC p8) | 10'. P(p) | 11'. R(p10')
a p rP
He is praying now. his sins will be atoned.
171
172 The Structure of Arguments
| rR | 12'. ifC T+ (p1 ) ifC t+ C P | 13'. then R(p1 & r 11') thenC rP | 14'. rR
rP is the result of his praying now. If I were to kill him now, then he would go to heaven. rP would be the result of my killing him now and his sins being atoned. Line 12: This is the conclusion of the articulation. Its outcome is equivalent to the outcome of the operation that is justiWed: Q(p1) in Line 3. No collateral operation — T + (q3 ) — need be appended to the outcome (see Chapter 5, Section 2.3, note 7). Line 13: The analysis here assumes that each of the two articulations — that in Lines 5–12 and that in Lines 14–19 — independently justiWes Q3 (see Chapter 4, Section 5.2 on independent eVects). Line 14: See comment to Line 1, above. The constituent element pk is targeted in Line 17 and in Line 21. Line 17: The Eduction is based on the fact that his father may have gone to hell (% r16) and that if he were to kill the king now, the latter would go to heaven (Lines 7–8). The collateral operation is a Comparison, K. Note that the Comparison is not between two q^p propositions “Revenge should be fair and equitable” and “It would be right to kill the King now”, nor is it made between the two p-propositions, but rather between the two constituent elements pk14 and pj1. Line 19: Again, there is no collateral operation; see above comment on Line 12. Line 21: What is being justiWed is the operation of making the Inference from q^p14 , and hence we write here J(E20), rather than J(Q∧P20), which would justify the positive Evaluation (Q) of killing the king (P20). The collateral outcome states that killing the king while he is sinning (pq20) is a case of someone exercising fair and equitable revenge (pk14). Lines 23–25: This is a warrant (not an articulation!) of the warrant in Line 21 and is constituted of two operations (one of which — if… then… — is a compound operation): That the king will go to hell if killed while he is sinning (Lines 23–24) does not by itself show that this is equitable revenge, but only in conjunction with the fact (Line 25) that then he will then have the same fate as Hamlet’s father (k25 ). The outcome in Line 16 was % rP, but the target of K (Line 25) is rP16 — without the degree-of-conWdence superscript — because what is being compared is ‘my father went to hell’, and not ‘my father may have gone to hell’.
Relations within and between arguments 173
The underlying structure displayed in the above analysis contains material that does not appear in the original text (the “expressed argument”). Here are some of the operations that the analysis has to include but have not been made explicit in the text, which can be understood without them: Operation 6: (Because he is a villain) he should receive severe punishment. Operation 9: (He will go to heaven) because he is praying, and his sins will be atoned. Operation 10: There is a contradiction between going to heaven and the severe punishment he merits. Operation 14: Revenge should be fair and equitable. Operation 17: There is a contradiction between fair and equitable revenge and killing him now. Operation 21: To do so would be fair and equitable revenge. Operation 25: There is a similarity between my father’s going to hell and the king’s going to hell. Also, the outcome of Operation 3 in the analysis (“It would not be right to kill him now”) is barely hinted at in the text by “No!” (Line 15 of the text; this outcome appears already in Operation 3 because we have opted for a regressive analysis, although the text is progressive; cf. Chapter 5, Section 6.1). Moreover, the sequence of operations in the analysis diVers at times from that of the corresponding Lines of Hamlet’s text. As noted in the foregoing, this soliloquy falls into several parts. This raises the question whether it constitutes a single argument. Now, it can be shown that all operations form a connected graph (Section 1.3). To do so, it will be convenient to group some of the operations into batches. A batch is deWned as any set of (one or more) operations which are either one of the following: 1. The operations in a conXation; 2. An operation and its collateral operation; 3. The operations forming a compound. These are the relations listed under (b), (c), and (f) in Section 1.2, above. 4. A single operation that is not included in one of the above, i.e., it is not part of a conXation, not a collateral operation and does not have a collateral operation, and is not part of a compound.
174 The Structure of Arguments
1 2 3 4 5 6 7/8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23–24 25
Figure 9.2 Targeting relations between batches in the Hamlet soliloquy.
Relations within and between arguments
It can easily be seen that any set of two or more operations written in a single line in the above formalization of the Hamlet soliloquy form a batch, and so do the implications, which are written in two lines (Lines 7–8, 23–24). If we now conceive of the batches in the formalization as nodes of a graph that represents the targeting relation, we can draw the graph in Wgure 9.2. The Wgure mirrors the fact that each batch — except the last one in Line 25 — either targets or is targeted by at least one other batch. Hence, since the operations within each batch are related, the graph depicting the argument is connected. In other words, the whole soliloquy is a single argument, according to our deWnition. It is true, though, that this argument might have been broken up and apportioned to several participants in a conversation; more on this in Section 3, below. The targeting relation imposes a partial order on operations, as can be easily seen in this graph. Thus, Operations 2 and 3 must both come after the conXated operations in Line 1, because each of them targets at least one of the conXated operations in it; but there is no targeting relation between Operations 2 and 3, which means that these two operations are not ordered relative to each other in respect to targeting. Inspection of the analysis shows that, at least in the present case, the sequence adopted is motivated by the content of the operations (try switching the sequence of these two operations!), but sometimes alternative sequences may be equally acceptable in an analysis.
2.
Relations between arguments
In this section we go beyond the boundaries of the single argument and deal with the relations between arguments in a discussion. A discussion, debate, or conversation consists, of course, of arguments; but do all the arguments that appear in it really “belong” to it? We often note that someone has gone oV at a tangent and her comment introduces material extraneous to the issue being discussed. Intuitively, an argument that does not relate to any other argument in the discussion — that is, it neither refers to nor is referred to by another argument — does not “belong” to the discussion. Further, when people converse, two (or more) discussions may be going on; that is, there are two (or more) disconnected sets of arguments, each of which forms a network of relations. The notions introduced in the previous section permit us to deal with this more formally.
175
176 The Structure of Arguments
2.1
Types of relations between arguments
Just like two operations in a given argument, two arguments may be either strongly or weakly related. Take two arguments, A and B. When there is an operation in A and another operation in B that are strongly related (in the sense explicated in Section 1.2), we say that the two arguments are strongly related; when there is only a weak relation between any two operations in A and B, the two arguments are weakly related; and when there is neither a strong nor a weak relation between any two operations in A and B, the arguments are unrelated. In eVect, the only way two arguments can be strongly related is by targeting: (a) in Section 1.2. The notions of strongly and weakly related arguments may form the basis for a much richer classiWcatory scheme for relations between two arguments. Take arguments A and B, and suppose that an operation in B targets an operation in A. Now, the type of that operation in B — whether it is an Interpretation, an Elaboration, a Designation, etc. — deWnes the type of relation between the two arguments. There may of course be more than one operation in B targeting an operation in A, and this problem will be taken up in the Wnal section of this chapter, which is concerned with the typology of arguments. 2.2
DeWnition of ‘discussion’
A discussion is an interchange of arguments, in which two or more people may take part.4 In Section 1.3 ‘argument’ was deWned in terms of relations. We now propose a similar deWnition of discussion. This deWnition permits us to identify an argument that does not belong at all to a given discussion, that is an ‘outsider’, so to speak: such an argument is unrelated to any other argument. I A discussion is an interchange between two or more people comprising (i) a set of two or more arguments, such that (ii) the strong and weak relations between these arguments form a connected graph.
A second deWnition introduces the distinction between fully belonging to a discussion and marginally belonging to it:
Relations within and between arguments 177
II An argument belongs fully to a discussion, if it is strongly related to at least one other argument in it. It belongs to a discussion marginally, if it is not strongly related to any other argument fully belonging to the discussion but is weakly related to at least one other such argument.
These deWnitions might be objected to as being too broad. According to them, one who interprets or evaluates Hamlet’s argument in his soliloquy (as literary critics, among others, do) is engaged in a ‘discussion’ with Hamlet. It might seem that this situation can be remedied by introducing into the deWnitions a pragmatic concept like ‘session’, corresponding to the concept ‘turn’ in the deWnitions of ‘argument’. But this raises the further question of how ‘session’ might then be speciWed so as to include, e.g., a discussion going on via internet, and the like. In this book no attempt will be made to deal with this question; instead, we rest content with conceiving of ‘discussion’ as a concept with fuzzy boundaries, and accept the foregoing deWnitions as they stand. 2.3
Load and Density
Two measures have been developed for the characterization of discussions, arguments, and operations: 1. load, which characterizes an element — either an operation in an argument or an argument in a discussion; 2. density, which is a property of an argument or a discussion as a whole. 1. Load. Operations in an argument will typically diVer in the degree to which they are, intuitively, central in the argument. In the next chapter, certain behavioral consequences of centrality will be discussed. This notion of centrality can be operationally deWned, and one of the ways to do so is in terms of the load of an operation. The load is deWned as the number of other operations that it either targets or that target it. 2. Density. Besides the load of an operation one can compute the load of an argument in a discussion, that is, the number of other arguments it is related to. Discussions can be described in respect to the degree to which their arguments are well-knit together. In a disjointed discussion, at the one extreme, few arguments relate to each other, and in a well-knit one there are many arguments that relate to each other. In Schlesinger (1974) a coeYcient of density has been proposed that captures this property of discussions and which will be described here brieXy. Consider a discussion constituted of m arguments. The maximum number
178 The Structure of Arguments
of pairs of related arguments is (m2-m) / 2; this value applies when each argument in the discussion is related to each other argument. The minimum number of related pairs is m-1; this will apply when each argument is related to only one other argument. Let n be the number of pairs actually related in a given discussion. Obviously, the greater the diVerence between n and the minimum number of pairs (m-1), the greater the density (in the intuitive sense of the term) of the discussion. The value of this diVerence is n-(m-1). Now, density is dependent also on the range of values that lie between the maximum and minimum numbers mentioned above. To obtain the coeYcient of density, D, we divide n-(m-1) by the diVerence between the maximum and the minimum, that is, by (m2-3m+2) / 2. We thus obtain the formula: D=
2(n-m+1) m2 -3m+2
D varies between 0 (minimum density) and 1 (maximum density).5 This measure is applicable to discussions of three or more arguments (when m〈 3, the denominator will be 0), but for shorter discussions the notion of density is of no interest. The coeYcient of density is discussed and illustrated in Schlesinger (1974), where the term ‘move’ is used instead of ‘argument’. In view of the distinction made in the foregoing between strongly and weakly related arguments, we can now compute two coeYcients: one for strong relations — call this the coeYcient of strong density — and one that does not discriminate between strong and weak relations, the coeYcient of weak density. As stated, the coeYcient of density is a characteristic of a discussion and is determined by the network of relationships between the arguments comprising the discussion. A similar coeYcient can be used to characterize an argument: by considering the number of pairs of operations within the argument that are either strongly or weakly related (for strong and weak coeYcients of density, respectively). Additional ways of characterizing discussions — segments, foci, and cut points — may also be used for operations within an argument. For details the reader is referred to Schlesinger (1974).
Relations within and between arguments 179
2.4
Chains of counter-arguments
The analysis of chains of arguments in a debate may necessitate a notational convention that has not been discussed so far. Each participant in the debate may advance an argument that confutes not only the last argument by her opponent but every counter-argument of her opponent and aYrms every argument she has marshaled herself (see also Rips 1998). Let us illustrate this with a simple, schematic case. Suppose we have two participants in a debate: the Proponent and the Opponent. The Proponent makes a claim; the Opponent presents a counter-argument; the Proponent challenges this counter-argument; the Opponent then defends this counterargument against this challenge. Such a chain of arguments may be presented schematically as follows: Proponent 1. … 2. … 3. X (…)
x
Opponent 4. … 5. … 6. X(… )
x: T– (x3)
Proponent 7. … 8. … 9. X (…) Opponent 10. … 11. … 12. X (… )
x: T– (x6 ) x: T+ (x3 )
x : T– (x9) x : T+ (x6 ) x : T– (x3 )
In Line 6, the Opponent refutes the Proponent’s argument: T– (x3 ). This move is countered by the Proponent, who claims that the Opponent is wrong in respect to T– in Line 6, and this implies that the Proponent was right in respect
180 The Structure of Arguments
to the outcome of Line 3 (refuted in Line 6): T+ (x3 ). Thus the outcome x in Line 9 is equivalent not only to the negation of the Opponent’s x6 but also to the aYrmation of the Proponent’s initial conclusion, x3. This requires a notational convention: we write the outcome x twice, each time with one of its collateral operations.6 Similarly, in Lines 10–12 the Opponent attacks the Proponent’s defense, and here the conclusion is: the Proponent is wrong in her defense (Line 9), so the Opponent was right in her attack (Line 6), so the Proponent was wrong in respect to the conclusion of her initial argument (Line 3). There are of course various other conWgurations of an interchange between two participants. For instance, instead of defending her counter-argument, the Opponent may, in Line 10–12, launch a diVerent attack on the Proponent’s position, e.g., one directed at the outcome of Line 3 rather than to those in the intervening Lines 6 and 9.
3.
“Encapsulated” dialogues
Peirce is reported to have written: “all thinking is dialogical in form. Your self of one instant appeals to your deeper self for his assent.” (cf. also Slade 1995).7 Thus, Hamlet’s soliloquy quoted in Section 1.4, above, could be reformulated as a dialogue; conversely, a dialogue can be reformulated as a single argument containing a sort of internalized dialogue. Another example of a dialogue with oneself that is encapsulated in a single argument has been given in Chapter 1, Section 3: I should remodel my house, because it has painful psychological associations for me. But really, I am not sure that remodeling would remove these. Well, even if it doesn’t, I could always resell it, perhaps at a proWt. (adapted from Freeman 1991: 163).
This would be analyzed as follows: Example 2 1. Q∧P(p) q∧p I should remodel my house. ∧ 2. J(Q P1) j 〈What justi¼es this is that 〉 | 3. P(p) p it has painful associations for me, and | 4. if T+ (p1) if t+ if I remodel it, | 5. then P(p) then p then these will be removed.
Relations within and between arguments
〈 But 〉 perhaps this is not a good reason to remodel it. % % – + 7. J( V6) j: T (if t 4 then p5) 〈 What justi¼es this Validation is that 〉 perhaps it is not true that remodeling will remove these associations. 8. E(% v–6 ) e: %T– (q∧p1) 〈It follows that〉 perhaps I should not remodel it. 〈 But 〉 I should (after all) remodel my 9. T+ (q∧p1 ) t+ :T– (e8 ) house. 10. J(T+9 ) j 〈 What justi¼es this is that 〉 + – + | 11. if [ T (p1 ) & T (p5 )] if [t & t– ] if I remodel my house and it is | not true that these associations | will be removed, | 12. then P(p) then p then I can resell it, perhaps at a | pro¼t. → | 13. E (if [t+ & t– ]11 & then p12) e 〈 Therefore〉 the Justi¼cation in Line 7 is not valid. Explanation: Lines 3–5: This is a warrant comprising more than one operation. Alternatively, one might formalize this as an articulation by appending an operation: E (p3 & if t+4 then p5 ) e: T+(q∧p1) It follows that I should remodel it. (Cf. the articulation in Lines 11–13). 6.
%V–
(J2 )
%v–
An “external” dialogue that parallels this argument would be as follows (the corresponding lines in the preceding analysis — in parentheses): Proponent: I should remodel my home. (Line 1) Challenger: I don’t see any reason for you to do so. --Proponent: The house has painful psychological associations (Lines 2–5) for me Challenger: But remodeling the house may not remove these. (Lines 6–8) Proponent: Even if my house retained its painful psychological (Lines 9–13) associations, I could always resell it, perhaps at a proWt.
Suppose now that — after deliberating the issue with herself or somebody else — the Proponent tells somebody why she has decided to remodel her house. The same argument may then be “wrapped up” so that the encapsulated dialogue is no longer evident:
181
182 The Structure of Arguments
I should remodel my house, because it has painful psychological associations for me, and even if remodeling doesn’t remove these, I still could resell it, perhaps at a proWt.
As stated in Chapter 1, Section 2, we accord diVerent underlying structures to arguments that are presumably arrived at by diVerent trains of thought. The train of thought in the next example is more compressed than that in Example 2 — the author comes straight to the point (and possibly, it reXects a later phase in the deliberation process). Since the trains of thought diVer, a somewhat diVerent underlying structure will be assumed: Example 3 1. Q∧P(p) q∧p ∧ 2. J(q p1) j | 3. P(p) | | 4. if T+ (p1 ) | 5. then %P(p) | 6. if [T+(p1 ) & T– (p5 )] | | 7. then P(p)
4.
I should remodel my house. 〈What justi¼es this is that 〉 p It has painful associations for me, and if t+ if I remodel it, % then p then these will perhaps be removed. if [t+ & t– ] If I remodel it and they are not removed, then p then I can resell it, perhaps at a pro¼t.
Toward a typology of arguments
Among the attempts at deWning types of arguments there are those based on the kinds of inference through which the conclusion is reached. The typology of arguments proposed in this section, rather than deploying such argumentinternal criteria, is based on the relations between arguments. Some writers have previously proposed such a relational typology for counter-arguments, that is, arguments that refute other arguments. Some of these attempts will be discussed in Section 4.1, and an alternative classiWcation of counter-arguments will be developed. An extension of this typology to all kinds of arguments (not only counter-arguments), which is also based on relations between arguments, will be proposed in Section 4.2.
Relations within and between arguments 183
4.1
Counter-arguments
Shaw (1996) distinguishes between three types of objections (i.e., counterarguments): ‘assertion-based’, ‘argument-based’, and ‘alternative-based’ objections. An assertion-based objection is one that refutes the truth of a premise that supports the conclusion, whereas an argument-based objection is one that claims that the conclusion does not follow from the premises. This distinction parallels that made by Pollock (1989: 126) between rebutting and undercutting defeaters. Shaw’s ‘alternative-based’ objection is one that claims that “the argument does not consider information that is relevant to determining the truth or utility of the conclusion”. Shaw’s classiWcation is similar to that proposed by Quiroz, Apothéloz, and Brandt (1992), whose classiWcatory scheme comprises four categories; their examples are (in a sequence diVerent from theirs): 1. Counter-argument concerning the plausibility of the reason: – Mary was in a very bad mood; she didn’t smile all evening. – Mary? She didn’t stop laughing. 2. Counter-argument concerning the completeness of the reason: – You should buy the same car as Peter. It is extremely comfortable. – It is much too expensive for me. 3. Counter-argument concerning the argumentative orientation of the reason – “A World Apart” is not a very good Wlm. It doesn’t teach us anything new about apartheid. – That’s precisely what makes it good. 4. Counter-argument concerning the relevance of the reason – I am not going to take this exam. I didn’t prepare for all the questions. – Just because you didn’t prepare for all the questions is no reason not to take the exam.
Quiroz et al.’s (1) would be an example of Shaw’s assertion-based objections, their (2) — of Shaw’s alternative-based objections, and their (3) — and possibly also (4) — of her argument-based objections. Shaw’s distinction between denying the truth of a premise (‘assertion-based objection’) and claiming that the conclusion does not follow from the premise (‘argumentbased objection’) parallels our distinction between denying the truth of a claim
184 The Structure of Arguments
(T– ) and denying the validity of a JustiWcation, or, in a progressive argument, of an Inference (V–). In our system, (2) — Shaw’s ‘alternative-based’ objections — would also be a counter-argument denying the validity of a JustiWcation.8 In our analytic framework there is a clear distinction between (3) and (4). The counter- argument in (3) is directed at a JustiWcation: “It doesn’t teach us anything new about apartheid” is a JustiWcation of the Wrst author’s opinion of the Wlm, and this JustiWcation is objected to by the author of the counterargument. Now take (4). “I didn’t prepare for all the questions” is an excuse; it is said to justify the decision of not taking the exam.9 However, in our system this is not a JustiWcation: a JustiWcation supports a statement in an argument, whereas not having prepared for all the questions is the reason for a certain behavior, for an action (or lack of it); see Chapter 5, Section 1.2. This reason — which serves here as an excuse — is formalized as an Accounting operation, and the counter-argument in (4) is therefore directed at this Accounting operation, not at a JustiWcation. In this respect it diVers from the counter-argument in (3). The distinction Quiroz et al. had in mind is a diVerent one, as shown by their labels for (3) and (4). Like many writers, they do not distinguish between JustiWcation and Accounting, regarding both as “reasons”. In the foregoing we have distinguished between counter-arguments denying the truth of a claim and those denying the validity of an operation. There is a third possibility, namely, counter-arguments based on a negative Evaluation, Q. One might oppose “I am not going to take this exam. I didn’t prepare for all the questions” in two ways: (i) by denying the truth of the reason “I didn’t prepare for all the questions” or, (ii), as has been done in (4), by claiming that this is not a good excuse, i.e., by a negative Evaluation (an Evaluation, remember, refers to some norm other than truth or validity). Example 4 Author 1 1. P(p) p 2. A(p1) aP aA
I am not going to take this exam. I didn’t prepare for all the questions. This is the reason for my not taking the exam.
Author 2 3. Q(aA2) q
This is not a good excuse for not taking the exam.
Relations within and between arguments 185
To summarize the discussion so far, the above four counter-arguments can be classiWed according to two dimensions: 1. The operation that rejects the proponent’s argument directly. This operation may be T– , as in (1), V– , as in (2) and (3), or Q (a negative Evaluation), as in (4). 2. The type of operation or outcome that is rejected. In (1), (2), and (3), the counter-arguments reject a JustiWcation, whereas in (4) an Accounting operation is rejected. Other types of operations can be rejected as well, as illustrated by Example 5, below. It is reasonable to expect that, as more and more counter-arguments are considered, lists like those of Shaw and of Quiroz et al. will have to be expanded again and again. A better strategy would be to look for a principled way of arriving at a classiWcation, and the foregoing discussion shows that this seems feasible within our formal system. It is suggested that a serviceable classiWcation of counter-arguments can be achieved by the two aforementioned dimensions. This will now be illustrated by analyzing a type of counter- argument discussed by Govier (1988: 217f) under the term “refutation by logical analogy”. Govier’s example is: – If Jane Fonda exercises, she is Wt. Jane Fonda is Wt; so Jane Fonda exercises. – If Mother Theresa is the richest woman in the world, then Mother Theresa is a woman. Mother Theresa is a woman; so Mother Theresa is the richest woman in the world.
The Wrst argument is based on an illegitimate inference from the truth of the consequent (‘Jane Fonda is Wt’) to the truth of the antecedent (‘Jane Fonda exercises’), in our terminology: a Backward Modus Ponens, B (Chapter 3, Section 1.1). The objection (‘If Mother Theresa…’) is a similarly constructed argument, which leads to a patently false conclusion, thus showing that the Jane-Fonda argument is not valid. Here is our analysis: Example 5 1. 2. 3. 4.
Author 1 if P(p) then P(p) T+ (p2) B(if p1 then p2 & t+3)
if p then p t+ b: T+ (p1)
If Jane Fonda exercises, then she is ¼t. Jane Fonda is ¼t. 〈It follows that〉 Jane Fonda exercises.
186 The Structure of Arguments
Author 2 5. if C V+ (B4) if C v+ If this inference would be valid, C + ∧ C + ∧ then v | if p then the following would (also) 6. then V | if P(p) | | be valid: | | If M. Ther. is the richest woman | | in the world, 7. | then P(p) | then p then Mother Theresa is a | | woman. 8. | T+ (p7 ) | t+ Mother Theresa is a woman. 9. | B(if p6 then p7 & t+8 ) | b: T+ (p6 ) 〈It follows that〉 Mother | | Theresa is the richest woman in | | the world. 10. J(if C V +5 thenC V +6 ) j: K(if P1 then P2 & T+3 & B4, if P6 then P7 & T+8 & B9) 〈What justi¼es this is that 〉 the Mother-Theresa argument and the Jane-Fonda argument have the same structure. 11. T+ (if p6 then p7 ) t+ The implication in Lines 6–7 is true; 12. T+ (t+8 ) t+ its consequent (M.T. is a woman -Line 8) is true, 13. T– (b9 ) t– and the conclusion (Line 9) is false. 14. E (t+11 & t+12 & t–13) e: T– (v+6 ∧[if p6 then p7 ] & t+8 & b9 ) 〈It follows that〉 it is not the case that the inference in Lines 6–9 is valid. 15. M(if C v +5 thenC v+6∧[…] & t-14) m: T– (v+5) 〈It follows by Modus Tollens that〉 it is not – m: V (B4) the case that the inference B4 is valid. Explanations: Line 4: A Backward Modus Ponens (B) may be an acceptable (though not a deductive) inference; see Chapter 3, Section 1.1, sub Class 5: Inference. Lines 6–9: The faulty Mother-Theresa argument is a conXated sequence; it cannot stand by itself, because Author 2 of course does not commit himself to the whole argument, but merely says that if the Jane-Fonda argument were acceptable, the Mother-Theresa argument would be as well. Line 10: This is a Comparison between two arguments. Each argument is represented as a conjunction of the operations that constitute it. See Chapter 4, Example 20b. Line 15: There are two (logically equivalent) collateral operations: one denies
Relations within and between arguments 187
the truth of the validation in Line 5 and the other states that the Backward Modus Ponens is invalid. See Section 2.4, above, for the notation.
The counter-argument advanced by Author 2 in this example can be characterized by a proWle across the two dimensions speciWed above: 1. The operation that leads directly to rejecting the preceding argument, namely, a negative Validation (Line 15). Note that of the two collateral operations in Line 15, T– (v5) rejects an outcome of Author 2’s own argument, and only V– (B4) rejects an operation of the Wrst author’s argument. In other words, while T– (v5) entails V– (B4), it does not refute the preceding argument directly. 2. The type of operation or outcome that is rejected: the operation Backward Modus Ponens in Line 4.10 The proWle of this counter-argument, then, is V– / B. The same proWle will be accorded to any counter-argument that claims that a Backward Modus Ponens is not valid. Things become more complicated when one considers that a counterargument may refute more than one operation in a given argument or more than one argument. In the schematic example given in Section 2.4, the argument in Lines 10–12 refutes two of the Proponent’s arguments. In such cases, more than one proWle will be required to characterize the counter-argument. Our typology, based on proWles across two dimensions, then, permits of an indeWnitely large number of types, unlike a Wxed set of types, like those proposed by Quiroz et al. or Shaw. It should be obvious, however, that some distinctions are not accommodated by our typology. Thus, we assign the same proWle, V– / J, to both Quiroz et al.’s (2) and their (3), and do not diVerentiate between diVerent reasons for the lack of validity (such as ‘completeness of the reason’ and ‘argumentative orientation of the reason’). This may at times be a drawback. In general, though, we make much Wner distinctions than both Quiroz et al. and Shaw. Thus, Shaw’s ‘alternative-based’ objections may have any one of several proWles in our classiWcation and there will be no way to indicate what they have in common. To provide for further distinctions would require additional dimensions.11 4.2
Other arguments
The typology proposed here for counter-arguments can be extended to certain other types of arguments. Let us call a supporting argument one that, instead
188 The Structure of Arguments
of refuting another argument (as a counter-argument does), supports it. Supporting arguments may be classiWed along the same dimensions that have been proposed in the foregoing for counter-arguments, but in Dimension 1 (the operation that rejects the proponent’s argument directly) the alternatives for supporting arguments will be T+, V+, and positive Evaluations (instead of T–, V–, and negative Evaluations, which Wgure in counter-arguments). An argument that neither refutes nor supports a preceding argument, but rather provides some additional information relevant to it (e.g., by an Elaboration or by a Designation), explains it (by an Interpretation or by an Accounting operation), or concludes something from it by an Inference, will be called a supplementing argument. Here is an example: Example 6 Author 1 1. P(p)
p
Someone murdered the ambassador in his garden yesterday night.
Author 2 2. P(p) 3. E(p2)
p e: % O(p1)
4. P(p)
p
5. E(p4)
e: % O(p1)
6. P(p)
p
7. E(e3 & e5 & p6 )
e: % O(p1)
Tim has a good alibi. 〈Therefore〉 it is unlikely that he was the murderer. The ambassador’s wife loved him, and they lived happily together. 〈Therefore〉 it is unlikely that she was the murderer. The only other person that has been near the garden is Ron. 〈Therefore〉 it is likely that the murderer was Ron.
Explanation: Recall that % stands for any degree of certainty, ‘quite unlikely’ ‘probable’, etc. (Chapter 3, Section 1.3).
Supplementing arguments may be classiWed along the same two dimensions as counter-arguments, and the alternatives in Dimension 1 will include, instead of Truth value and Validation, other types of operations. (Note that when an argument contains an Evaluation of an operation in a previous argument, it may also be a supplementing argument and not only a counter-argument or supporting argument.)
Relations within and between arguments 189
In this example, several operations in the supplementing argument (viz. those in Lines 3, 5, and 7) target the same operation in the preceding argument. There may be arguments where several types of operations target one or more operations in a preceding argument (or several preceding arguments); for instance, an author may elaborate on one operation and infer something from another. What is true of counter-arguments and supporting arguments is therefore true also for supplementing arguments: more than one proWle may be required to characterize them. Furthermore, the categories counter-arguments, supporting arguments and supplementary arguments are not mutually exclusive ones. An argument may, for instance, both infer something from an operation in another argument and refute another (or even the same) operation in that argument; or it may support one operation and refute another one (as when in saying “I agree with you that…, but you are wrong in saying…”). Here, again, there will be more than one proWle. Dimensions 1 and 2 are relevant only to counter-arguments, supporting arguments and supplementing arguments, because these are strongly related to other arguments. Arguments that neither target an operation in a previous argument nor are connected to it — such as the Wrst argument in a discussion or an isolated argument — obviously cannot be assigned a proWle across Dimensions 1 and 2. Arguments that are only weakly related (see Section 1.2, above) to others may be classiWed according to the various types of connections (Chapter 8) — Contrast, Similarity, and so on — which deWne various types of relationships between an argument and a preceding one. Take, for instance, Example 9 of Chapter 8, reproduced here: Example 7 Author 1 1. P(p) p 2. ?O (p1) ?O Author 2 3. O(p1) o Author 3 4. P(p) p
Somebody sent Beatrice ½owers. Who sent her ½owers? One of her admirers did. Rsp {o, ?O2 } Norman certainly did not. Rsp {p, ?O2 }
[= backdrop]
190 The Structure of Arguments
Author 2 presents a supplementary argument to the Wrst argument, which is strongly related to it: O targets p1. Its proWle is therefore O / P. By contrast, the operation in Author 3’s argument does not target any other operation (as shown in Chapter 8, Section 2, it is not an Elaboration of p1). This argument is only weakly related to the Wrst argument, namely, by a Response connection. It is therefore classiWed as: Rsp {p, ?O}.12 Figure 9.3 schematically describes types of arguments. The categories in the Wgure, except that of unrelated arguments, may be further subdivided into types as described in the foregoing, by proWles or, as in Example 7, by indicating the relevant connection. Arguments that are
unrelated to others
counter-arguments
strongly related to others
supporting arguments
Figure 9.3 Types of arguments
weakly related to others
supplementing arguments
Chapter 10
Expressed arguments
Signs are small measurable things, but interpretations are illimitable. – George Eliot, Middlemarch
The preceding chapters have dealt with the underlying structures of arguments. This chapter deals with expressed arguments, why their expression involves omission of operations (Section 1), and which operations tend to be omitted (Section 2). We also discuss some characteristics of précis writing (Section 3). The Wnal section deals with operations that target the expressed argument.
1.
Arguing and understanding arguments
1.1 Omitting and bridging It will be recalled from Chapter 1 that when one expresses an argument verbally, one often “condenses” its underlying structure, that is, one omits some of the operations (see the discussion in Herrmann and Grabowski, 1994: 59– 60, 349–350). Accordingly, in the arguments we analyzed in the preceding chapters we often had to add operations that are not explicitly stated in their verbal expression. It seems intuitively clear why the author of an argument should omit some operations in the process of formulating it. It would often be very tedious to verbalize every single operation (as shown, incidentally, by the verbal descriptions in many of our examples), and to do so would be wasting time and eVort unnecessarily. Unnecessarily, because normally the hearer is perfectly able to understand the argument without the unstated operations. Such redundant verbalization would therefore infringe on Grice’s (1975) conversational maxims. As Voltaire says, “The secret of being a bore is to say everything”.
192 The Structure of Arguments
So much for the author of an argument (who, in this chapter will be referred to as the ‘speaker’, which is not intended to exclude the writer). As for the hearer (a term that will be used here also for the reader), omission of operations in the expressed argument may result in misunderstandings; these will be brieXy dealt with in the Wnal section of this chapter. But more often than not, the hearer will understand the argument correctly in spite of such omissions. Communication succeeds, normally, because the speaker tends to omit only those operations that the hearer is able to bridge. In the course of their experience in communicating with each other, people learn when operations can be omitted without impairing understanding. When the argument has been correctly understood, the hearer has bridged the missing operations. Bridging may occur in either one of two ways: 1. The hearer Wlls in the omitted operation(s) mentally. This does not necessarily involve awareness on part of the hearer. 2. It is reasonable to suppose that occasionally the hearer may understand the argument as presented, without his processing in any way the content of the omitted operations. For instance, Hamlet (Chapter 9, Section 1.4) does not say explicitly why he thinks he ought to kill the king while he is sinning. Again, in our analysis of Hamlet’s monologue (Example 1) the outcome of Operation 25 reads: ‘There is a similarity between my father’s going to hell and the king’s going to hell’, but this does not appear in the monologue. Now, a hearer who fails to supply this operation mentally may still be said to have understood the monologue correctly (albeit not “completely”). There is in fact some research that suggests that hearers may fail to supply the missing inferences (Noordman, Vonk, and KempV, 1992).1 1.2
Accessibility
While one may be aware of omitting an operation in formulating an argument, one frequently will be quite unaware of doing so: “We know more than we can say”, as William James (1890/1981: 168) observed at the turn of the century. Likewise, the hearer will not always be aware of bridging an unstated operation. Awareness is a matter of degree. The presently available empirical techniques are limited in their eYciency in tapping degree of awareness directly, but one can get a clue from studying a variable that is closely related to awareness and which we will call accessibility. Accessibility pertains to the ability of the speaker or hearer to state, after
Expressed arguments 193
the argument has been formulated or understood, what operations have been omitted. The speaker may be able to do so even if the omission occurred without awareness, and likewise, the hearer may be able to do so even if bridging occurred without awareness. In fact, the analyst who formalizes an argument is in the position of the hearer: at Wrst she may understand the argument but be unaware of some omitted operations, and then she retrieves them, often laboriously. 1.3
Determinants of omission and accessibility
As stated, in formulating an argument, people generally omit what their audience can be expected to bridge easily. How much is omitted from an argument will therefore depend, among others, on the degree to which the speaker and the hearer know each other: as Vygotsky (1987) points out, the more familiar they are with each other, the more abbreviated their sentences tend to be. The tendency to omit operations will also be dependent on the degree to which the speaker thinks that the hearer is familiar with the content of the argument, the speaker’s alertness when formulating the argument, and the genre of the discourse. These are situation-bound factors, they vary from context to context and from speaker to speaker. We believe that beyond these there are some very general factors that apply to any situation and can be formulated in terms of the constructs of our system. It is to these that we turn in this Wnal chapter. Intuitively, the more central an operation is in the argument, the less likely it is to be omitted. This intuition will of course give us little mileage unless the notion of centrality is explicated. This can be done in terms of the concepts of our analytical framework. Centrality of an operation, we suggest, is determined by its type and by its place in the network of relationships between operations. It is proposed that degree of centrality of an operation depends, among others, on the following: 1. JustiWcations will be, on the whole, less central than other operations. Delete a JustiWcation from an argument, and it may still hold together and be understood (Sprott, 1992, claims that a justiWcation is subordinate to a “head act”, i.e., to the statement claim it justiWes). 2. Whether the operation is a terminal one — roughly, one that is not targeted — or a transmitter, i.e., one that is targeted by at least one other operation
194 The Structure of Arguments
(these two terms will be more precisely deWned further on). Because there are other operations that “depend” on them, transmitters are on the whole more central than terminal operations. In terms of the processing of arguments, an operation that is targeted — i.e., a transmitter — has to be reverted to in processing the argument and it thus attains a sort of saliency. 3. The load of the operation, that is, the number of other operations that it is targeted by plus the number of other operations that it targets (see Chapter 9, Section 2.3). The greater the number of operations with which a given operation is related by targeting, the more crucial it will presumably be, on the whole, to the structure of the argument. It stands to reason that centrality it is a determinant not only of omissions but also of the accessibility of an operation: the less central the operation, the harder it will be for the speaker to recover it after the argument has been expressed and by the hearer after it has been comprehended. Centrality is presumably not the only determinant of omission and accessibility. In a given argument, there may be operations that are self-understood and need not be verbally expressed (we think primarily of conclusions of arguments); these may be easily bridged by the hearer. Conceptually, this factor is independent of that of centrality (but there may of course be operations that will tend to be omitted because they are both not central and selfunderstood).2 The degree to which an operation is self-understood will depend on various factors having to do with the subject matter of the argument, and the knowledge shared by the speaker and his audience. It can therefore not be deWned in terms of the constructs of our system, and we have done no further work on it. 1.4
Terminals and transmitters
We deWne transmitter as an operation that is targeted; that is, either the operator of the operation or its outcome is targeted. An operation that is not a transmitter will be called a terminal. To illustrate, X is a transmitter if it is targeted by an operation Z in one of the ways speciWed in Table 10.1. The symbol / in the table stands also for //. Likewise, if … then … in the table stands for all implications, i.e., for ifC … thenC, iV … then, and iVC … thenC (see Chapter 4, Sections 1 and 2 on the use of these symbols).
Expressed arguments 195
Table 10.1 Targeting that turns operation X into a transmitter Operator X is targeted
Outcome x is targeted a
Simple target
Z (X )
Z (x )
Multiplex target
Z (X , …) Z (… , X) Z (X & …) b Z (… & X ) Z (X / …) b Z (… / X ) Z ( if X then …) Z ( if … then X ) Z (…..∧ X ) b Z (X ∧ … ) Y (…) y: Z (… X …)
Z (x , …) Z (… , x) Z (x & …) Z (… & x) Z (x / …) Z (… / x) Z ( if x then …) Z ( if … then x ) Z (….∧ x ) Z (x∧ … ) Y (…) y: Z (… x …)
Compound target
ConXation Collateral operation c
Notes a. In this table, x includes any one of the partial outcomes of Interpretation and Cause, viz., iP , iI, aP, aA, rP, and rR. It also includes constituent elements of outcomes. b. For explanation of symbols & and / see Chapter 4, Sections 2 and 3; ∧ is explained in Chapter 6, Section 1. c. Here X and x may be a either a simple or a part of a multiple, compound, or conXated operation/ outcome.
An operation may be targeted by another operation in the same argument, or by one in another argument in the discussion; the latter case will be called inter-argument targeting.3 Transmitters in compound operations and conXations When an operation X is a conjunct or a disjunct in a compound, targeting X turns only X into a transmitter and not the operation compounded with it. In other words the operations in implications (if… then…), conjunctions, and disjunctions are treated as separate operations. Further, the operations in a conXation are treated as separate operations, like compounds. These rules are illustrated in Table 10.2. The Wrst lines of the table should be read thus: In an implication ‘if X (…) then Y (…)’, when either X or x is targeted, only operation X is a transmitter, and when either Y or y is targeted, only operation Y is a transmitter. For more complex structures — like, e.g., [X/Y]∧Z — the same principles as those illustrated in the table hold.
196 The Structure of Arguments
Table 10.2 Transmitters in compound operations and conXations Operation
Targeted operator/outcome
Transmitter
Implication
if X (…) then Y (…)
Conjunction
X (…) & Y (…)a
Disjunction
X (…) / Y (…)a
ConXation b
X ∧Y (…)
X or x Y or y X or x Y or y X or x Y or y Y or y X∧Y or x∧y
X Y X Y X Y Y X and Y
Notes a. For explanation of symbols & and / see Chapter 4, Sections 2 and 3. b. See Chapter 6 on conXations. The conXating operation by itself cannot be targeted (Chapter 6, Sections 2.1 and 2.4).
Table 10.3 Transmitters in collateral operations Operation Y (…) y: X (…)
Targeted operator
Targeted outcome
Y X x y
Compounds a
Z (…) z: X (…) & Y (…)
X Y
z
x∧y
X and Y Y Z, X, Y
Z ConXations
Z (…)
X∧Y Yb
Y X X and Y Y and X X Y X Y X, Y, Z Z Z, X, Y
x y x and y
z: X ∧Y (…)
Transmitter
y Z z
Y Z Z, X, Y
Notes a. The examples are of conjunctions, but the same rules apply (mutatis mutandis) to disjunctions and implications. b. The conXating operation by itself cannot be targeted (Chapter 6, Sections 2.1 and 2.4).
Expressed arguments 197
Transmitters in collateral operations A collateral operation and its “main” operation are also treated as two separate operations in respect to their status as transmitters. Thus, when the “main” operator is a transmitter, the collateral one may be a terminal, or vice versa. However, the outcome of the collateral operation is identical to that of the “main” operation; hence, when one of these outcomes is targeted, the other is targeted as well. When the collateral operation is a compound or a conXation, the rules stated in the foregoing apply to it. This is illustrated in Table 10.3, the Wrst lines of which should be read thus: Given an operation Y with a collateral operation X, when the operator Y is targeted, only operation Y is a transmitter, …, if the outcome y is targeted, both operations Y and X are transmitters… . Transmitters in JustiWcations A warrant of one line (see Chapter 5, Section 2.3) may involve a collateral operation, and the foregoing rules for collateral operations apply to it. Each operation in a warrant of more that one line or in an articulation is regarded as separate in respect to its status as transmitter. The operation that is justiWed is always a transmitter, since it is targeted by J, the JustiWcation. In an articulation, the outcome of the conclusion is equivalent to the outcome of the Table 10.4 Transmitters in articulations a Articulation Z(…) J(Z) | X (…) | …. (…) → | Y (…)
Targeted operator / outcome
Transmitter
z j x … y Jb X or x Y y zc
J X Y Y and Z Z and Y
Notes a. The same rules apply to warrants of more than one line (except for those involving Y and y, because warrants have no conclusions). b. In an articulation, the outcome j cannot be targeted; see Chapter 5, Section 4.2. c. The justiWed operation, Z, is always a transmitter, because it is targeted by J.
198 The Structure of Arguments
operation justiWed by the JustiWcation. Hence, when either one of these outcomes is targeted, both operations are transmitters. However, targeting the operator of the justiWed operation does not turn the conclusion into a transmitter, because the two operators are not equivalent. These rules are illustrated in Table 10.4 for articulations.
2.
An experimental study of omissions
The study reported on in this section was designed to corroborate our hypotheses regarding the eVects of terminality and JustiWcations on omissions (see Section 1.3, above). The procedures used had never been tried out before, to our knowledge. These studies were therefore regarded as exploratory and only a small number of subjects participated in them. 2.1
Text materials
The Hebrew texts used in these studies were taken from published juridical protocols. One text (henceforward: Admission), was based on a verdict dealing with the admission of candidates to the university; from this verdict Wve arguments were extracted. The other text (henceforward: Medicine), was based on a verdict pertaining to the admissibility of administering an experimental drug to a terminally ill patient; from this verdict Wve arguments were extracted. Two texts were used so that the Wndings could be replicated, permitting generalization. For the experiments, a ‘Standard’ version of the text was prepared, based on our formalization of the underlying structures of the arguments extracted from the texts: the text was reformulated so that all the operations in the formalization were mentioned explicitly. The eVects of terminality and JustiWcations were assessed in this study.4 Our texts included operations of the four possible combinations: terminal operations that are JustiWcations: terminal operations that are not JustiWcations: transmitters that are JustiWcations: transmitters that are not JustiWcations:
+T +T –T –T
+J –J +J –J
As stated, the texts in this study included several arguments. Operations that were the objects of inter-argument targeting (Section 1.4, above) were re-
Expressed arguments 199
garded as transmitters for the purpose of this study. The rationale for this was that each subject read the text as a whole, so the fact that it contained more than one argument therefore presumably did not aVect performance in the experimental tasks (described below). The number of operations in each of these categories is given in Table 10.5. Table 10.5 Number of operations in each category – Omission study Admission +T –T Total
2.2
+J 4 7 11
–J 5 22 27
Medicine Total 9 29 38
+T -T Total
+J 8 4 12
–J 2 19 21
Total 10 23 33
Procedures
The most direct way to study omissions is to analyze actual arguments in respect to the operations that have been left unexpressed. Because of the need to perform a separate analysis of each argument, however, this is a very timeconsuming method, and we therefore opted for a diVerent approach: presenting experimental subjects with a text and asking them to recall it from memory (see van Eemeren, de Glopper, Grootendorst and Oostdam, 1995, for a diVerent experimental procedure).5 There is a problem here: the subject’s output may give a somewhat distorted picture of omissions in arguing, because in this particular task it may be aVected also by memory of operations included in the presented text. This is discussed below. Experimental tasks Two experimental tasks were deployed in our study: Reconstruction (R). Subjects were given the Standard version of a text and then asked to reproduce it in writing from memory. The reproduced text was then compared with the one they had read. The subject in this task is in a situation similar to that of a person who produces a text: in both cases some message is conveyed and formulated verbally. It may be assumed, therefore, that in our reconstruction task people will tend to omit the same kinds of operations they tend to omit in production. True, the subject who reconstructs a text may omit fewer operations, because he may remember speciWc operations that appeared
200 The Structure of Arguments
in the text read; but what is of crucial interest here is not the number of omissions but the kinds of operations omitted (+T vs. –T, +J vs. –J), and there seems to be no reason why remembering the text should aVect also the type of operations omitted. The reconstruction task, then, may provide us with a clue as to what operations speakers tend to omit.6 Expansion of reconstructed text (ER). This task was carried out by the same subjects who performed the Reconstruction task (R), and after the subject had performed the latter. Each subject was asked to expand his or her output of the reconstruction task, that is, to add to it “missing” operations (an example of such an expansion, taken from a diVerent text was given). We conceived of this as another reconstruction task, showing what operations the speaker tends to omit even after prompting.7 To summarize, two tasks, Reconstruction (R) and Expansion of reconstructed text (ER) were deployed to assess the eVect of terminality and of JustiWcations on omissions by the speaker.8 Subjects In view of the exploratory nature of this study it was carried out with only a small number of subjects. In the two experimental tasks, eight subjects were tested individually (all but one were university freshmen). They were given a text and asked to reconstruct it (R). Then each subject was asked to expand the product of his or her reconstruction (ER). Four of the eight subjects performed these tasks on the Admission text and the four others — on the Medicine text. Coding The unit of analysis was an operation. An exception were the operations constituting collateral operations. In the R-task and the ER-task there is no need for the subject to mention both the collateral operation and its ‘main’ operation. For instance, in the outcome ‘Therefore the University’s action was illegal’ — formalized as e: Q(p) (see Line 6 of the analysis of the Admission text, Appendix B) — the subject who mentions the illegality of the University’s action may be credited with both the outcome e and the outcome of the collateral operation, Q(p). Collateral operations were therefore dealt with as single unit (that is, they were treated as a ‘batch’; see Chapter 9, Section 1.4). Texts written by the subjects in each of the two tasks were analyzed by two coders, who determined for each subject and each task which of the operations were mentioned. DiVerences of opinion were settled by discussion.9 At the
Expressed arguments 201
time of coding, the coders did not know whether a given operation was terminal or not. Tests of our hypotheses are based on the assumption that subjects correctly understood the text and only failed to provide certain operations. In fact, there were no indications that any one of the subjects had misunderstood an argument. 2.3
Results
The hypotheses tested in this study were: In the Reconstruction task and in expanding the reconstructed text 1. The probability of recalling a terminal operation (+T) would be greater than that of recalling a transmitter (–T). 2. The probability of recalling an operation in a JustiWcation (+J) would be greater than that of recalling other operations (–J). In comparing the eVects of terminality and JustiWcations, account has to be taken of the possibility of confounding. Suppose, for instance, that the experimental data show both that terminals are more likely to be omitted than transmitters and that JustiWcations are more likely to be omitted than operations that are not JustiWcations. Then it is possible that the higher omission rates of terminals is due to the fact that some terminals are JustiWcations, and not because terminals as a whole were omitted more frequently (and vice versa for JustiWcations, which may tend to be omitted only because some of them are also terminals). We therefore tested for the signiWcance of the interactions between terminality and JustiWcation. The probabilities of mentioning operations in each category were computed as follows. For each subject, the number of operations of a given category that he or she mentioned was divided by the total number of operations in that category (as given in Table 10.5). The mean of these proportions over subjects was computed. These mean proportions are given in Tables 10.6–10.7 Table 10.6 Reconstruction (R) – Probability of mentioning an operation Admission +T –T Total
+J 0.438 0.607 0.546
–J 0.300 0.609 0.550
Medicine Total 0.361 0.609 0.549
+T –T Total
+J 0.446 0.646 0.509
–J 0.250 0.567 0.535
Total 0.406 0.579 0.525
202 The Structure of Arguments
Table 10.7 Expansion of reconstructed text (ER) – Probability of mentioning an operation Admission +T -T Total
+J 0.500 0.512 0.500
–J 0.500 0.550 0.541
Medicine Total 0.497 0.542 0.529
+T -T Total
+J 0.469 0.729 0.555
–J 0.250 0.585 0.552
Total 0.425 0.611 0.554
Due to the small number of subjects involved, a non-parametric test, the Wilcoxon matched-pairs signed-ranks test, was used to analyze the signiWcance of the obtained diVerences. As a Wrst step, the signiWcance of the interactions between terminality and JustiWcation was tested.10 The Wilcoxon test showed that for each of the two tasks and for each of the two texts the interaction eVect, if any, was not statistically signiWcant. It was predicted that terminal operations would be more likely to be omitted than transmitters. DiVerences in this direction were obtained in both tasks and for each of the two texts. As for the statistical signiWcance of these diVerences, it should be borne in mind that for N=4, the smallest p-value that can be obtained by the Wilcoxon test is 0.0625. For the terminality factor, this value was obtained in the R-task for both texts, and in the ER-task for the Medicine text. Due to the small number of subjects in this exploratory study, then, the diVerences did not quite reach a generally accepted level of signiWcance; but the general trend of the data is deWnitely in accord with our hypothesis, and the fact that in the reconstruction task the same eVect was replicated increases our conWdence in the Wndings. It was further predicted that operations in JustiWcations would be more likely to be omitted than operations not in JustiWcations. While all but one of the diVerences were in the predicted direction (in one case no diVerence in rank order was obtained) none of them even approached signiWcance (the pvalues being 0.44 or higher). In view of these results it was decided to explore further the two factors, terminality and JustiWcation, with much larger numbers of subjects. Because of the large amount of labor involved in coding data obtained in Reconstruction and Expansion tasks, it seemed advisable to use a diVerent task in the experiments presently to be reported on.
Expressed arguments 203
3.
Experimental studies of précis writing
It is commonly observed that in taking notes — say, at a lecture — one abbreviates the heard argument. Later, when the person who took them, or someone else, reads these notes, she bridges the operations that have been omitted. There are hardly any empirical studies of what gets omitted in such précis writing.11 In the following we report on some preliminary research addressed at this question. The hypotheses tested in these studies parallel two of those formulated for the reconstruction and expansion task studies reported earlier on, and in addition include a hypothesis regarding load (Section 1.3, above): 1. In abbreviating a text, terminal operations tend to be deleted more frequently than transmitters; and 2. JustiWcations (including all operations in an articulation or a warrant) tend to be deleted more frequently than other operations. 3. The greater the load of an operation, the less likely it is to be deleted. In this study subjects were presented with a text and instructed to abbreviate it, as in summarizing a lecture, so as to enable someone else to reconstruct the abbreviated text subsequently. 3.1
Deletion study
Parts of the two Hebrew texts used in the previous study served in the present one: two arguments from the Admission text and four of the Medicine text (see Section 2.1). The analyses of these arguments are given in Appendix B. Each text was divided into units, which were separated by asterisks.12 Each unit was a batch, in the sense of the term deWned in Chapter 9, Section 1.4. Two or more operations in a conXation or in a compound belong to the same batch, as do an operation and its collateral operation (a rule-of-thumb: operations that in the analysis are written in the same line belong to the same batch, and so do the two operations in an implication, which for convenience, appear in two lines). A batch is regarded as terminal if none of the operations in it is targeted; otherwise it is regarded as a transmitter. The numbers of batches in each of the four categories, +T +J, +T –J, –T +J, and –T –J, are given in Table 10.8. Two parallel forms were prepared, diVering in the sequence in which the two texts were presented (Admission – Medicine or Medicine – Admission).
204 The Structure of Arguments
Table 10.8 Number of batches in each category – Deletion study Admission +T –T Total
+J 2 3 5
–J 3 9 12
Medicine Total 5 12 17
+T –T Total
+J 3 4 7
–J 1 9 10
Total 4 13 17
Instructions Subjects were instructed to abbreviate the text so that it would be possible for someone else to recover its content subsequently. This was to be done by deleting units (a unit being a stretch of text between two asterisks), with the provision that (a) only whole units, and not parts of units, be deleted, and (b) where necessary, connecting words or phrases, like “and”, “but”, “because”, and so on could be added to or deleted from any unit, so as to ensure continuity of the remaining text. The latter provision was made so that subjects would not refrain from deleting a unit because of any lack of such a phrase or because of a “dangling” phrase after a deleted unit. Subjects Subjects in this study were 77 students at the Hebrew University, who participated either in partial fulWllment of their course requirement or for a small remuneration. They were tested on an individual basis. About half the subjects were given each of the two parallel forms. Results Terminality and JustiWcation. The results are represented as probabilities of not deleting a batch of a given category, so that the numbers are comparable to those in the previous experiment. The probabilities of not deleting batches of each category, +T +J, +T –J, -T +J, and –T –J, are given in Table 10.10 for each of the two texts (probabilities being computed as in the two previous studies). As in the previous study, for each subject, the number of operations of a given category that he or she mentioned was divided by the total number of operations in that category; then the mean of probabilities over subjects was computed.
Expressed arguments 205
Table 10.9 Probability of not deleting a batch – Deletion study Admission +T -T Total
+J 0.461 0.615 0.553
–J 0.602 0.771 0.728
Medicine Total 0.545 0.732 0.677
+T -T Total
+J 0.394 0.841 0.649
–J 0.377 0.831 0.786
Total 0.390 0.834 0.730
The table shows that the eVects of terminality and of JustiWcation were in the predicted direction in both texts. The signiWcance of diVerences was assessed by t-tests. In neither one of the texts was the interaction between the two factors (terminality and JustiWcation) signiWcant (see note 10 on testing the signiWcance of interactions.) The diVerences due to terminality and to JustiWcation were all highly signiWcant: The diVerences between the probabilities of +T and -T were t= –7.37, p<0.001, for the Admission text, and t= –12.66, p<0.001 for the Medicine text. The diVerences between the probabilities of +J and –J were t= -6.09, p<0.001 for the Admission text, and t= -5.32, p<0.001 for the Medicine text.13 Load. The data were also analyzed for the eVect of load on omissions — deleting batches, in this case. Correlations were computed between load of batch and the proportion of subjects who mentioned this batch (that is, the number of subjects who did not delete it). Pearson correlation coeYcients were positive but low, and failed to reach signiWcance: 0.326 for the Admission text and 0.160 for the Medicine text.14 Since the correlations were computed for only 17 batches in each of the texts, much higher coeYcients would have been required to obtain signiWcant correlations. (The correlation coeYcient for the two texts combined, 0.228, was also not signiWcant.) We therefore performed an additional analysis: for each of the subjects we computed the correlation between load and omissions. For the Admission text, the correlation coeYcients of 59 of the 77 subjects were positive and those of only 18 subjects negative. For the Medicine text, positive coeYcients were obtained for 51 of 76 subjects (one subject did not delete any batch and was therefore not included in the analysis) and negative ones for only 25. These diVerences were highly signiWcant by a t-test — t=6.412, p<0.001 for the Admission text and t= 3.160, p<0.002 for the Medicine text — and can thus be generalized to a population of subjects (but not of batches). However, the
206 The Structure of Arguments
coeYcients were mostly very low. Load, as deWned in Section 1.3, above, and terminality are of course not entirely independent measures. By deWnition, a transmitter is targeted, whereas a terminal is not. In fact, the Pearson correlations between these two variables were 0.35 for the Admission text and 0.44 for the Medicine text. The question therefore arises whether load has any eVect beyond that of terminality. In view of the small number of batches, it seemed unadvised to compute partial correlations, but the following table shows that when terminality is held constant, load seems to have little or no eVect. In the table, the 17 batches in each of the two texts are classiWed according to load (from 1 to 6) and terminality; some of the cells represent more than one batch, and in each cell the mean proportion of subjects that did not delete the batch is given. Table 10.10 Mean proportion of subjects not deleting a batch – Deletion study Load 1 2 3 4 5 6
3.2
Admission Terminals Transmitters 0.56 0.52 0.62 -------
--0.72 0.73 0.57 --0.96
Medicine Terminals Transmitters 0.37 0.42 ---------
0.94 0.94 0.76 0.76 0.78 0.82
Highlighting study
A replication of the previous study was conducted by Gazit Kahana with diVerent experimental materials and a diVerent technique.15 The text for this study was taken from an article on archeology. Instead of deleting parts of the text, as in the previous study, subjects were instructed to highlight with a color marker those parts of the text that would enable them to understand it when rehearsing the text. The text was not divided into units (unlike that in the previous study); and there was no constraint on the size of the stretches of text subjects could highlight. Unlike the analyses of the deletion study, those of the present study were therefore performed on operations, rather than on batches. The number of operations in each category are given in Table 10.11.
Expressed arguments 207
Table 10.11 Number of operations in each category – Highlighting study +T –T Total
+J
–J
Total
7 -7
14 10 24
21 10 31
The subjects were 37 students who volunteered for this study. To ensure some familiarity with the kind of subject matter of the text, participation was limited to students of archeology, geography or history. They were tested on an individual basis. The results are given in Table 10.12. In this particular text there were no –T +J operations. To ensure that the obtained diVerences were not due to an interaction between the two factors, terminality and JustiWcation, signiWcances were tested with one factor held constant. Thus, to assess the eVect of terminality, the proportion of highlighted +T –J operations was compared with that of –T –J operations (i.e., the right-hand column of Table 10.12); the diVerence was in the predicted direction with t=7.22, p< 0.001. Likewise, a highly signiWcant eVect of JustiWcations was found: comparing the proportions of highlighted +T +J and +T –J operations (i.e., the Wrst row) yielded t=3.68, p<0.001. Table 10.12 Probability of highlighting a batch +T –T
+J
–J
0.185 ---
0.278 0.527
In making a précis of a text, it is common practice to highlight parts of the text, rather than delete parts of it. But are there any systematic diVerences between the highlighting and the deletion tasks? To answer this question, Gazit Kahana carried out a replication of the preceding study with the same text with 25 students of archeology, geography or history at the Hebrew University, and using the deletion technique described in Section 3.1. But unlike the materials used in that study, the text was not divided into sections by asterisks, and the units of analysis were therefore operations rather than batches. It was found that there was more than twice as much undeleted material in the replication study than highlighted material in the highlighting study and this diVerence was highly signiWcant (subjects apparently tend to be “conservative”, being a bit reluctant either to delete or to highlight). Apart from this, the same pattern of results was obtained, and the diVerences were in the expected direction.
208 The Structure of Arguments
Those for terminality were statistically signiWcant, but those for JustiWcations were not. 3.3
Terminality and JustiWcations reconsidered
A consistent eVect of terminality was obtained in all the studies reported here. In the pilot study, subjects were asked to recall a text or to expand a reconstructed text (Section 2). For each of the two experimental texts, the signiWcance level of the diVerence between terminal operations and transmitters was 0.0625 (Wilcoxon test) — as high a level as could have possibly been attained with the small number of subjects who participated. In the Deletion study (Section 3.1), which was carried out with a much larger sample, a highly signiWcant diVerence was obtained for each of the texts. Likewise, in the Highlighting study (Section 3.2), in which a diVerent experimental text was deployed, a highly signiWcant diVerence was obtained. The eVect of JustiWcation was also highly signiWcant in both the Deletion and the Highlighting studies, but failed to reach signiWcance in a replication of the latter (Section 3.2). In the pilot study with the Reconstruction and Expansion tasks, no signiWcant diVerences between JustiWcations and other operations were obtained. It seems to us, in retrospect, that a distinction ought to be made between JustiWcations that include several operations and those that are warrants constituted of a single operation each (as were all JustiWcations in the highlighting study). It may well turn out that JustiWcations that include several operations tend to be more central in the argument than single-operation warrants.
4.
Targeting the expressed argument
In this Wnal section, operations will be discussed that target the expressed argument, or parts of it, rather than parts of the underlying structure. A notational convention is introduced for such operations, and some minor revisions in our system are proposed. 4.1 The nature of Interpretations In everyday parlance, the word “interpretation” is used in a variety of ways. One “interprets” Xuctuations on the stock market as reXecting, say, expecta-
Expressed arguments 209
tions of wage increases, an X-ray picture as indicating a tumor, a shifting glance as reXecting insincerity, and so on. In our system these would be analyzed in terms of Accounting, Result, and compound ‘if___ then ___’ operations; the term ‘Interpretation’ is not used for the explanation of such non-verbal phenomena. Instead, ‘Interpretation’ serves as a technical term in a sense that is close to what was presumably the original one of this word, namely, the translation and elucidation of texts. An Interpretation, roughly speaking, aims at rendering a text in diVerent (presumably easier to understand or less ambiguous) words, according to the intention of its author, without “adding” anything to it. Observe now that this conception of Interpretation as aimed at a text has an important implication for its formalization, one that we have not paid attention to in our preceding discussions: an Interpretations targets the expressed argument, not its underlying structure. Further on we will see how this can be taken into account by our notation. Unlike Interpretations, most other operations typically target the underlying structure, or parts of it; exceptions will be discussed in Sections 4.4–4.5, below. Some Interpretations are implicit, that is, one can infer from the author’s words how he understands a previously occurring text, without the author having verbalized his Interpretation of this text. But often an Interpretation is explicit, that is, it is verbalized. The act of interpreting a text may take various forms, which are all categorized as Interpretations in our system. Thus, an author may explain an obscurely phrased sentence occurring in a previous argument, or a word or phrase in such a sentence, or he may translate a sentence, phrase or word that appeared in a foreign language. Again, an Interpretation may also furnish a “deeper” (perhaps metaphorical) meaning of the text; for instance, an author may say that the line by Yeats, “Things fall apart, the centre does not hold”, refers to the social and political deterioration of his time. Each of these is an explicit Interpretation, and as stated, it targets the expressed argument and provides a sort of verbal description of its meaning. Note now that this is exactly what the analyst does when she formalizes an argument. Every formalization is based on an interpretation of the argument: it takes the expressed argument as input and outputs an underlying structure that accords with the presumed intention of the author. But this is a sort of ‘meta-interpretation’, which is not itself part of the argument. The analyst does not function as a participant in the discussion, and therefore her interpretation does not appear in the formalization as a separate operation.
210 The Structure of Arguments
Not only the analyst, but every participant in a discussion imposes an interpretation on other participants’ arguments that she relates to; she construes it implicitly. In other words, she takes an expressed argument as input, and outputs an underlying structure, which she then relates to. In most cases this interpretation is an implicit one: when referring to a previous argument, the participant does not state explicitly “by this she means ….”. Normally, such an implicit interpretation of a previous expressed argument will be similar to the analyst’s interpretation of that argument. This is why in all our analyses so far there is no formalization of the implicit interpretation applied by an author to a preceding argument: including an Interpretation operation would result in an unnecessary repetition of the formalization of the preceding argument provided by the analyst and would clutter up the formalization. However, whenever the analyst discerns the occurrence of a misunderstanding, he must include in the formalization an Interpretation operation showing how the author has construed the preceding argument (incorrectly). Examples of this will be given further on. To summarize, implicit Interpretations have to be formalized only when they are incorrect, that is, when they do not correspond to what the analyst holds to be the intended meaning. Explicit Interpretations, by contrast, must always be formalized, whether they are correct (according to the analyst) or not. These principles will be illustrated in Section 4.3. Further on, a notation will be introduced for operations (Interpretations or others) that target expressed arguments or parts of them: the target will be indicated by line number(s) in square brackets. The usefulness for this notational convention will become apparent in the analyses in the next subsection. 4.2
Misunderstandings
Let us start with a concrete example. Suppose Carol says to Donald: – Why don’t you come and see me sometimes?
There may be two ways to construe Carol’s meaning: (i) as an invitation, and (ii) as a complaint. Suppose now that the analyst has reason to believe that she intended (ii) and that Donald imposes an implicit Interpretation on Carol’s argument according to which she meant (i). This is a misunderstanding, and the fact that it has occurred must be reXected in the formalization of Donald’s argument. What makes the analyst decide that a misunderstanding has oc-
Expressed arguments
curred? As pointed out by Heritage (1984: 255–259), when a participant has been misunderstood, this will usually become evident from her subsequent response. This may be illustrated by a dialogue (adapted from Heritage): Carol: Donald: Carol:
Why don’t you come and see me sometimes? I would like to. Yes, but why don’t you?
Carol’s rejoinder makes it clear that she had been complaining. Her argument was 1. P(p) 2. Q(p1) 3. ?A (p1)
p q ?A
You have not visited me. This is blameworthy. What made you behave like this?
Donald, however, implicitly interprets her argument as meaning DO ∧P(p)
dO ∧p
You should come and visit me.
The latter statement will be formalized as the collateral operation of an Interpretation. Consider now what is the target of this Interpretation. To write I(p1 & q2 & ?A3) would be misleading: p, q, and ?A represent what Donald fails to understand; he does not refer to a Presentation- Evaluation-Question argument, because this is not how he understood Carol’s argument. We therefore introduce the convention that when an expressed argument or part of it is targeted, it will be symbolized by the relevant line numbers in square brackets, as shown in Line 4: Example 1 Carol 1. P(p) 2. Q(p1) 3. ?A (p1) Donald 4. I[1–3]
5. P(p)
p q ?A iP: DO ∧P(p) iI
You have not visited me. This is blameworthy. What made you behave like this?
You should come and visit me This is what “Why don’t you come and see me sometimes” means. p I accept this invitation. Rsp {p, [1–3] }
211
212 The Structure of Arguments
Carol 6. T– (iI4)
t–
7. ?A (p1)
?A
It is false that this is what “Why don’t you come and see me sometimes” means. What made you behave like this?
Explanations: Line 5, Rsp{p, [1–3] }: Donald’s accepting Carol’s (presumed) invitation is a Response (a connection symbolized Rsp; see Chapter 8, Section 3). If this would have been a Response to what Carol really had intended (that is, to the underlying structure of Lines 1–3), one would have to write here Rsp {p, p1 & q2 & ?A3}. As it is, his Response is to the expressed argument (on Donald’s erroneous Interpretation), that is, to [1–3]. Line 6: Carol does not relate to iP in Line 4 (the content of Donald’s Interpretation); instead, she argues that this is not what “Why don’t you come and see me sometimes?” means, i.e., that iI is false. Line 7: Carol’s rejoinder not only points out that there has been a misunderstanding but repeats the demand for an appropriate response to her complaint: “… but why don’t you?”. Arguably, Carol’s underlying structure includes also: ‘Your answer is not relevant to my question’. This would be symbolized as a Status operation (Chapter 3, Section 1.1, sub Adjudgments).
Suppose now that on another occasion Carol asked the same question, but with a diVerent intention, and her rejoinder makes it clear that she has, again, been misunderstood: Carol: Ernie: Carol:
Why don’t you come and see me sometimes? I have been terribly busy for a long time now. No. I wasn’t complaining, I just want you to visit me.
Here the roles are reversed, in a way: Carol’s rejoinder makes it clear that she had extended an invitation (as Donald, in the preceding example, thought she did), whereas Ernie’s excuse shows that he thinks she is complaining (as Carol actually did in the preceding example). In the analysis, Ernie’s Interpretation comprises three suboperations, and for these we use the notation adopted for articulations and for the suboperations of Accounting (Chapter 5, Sections 2.3 and 5.2).
Expressed arguments 213
Example 2 Carol 1. DO ∧P(p) Ernie 2. I [1] | 3. P(p) | 4. Q(p3) | 5. ?A (p3)
6.
A(p3)
7. E(a6) Carol 8. T– (iI2) 9. DO ∧P(p)
dO ∧p
Please come and visit me.
iP p q ?A
You have not visited me. This is blameworthy. What made you behave like this? iI This is what “Why don’t you come and see me sometimes?” means. aP I have been terribly busy for a long time now. A a This is the reason for my not visiting you. Rsp{a, [1] } e: T– (q4 ) 〈Therefore〉 it is not true that my behavior was blameworthy. t– dO ∧p
It is false that this is what Line 1 means. Please come and visit me.
Explanations: Line 6: In our system, excuses like this are analyzed as Accounting, see Chapter 5, Section 1.2 Rsp {a, [1] }: See the explanation to Example 1, Line 5, above. Line 8: On the target iI2 see Explanation to Line 6 in Example 1. Line 9: Carol repeats the request. While she used word that diVer from those in Line 1, the underlying structure is the same.
The misunderstandings in the preceding examples involved substituting a type of operation that diVered from the intended one: in Example 1, DO ∧P(p) was the Interpretation of the expression corresponding to operations P, Q, and ?A (and conversely for Example 2). In other instances, a participant’s Interpretation may assign types of operations that are identical to those in the analyst’s formalization of that argument, and the locus of the misunderstanding is in the verbal description of these operations. Consider this dialogue: Arthur: When he heard this story, he died of laughter. Barbara: O, how sad!
Assuming that Barbara was not being sarcastic, this may be analyzed as:
214 The Structure of Arguments
Example 3 Arthur 1. P(p)
p
When he heard this story, he laughed immoderately.
iP
When he heard this story, he laughed so much that he died. This is what “When he heard this story, he died of laughter” means. This is sad.
Barbara 2. I[1]
iI 3. Q(iP2)
q
Here the misunderstanding becomes manifest only in the verbal descriptions; both Arthur’s argument and Barbara’s construal of it, iP, are Presentations (we might have written here iP: P(p), but this would have been superXuous; see Chapter 5, Section 2.2). To conclude, misunderstanding is not a separate category in our formal system. Rather, a misunderstanding is reXected in the formalization as a discrepancy between the analysis of an argument and its Interpretation by a participant in the discussion. DiVerent degrees of misunderstanding — and misunderstandings, after all, admit of degrees (Dascal, 1999) — will be reXected by diVerent degrees of discrepancy. The notation adopted in the foregoing for the targets of incorrect Interpretations will also be used for those of correct ones, as shown in the following. 4.3
Implicit and explicit Interpretations
In the previous subsection, we discussed examples of implicit Interpretations, i.e., those that are not stated explicitly by their authors and have to be inferred from what they did state. An Interpretation may also be explicit, as in Example 4: Example 4 Author 1 1. P(p) p
He committed a terrible faux pas.
Author 2 2. I[1] iP iI
He made a big blunder. This is what “he committed a terrible faux pas” means.
Expressed arguments 215
Observe now that the explicit-implicit distinction has implications for the analysis: Implicit Interpretations are included in the analysis only if, as in Examples 1–3, they are incorrect (according to the analyst’s understanding of the interpreted argument). As stated, (Section 4.1), when the author’s implicit Interpretation of a preceding argument is correct, it is identical to the way the analyst understood and formalized it, and its inclusion in the analysis would be a useless repetition. To illustrate, take Dialogue I (a slight modiWcation of an example analyzed in the preceding chapter, Section 4.1): Dialogue I. – I didn’t prepare for all the questions. – Just because you didn’t prepare for all the questions is no reason not to take the exam.
The author of the counterargument assumes — without saying so explicitly — that the Wrst author intends not to take the exam. Suppose now that this implicit Interpretation is correct, that is, it is identical to the analyst’s construal of the Wrst argument. Then the formalization of the counterargument will not include any Interpretation: Example 5 Author 1 1. P(p) p 2. A(p1) aP aA Author 2 3. Q(aA 3) q
I am not going to take this exam. I didn’t prepare for all the questions. This is the reason for my not taking the exam. This is not a good reason for not taking the exam.
Unlike an implicit Interpretation, an explicit one will be formalized whether it is correct or not, by the analyst’s lights. What has been said explicitly cannot just be discarded in the analysis. Take Dialogue II. Dialogue II. – I didn’t prepare for all the questions. – You mean you are therefore not going to take the exam. Just because you didn’t prepare for all the questions is not a good reason for that.
Author 1’s argument will be formalized as in the preceding example, but the formalization of the counterargument will now contain a correct Interpreta-
216 The Structure of Arguments
tion, that is, one that is identical to the analyst’s construal: Example 6 Author 1 1. P(p) p aP 2. A(p1) aA Author 2 3. I [1–2] iP | 4. P(p) | 5. A(p4) | iI 6. Q(aA 5)
I am not going to take this exam. I didn’t prepare for all the questions. This is the reason for my not taking the exam.
p aP aA
q
I am not going to take this exam. I didn’t prepare for all the questions. This is the reason for my not taking the exam. This is what “I didn’t prepare for all the questions” means. This is not a good reason for not taking the exam.
Explanation: Line 3: Author 2 interprets the words “I didn’t prepare for all the questions” (Line 1), but the analysis of these words appears in both Line 1 and Line 2.
Turning to incorrect explicit Interpretations, suppose that the analyst, for some reason or other, holds that the Wrst speaker in Dialogue II merely stated a fact, without intending to imply that she is not going to take the exam. Then it is Author 2 — not the analyst — who (incorrectly) interprets “I didn’t prepare for all the questions” as in Lines 1–2 of the preceding example: Example 7 Author 1 1. P(p) p Author 2 2. I [1 ] iP | 3. P(p) | 4. A(p3) | iI 5. Q(aA 4)
q
I didn’t prepare for all the questions.
p aP aA
I am not going to take this exam. I didn’t prepare for all the questions. This is the reason for my not taking the exam. This is what “I didn’t prepare for all the questions” means. This is not a good reason for not taking the exam.
The following table summarizes the four possibilities considered.16
Expressed arguments 217
Table 10.13 Explicit and implicit, correct and incorrect Interpretations correct
incorrect
Explicit
formalized (as in Example 6)
formalized (as in Example 7)
Implicit
not formalized (as in Example 5)
formalized (as in Examples 1–3)
Occasionally, the analyst does not commit herself to an Interpretation’s being correct (or incorrect). Such an Interpretation will have to be formalized even when it is implicit, as will be illustrated in the following subsection, Example 11. 4.4
Designations targeting expressed arguments
The distinction introduced in the foregoing between targeting underlying structures and targeting expressed arguments has been introduced to deal with Interpretations. It will be useful also in the case of other types of operations. Designations will be dealt with Wrst. Compare these two sentences: Oliver Goldsmith wrote: “The true use of speech is not so much to express our thoughts as to conceal them”. My neighbor says that the true use of speech is not so much to express our thoughts as to conceal them.
Oliver Goldsmith is credited with writing certain words; my neighbor is only said to have expressed the same idea, and there is no commitment as to the exact wording she used. The distinction here corresponds to that between direct and indirect speech. An author Designation, then, may target either the expressed argument, as when the aphorism is said to have been enunciated verbatim by Goldsmith,17 or the underlying structure of this quote, as when my neighbor is said to ascribe to this view. When the target is the expressed argument, it will be put in square brackets, like the target of an Interpretation (Author 2 in Example 8 and Author 1 in Example 9), whereas when the underlying structure is targeted, we deploy the usual parentheses (Author 3 in Example 8 and Author 2 in Example 9).
218 The Structure of Arguments
Example 8 Author 1 1. P(p) p Author 2 2. DA [1] dA Author 3 dA 3. DA (p1)
The true use of speech is not so much to express our thoughts as to conceal them. Oliver Goldsmith wrote these words. My neighbor also claims that p1 . Sim {dA , dA2 }
Explanation: Line 3: There is a Similarity connection (Chapter 8, Section 4) between this outcome and that in the previous argument.
Suppose now that instead of stating who is the author of a previously mentioned text, as in this example, one quotes Oliver Goldsmith as having written this aphorism. This would involve a conXation of DA and P. An additional convention is required here: the target of P (which, it will be recalled from Chapter 2, Section 1, is not a “real” target) will be enclosed in square brackets to indicate that the verbal expression of the Presentation is referred to; see the following example. Example 9 Author 1 1. DA ∧ P[p] dA ∧ p
Author 2 2. DA (p1) dA
Oliver Goldsmith wrote: “The true use of speech is not so much to express our thoughts as to conceal them”.
My neighbor also claims that p1 . Sim {dA , dA ∧ p1 }
Unlike Line 1 in this example, the Presentation in Example 8 is P(p), with p in parentheses, not square brackets, because the sentence “The true use of speech…” is not presented as a verbatim quote. If Author 1 of Example 8 had indicated somehow that it was a word for word quote, without disclosing its source, this would have been a Designation of an indeWnite author: DI ∧P[p]. Normally, an analysis imposes an interpretation on the expressed argument (see Section 4.1, above). There are cases, however, where the analyst will decide on a verbal description that is uncommitted to any Interpretation. This
Expressed arguments 219
is illustrated by the following example. Example 10 Author 1 1. P(p) p
Things are going from bad to worse.
Author 2 (to Author 3) ?I What does he mean? 2. ?I [1] Author 3 3. I[1] iP iI
His stocks are falling on the market. This is what “Things are going from bad to worse” means. Rsp {i, ?I2 }
Explanations: Line 1: The analyst does not commit herself to any speciWc Interpretation of Author 1’s gloomy comment, and there is no way of telling whether she considers Author 3’s Interpretation in Line 3 to be correct or not. See also Example 4. Line 2: But when the Interpretation Question pertains to a sentence that has not been mentioned previously (“What does `Things are going from bad to worse’ mean?”), it is formalized as a conXation: ?I ∧ P[p] ; see Chapter 7, Example 11. Such a conXation is inappropriate, however, when the Question is about the meaning of a phrase or a word, because P[p] refers to a whole proposition. Instead, one will then have to introduce a backdrop (Chapter 7, Section 2), in which the phrase or word Wgures as a constituent, and the Question targets this constituent.
In general, when an Author gives a verbatim report of what someone else said or wrote, the analyst, too, will have to present this quote verbatim without paraphrasing it; the formalization will then be: DA ∧P[p] dA ∧ p — with square brackets. Consider now an Inference made from such a verbatim report: – Yeats wrote: “Things fall apart, the centre does not hold” – This shows that Yeats was pessimistic about the political fate of the Western world.
To infer something from the quote, the second author has to impose an (implicit) Interpretation on it. The analyst, by contrast, does not commit
220 The Structure of Arguments
herself to any speciWc Interpretation of “Things fall apart…”. Unlike correct implicit Interpretation (Section 4.3, above), the second author’s Interpretation must be formalized, because it is not redundant: Example 11 Author 1 1. DA ∧ P[p]
dA ∧p
Yeats wrote: “Things fall apart, the centre does not hold”
Author 2 2. I[1p]
iP
Our time is marked by the political deterioration of the Western world. This is what “Things fall apart, the centre does not hold” means. 〈 One may infer from the fact that Yeats wrote this that 〉 Yeats was pessimistic about the political fate of the Western world.
iI 3. E(dA ∧p1 & i2)
e
Explanations: Line 2: The Interpretation does not pertain to the verbal expression formalized by the whole conXation in Line 1 (“Yeats wrote” is not being interpreted here), but only to the quote p. The target is therefore symbolized by [1p], that is, the p in the outcome dA ∧p of Line 1. When I targets a constituent element, the latter is also enclosed in square brackets; see Appendix B, Admission text, Lines 7–8. Line 3: Author 2’s Interpretation, i2, Wgures in the outcome, because the Inference he makes is from what he believes the poet to have intended, which is not necessarily what he actually intended.
4.5
Other operations targeting expressed arguments
There are other operations, besides Interpretations and Designations, that may target an expressed argument. Take Inferences. Usually, one infers something from a proposition contained in the underlying structure; the Inference made from the proposition does not depend on the way it is verbalized. However, there are instances where an Inference targets the expressed argument. One may infer something from the linguistic form in which an operation is expressed, as when one infers from someone’s choice of words that she is in a bad mood. This is not an Inference from the content of an outcome; neither is it an
Expressed arguments 221
Interpretation, because nothing she has said can be interpreted (in the sense in which ‘Interpretation’ is used in our system) as meaning “I am in a bad mood”; it is not what she said but how she said it that is inferred from. This, then, is an Eduction that targets the linguistic expression, not the underlying structure.18 Which other types of operations may target expressed argument, is an issue that awaits investigation. Examples that come to mind are Accounting, as when one gives a reason why an argument was expressed in a particular way, and Evaluation, as when one claims that the linguistic formulation of an argument is impressive, infelicitous, Status, as when one says something about the verbal form of the operation, etc. It seems that Truth value, Validation, and Confrontation can be ruled out in principle, because they pertain, by deWnition, to propositions, and not to the way these propositions are verbally formulated. 4.6
Some requisite revisions
The preceding discussion requires certain minor revisions of the deWnitions given in the previous chapter. First, the deWnition of ‘strongly related’ (Chapter 9, Section 1.2) must be expanded to include targeting an expressed argument or part of it. Accordingly, the operation in Line 3 of Example 6 is strongly related to the operations in Lines 1–2, and hence the two arguments are also strongly related. Second, Criterion (e) for strong relationships given in Chapter 9, Section 1.2, must be expanded to include the sub-operations of an Interpretation (like those in Lines 4–5 of Example 6). According to the revised criterion, a strong relation holds between two operations X and Y, if X is a Cause or Interpretation operation, and Y is one of its sub-operations. Third, consider the two operations in Donald’s argument in Example 1 (Lines 4–5). While these are related neither by a targeting relation nor a connection, the Interpretation in Line 4 is indispensable for p5, the Response to Carol’s question. It would therefore be counter- intuitive to regard these as two unrelated arguments. Now, since p5 is connected to the argument in Lines 1–3 (as a Response), and Line 4 is Donald’s Interpretation of these lines, it is reasonable to regard p5 as connected to this Interpretation. According to this reasoning, the operations in Lines 4–5 are weakly related, and this accords with our intuition that they form a single argument. This can be generalized as follows: If an argument contains an Interpretation of x, where x is contained in a previous argument, and also an operation that is related to x, then the latter
222 The Structure of Arguments
operation is weakly related to the Interpretation. A very similar case is that of the two operations in Carol’s rejoinder: Lines 6–7 in Example 1. While these do not appear to be related, they intuitively constitute a single argument. Here the foregoing generalization does not apply, however. It seems to us that between these two operations there is a certain connection, of a type that has not been dealt with in Chapter 8. The two operations would accordingly be weakly related, which implies that they belong to the same argument. Apparently there is a whole class of questions — not only in arguments involving Interpretations — that somehow bear on preceding operations, and perhaps all these belong to this type of connection. DeWning this type of connection remains a task for the future. Coda Our fundamental intellectual impulse is to search for diYculties — or even to invent diYculties in order to overcome them. - Karl Popper
Notes
Notes to Chapter 1 1. In our system, A represents a single argument. This follows from the formal deWnition of ‘argument’ given in Chapter 9, Section 1.3. 2. See also O’Keefe (1982) and Öhlschläger (1979: 22- 32). 3. While this construct should not be confused with that of underlying (or deep) structure in transformational grammar, there are obvious similarities between them. Both pertain to something that “leads to” the linguistic expression. Unlike their linguistic counterparts, however, our underlying structures are not “generated”, but must be constructed by the analyst on the basis of her interpretation of the argument. 4. Cf. Wittgenstein (1980b: 42): “Virtually, in the same way as there is a diVerence between deep and shallow sleep, there are thoughts which occur deep down and thoughts which bustle about the surface.” See also Pollock (1998: 118–120) on “quick and inXexible” processes. 5. Analyses by other authors (e.g., van Eemeren et al., 1993) are also based on rational reconstructions, albeit of a diVerent nature. 6. Sue’s assertion and Ted’s reply are regarded in our system as arguments, although none of them comprises any proposition supporting its conclusion; cf. Introduction, Section 1. 7. Not all presuppositions of a statement can be included in the analysis. Here, as ever so often, the analyst will have to exercise his judgment in deciding what to include. 8. In discussing implicit assumptions, Ennis (1982) makes the (conceptually important) distinction between those that are “needed” — that is, those that have to be true for the argument to be “as good as can be” — and those that are “used” in the thinking of the person who formulates the argument. Our analyses may include both needed and used assumptions, and we suggest that there can be no hard-and-fast guidelines as to which of these two kinds takes precedence over the other in a given analysis. Ennis proposes criteria for identifying used assumptions and for identifying needed ones, but his treatment shows that how these criteria are to be applied will depend in each case on the analyst, the information available to him, and his informed guesses. 9. The common practice of diagramming an argument as premises leading to conclusions is neutral in respect to progressivity or regressivity of the argument (see, e.g., Freeman,
224 The Structure of Arguments
1991). In this respect, our approach aspires to a more psychologically real description. 10. The version of the WhorWan hypothesis proposed by Slobin (1996: 76) claims that “the activity of thinking takes on a particular quality when it is employed in the activity of speaking. … one Wts one’s thoughts into available linguistic frames.”. It seems plausible that there is a phase that precedes the one of “thinking for speaking”.
Notes to Chapter 2 1. And also to the “speaker” of Sign Language or of gesture language. The term “author” is preferable to “participant”, because the latter implies actual presence or participation, whereas it may be a text of an absent person that is being discussed. Authors will henceforward be referred to by “he”, irrespective of gender. 2. The term ‘argument’ has been used in various ways (see O’Keefe 1982). Among others, the word is often used for a verbal altercation (“we had an argument about …”). In this book, the term will not be used for a debate or discussion as a whole, but rather for a single turn in the discussion. A formal deWnition of argument will be given (in the terms of our analytic system) on Chapter 9, Section 1. 3. Although the symbol for the outcome is completely determined by that for the operation, it has to be included, as will become clear in Chapter 3, Section 3. 4. At Wrst blush, one might write T–(q3 ): Author 2 refutes the outcome in Line 3. But this is inappropriate: what Author 1 says in Line 3 is that ‘his attendance at this party is reprehensible’, not just that he did something reprehensible. Once Author 2 establishes that there was no such attendance, the former claim becomes meaningless (like “The present king of France is bald”), not false. This is an example of the Wne logical points that frequently have to be considered in an analysis; in fact, performing such analyses may serve to hone one’s logical discrimination. 5. Considerations of normativeness, however, enter into the reconstruction of the underlying structure; see Chapter 1, Section 1.2. While no distinction is made between ‘bad’ and ‘good’ arguments, the formalizations themselves are of course subject to rules (i.e., they may be well-formed or not). 6. This symbolization is possible only if x is the outcome of a previous operation, X; otherwise the notation will be somewhat diVerent; see Chapter 6, Section 1. 7. In some systems, though, such a distinction is made (cf. Lyons (1977, vol. 2: 768). But within our system they will be treated as notational variants. As will be shown in the following chapter (Section 3.1), our system also provides for marking diVerent probabilities of propositions, Truth values, and other operations.
Notes 225
Notes to Chapter 3 1. What we are dealing with in this chapter are types of operations and of operators, rather than speciWc operations and operators appearing in diverse arguments (tokens). Occasionally, we will refer to these types by the terms “operations” and “operators”, tout court. 2. In Chapter 10, Section 4.2 we introduce a slightly diVerent convention for the target of an Interpretation. A more precise analysis of the Hamlet quote would be with an Evaluation operator (see below, Class 7). This requires a notational convention that will be introduced in Chapter 6. 3. We adopt the term ‘Accounting’ rather than ‘Explanation’, because the latter term might be easily misconstrued. Causal statements have to be distinguished from conditionals, like “if you go one step further, I’ll shoot”, are analyzed with an “if___ then___” functor (Chapter 4, Section 1). Sometimes such a statement is based on a causal relation (e.g., “if you touch it, you’ll get burned”), but this may be disregarded in the analysis, unless the analyst considers that the speaker to intended to communicate that there is such a causal link. 4. We use superscripts to subcategorize operations. These diVer from the superscripts to the Truth value operator, + and –, which do not subcategorize, but indicate values of the outcome (the outcome of T–(x) states that x is not true). 5. “I assert that…” will not be analyzed as DP (it is regarded as the default value, so to speak). “I believe that …” may mean more or less the same as “I assert that…”, and then it will not be symbolized by DP. But when “I believe that…” signals a lower degree of certainty, it will be formalized by a degree-of-conWdence superscript (Section 1.3 of this chapter) like statements qualiWed by “presumably”, “probably”, “almost certainly”, and the like. In some instances one may resort to the Formalization principle (Chapter 2, Section 2.2) and analyze a statement about hoping, fearing, etc. without DP , disregarding the propositional attitude altogether (provided, of course, that the latter does not have to be targeted subsequently). Take, for instance, the statement “Macbeth feared that Banquo’s son might become king”, and suppose it is later targeted only in its entirety. This may then be regarded as a single assertative statement concerning Macbeth’s state of mind. 6. Clarke (1985) deals with “intend” and “plan” as “projectives” and shows that they exhibit a special logic. 7. Imperative sentences that are tangential to a given discussion (“Listen to me”; “It is stuVy in here; open the window, please”) will not be analyzed as operations, unless they are subsequently targeted (“The fact that you said so shows that …” ); cf. Chapter 9, Section 1.2. 8. An author may give examples without making a general statement; e.g., “I would like to buy something like a or b”. The analyst will then either construe an appropriate general statement, or analyze this as a disjunction (see next chapter on the notation for disjunctions), i.e., “I would like to buy a, or I would like to buy b, or I would like to buy something that is similar to a and b” (where the fact that there is some similarity will be indicated by a Comparison). The choice between these two possibilities parallels that between an analogy that is analyzed via a Generalization and one that is not; see discussion under Class 5, above.
226 The Structure of Arguments
When an example serves to explain a preceding general term it may be analyzed as an Interpretation. 9. To specify more precisely the degree of conWdence — e.g., to distinguish between “it is very likely that” and “there is a slim chance that” (or between probably and certainly) — additional superscripts may be appended to % . The degree-of-conWdence concept largely parallels QualiWcation in Toulmin’s (1958) system. There are operations that have a degree-ofconWdence marker in their outcome, and the latter Wgures in a subsequent target without %: %X(…) %x .....
.....
Y (x)
y
See, for instance, Chapter 9, Example 1, Line 25. 10. Of course, “a contains a contradiction between … and …” does make sense, but this will have to be formalized by a Confrontation, the terms of which are parts of this a. That an operation inherently requires more than one term means that it is multiplex. Some types of operations may be based on more than one statement — e.g., some Inferences are made from two premises — and then their targets are not multiplex but compound (Chapter 4), that is, they involve conjunctions; see examples in Chapter 5, Section 1.3. 11. This is an Eduction — an Inference made by the author from x — not a Result operation, which is a claim that something occurs as a consequence of x. This distinction is discussed at length in Chapter 5, Section 1.3. 12. Certain more complex Result and Accounting operations do not have such bipartite outcomes, as will be seen in Chapter 5, Section 5.2. 13. The claim that there are insuYcient grounds for giving a reason should be distinguished from the claim that the reason given is not a good (suYcient) one. What has been said here about the author’s commitments does not imply, of course, anything about his intentions. An interesting treatment of the distinction between commitments and intentions can be found in Hamblin (1987: 240f). 14. A special type of collateral operation will be discussed in Chapter 9, Section 2.4.
Notes to Chapter 4 1. Negation, which is a connective in logic, does not serve to compound two expressions, and hence it is not a functor, in our sense, but an operation: T–. As such, it is part of a continuum that extends from T+, through various degrees of probability, to T– (cf. Chapter 3, Section 1.3). 2. Some philosophers of logic therefore oppose the truth-functional account of conditionals (Read 1995; see also Kienpointer 1992: 57–64). On the relationship between logic and argumentation see Toulmin (1958) and Vorobej (1995b: 28V). 3. If we were to write the implication in a single line, the two Presentations in our example would have to be distinguished by superscripts — e.g., if P1 (p) then P2 (p) — and these
Notes 227
would have to be retained in any subsequent target, e.g., V+ ( P11) or T– (p11) . 4. Various sentences that are phrased as conditionals have underlying structures that do not involve any implication. For instance, “If he cheats on her, that will be a terrible thing for him to do” only looks like an implication (cheating on her is a terrible thing to do, not only if he does it. This sentence may be analyzed as an Evaluation. 5. Fisher (1989: 412–413) says that “it has to be shown that [suppositions] can always be paraphrased out without loss“ in this manner, but he does not give any evidence that they cannot. What he does show is that such reduction would often be “very unnatural and cumbersome” and “awful to read” (p. 407). 6. This is illustrated by the following anecdote (quoted by Peter Geach 1976: 26): Teacher: “Suppose y is the number of eggs, …” Student: “But Sir, please, Sir, suppose y isn’t the number of eggs?” 7. Implications may also be enclosed in square brackets, e.g., X / [if Y then Z] (“Either you do the dishes now, or if guests come you have to take them out to eat.”). The implication (“if… then…”) will then have to be written in a single line. It is well-known that a disjunction can be reformulated as an implication and vice versa. It will be convenient, however, to retain both the functor “if___ then ___ ” and the functor for disjunction. 8. The single slash will be used also for operations regarding which the analyst (and perhaps even the author) is uncertain whether inclusive disjunction (the “and/or” of legal jargon) or exclusive disjunction (“either /or, but not both”) is intended. 9. In Example 12 it is not permissible to write P1 (p) & P2 (p) instead of Lines 1–2, because this would open the door to conjoining any two operations, and to prevent this, special elaborate rules would have to be introduced. Without such rules it would then be diYcult to give a formal deWnition of ‘argument’; see Chapter 9, Section 1. Unlike conjunctions, implications cannot be broken down into two operations. The antecedent of an implication (“if …”) is not asserted by itself, in fact it does not have any meaning by itself; only the compound in toto (“if … then …”) is asserted by the author. That the implication is written in two lines is only a matter of notational convenience. 10. Compound targets should be distinguished from the multiplex targets of Comparison (K), Confrontation (C), and Subsumption (U); see Chapter 3, Section 2.1. 11. Apart from this, the order of operations in Author 1’s argument is immaterial: if the relative order of P1 , P2 , and P3 (or of E4 and E5) would have been changed, this would still be a formalization of the same underlying structure (and the sequence exhibited in our example may have been adopted only because it mirrors the order of clauses in the expressed argument). 12. Similar to our distinction between dependent and independent eVects is that between linked and convergent arguments often made in the literature. The latter distinction has been shown to be problematic, and authors disagree in respect to the classiWcation of certain arguments (see, e.g., Freeman 1991: 9–14, Vorobej 1995a). A recent attempt at clariWcation has been made by Walton (1996), but see the critical review by Vorobej (1998). We therefore prefer to eschew the use of these terms and use less controversial ones instead.
228 The Structure of Arguments
This does not imply, however, that the boundary line between dependent and independent eVects is sharper than that between linked and convergent arguments. Vorobej (1995b) introduces the concept of subjective convergence in order to deal with problems raised in regard to the concept of objective convergence. Objective convergence is of interest in the context of argument validity, and since the present work limits itself to the description of arguments, without reference to questions of validity and acceptability, it is subjective convergence that concerns us. 13. Some arguments involve situations where the eVect of two factors is greater than that of each one taken by itself. Thus, heavy smoking reputedly increases the risk of heart disease and so does eating fat meats; and the risk incurred by both smoking and eating fat meat is greater than that incurred by only one of these vices. In cases like this, the analysis requires an additional Comparison (K) operation (Chapter 3, Section 1.1, sub Adjudgment). This operation has a multiplex target, comprising the eVect of smoking, the eVect of eating fat meat, and the eVect of doing both. These eVects may have to be introduced by additional Presentations, so that constituent elements of their outcome can Wgure in the target of K.
Notes to Chapter 5 1. In English, “why” may be used to inquire either about causes and motives or about the justiWcation for making a statement (cf. Hamblin 1987: 223). The same holds for the Hebrew question word “lama”. In German there are two words: “warum”, which is used primarily for reasons and motives, and “wieso”, which serves primarily for justiWcations (cf. Grimm 1960, s.v. warum and s.v. wieso). 2. JustiWcation and Accounting usually diVer in the conWdence one has in what is being justiWed or accounted for. When one gives a reason or motive for some event or state, one is typically more or less certain that this event or state occurred, whereas one often advances a JustiWcation for an operation without being quite certain about it. In principle, however, the degree of conWdence of an operation (Chapter 3, Section 1.3) is independent of the distinction between JustiWcation and Accounting: one can be quite certain of the claim one justiWes, and, conversely, one may be not quite certain whether the explained event or state of aVairs has indeed occurred (or will occur). 3. Again, the distinction here is independent of degree of conWdence; cf. Note 2. 4. Recall that for the same reason we do not divide the outcomes of Inferences into two parts (Chapter 3, Section 3.1). 5. However, when the operator P is subsequently targeted, the collateral operation, P(p) must be appended to j; see, for instance, Example 19 (Section 4.1). 6. The term ‘warrant’ is used here in a somewhat wider sense than that in which Ryle (1950) uses “inference warrant” (i.e., hypotheticals) and in which Toulmin (1958) uses “warrant”. Toulmin’s “backing” is, in our system, also part of the JustiWcation. For critical discussion of Toulmin’s concepts of warrant and backing see Öhlschläger (1979, pp. 79–88, 108–110), van Eemeren, Grootendorst, and Kruiger (1987: 199–207), and Freeman (1991: 3–8, 50– 88). Ducrot (1996: 140f) uses the Aristotelian term ‘topos’ instead of ‘warrant’. Pollock’s
Notes 229
(1989: 126–127) distinction between justiWcation and warrant does not pertain to our underlying structures but rather to the evaluation of a belief of the author of the argument: whether it is actually justiWed from the author’s perspective (justiWcation) or would be arrived at by an idealized author (warrant). 7. The conclusion is indicated by a small arrow, and it is therefore not necessary to indicate this equivalence by appending a collateral operation. 8. Accounting, like JustiWcation, is a regressive operation, and it, too, may have to be broken down into “sub-operations”, as illustrated in Examples 24–26, below. 9. See Note 5 on Ryle’s (1950) “inference warrants”. Toulmin (1958) regards the major premise as a “warrant”. For Öhlschläger (1979: 88–101) the major premise is a sort of presupposition, which licenses the conclusion (not the inference, as in Ryle). Our purpose here is diVerent from that of these writers, and their arguments for not according a more independent status to the major premise do not apply to the present framework. It has been remarked that syllogisms do not add any new information; in a sense, they are circular: “All politicians are shrewd” can be true only if Carl Caldwell (being a politician) is shrewd. A syllogism cannot be said, therefore, to justify the conclusion, in the ordinary sense of “justify” (see Neumann 1986: 30–31). However, “JustiWcation” is used here as a technical term, and it means neither more nor less than what has been explicated in Section 1. Syllogisms with a premise that states what holds for “some” xs (e.g., “All A’s are B’s; some A’s are C’s; therefore some C’s are B’s”) deploy a Subsumption operator with a superscript: US (Chapter 3, Section 1.1). An example of a more complex syllogism is analyzed in Appendix C. 10. In a logical notation, a syllogism may have a form paraphrasable as: “For every x, if x is a politician, then x is shrewd”. For such an implicational analysis, quantiWers as well as a variable would be required to forge the link from “if x is a politician” to “Carl Caldwell is a politician”. It was not considered advisable to introduce into our system quantiWers and variables, since these are not needed for any other purpose. Accordingly, our analysis of a Modus Ponens diVers from that of a syllogism. Our analytic framework does not focus on logic, and so arguments that are similar in their logic do not have to be analyzed in the same manner. 11. Refuting the operation targeted by a JustiWcation — e.g., V– (P1) in the above example — means that the operation is not well-founded. This is a slightly stronger claim than refuting the JustiWcation, V– (J3), which means that this particular JustiWcation fails to attain its purpose of justifying the targeted operation. The distinction is a subtle one, and in many instances either one of the two analyses will be appropriate. 12. See Chapter 4, note 12 on this distinction in relation to that between convergent and linked arguments. 13. Accounting can also have suboperations without a conclusion, i.e., that are like a warrant (see the warrants in Chapter 9, Example 1, Lines 22–25 and Example 2, Lines 2–5). 14. Deductive proofs are authorized by what Toulmin (1958: 134) calls our “basic rational competences” and thus have no JustiWcations. But what about other, non-deductive proofs? See also Feigl (1950: 129) on the “limits of justiWcation”.
230 The Structure of Arguments
Notes to Chapter 6 1. As Peter Winch (1987: 182) remarks, one can say “He believes that…, but he is wrong”, but one cannot say “I believe that…, but I am wrong”. 2. Some of these designations may also appear with author Designations (where the author is not the speaker): DA, P ∧ P(p) may stand for, e.g., “Lucy wanted to pass the exam” and DA, D ∧ P(p) — e. g., “Lucy intends to pass the exam”. See the discussion in Appendix A. 3. We do not intend, however, to take a stand regarding the debate over the correct analysis of performatives (see Lyons 1977: 778f, on this issue). Since our analyses pertain to the underlying structure rather than to the verbal expression, sentences like “I wouldn’t smoke, if I were you” (when intended as an advice or command) will also be analyzed with DO. 4. We note parenthetically that DO may appear in the consequent of an implication. Thus, “Don’t drink coVee in the evening, if you want to go to bed early” will be symbolized: if P(p) then DO ∧P(p). It is important here not to let oneself be misled by the verbal expression. The similarly worded advice “Don’t go through the park, if you don’t want to get mugged” will be symbolized by 1. DO ∧P(p) 2. J(DO ∧P1)
dO ∧p j: if T+ (p1) then %P(p)
Don’t go through the park. 〈What justiWes giving this advice is that〉 if you go through the park, then you might get mugged.
“Don’t buy at this store, if you want my advice” is simply DO ∧P(p) (the “if”-clause indicates that this is an advice rather than, say, a command). Van Dijk (1981: 170V) discusses these and similarly constructed sentences from the point of view of their verbal expression. 5. The meaning of “ought” here (or “must” in similar arguments) presents a logical problem; see von Wright (1983). This is called by Clarke (1985: 29) a retrospective prudential inference. It is immaterial here whether Ted said that he wanted to pass the exam, or whether the author just concluded this from his behavior; see Appendix A. 6. In discussing Walton and Krabbe’s (1995) system, Rips (1998) notes that “… the dialogue-game framework makes it diYcult to represent the embedded or recursive structure of support that is often typical of argumentation.” Our example illustrates how such structures are tackled in our system.
Notes to Chapter 7 1. Uwajeh (1996) also deWnes a question as performing “the illocutionary act of information-seeking”. Uwajeh diVers from us in holding that a rhetorical question “may be a question indeed.” [p. 98]. 2. Not surprisingly, there are utterances that can be construed either as questions or as some other kind of request or both; see Uwajeh (1996). Here, as everywhere, it is up to the
Notes 231
investigator to decide how the utterance is to be interpreted and analyzed. 3. Chapter 10, Section 4, introduces a diVerent notation for the target of Interpretations and Interpretation questions. 4. Questions like “What happened yesterday?” are not Presentation Questions; in Section 2 we show how these are formalized. That there are no Nescience Questions is shown in Note 16. 5. If necessary, the convention may be introduced of adding superscripts to ?O so as to specify the kind of Elaboration asked for. 6. Sometimes the analyst may take her clue from the answer to the question, but then she assumes that the respondent understood the question in the way the questioner intended it to be understood, whereas the object of the analysis is, of course, the question as intended by its author. A question the ambiguity of which might be resolved by the context is “So what?”. This may be used to ask about an Inference (“What follows from this?”), about a result (“So what will happen because of this?”), or about a JustiWcation (“How does this support what you said?”). See the discussion in Rips (1998: 414). 7. A backdrop is a certain kind of presupposition of a Question; however, not every presupposition of a Question is a backdrop, but only those that are subsequently targeted by that Question. See also Examples 14 and 15, further on. 8. Backdrops are also deployed in analyzing Questions that target constituent elements; see Example 10. Nothing would be gained therefore by liberalizing the concept of conXations and providing for the possibility of having conXated operations that the author does commit himself to. 9. We note in passing that there is a diVerence in nuance between this question and “Don’t gargoyles speak English?”. The latter will have the same analysis, but ?T ∧P(p) in Line 1 will be glossed: ‘Is it true that gargoyles do not speak English?’. 10. As shown in Example 15, above, one can apply a Presupposition restoring operation to a Question. In Chapter 3, Section 1.1 we discussed Presupposition restoring as a subclass of the Inference class, but it is a very special kind of inference. It is also possible to make an Inference from the backdrop of a Question; it is only the Question itself that cannot be inferred from (except, as stated, when the inference is based on the fact that the Question has been asked: d∧?). 11. The JustiWcation of a Question can only be a warrant (consisting of one or more operations). It will not be possible to reformulate this warrant as an articulation (Chapter 5, Section 2.3), because the conclusion of such an articulation would have to be identical to the Question that is being justiWed and no chain of reasoning can lead to a Question. 12. For instance “Is this a Rottweiler? I am told that is a particularly vicious breed of dogs and I am scared.” The formalization has to include an extra operation (as in Example 19): DA (?T )dA
I asked this Question.
and this permits A(dA ) a p aA
I am told that this is a particularly vicious breed … This is the reason why I asked this question.
232 The Structure of Arguments
13. Consider also that a JustiWcation (unlike an Inference) does not target an outcome but an operation, and thus relates implicitly to the author of that operation. 14. Even when the Question comes last (e.g., “I am a stranger here. Can you tell me how to get to …?”), we do not have an Inference (the request for information cannot be inferred from the fact that one is a stranger); instead, “I am a stranger here” serves as the JustiWcation for that particular person asking the Question. This requires an extra operation: (DA (?T) dA I asked this Question), as in note 11, which is then targeted: J(DA ). Statements like “I do not know whether…” or “ I am not sure about…” are formalized as Nescience operations. Such a statement may function as the felicity condition for a question, but the question can in no way be inferred from it. 15. The relation between the outcomes in Lines 2 and 4 is symbolized as a ‘connection’; see Chapter 8, Section 3. Ruth Manor (1982) distinguishes between direct and eliminative answers. A direct answer to the Question in Example 21 would be “Jack did”. Eliminative answers would include those like “One of her admirers”, “Jack or Jerry” — both Elaborations, in our system — and also “Norman certainly did not”, which is not an Elaboration. In the Who-question that she gives as an example, direct and eliminative answers can be clearly distinguished. In some other types of questions, there is no sharp boundary line between the two categories. Consider the following answers to the question “When did the Allies land in France?”: “In the summer of 1944”, “In June 1944”, “On June 6, 1944”; which of these is direct and which eliminative? 16. Nescience ascribed to someone else — ‘He/she does not know’ — will be formalized DA ∧ /?/X (y); see the discussion in Appendix A. 17. Note that we are dealing here only with not knowing what, whether, etc. … or that something is the case. Very general statements like “I don’t know something about…”, “there is something you don’t know”, cannot be analyzed with a Nescience operator and will instead be treated simply as Presentations. Accordingly, Questions like “What don’t you know?” will be Elaboration Questions targeting such Presentations, and the latter may have to be introduced as backdrops.
Notes to Chapter 8 1. Alternatively, one might analyze the confuted statement as a constituent element (Chapter 3, Section 3.3) of a Presentation comprising both sentences in Example 1. But besides being more cumbersome, such an analysis would be less informative than one that indicates, by a connection, an additional link between parts of the argument. 2. Of course, when the added information is inferred from the preceding statement, it is analyzed as an Inference operation, when it states its result — as a Result operation, etc. 3. The diVerence between Examples 4a and 4b is a superWcial one and does not pertain to the underlying structure. This is why we do not add a ‘reversed’ concession (“Counterconcession”?) to our list. The same holds good for Seriation, where the diVerence between,
Notes 233
e.g., ‘a before b’ and ‘b after a’ does not pertain to the formal aspect of the underlying structure. In the case of Concessions, underlining makes for greater perspicuity of the notation. In the case of temporal Seriations, unlike in that of Concessions, the direction is immediately obvious, and there seems to be little need to indicate it by underlining. 4. Suppose the author says only “Maggie’s son is not really a genius” (without the additional “however, he is very bright”). Paralinguistic and contextual cues may make the intended meaning clear (i.e., either that he is very bright or that he is dumb), and then this will be an additional operation in the underlying structure that has to be formalized. In Chapter 6, Line 4 of Example 20 is connected to Line 3 by a Concession. 5. A speaker may say something that she then recognizes to be completely wrong (“He spent Wfty … I mean Wve hundred …”), but such lapses pertain to the expression of the argument and are not represented in its underlying structure (see Chapter 1, Section 1) 6. When a Question and its answer are quoted, the Response may occur in the same argument as the Question. For instance: “Jean asked whether …., and Jack answered that …”. The formalization then involves a conXation — DA ∧?T (…) and DA ∧ Y(…), with the connection marker Rsp {dA ∧y, dA ∧?T ). 7. This is not a concession connection, because his brother’s having attained self-fulWllment does not counter any expectation that might be raised by David’s having gained appreciation. 8. See Ducrot (1996: 188f) for a treatment of “but”. 9. For a while we considered, but then decided against, including three additional connections in our list: (a) Replication: An operation may have an outcome that is identical to the outcome of another operation. One may, for instance, arrive at a conclusion by way of an analogy and subsequently arrive at the same conclusion by way of a logical deduction. However, the identity of outcomes will be indicated by a collateral T + operation: X(…) x: T + (…), and no connection is required to represent it. (b) Repetition: An author may repeat what has been said in a previous argument, and this repetition fulWlls the same function, i.e., it is analyzed as the same kind of operation with the same target. But this does not require a special type of connection, because the fact that this is a repetition is evident from the repetition of the same line — operation, outcome and verbal description — in the analysis of the second argument. When the repetition occurs in the same argument, it will normally be part of the expressed argument, not of its underlying structure. (c) Instantiation. Compare A to B: A – Mammals nurse their young. – Cats are mammals. B – Animals who nurse their young are called mammals. – Cats, for instance.
234 The Structure of Arguments
In both A and B, cats are said to be a subclass of mammals. In A we have a typical Subsumption. In B, however, the second author does not want to tell us something about cats (‘be it known that cats are mammals’), but to give an example that illustrates the preceding general statement. In “Cats, for instance” the focus remains on the whole (mammals), and in this respect this statement diVers from a typical Subsumption, where the focus is on both the whole and the part included in it (cats). At Wrst blush this seems to suggest that what we have here is a toned-down Subsumption, i.e., a connection. Note, however, that in B the relation between the two statements is quite explicit (just as in A), and in this respect it is unlike the relations formalized by other toned-down operations, where the relation is merely hinted at. Take the Similarity connection: – John bought a video set. – Jane bought a new hat. These are two Presentations — “Jane bought a new hat”, taken by itself, does not say anything explicitly about its relation to the Wrst statement — and we detect, in addition, that the juxtaposition of the two statements serves to point out some similarity. This is indicated by a Similarity connection. In B, by contrast, where the relation is explicit, no connection is in order. We therefore analyze B, as well as A, as a Subsumption.
Notes to Chapter 9 1. While an argument may ‘occupy’ less than one turn, it will not comprise more than one turn, with two exceptions: (1) Two authors may concoct a single argument: e.g., A completes the idea that B has begun to express, or A indicates assent or comprehension in the course of B’s expressing the argument; see Clark (1992: 110–115) for examples. We may view these as “corporate” authors. (2) A attempts to complete B’s argument, but B rejects this completion and corrects it; see Antaki, Diaz, and Collins (1996) for examples. Similarly, in a Socratic dialogue, one of the participant spins out an argument while being interrupted by the other merely by assenting comments or simple questions (see Blair 1998). These cases may be regarded as interrupted arguments. On the deWnition of ‘turn’ and the diVerence between turn and move, see Edmondson (1981: 6–7, 86). 2. As we have seen in Chapter 4, Section 3, two operations are ordinarily not conjoined (for otherwise almost any two operations could be regarded as a single compounded one). Criterion (f) thus concerns mainly disjunctions and implications. 3. This term is being used here in a diVerent sense than that in Rips (1998). 4. Apostle (1982) would include also monologues in discussions. He uses the term ‘polylogue’ for discussions with more than two participants (the Greek word, though, means garrulity). Note, however, that ‘dialogue’ is not restricted to only two participants.
Notes 235
5. In that paper it was proposed to weight this number by the distances of the arguments from each other. Green and Jackson (1976) discuss this measure and propose a somewhat diVerent one. 6. Note that this cannot be formalized as: x: T– (x6 ) & T+ (x3 ), because the outcome x is not equivalent to the conjunction of T– (x6 ) and T+ (x3 ) but to each of these by itself. 7. Ducrot (1996: 96) goes even further when he argues that: “… every utterance is a sort of mini-dialogue.” 8. Why is this a JustiWcation and not an Accounting operation? “You should buy…” is an advice, and an advice is an imperative of sorts (cf. Hamblin 1987: 10). An imperative can have only a JustiWcation, not a motive or reason (though, of course, there may be a motive for issuing the imperative). 9. Besides being an excuse, it may also be a (possibly true) report of what led to her not taking the exam. Such reports of reasons are of course also analyzed as Accounting. 10. For both dimensions, conXations rather than simple operations may be selected. 11. Ultimately, of course, a typology that does justice to all possible distinctions would involve characterizations just as complex as the full analysis of the arguments. 12. A Question is strongly related to a preceding operation (i.e., the one the question is about). Answers to questions (like Author 3’s argument) are weakly related to the corresponding Question, but will typically be strongly related to the operation targeted by the question. See Chapter 7, Section 5, and Chapter 8, Section 3.
Notes to Chapter 10 1. The term ‘bridging’ has been used in the literature in a more limited sense, for inferences made by the hearer. Singer and Halldorson (1996) and Singer, Harkness, and Stewart (1997) deal with bridging inferences of causes and motives. But there are other kinds of operations that may be omitted by the speaker, and hence have to be bridged, in our sense of the term, by the hearer. Thus, our analysis of Hamlet’s monologue (Chapter 9, Section 1.4), includes an Eduction, a Comparison, and a Subsumption (Operations 6, 10 and 21, respectively), among others, which were not explicitly stated in the text; these are presumably bridged by the hearer. 2. In Schlesinger (1992), this factor was discussed under the term ‘automaticity’, and was proposed as an explanation of the eVects of centrality. We now believe that this explanation is faulted. 3. Observe that the only factor determining whether an operation is a transmitter or a terminal operation is targeting. Thus, neither a connection (Chapter 8) nor an annotation to a constituent element (Chapter 3, Section 3.4) turns an operation into a transmitter. 4. At the time these texts were excerpted and formulated, the notion of terminal operation had not yet been fully developed, and hence the results could not have been inXuenced unwittingly by the investigator’s preparation of the texts. The experiment was originally
236 The Structure of Arguments
conducted with yet another text (yielding similar results), but due to problems in the formulation of this text and its formalization, these data will not be analyzed here. 5. We have also experimented with a production task, in which subjects were given a text posing an ethical dilemma and asked to write down their reasoned opinion of how it should be solved. The subjects’ productions were very stereotyped and did not permit testing of our hypotheses. 6. Before reproducing the text, subjects must have read it, that is, they are also hearers. But since the text that is read is the Standard version, there are no operations that have to be bridged in reading it, and hence an omission in producing the text cannot be laid down to previous failure of bridging. 7. Alternatively, it may be viewed as tapping the accessibility (Section 1.2, above) of the operations previously omitted in performing the reconstruction. This may involve some overestimation of accessibility, because in expanding, the subject may remember the operation that were expressed in the text read (and reconstructed); but the relative accessibility of terminals and transmitters, JustiWcations and other operations, will presumably be reXected by the data obtained in this task. We accordingly also examined which of the operations omitted in the Reconstruction task were subsequently supplied by the subject in the Expansion task. But due to the small number of omissions in the Reconstruction task, no signiWcant diVerences between expanded terminals and transmitters or between JustiWcations and other operations were obtained. 8. Some of the materials were prepared by Smadar Sapir-Yogev, who also conducted a pilot study. Another task we tried out was to present subjects with the original version of our texts — i.e., the one that was expanded by us into the Standard version (Section 2.1) — and ask them to expand it, that is to add missing links (i.e., operations) in the argument. This task taps the accessibility to the hearer of operations omitted by the speaker. But since the number of operations that could have been expanded was very small (between zero and seven in each of the four types, +T +J, +T –J, –T +J, –T –J; see Table 10.5), we found no signiWcant diVerences in the tendency to expand terminals and transmitters, or JustiWcations and other operations. 9. In an articulation, the Wrst line contains j without a collateral operation; cf. Line 13 of the Admission text and Line 17 of the Medicine text in Appendix B. In coding the text, it will usually be diYcult, if not impossible, to decide whether this JustiWcation has been mentioned or not, and the J operations (but not the articulations) were therefore dropped from the analyses. 10. The interaction was computed by a diVerence score for each subject in the following manner. Let p(+t +j) be the probability of a given subject mentioning a batch of the category +T +J; p(+t -j) — the probability of mentioning a batch of the category +T –J, and so on. For each subject a diVerence score was computed: [p(+t +j) – p(+t –j)] – [p(–t +j) – p(–t –j)]. The null hypothesis was that the mean of these diVerence scores, over subjects, is zero. 11. Van Dijk (1980) has proposed certain “macrorules” according to which changes are made in such tasks. Previous work mentioned in O’Keefe (1982: 20) has dealt with the
Notes 237
motives for omitting or supplying missing links. In our work the emphasis is on the determinants of omitting operations, rather on the motivation for doing so. 12. The technique deployed in this study was suggested by Hadas Shintel, who carried out a pilot study and collected the data for this study with Niva Lieberman. Niva Lieberman and Arnon Keren analyzed the data. Thanks are due to Ronit Nirel, Malka GorWne, and Yacov Schul for statistical advice. 13. While column totals for the Medicine text show that the tendency of not deleting a batch was higher for –J than for +J, as predicted, the cells in the table have larger numbers for +J than for –J. This is due to the discrepancy in the numbers of operations in the cells (see Table 10.8): there were nine –T–J operations as against only one +T–J operation, and the former thus weighed more heavily in the computation of the column total. 14. Several batches in each of the texts had a low load and were rarely deleted. It turns out that most of these batches included a Presentation (in a conXation or otherwise). Now, a Presentation may be a central operation in the argument (according to an intuitive notion of centrality). But Presentation diVers from other operations in that it does not, by deWnition, target any other operation, and its load will therefore tend to be smaller than that of other operations. Our hypothesis concerning load does not take this into account. 15. The data of this study were analyzed by Niva Lieberman and Arnon Keren. The text in this study consisted of a single argument (according to our deWnition of argument, in Chapter 9, Section 1), unlike the texts used in the previous studies (see Section 2.1, above), and all transmitters were therefore intra-argument transmitters. 16. We note in passing that similar rules apply to Presupposition restoring (H). Suppose that in responding to Author A’s argument, Author B imputes to it a certain presupposition. When Author B states this presupposition explicitly (“You seem to assume that…”, or the like), the analysis of his argument must always include a Presupposition restoring operation. Suppose now that Author B does not state this presupposition explicitly (i.e., restores it only implicitly). Then the analysis of his argument will not always include a Presupposition restoring operation, H; rather, we will have to distinguish the following cases: (i) The presupposition which Author B imputes to Author A does not appear in the analysis of Author A’s argument (see Chapter 3, Example 6). (ii) Author B misunderstands Author A, imputing to him a presupposition that diVers from that appearing in the analysis of Author A’s argument. (iii) Author B imputes to Author A a presupposition that is the same as that appearing in the analysis of Author A’s argument. In cases (i) and (ii), a Presupposition restoring operation, H, will appear in the formalization of Author B’s argument, so that he can then relate to (i.e., target) its outcome, h. By contrast, in case (iii), the analysis of Author B’s argument will not include a Presupposition restoring operation, H. This is because B’s referring to the presupposition can be formalized as targeting the presupposition that appears in the analysis of Author A’s argument. 17. Whether the words were spoken or written will of course not aVect the analysis.
238 The Structure of Arguments
18. In general, the line between operations targeting an outcome (or an operator) and those that target the expressed argument is not always easy to draw. Take the argumentum ex silencio — an argument to the eVect that since the author claimed, say, that something applies to cases A and B, he implies that it does not apply to an unmentioned case C. At Wrst blush one might regard this as an Inference from the way the argument was verbally expressed. It appears to us, however, that this inference is from the fact that the author made a certain assertion, comprising A and B, rather than a diVerent one, comprising A, B, and C: 1. D∧P(p) 2. T– ∧ D ∧ P(p) 3. E(d∧p1 & t– ∧d∧p2 )
d∧p t– ∧d∧ p e
He said that … A and B… . He did not say that ….. A, B, and C…. . 〈From this it follows that〉 his assertion does not apply to C.
References
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Appendices
Appendix A. A note on reported arguments In analyzing an argument, we take into account not only what has been said, but also what has been left unsaid: the tacit line of reasoning that may be assumed to underlie the verbal expression (see Chapter 1). In a way, then, an argument, in our system, has a dual nature: it is both verbal and mental. Words that are not intended to convey a message (such as the recital of nonsense rhymes) will not be regarded as arguments, nor will be thoughts that remain without any verbal realization. Reported arguments of a certain type are a borderline case. Compare the following two statements: A Bill says that there is a ghost in the attic. B Bill thinks that there is a ghost in the attic. The author of A reports on an argument made by Bill, but the author of B only reports on what Bill thinks. Nevertheless, because it is reported by someone else, this thought (not verbalized by Bill) will have to be treated in our system as an argument. To understand the reason for this, consider what would be a possible alternative. The assertion of Bill’s belief, one might argue, should be analyzed as a Presentation, just like, say, the assertion “Bill is superstitious”. But such an analysis would have unacceptable consequences. Consider C Celia says that there is a ghost in the attic. Bill thinks that this is true. If we were to conceive of the second sentence as a Presentation of a mental state, the analysis would be: (*) 1. DA∧P(p) 2. P(p)
dA ∧ p
p
Celia says that there is a ghost in the attic. Bill thinks that this is true.
But this is problematic, because there is no targeting relation between the operations in the two lines, and two unrelated operations are regarded as belonging to two separate argu-
248 The Structure of Arguments
ments (Chapter 9, Section 1.3). This runs counter to our intuition that these two operations are closely related. It might be objected that while the two operations are not strongly related, there is a Seriation connection (Chapter 8, Section 2) between them: Celia said… and then Bill thinks that this is true. That is, they are weakly related and thus belong to the same argument, according to our deWnition in Chapter 9, Section 1.3. However, there will be cases where no such weak relation holds (suppose, for instance, that without hearing what Celia had said, Bill believes that there is a ghost in the attic). Furthermore (and perhaps more importantly), adding such a weak relation does not capture our intuition that “Celia said… ” and “Bill thinks that this is true” belong to the same argument because they refer to the same proposition: what Bill believed is what Celia claimed, namely, the existence of the ghost (but see the reservation in Pollock, 1989: 106–109). It is this content of the claim and of the belief, rather than any weak relation, that constitutes the link between the two operations. The correct way to deal with arguments like this is therefore to stipulate that DA (and DI ) may apply also to non-verbalized beliefs (as in B) that an author ascribes to someone. That is, the formalization of C will be: Example 1 1. DA ∧ P(p) 2. DA ∧ T + (p1 )
dA ∧ p d A ∧ t+
Celia says that there is a ghost in the attic. Bill thinks that this is true.
In arguments like B, where there is only one operation, the problem of unrelated operations (discussed in the foregoing) does not arise, of course. But in line with our stipulation concerning author Designations, B will also be analyzed with DA as conXating operation: Example 2 1. DA ∧ P(p)
dA ∧ p
Bill thinks that there is a ghost in the attic.
Other kinds of operations will be treated similarly. Suppose an author states that John made an Inference, without John having said anything that might be construed as his having made it). This will be formalized like a verbally expressed inference, e.g., DA ∧ E(x).
Appendix B. Analysis of texts deployed in the précis study - Chapter 10 Admission text Author 1: Plainti¬ 1. DR∧P(p) dR ∧ p p:…
pl pm pn
According to paragraph 9 of the Board of Higher Education, an institute of higher education may not, in its admittance policy, discriminate on the basis of race, sex, religion, or discriminate on the basis of social class.
Appendices 249
The University has admitted to its Law School pq r while not admitting the plainti¬. a graduate of Pq a higher Yeshiva institute. pr N(dR ∧p1) n: … According to paragraph 9, being a nq r is not a legitimate criterion of admittance. nq (= pq2) graduate of nr (= pr2) a higher Yeshiva institute. j: U(nq r3, pn1) 〈 What justi¼es this claim is that 〉 a graduate of a J(N3) higher Yeshiva is a member of a speci¼c social class. E(p2 & n3) e: Q(p2) 〈 One may infer from this that 〉 the University has acted in violation of paragraph 9. E(q5) e: Q(p2) 〈 Therefore 〉 the University’s action was illegal.
2. P(p)
3.
4. 5. 6.
p: …
Author 2: Defendant 7. S∧I[1pl ] s∧i 8. S∧I[1pn]
Cnt{s, s7} aP: %DC ∧I [1pn] The term “social class” is perhaps taken from regulations in countries like England, where there are sharp social distinctions, i: … where it denotes, e.g., i’ the upper class, the middle class. This is the reason for s∧i8 . aA % I[1pn] %i: … In our country the term applies perhaps to populations like i” new immigrants. J( % I10) j: K(i”10, i’9) 〈 What justi¼es this claim is that 〉 new immigrants are similar in the relevant respects to the social classes in countries like England. t– At any rate, contrary to the plainti¬’s claim, a T– (u4) graduate of a higher Yeshiva cannot be regarded as a member of a speci¼c social class. Deg{t –, % i10} J(T –12 ) j 〈 What justi¼es this claim is that 〉 | 14. P(p) p: … a graduate of ps cannot be regarded as a | member of a speci¼c social class. | ps a secular institute of higher education | 15. W(p14) w: … 〈 Analogously, 〉 a graduate of wk cannot be | regarded as a member of a speci¼c social class. | wk (= nr3) a higher Yeshiva institute.
9. A(s∧i8)
10.
11.
12.
13.
→
s∧i
The interpretation of paragraph 9 in respect to discrimination on the basis of race, sex, religion is not controversial. By contrast, one may raise doubts regarding the interpretation of “social class” in paragraph 9.
250 The Structure of Arguments
| 16. J(W15) j: K(wk15, ps14) 〈 What justi¼es this claim is that 〉 these | institutions are alike in that they impart | knowledge. e: T– (e5) 〈 Because a Yeshiva graduate cannot be so 17. E(t–12) regarded,〉 the University did not contravene paragraph 9. 18. E(e17) e: T– (q6) 〈 Therefore 〉 the plainti¬’s claim that the University has acted illegally cannot be accepted. Explanations: Line 1: DR stands for a law, rule or regulation as “author” (Chapter 3, Section 1.1). The whole outcome dR^p does not have any constituent elements, but p does. Line 4: The two superscripts in nq r direct us to combine “a graduate of “ (n q) with “a higher Yeshiva institute“ (n r ). Line 5: Recall that an Evaluation, Q, may pertain to conformity with or violation of any norm. Line 7–8: Claiming that the interpretation of a clause is (or is not) controversial is a Status operation. There is a Contrast connection (Cnt) between the operations in these two lines; see Chapter 8, Section 2. On the square brackets enclosing targets of I see Chapter 10, Sections 4.1–4.2. Line 9: DC is a Designation of situation or context (Chapter 3, Section 1.1). Lines 9–10: Note that the Interpretations, I, in these two lines diVer. In order not to encumber this analysis too much we have omitted here the partition of the outcome of I into i p and i I Line 12: The phrase “At any rate” signals a Degression (Deg); see Chapter 8, Section 4.
Medicine text Author 1: Representative of the state DR∧P(p) dR ∧ p: … According to paragraph 3 of the Statues, it impermissible to administer any medicine not included in the register for pq medicines. 2. DR∧P(p) dR ∧ p: … According to paragraph 5, one may not include in the register pr any medicine concerning which it not clear that it cannot cause harm and that it is e~cient for the purpose it is designed for. 〈 It follows that 〉 according to paragraph 5, one 3. N(dR∧p2) n: … should not register nl the medicine under discussion. 4. J(N3) j: U(nl3, pr2) 〈 What justi¼es concluding this is that 〉 regarding the medicine under discussion it is not clear that it cannot cause harm and that it is e~cient for the purpose it is designed for. 1.
Appendices 251
5. N(n3 & dR∧ p1)
n:… 〈 It follows that 〉 it is impermissible to administer nk (= nl3) the medicine under discussion.
Author 2: Plainti¬ 6. P(p) p
7.
8.
9.
10.
The Director General of the ministry is entitled to permit a physician-researcher to use a medicine that does not meet the requirements of paragraph 5. j: DR∧P(p) d∧p 〈 What justi¼es this is that 〉 according to the J(P6) regulations concerning pharmacists pk (= p2) the said restrictions do not apply to medicines used for research. ps %A(dR∧p ) aP It is assumed that medicines for research, the use of 7 which is restricted and controlled, need not be subject to the restrictions imposed on medicines that are marketed freely. %aA Apparently this is the reason for the regulations that … [Line 7]. N(p6 & p7) n: T– (n5) n: … 〈 It follows that 〉 the Director General may permit use of the medicine under discussion. nm (= nl3 ) J(N9) j: U(nm9, ps7) 〈 What justi¼es this is that 〉 the medicine under discussion is used for research.
Author 1: Representative of the state 11. T– (u10) t– It is not true that the said medicine is to be used for research. j 〈 What justi¼es this is that 〉 12. J (T –11 ) | 13. D∧P(p) d∧p The plainti¬ stated that it is to be used as a cure. | 14. C(p13, j10) c and this contradicts the claim that it is to be used for research. 15. E(t–11 ) e: T– (n9 ) 〈 It follows that 〉 the plainti¬’s claim [Line 9] is wrong. e: T+ (n5 ) Author 2: Plainti¬ 16. T+ (n9) t+ : T – (e15) The plainti¬’s claim [Line 9] is correct (i.e., e15 and n5 are false). t+ : T – (n5) 17. J(T+16) j 〈 What justi¼es this is that 〉 According to the Helsinki |18. DR∧if P1(p) then P2(p) dR∧if p1 then p2 | accord, if the physician has | hope that this will help the | patient, he “shall be free” to | use a new medicament.
252 The Structure of Arguments
|19. T+ (p118) |
t+
and this is a case where this is so.
Explanations: Lines 12–14: This is a warrant comprising more than one operation (Chapter 5, Section 2.2). It is not an articulation, because there is no conclusion that is identical to T–11, the operation targeted by J. Lines 15–16: Since it follows (Line 15) that n9 is wrong, n5 is right (and similarly for Line 16); see Chapter 9, Section 2.4. Lines 18–19: Another warrant with two operations. To turn this into an articulation a conclusion would have to be added: N(dR∧if p1 then p218 & t+19 ) …
Appendix C. Embedded collateral operations A given operation may have two — in principle, even more — embedded collateral operations. Here is an example. 1. P(p) 2. P(p) 3. N(p2 ) 4. J(N3 )
p: pq … p: pr … n: ns
Jack has been employed by the company for ¼ve years. Worker employed by this company for 20 years have full pension rights. 〈 It follows by Modus Ponens that 〉 15 years from now Jack will have full pension rights. j: L(p1 ) l: U(pq1, pr2) 〈 What justi¼es saying so is that 〉 〈 it follows from p1 that 〉 15 years from now Jack will have been employed by this company for 20 years.
Explanation: Line 4: What is inferred (by a Deduction, L) from p1 is the Subsumption, U, of Jack (pq 1) under the category of workers employed for 20 years (pr2). This is what justiWes the Modus Ponens in Line 3.
Author index
A Allen 43, 239 Antaki 234, 239 Apostle 234, 239 Apotheloz 183, 239, 243 B Blair xiv, 234, 239, 242 Blickle xiv, 243 Brandt 183, 239, 243 Buchler 30, 239 Bybee 30, 239 C Chittleborough 33, 239 Clark 157, 234, 239 Clarke 66, 230, 239 Coleman 4, 239 Collins 2, 234, 239 Copi 65, 239 Cox xvi, 239 Cummins 68, 240 D Dascal 214, 240 Delahunty 114, 240 Diaz 234, 239 van Dijk 230, 236, 240 Ducrot 229, 233, 235, 240 E Edmondson xiv, 234, 240 van Eemeren xiv, xvi, 4, 6, 154, 199, 223, 228, 240 Ennis 5, 223, 240
F Feigl 79, 229, 240 Finocchiaro xv, 240 Fisher xvi, 227, 240 Fleischmann xiv, 241 Freeman xiv, xv, xvi, 3, 9, 13, 154, 180, 223, 227, 228, 240 G Geach 81, 110, 227, 240 Gilbert 10, 240 Ginzburg 140, 158, 241 de Glopper 6, 199, 240 Govier 31, 81, 185, 241 Grabowski xvi, 4, 191, 241 Green 1, 235, 241 Grice 191, 241 Grimm 229, 241 Groeben xiv, 243 Grootendorst xvi, 6, 199, 228, 240 H Halldorson 235, 243 Hamblin xvi, 38, 81, 135, 166, 226, 228, 235, 241 Harary 164, 241 Harkness 235, 243 Harrah 144, 158, 241 Heritage 211, 241 Herrmann xvi, 4, 19, 191, 241 Hilton 82, 241 Hitchcock 4, 241 Hoaglund 81, 241 Hofer xiv, 241
254 The Structure of Arguments
J Jackson, S. xiv, 240, 241 Jackson, P. R. 235, 241 Jacobs xiv, 240, 241 Jacquette 5, 242 James 2, 8, 192, 242 Janik 29, 244 Jespersen 129, 242 Johnson xiv, 242
P Peirce 10, 30, 180, 242 Perelman xiii, xvi, 29, 31, 242, 243 Pikowsky xiv, 241 Pollock 69, 183, 223, 228, 243, 248
K Kempff 192, 242 Kienpointer 29, 65, 226, 242 Klein xvi, 242 Klug 31, 242 Krabbe 230, 244 Kruiger xvi, 228, 240 Kuhn 1, 2, 242
R Read 226, 243 Rieke 29, 244 Rips xiv, xv, 2, 46, 166, 179, 230, 231, 234, 243 Roth 1, 243 Ryle 228, 229, 243
L Lederer 160 Levi 6, 242 Levinson 33, 242 Lyons 38, 125, 224, 230, 242 M Macaulay 129, 242 Mann 3, 242 Manor 232, 242 Meiland xvi, 4, 242 Michalski 2, 239 N Neumann 229, 242 Newman xvi, 33, 239 Noordman 4, 192, 242 Novak 30, 242 O Öhlschläger 223, 228, 229, 242 O’Keefe 223, 224, 236, 242 Olbrechts-Tyteca xiii, 29, 243 Oostdam 6, 199, 240
Q Quirk 152, 243 Quiroz 183, 185, 187, 239 243
S Salmon xv, 3, 91, 154, 243 Sayles xvi, 227, 240 Schlesinger 10, 177, 178, 235, 243 Schreier xiv, 243 Scriven 5, 243 Searle xvi, 243 Shaw 46, 183, 185, 187, 243 Singer 4, 235, 243 Slade 180, 244 Slobin 224, 244 Spranz-Fogasy xiv, 241 Sprott 193, 244 Stewart 235, 243 Strawson xvi, 32, 65, 244 Svevo 8, 244 T Thomas 13, 244 Thompson 3, 242 Toulmin xiii, xv, xvi, 13, 29, 66, 226, 228, 229, 244 U Uwajeh 230, 244
Author index 255
V Vonk 192, 242 Vorobej 226, 227, 228, 244 Vygotsky 1, 10, 193, 244
Willard xvi, 239 Winch 230, 244 Wittgenstein 81, 223, 244, 245 von Wright 230, 245
W Wachbritt 29, 244 Walton 5, 30, 31, 81, 227, 230, 244
Z Zeitz xv, 3, 91, 154, 243
Subject index
A a fortiori 32, 41, 97–98 abduction 30 accessibility 192–194, 236 Accounting 28, 44, 52, 54, 81–82, 104, 121, 160, 221, 228–229 See also Cause dependent 102 independent 102 Accrual 148–150 adjacency pair 157 Adjudgment 34–39, 47, 49, 53, 60 Alternate 158 Analogy 31, 94–97 See also Inference annotation 57–58, 165 answer 131, 143–144 direct 232 eliminative 232 alternative-based objection 83–184, 187 argument xvii, 17, 224 convergent 227 counter-argument 179–180, 183– 187, 189 definition of 163–175, 177 expressed 6, 10, 11, 14, 104–105, 191–222, 233 expressed, as target 208–222 linked 227 relations between arguments 175– 180 relations within 164–167 reported 247–248 strongly related 176, 189, 221
sub-argument 167 supplementing 188–189 supporting 187, 189 typology of 182–190 unrelated 176 weakly related 176, 189, 222 argument-based objection 46, 183 argumentation (arguing process) 1–11 argumentum ex silencio 238 articulation 87–91, 95, 97, 100 See also Justification assertion-based objection 46, 183 author 13 B backdrop 134–136, 138, 145, 231 Backward Modus Ponens 30, 185–186 See also Inference batch 173 biconditional 67–68 bridging 191–192 C Cause 28, 47, 54, 60, 120, 142, 165 dependent vs. independent 102– 103 centrality (of operation) 193, 194 collateral operation 58–62, 89, 164, 180, 197, 211 conjoined 76 embedded 252 in Justification 87 Comment 150 Comparison 31, 35–36, 44–45, 48–49,
N. B. : Terms in our formal system are capitalized.
258 The Structure of Arguments
120, 159, 170, 228 See also Adjudgment compound 65–77, 127–128, 165, 195 Concession 152 conclusion 88 conditional 227 conflation 164, 195 as target 110–116 interpretation of 116–118 outcome of 110–116 with compounds 127–128 with Question 136–139 with sequences 127–128 Confrontation 35, 44–45, 47, 120 See also Adjudgment conjunction 71–73, 152, 155 connection 147–161, 222 as toned down operations 159– 161 between arguments 157–159 “unrestricted” 149–156 constituent element 55–57, 96, 232 Contrast 159 convergent argument 227 Correction 155 counterargument 183–190 counterfactuals 68 counter-considerations 154 D Deduction 30 See also Inference defeater 46, 183 degree of confidence 41–44, 94, 133 Degression 151 density 177–178 deontic statement 35 dependent effects 75–76, 100–104 Designation 36–39, 45, 48, 217–220 See also Adjudgment conflating 122–127 dialogue See discussion “encapsulated” 180–182 discussion 20, 176–177 disjunction 70–71 disjunctive Question 138
“dont know” 40, 145–146 See also Nescience E Eduction 14–15, 18 See also Inference Elaboration 27, 37, 47, 51, 54, 150, 120–121 Elaboration Question 132 Evaluation 14–15, 35, 38, 48, 188, 120, 125, 221 See also Adjudgment excuses 184 explanation 225 See also Accounting expressed argument 6, 10, 11, 14, 104– 105, 191–222, 233 as target 208–222 F felicity condition 7 formalization 17–20, 104–105, 107, 209 Formalization principle 19, 107 functors 65 G Generalization 30 See also Inference H hedges 34 I illocutionary force 34, 37–39 Impediment 156 imperative 38, 125, 225, 235 imperative Question 135 implication 65–70 independent effects 76–77, 100–104 Inference 29–33, 42–43, 47, 54, 60, 79– 81 83, 120, 142–143, 220 from Question 141, 231 inferencing, forward and backward 8 instantiation 233 intention to act 38 Interpretation 26, 44, 47, 50, 52, 54, 117, 120–121, 160, 219, 221 explicit vs. implicit 209–210, 214– 217
Subject index 259
Interpretation Question 133 interpretation, analyst’s 6, 209–210 J Justification 33–34, 52, 60, 79–108, 121, 142–143, 164, 193, 197–198, 202, 204–205, 207–208, 228 as target 98–100 dependent vs. independent 100– 102 of “dont know” 146 of Question 141–142 outcome of 86–87 L linked argument 227 load 177–178, 194, 205–206 M misunderstanding 210–214 Modus Ponens (and syllogism) 4, 29, 90–94, 229 See also Inference Modus Tollens 30, 87 See also Inference N negation 226 Nescience 40, 48, 129–146 See also Question; “don’t know” O objection 46, 183, 185 See also counterargument alternative-based 183–184 argument-based 46, 183 assertion-based 46, 183 omission 191–193, 198–202, 205 operation 13–24, 25–41 as target 45–50 bridging of 191–192 centrality of 193, 194 conjoined 71–73 disjunct 70–71 omission of 191–193, 198–202, 205 sequence of 71
scope of meaning 41 strongly related 164 sub-operation 89, 102, 103, 165, 171, 229 unrelated 164, weakly related 165 operator 14–15, 25–44, 45 orienters 166, 168 outcome 14–15, 51–62 as target 45–50 bipartite 112–114 constituent elements of 55–57, 96, 232 meaning of 53–55 part of 51–53 P pragmatics xiv-xv, 38, 177 See also Speech acts; Illocutionary force Precedence principle 60 précis writing 203–208 performatives 38 Presentation 14–15, 26, 61, 72, 120, 237, 247 Presupposition restoring 32, 138–139, 231, 237 See also Inference presupposition 134 of a Question 138 See also backdrop Progression 150 progressive mode 7–8, 19, 80, 91–94, 96, 104 propositional attitude 37 Q qualification 226 qualifiers 229 Question 40, 129–146 See also Nescience ambiguous 133 conflated and conflating 136–139 disjunctive 138 imperative 135
260 The Structure of Arguments
Justification of 141–142 yes-no question 137 quotes 219 R reasoning (process) xvii, 1–12, 13, 51, 104 implicit steps in xv-xvi, xvii-xviii, 3, 4–5 phases of 9–11 rebuttals 66 rebutting defeaters 46 reductio ad absurdum 69 regressive mode 7–8, 19, 80, 82, 91–94, 96, 104 repetition 233 replication 233 Response 144, 157 Result 28, 44, 52, 54, 83, 104, 121 See also Cause dependent vs. independent 104 S Sequel 160 Seriation 151, 160 Similarity 159 Solution 155 speech acts 38 See also illocutionary force Status 35, 47, 75, 119, 166, 221 See also Adjudgment sub-operation 89, 102, 103, 165, 171, 229 Subsumption 39, 44, 48, 50, 92, 120, 229 See also Adjudgment Subsumption Question 134 Summarizing 155 supposition 69 syllogism 4 See Modus Ponens T target 14–15, 44–51, 148–149 compound 74–75 conflated operators as 116
conflating operators as 116 expressed argument as 238 Justification as 98–100 meaning of 53–55 multiplex 44 of Question 131 operator as 45–50 outcome as 238 Question as 140–143 simplex 45 warrants as 98–99 targeting See target inter-argument 195 terminal 193–198, 202, 204, 206–208 transmitter 193–198, 202 Truth value 17, 34–35, 45–47, 52, 99, 118, 188 See also Adjudgment Truth value Question 133, 137 turn 17, 163–166, 177 U undercutting defeaters 46 underlying structure 2–7, 14, 17–19, 209, 217 reconstruction of 4–7, 8, 17 V Validation 35, 45–46, 61, 99, 118, 188 See also Adjudgment validity, logical xiv See also Validation variables (for operators / outcomes) 229 verbal description (of argument) 3, 18, 213 verbal expression 218 See also argument, expressed W warrant 87–91, 97–99, 101 See also Justification Whorfian hypothesis 10
List of symbols
X, Y, Z, and x, y, z are variables standing for operators and outcomes, respectively. Lower case x, y, z may also stand for subscript digits. Operations /operators A Accounting 28 B Backward Modus Ponens 30 C Confrontation 35 D Designation 36–39 also: Designation of the author 36 DA Designation of the author 36 DC Designation of the context 37 DD Designation characterizing intention to act 37 DF Designation characterizing performative 37 DI Designation of indefinite author 36 DL Designation of the location 37 DO Designation characterizing imperative 37 DP Designation characterizing propositional attitude 37 DR Designation of the author when it is a law, regulation or rule 36 DT Designation of the time 37 E Eduction 14–15, 32 G Generalization 30 H Presupposition restoring 32 I Interpretation 26 J Justification 33–34 K Comparison 35–36 L Deduction 30 M Modus Tollens 30 N Modus Ponens 29 O Elaboration 27 P Presentation 14–15, 26 Q Evaluation 14–15, 35 R Result 28 S Status 35 T Truth value 16, 34–35 T+ true 34–35 T– false 34–35
262 The Structure of Arguments
U
Subsumption 39 US partial Subsumption 39 V Validation 35 V+ well founded, valid 35 V– not well founded, invalid 35 W Analogy 31 ?X Question of type X 130–131 ?X/Y ambiguous Question 133 /?/X “I don’t know” operation of type X 130–131, 145 Outcomes The above symbols in lower case stand for the corresponding outcomes. 14-15 ?X (underlined) stands for the outcome of a Question operation of type X. 131 /?/X (underlined) stands for the outcome of a “don’t know” operation of type X 145 the presentation part of the interpretation 26, 51 iP the interpretation part of the interpretation 26, 51 iI the presentation part of the result 28, 51 rP the result part of the result 28, 51 rR the presentation part of the accounting 29, 51 aP aA the accounting part of the accounting 29, 51 x: xy constituent elements of outcomes 56–57 xz Targets (xy) outcome x in line y of underlying structure is targeted 14–15 (Xy) operator X in line y of underlying structure is targeted 45–46 [1-3] outcome of expressed argument is targeted; digits refer to line numbers 211 Compounds X(…)&Y(…) conjunction 71–73 X(…) / Y(…) inclusive disjunction 70–71 X(…) // Y(…) exclusive disjunction 70–71 if X(…) thenY(…) simple implication 65–66 iff X(…) then Y(…) biconditional implication 67–68 if c X(…)thenc Y(…) counterfactual 68 if s X(…) thens Y(…) supposition 69 Connections Acc {x, y} Accrual 148–149 Alt {x, y} Alternate 158 Cmm {x, y} Comment 150 Cnc {x, y} Concession (statement countering the expectation is underlined) 152 Cnt {x, y}Contrast 159
List of symbols 263
Cor {x, y} Correction 155 Deg {x, y}Degression 151 Imp {x, y}Impediment 156 Pro {x, y} Progression 150 Rsp {x,y} Response 157 Seq { x, y, z, ...} Sequel 160 Ser {x, y, z, ...} Seriation 151 Sim { x, y} Similarity 159 Sol {x, y} Solution 155 Sum {x & y & z...} Summarizing 155 Various (X1 ), (x2) subscript digits refer to line numbers 15, 46 %X, %x degree of confidence (of operation / outcome) 41–44 X^ Y conflation 109 X(…) x: Y(…) collateral operation (following the colon) 58–62 | vertical lines indicate subsets of operations in articulations, warrants, | Accounting, Interpretation, etc. 88, 102, 128, 161 | | → | the conclusion of the articulation X1(…)/ X2 (…) x1/x2
two operators/outcomes of same type in one line are distinguished by digits 70 X’(…)/ X” (…) x’/x” as in above – distinction can be made by apostrophes 122 annotation 57–58 X(…) x: y’ (=z”) [] square brackets indicate the scope of operators and functors 70 <> explanations added to verbal description 15
In the series HUMAN COGNITIVE PROCESSING (HCP) the following titles have been published thus far or are scheduled for publication: 1. NING YU: The Contemporary Theory of Metaphor. A perspective from Chinese. 1998. 2. COOPER, David L.: Linguistic Attractors. The cognitive dynamics of language acquisition and change. 1999. 3. FUCHS, Catherine and Stéphane ROBERT (eds.): Language Diversity and Cognitive Representations. 1999. 4. PANTHER, Klaus-Uwe and Günter RADDEN (eds.); Metonymy in Language and Thought. 1999. 5. NUYTS, Jan: Epistemic Modality, Language, and Conceptualization. A cognitivepragmatic perspective. 2001. 6. FORTESCUE, Michael: Pattern and Process. A Whiteheadian perspective on linguistics. 2001. 7. SCHLESINGER, Izchak, Tamar KEREN-PORTNOY and Tamar PARUSH: The Structure of Arguments. 2001. 8. SANDERS, Ted, Joost SCHILPEROORD and Wilbert SPOOREN (eds.): Text Representation. Linguistic and psycholinguistic aspects. n.y.p.
