THE LVOV-WARSAW SCHOOL – THE NEW GENERATION
POZNAē STUDIES IN THE PHILOSOPHY OF THE SCIENCES AND THE HUMANITIES VOLUME 89
EDITORS Jerzy BrzeziĔski Andrzej Klawiter Krzysztof àastowski Leszek Nowak (editor-in-chief) Izabella Nowakowa Katarzyna Paprzycka (managing editor)
Marcin Paprzycki Piotr Przybysz (assistant editor) Mikoáaj SĊdek Michael J. Shaffer Piotr Ziemian
ADVISORY COMMITTEE Joseph Agassi (Tel-Aviv) Étienne Balibar (Paris) Wolfgang Balzer (München) Mario Bunge (Montreal) Nancy Cartwright (London) Robert S. Cohen (Boston) Francesco Coniglione (Catania) Andrzej Falkiewicz (Wrocáaw) Dagfinn Føllesdal (Oslo) Bert Hamminga (Tilburg) Jaakko Hintikka (Boston) Jacek J. Jadacki (Warszawa) Jerzy Kmita (PoznaĔ)
Leon Koj (Lublin) Wáadysáaw Krajewski (Warszawa) Theo A.F. Kuipers (Groningen) Witold Marciszewski (Warszawa) Ilkka Niiniluoto (Helsinki) Günter Patzig (Göttingen) Jerzy Perzanowski (ToruĔ) Marian PrzeáĊcki (Warszawa) Jan Such (PoznaĔ) Max Urchs (Konstanz) Jan WoleĔski (Kraków) Ryszard Wójcicki (Warszawa)
PoznaĔ Studies in the Philosophy of the Sciences and the Humanities is partly sponsored by SWPS and Adam Mickiewicz University
Address:
dr Katarzyna Paprzycka . Instytut Filozofii . SWPS . ul. Chodakowska 19/31 03-815 Warszawa . Poland . fax: ++48 22 517-9625 E-mail:
[email protected] . Website: http://PoznanStudies.swps.edu.pl
POLISH ANALYTICAL PHILOSOPHY
Volume VI Editors: Jacek Juliusz Jadacki (editor-in-chief) Leszek Nowak Jan WoleĔski Jerzy Perzanowski Ryszard Wójcicki
THE LVOV-WARSAW SCHOOL – – THE NEW GENERATION
Edited by Jacek Jadacki and Jacek PaĞniczek
Amsterdam - New York, NY 2006
The paper on which this book is printed meets the requirements of "ISO 9706:1994, Information and documentation - Paper for documents Requirements for permanence". ISSN 0303-8157 ISBN-10: 90-420-2068-7 ISBN-13: 978-90-420-2068-9 ©Editions Rodopi B.V., Amsterdam - New York, NY 2006 Printed in The Netherlands
CONTENTS Jacek Jadacki, Jacek PaĞniczek, The Lvov-Warsaw School: Its Contemporary Inheritors and Investigators in Poland and Abroad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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PART I. THE SCHOOL: ITS ORIGINS AND SIGNIFICANCE
Barry Smith, Why Polish Philosophy Does Not Exist . . . . . . . . . . Jacek Jadacki, The Lvov-Warsaw School and Its Influence on Polish Philosophy of the Second Half of the 20th Century . . . .
19 41
PART II. OBJECTS AND PROPERTIES
John T. Kearns, An Elementary System of Ontology . . . . Jacek PaĞniczek, Do We Need Complex Properties Ontology? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrzej Biáat, Objects, Properties and Russell’s Paradox . . Joanna OdrowąĪ-Sypniewska, On the Notion of Identity . .
.. in .. .. ..
. . . . 87 Our . . . . 113 . . . . 129 . . . . 143
PART III. PROGNOSES, NORMS AND QUESTIONS
Tomasz Placek, A Puzzle about Semantic Determinism: àukasiewicz’s “On Determinism” Years Later . . . . . . . . . . . Max Urchs, Causality in Chaotic Environment: Does Strong Causality Break Down in Deterministic Chaos? . . . . . . . . . . . Jan WoleĔski, Three Contributions to Logical Philosophy . . . . . . . Andrzej WiĞniewski, Reducibility of Safe Questions to Sets of Atomic Yes-No Questions . . . . . . . . . . . . . . . . . . . . . . . . .
171 187 195 215
PART IV. CATEGORIAL GRAMMAR
Peter Simons, Languages with Variable-Binding Operators: Categorial Syntax and Combinatorial Semantics . . . . . . . . . . 239 Urszula Wybraniec-Skardowska, On the Formalization of Classical Categorial Grammar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
6 PART V. INTENTIONALITY, SENSE AND CONSEQUENCE
Liliana Albertazzi, Retrieving Intentionality: A Legacy from the Brentano School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kazimierz TrzĊsicki, Logical and Methodological Assumptions of the Ajdukiewicz’s and Kripke-Putnam’s Views of Meaning . . . Anna Jedynak, On Linguistic Relativism . . . . . . . . . . . . . . . . . . Dale Jacquette, Tarski’s Analysis of Logical Consequence and Etchemendy’s Criticism of Tarski’s Modal Fallacy . . . . . . . .
291 315 325 345
PART VI. TRUTHS AND FALSEHOODS
Arianna Betti, Sempiternal Truth. The Bolzano-TwardowskiLeĞniewski Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Artur Rojszczak, From the Act of Judging to the Sentence: The Truth-Bearer and the Objectivisation of Truth . . . . . . . . . . . . Wojciech ĩeáaniec, What does “Truth in Virtue of Meaning” Really Explain? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Józef Misiek, Do We Need a Definition of Truth? . . . . . . . . . . . .
371 401 421 445
PART VII. RATIONALITY: ITS CRITERIA AND DEFINITION
Ryszard Kleszcz, Criteria of Rationality . . . . . . . . . . . . . . . . . . . 469 Mieszko Taáasiewicz, On the Concept of Rationality . . . . . . . . . . . 485
THE LVOV-WARSAW SCHOOL: ITS CONTEMPORARY INHERITORS AND INVESTIGATORS IN POLAND AND ABROAD
Habent sua fata libelli. According to our original plans, this book was scheduled as the symbolic closure of the 20th century within the sphere of influence of the Lvov-Warsaw School. A serious illness suffered by one of us and the sudden violent death of our young friend, Artur Rojszczak, completely changed those plans. However, despite the various difficulties, this book is to finally appear in press. Let us treat it, therefore, in this altered situation, as our “tvardovskian,” symbolically tardy inauguration of the 21st century. We propose below a short survey of the content of this anthology.
Part I. The School: Its Origins and Significance The assumption in the title of Barry Smith’s article “Why Polish Philosophy Does Not Exist” is that there is no Polish philosophy. Through the process of exposition and commentary, this, initially provocative, assumption turns out to be a great compliment to the (scientific) style of philosophising in the Lvov-Warsaw School. There is no Polish philosophy in Poland because in Poland, especially since Twardowski’s times, it is philosophy per se that has been pursued, which is thus a constituent of world philosophy. Smith’s article gives a brilliant introduction to the extraordinary phenomenon of Twardowski’s circle, which brought Polish philosophers into the world stream of modernisation in philosophy. The significance of the School is sketched in Jacek Jadacki’s study “The Lvov-Warsaw School and Its Influence upon Polish Philosophy of the Second Half of the 20th Century.” The author advocates the view that, independently of the long ideological pressure of the communist regime, the School’s influence on Polish philosophy of the last fifty years turned out to be decisive. Jadacki proposes a certain division of the
In: J.J. Jadacki and J. PaĞniczek (eds.), The Lvov-Warsaw School – The New Generation (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 89), pp. 7-15. Amsterdam/New York, NY: Rodopi, 2006.
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history of this influence and he gives an overview of the most important achievements of the School in the domains of formal logic, ontology, epistemology, methodology, praxiology, philosophy of science, and axiology.
Part II. Objects and Properties LeĞniewski’s system of logic still captivates logicians and philosophers because of its formal elegance and ingenuity and stimulates them to further developments and new interpretations. LeĞniewski’s Ontology is frequently criticised for lacking a category of referring expressions which makes it incapable of accommodating expressions for collections of individuals. In his paper “An Elementary System of Ontology,” John T. Kearns develops a natural deduction system which is a restricted version of LeĞniewski’s Ontology and proves its soundness and completeness. Although the semantic account he provides treats nouns as predicates (as expressions with no ontological commitment), yet there is a way to conceive the language of Ontology as a truncated version of a larger language which does contain referring expressions. A revised system which contains such expressions is sketched. Philosophers sometimes wonder whether, apart from simple properties like for example being a cat or being black, there exist complex properties like being a non-cat or being a black cat. Putting aside the metaphysical issue of the existence of such properties, Jacek PaĞniczek, in his paper “Do We Need Complex Properties in Our Ontology?”, argues that complex properties could be a very fruitful ontological concept when conjoined with a liberal ontology of objects. Roughly speaking, complex properties may be used as a means for the categorisation of objects. PaĞniczek considers an algebra of properties which consists of simple properties and which is closed under Boolean operations. The principles that express possible dependencies between simple and complex predication are then enumerated and several categories of objects that obey all or only selected principles are discussed (particularly important among them are the categories of individuals, incomplete, and inconsistent objects). Russell’s paradox has been a recalcitrant problem in philosophical logic and has provoked philosophers to a constant search for still another “solution” to it. The so-called Russell’s property, which appears in this paradox, is often considered to be an abnormal property which needs to be somehow dismissed. Andrzej Biáat claims in his paper “Objects,
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Properties and Russell’s Paradox” that there are properties that are not objects and that the Russellian property is one of them. His argumentation is based on a formal-ontological system that allows for at least some properties not to be objects. When one tries to display Russell’s paradox within this system one comes to the conclusion that the property that applies to those and only those properties that do not apply to themselves is not an object. Apart from the paradox itself, Biáat’s system offers an interesting unorthodox ontological approach to objects and properties (usually it is assumed either that the classes of objects and properties are disjoint or that every property is an object). The principal aim of Joanna OdrowąĪ-Sypniewska’s paper “About the Notion of Identity” is to analyse the notion of identity and to clarify the terminology relevant to this notion. OdrowąĪ-Sypniewska characterises two main types of identity relevant to objects: abstract identity and numerical identity. She introduces further subtypes and points out some of the relations between objects which are identical numerically, and those which are identical abstractly. After describing some of the qualities of identity, the author examines the relationships between identity and such relations as sameness, kinship, likeness, equivalence, equality and difference. The author also proposes a criterion that would make the identification of identity possible.
Part III. Prognoses, Norms and Questions The subject of Tomasz Placek’s considerations in “A Puzzle about Semantic Determinism” are the ontological aspects of the discussion of truth, conducted by Twardowski and his pupils. Starting with àukasiewicz’s remarks that the thesis of the eternity of truth implies determinism, Placek expresses the view that the consequence of this thesis is the semantic but not ontological (fully-fledged) determinism. He demonstrates that àukasiewicz’s incorrect conclusions are due to his interpretation and formal characterisation of the phrase ‘it is true at a given time’ (depending on whether it is an operator or rather a predicate that ascribes a logical value; depending further on whether negation commutes with it or does not). Placek’s considerations appeal to a variety of possible intuitions: from intuitive ones to those proposed by the proponents of the logic of vagueness. The historical moral of Placek’s paper is that the birth of many-valued logic was polluted by the sin of imprecision.
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The question whether it is possible to build a bridge between deterministic (in particular causal) and chaotic visions of the world is undertaken by Max Urchs in his article “Causality in Chaotic Environment. Does Strong Causality Break Down in Deterministic Chaos?” Difficulties appear because chaos theories deny the validity of the principle of invariance of similarity, which lies at the basis of determinism in science. In the author’s opinion the solution is to consider causal and chaotic perspectives only as perspectives that can not be used together in one description of our world. His conclusion is, “There is no such thing as chaotic causality nor causal chaos.” Jan WoleĔski’s text “Three Contributions to Logical Philosophy” contains three short analytical arguments. In the third argument, “Determinism and Sentences about the Future,” WoleĔski shows (referring to Twardowski, LeĞniewski and Jordan) that the thesis on sempiternality of truth has nothing to do with the controversy between traditional determinism and indeterminism or, strictly speaking, that this thesis is compatible with both positions. The second argument, “God, Foreknowledge and Freedom,” presents the author’s formal criticism of a contemporary version of theodicy. The main aim of the first argument, “Permissions, Prohibitions and Two Legalisms,” is logical analysis of British legalism (lack of prohibition implies permission) and German legalism (lack of permission implies prohibition). Although non-classical logics were not the main interest of the LvovWarsaw school, it is well known that important results in many-valued logic, (alethic) modal logic, intuitionistic logic and paraconsistent logic were achieved by the representatives of the school. It is less well known, however, that Ajdukiewicz was one of the pioneers of the contemporary logic of questions (and answers). His first paper on questions appeared in 1926 and his most influential contribution to the field was published in 1934. After the war, the logic of questions was still an area of interest for Polish logicians; names such as Henryk HiĪ, Leon Koj, and Tadeusz KubiĔski are the first to be mentioned in that context. This volume includes a paper by Andrzej WiĞniewski, a student of KubiĔski, entitled “Reducibility of Safe Questions to Sets of Atomic Yes/No Questions.” WiĞniewski’s paper gives an example of the Polish-style approach to the logic of questions: formal tools are applied in order to solve a problem that is important not only to the logic of questions itself but also to philosophy.
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Part IV. Categorial Grammar Kazimierz Ajdukiewicz has been recognised as the founder or cofounder (with Bar-Hillel) of the theory of categorial grammar whose relevance for contemporary linguistics and philosophy of language can hardly be overestimated. Two articles in our book refer to Ajdukiewicz’s ideas in this domain. Peter Simons in his article “Languages with Variable-Binding Operators: Categorial Syntax and Combinatory Semantics” proposes an original method of surmounting the difficulties connected with the description of languages containing variable-binding operators in terms of categorial grammar. The main idea of this method is to construct an extended categorial grammar based on distinguishing the role of place marking and place filling. Simons also presents an outline of combinatorial semantics for languages with operators. On the other hand, Urszula Wybraniec-Skardowska in her article “On the Formalisation of Classical Categorial Grammar” takes into consideration LeĞniewski’s and Ajdukiewicz’s views on language in discussing the latter philosopher’s conception of classical categorial grammar in a historical context. She aims to accommodate this conception in an axiomatic system. The system of categorial grammar developed in this paper represents the concretistic approach to language, according to which tokens are the basic elements of language as opposed to the more frequently considered Platonist approach, which assumes type-tokens as basic.
Part V. Intentionality, Sense and Consequence Liliana Albertazzi, in her paper “Retrieving Intentionality. A Legacy from the Brentano School” shows that the conception of intentionality developed by Kazimierz Twardowski and his successors can serve as a tool for resolving some important problems in contemporary cognitive science. One of them, according to her, is the question of how to explain our specific (scil. dynamic) perception of immobile things (like the Leaning Tower), various immobile depictions of one object or symbols of mobile things (like mural representations of galloping horse, or exit signs), or the apparent movement of static phenomenal figures (like a moving spiral). To explain such perceptual situations, in which we transform sense data into meaningful experience events, one needs to use the subtle conceptual apparatus of intentional acts. Thanks to this
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apparatus, traditional controversies concerning the objective/subjective and the perceptual/intellectual character of duration can be precisely formulated. The main focus of Kazimierz TrzĊsicki’s contribution is indicated by his title “Ajdukiewicz’s Logical and Methodological Assumptions and the Conceptions of Meaning in Kripke and Putnam.” In Ajdukiewicz’s conception of meaning, the following (reconstructivist) assumptions are the most important. Firstly, all the semantic functions of expressions (including natural functions) must be relativised to the respective language. Secondly, natural languages are considered as an extrapolation of formal (logical) language, which is the only language in the proper sense of the word. Thirdly, the subject of the logical theory of language is language understood as a product. The problem of the relation between languages used by us and our world perspectives – posed in the thirties by Ajdukiewicz – is analysed by Anna Jedynak in her paper “On Linguistic Relativism.” According to linguistic relativism, using different languages results in different visions of world, and sums of those visions are mutually inconsistent. In consequence, different languages cannot be used simultaneously. Jedynak argues for the thesis that it is possible to compile the conceptual apparatuses of languages that are believed to be incommensurable without the risk of cognitive conflict. The impression that it is not possible arises only for pragmatic reasons. Alfred Tarski’s groundbreaking classical semantical works are still in the centre of philosophical discussions within the philosophy of language. Recently, John Etchemendy in his book The Concept of Logical Consequence (Cambridge: Harvard University Press: 1990) objected against Tarski’s identification of the logical relation of consequence with its ordinary intuitive counterpart and diagnosed Tarski’s position as an instance of “modal fallacy.” Roughly, the identification depends on the extent of the logical and extralogical terms that can be involved in the consequence relation. Dale Jacquette, in his paper “Tarski’s Analysis of Logical Consequence and Etchemendy’s Criticism of Tarski’s Modal Fallacy,” carefully analyses Etchemendy’s argumentation comparing it with Tarski’s understanding of consequence. He shows that Etchemendy’s objections can be avoided by an appropriate restriction of the terms relative to which the satisfaction of the consequence relation is determined. He stresses that Tarski’s views concerning the concept of consequence need not require a defence so long as we carefully follow Tarski’s intentions.
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Part VI. Truths and Falsehoods The historical origin of the Lvov-Warsaw School’s famous discussion on the absoluteness and the eternity as well as the sempiternity of truth is elucidated in “Sempiternal Truth. The Bolzano-Twardowski-LeĞniewski Axis” by Arianna Betti. She finds the seed for Twardowski’s and LeĞniewski’s ideas in Bolzano’s writings. As it appears, the thesis of the sempiternity of truth serves as a basis for three different ontological systems that differ, among others, in what they consider to be the truth bearers: for Bolzano, a Platonist realist, the truth bearers are ideal propositions-in-themselves; for Twardowski, an Aristotelian realist, they are typical judgements (abstracted from particular utterances); for LeĞniewski, a nominalist, they are concrete (uttered or written) sentences. Thus, for Bolzano and Twardowski, truth is atemporal whereas, for LeĞniewski, it is omnitemporal. Betti’s analysis throws an interesting light on the controversy between KotarbiĔski and LeĞniewski concerning the role of free creation in determining the ontological status of logical values as well as of their bearers. The problem of truth bearers in the Bolzano-Tarski tradition is examined also by Artur Rojszczak in his work “From the Act of Judging to the Sentence. The Truth Bearer and the Objectivisation of Truth.” It is an instructive appendix to Betti’s analysis. According to Rojszczak, the problem’s background consist in the so-called objectivisation of knowledge, i.e., in regarding it (or rather its parts) as being absolute (timeless, non-spatial) and independent from knowers (or, rather, their cognitive acts). Similarly, the objectivisation of truth can be described as the absolutisation of truth bearers or truth makers – making them independent, in other words. Wojciech ĩeáaniec’s article “What does ‘Truth in Virtue of Meaning’ Really Explain” takes up the old issue of analytic propositions. The author attempts to show in what “technical” sense propositions judged to be analytic by the logical empiricist tradition, up to and including Quine, can actually be demonstrated to be analytic. He delineates the procedures for showing that a given proposition is analytic in virtue of its logical form and the meaning of its constituent expressions, thereby giving more distinct contours to the somewhat hazy concept. Yet, the final conclusion is meant to convince the reader not to acquiesce to the logical empiricist account of analytic propositions by showing that the “truth in virtue of meaning” of some analytic propositions can be established only at the price of accepting other non-empirical propositions, the analyticity of which would have to be shown first. Thereby, a distinction among
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analytic propositions is introduced which is remotely reminiscent of the old analytic-synthetic a priori distinction. It has been said that analytical philosophy has had an advantage over non-analytical philosophy because of its ability to . . . analyse its own mistakes and prejudices. The essay “Do We Need a Definition of Truth?” is a brilliant illustration of this point. It is commonly known that one of the sources of Tarski’s semantical achievements in the thirties was the liar antinomy in àukasiewicz’s formulation. Józef Misiek argues that the attitude of analytical philosophers to this antinomy was actually the cause of a chain of misunderstandings, which paralysed their inquiry for years. Misiek’s answer to the title question of his paper is negative. The view according to which clarity is to be identified with definability is a harmful superstition. A humorous, coincidental corollary of the paper is that “the liar antinomy [. . .] is [only] a problem for the liar himself.” The more serious aspect of Misiek’s considerations consists in an adroit explanation of some vital facts in the history of philosophy of the last few decades.
Part VII. Rationality: Its Criteria and Definition According to the standard model of rationality accepted in the LvovWarsaw School and expressed by Ajdukiewicz and then Szaniawski (among others), our beliefs are rational when they fulfil three criteria: when they are articulated precisely, when they fulfil logical requirements (i.e., when they are related deductively and when there are no contradictions between them), and when they are sufficiently justified. Because many difficulties have been encountered in connection with these criteria, Ryszard Kleszcz in his paper “Criteria of Rationality,” tries to evade the problems by modifying the criteria. His modifications are twofold. Firstly, he proposes to implement different sets of criteria in different belief domains. Secondly, he argues that particular sets of criteria be weakened depending on the degree to which a given domain is theoretically complex. Kleszcz discusses in detail various versions of the three criteria mentioned above; in addition he discusses another two criteria, namely: (self)criticism and solvability of examined problems. The aim of Kleszcz’s strategy is to avoid the destructiveness of methodological relativism. The problem of a non-criterial definition of ‘rationality’ is considered by Mieszko Taáasiewicz’s in “On the Concept of ‘Rationality’.” He starts by distinguishing ontical and non-ontical (epistemic or pragmatic)
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rationality. Then, he points out that the variability of the criteria of rationality does not exclude the invariability of the notion of rationality. The desired definition of ‘rationality’ should ensure that the question of possessing respective (non-graded) properties is decidable and that logically incompatible theories are suitable simultaneously. Taáasiewicz considers as a candidate the definition of rationality as identified with what stands to reason. *** We hope that the texts presented above provide sufficient evidence to judge the accuracy of the opinion expressed in Smith’s introductory essay that they meet the contemporary “international standards of training, rigour, professionalism and specialisation” in philosophy. Jacek Jadacki Jacek PaĞniczek
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PART I THE SCHOOL: ITS ORIGINS AND SIGNIFICANCE
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Barry Smith WHY POLISH PHILOSOPHY DOES NOT EXIST
1. The Scandal of “Continental Philosophy” There are many hundreds of courses taught under the title “Continental Philosophy” (C.P.) each year in North-American universities. Such courses deal not with philosophy on the continent of Europe as a whole, however, but rather with a highly selective portion of Franco-German philosophy, centred above all around the person of Martin Heidegger. Around him is gathered a rotating crew of currently fashionable, primarily French thinkers, each successive generation of which claims itself the “end” of philosophy (or of “man,” or of “reason,” of “the subject,” of “identity” etc.) as we know it. A sort of competition then exists to produce ever wilder and more dadaistic claims along these lines, a competition that bears comparison, in more than one respect, with the competition among Hollywood film directors to outdo each other in producing ever more shocking or brutal or inhuman films. The later Husserl, Heidegger’s teacher, is sometimes taken account of in courses of this “Continental Philosophy”; not, however, Husserl’s own teacher Brentano and not, for example, such important twentieth-century German philosophers as Ernst Cassirer or Nicolai Hartmann. French philosophers working in the tradition of Poincaré or Duhem or Bergson or Gilson are similarly ignored, as, of course, are Austrian or Scandinavian or Czech philosophers. What, then, is the moment of unity of this “Continental Philosophy”? What is it that Heidegger and Derrida and Luce Irigaray have in common, which distinguishes them from phenomenologists such as Reinach or Scheler or the famous Daubert? The answer, it seems, is: antipathy to science, or more generally, antipathy to learning and to scholarly activity, to all the normal bourgeois purposes of the Western university (and we note in passing that, as far as phenomenology is concerned, it was Heidegger who was responsible for terminating that previously
In: J.J. Jadacki and J. PaĞniczek (eds.), The Lvov-Warsaw School – The New Generation (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 89), pp. 19-39. Amsterdam/New York, NY: Rodopi, 2006.
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healthy scientific line which had brought forth such masterpieces as Brentano’s Psychology form an Empirical Standpoint and Husserl’s Logical Investigations). This rejection of the values associated with normal scholarly activity is combined, further, at least in the case of those French thinkers accredited as “Continental Philosophers” – with a substitution of politics for science (where politics, too, is to be understood in a broad sense a sense broad enough to include also the adolescent fringe). Philosophy thereby becomes transformed into a strange type of ideologically motivated social criticism. This transformation is sometimes defended, especially by American apologists for “Continental Philosophy” such as Richard Rorty, by appeal to an argument along the following lines: i. ii.
All scientific activity is in any case an exercise of social power (here the work of Kuhn is often called in aid). The putative distinctions between “knowledge” and “power” or between “descriptive” and “performative utterances” are therefore spurious such distinctions must be “deconstructed” (in the manner of Foucault et al.).
Hence: iii.
Philosophers should cast aside the pretension that they are seeking knowledge and should instead engage exclusively in the struggle to shift the relations of power in society (and here we note that it is above all radical feminist groupings who have gained most from the widespread acceptance, in North America, of different versions of this argument).
(The problems with the argument are, of course, legion. To mention just one obvious stumbling block: if this is indeed an “argument” in defense of what might best be described as a grab for power on the part of certain groups, then this can only be because there is, after all, a distinction between descriptive and performative utterances, for if its premises did not themselves have validity as descriptive truths, then the argument would lose all force as justification.) That the discipline of philosophy has been subject in certain circles to a transformation of the sort described is at the same time masked by the use of new styles of writing which are designed to fool outsiders and to protect the circles of initiates from potentially damaging criticism. The most prominent mark of such styles of writing is the heavy use of pseudo-scientific jargonizing inspired by sociology and psychoanalysis. In addition, and especially in “post-modern” circles, they
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are marked by the utilization of various tricks of irony and self“quotation,” by means of which the authors of the new philosophy seek to distance themselves from the responsibility of making assertions which might be judged as true or false. Finally, however, the new writing style is often marked by the use of what can only be called pornographic devices. Consider the following characteristically pretentious passage, chosen at random from Derrida’s Spurs, in which the French Doctor Criminale undertakes to “deconstruct” the petit-bourgeois assumption according to which the two concepts of truth and castration would be somehow distinct: The feminine distance abstracts truth from itself in a suspension of the relation with castration. This relation is suspended much as one might tauten or stretch a canvas, or a relation, which nevertheless remains – suspended – in indecision. In the HSRFȒ. It is with castration that this relation is suspended, not with the truth of castration – in which the woman does [not 1] believe anyway – and not with the truth inasmuch as it might be castration. Nor is it the relation with truth-castration that is suspended, for that is precisely a man’s affair. That is the masculine concern, the concern of the male who has never come of age, who is never sufficiently sceptical or dissimulating. In such an affair the male, in his credulousness and naivety (which is always sexual, always pretending even at times to masterful expertise), castrates himself and from the secretion of his act fashions the snare of truth-castration. (Perhaps at this point one ought to interrogate – and “unboss” – the metaphorical fullblown sail of truth’s declamation, of the castration and phallocentrism, for example in Lacan’s discourse.) (Derrida 1978, pp. 59f )
Or consider this pudding of similar nonsense from Luce Irigaray: Gynecology, dioptrics, are no longer by right a part of metaphysics that supposedly unsexed anthropos-logos whose actual sex is admitted only by its omission and exclusion from consciousness, and by what is said in its margins. And what if the “I” only thought the thought of woman? The thought (as it were) of femaleness? And could send back this thought in its reflection only because the mother has been incorporated? The mother that all-powerful mother denied and neglected in the self-sufficiency of the (self) thinking subject, her “body” henceforward specularized through and through. (Irigaray 1985, p. 183)
Or again:
1
The ‘not’ is left out by the translator, to no apparent consequence.
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Inside Plato’s or Socrates’ cave, an artificial wall curtain reenactment, reprise, representation, of a hymen that has elsewhere been stealthily taken away, is never, ever crossed, opened, penetrated, pierced, or torn. (Irigaray 1985, p. 249)
As Ms. Irigaray explains: Any hint, even, of theory, pulls me away from myself by pulling open and sewing up unnaturally the lips of that slit where I recognize myself, by touching myself there (almost) directly. (Irigaray 1985, p. 200)
(It is, incidentally, one not inconsiderable victory of radical feminism in the Anglosaxophone countries that the C.P.-obsession with sex, as revealed in passages such as the above, has been introduced into the pages of even the most technical scientific journals via the banishment of the unmarked personal pronoun and its replacement with a pervasive and senseless switching back and forth of gendered “she’s” and “he’s.”)
2. Philosophy in Poland What, now, of the fate of philosophy in Poland? We note in passing how sad is the spectacle presented by the host of young students of philosophy in Poland currently devoting its energies to deconstructionist and to other non-serious and ultimately corrosive philosophical fashions. More important for our purposes, however, is the degree to which Poland’s own philosophers have fared so badly as concerns their admission into the pantheon of “Continental Philosophers.” Why should this be so? Why, to put the question from the other side, should there be so close an association in Poland – at least since 1894 – between philosophy and logic, or between philosophy and science? 2 One can distinguish a series of answers to this question, which I shall group together under the following headings: (a) (b) (c) (d) (e) 2
the role of socialism; the disciplinary association between philosophy and mathematics; the influence of Austrian philosophy in general and of Brentanian philosophy in particular; the serendipitous role of Twardowski; the role of Catholicism.
What other country – to mention just one symptom of the association I have in mind – would publish an encyclopedia entitled Philosophy and Science (Cackowski, Kmita and Szaniawski, eds. 1987)?
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3. Socialism and Scientific Philosophy Much of what needs to be said about the Polish case can be derived, with suitable modifications, from considering the case of Austria. Consider, in this light, the following passage from the autobiography of A. J. Ayer, who in 1932 spent a protracted honeymoon of just over three months in Vienna before returning to Oxford to write Language, Truth and Logic: The members of the Vienna Circle, with the notable exception of Otto Neurath, were not greatly interested in politics, but theirs was also a political movement. The war of ideas which they were waging against the Catholic church had its part in the perennial Viennese conflict between the socialistic and the clerical reaction. (Ayer 1977, p. 129)
A more explicit version of the same thesis put forward by Johannes Dvorak (also quoting Neurath): In light of the fact that the bourgeoisie – especially in Central Europe – had discharged itself of all enlightenment traditions and paid homage rather to the cults of irrationalism, while the proletariat struggled for a rational formation of society, the hope certainly prevailed that “It is precisely the proletariat which will become the carrier of a science without metaphysics.” (Dvorak 1985, p. 142)
Not only Neurath and Dvorak but also other scholars working on the background of the Vienna Circle have defended a view according to which the flowering of scientific philosophy in Central Europe between the wars is to be regarded precisely as part of a wider struggle between left and right, between science and reaction. I do not believe that we need spend too much time on this purported explanation as far as Poland – a land not of proletarians but of peasants and nobility – is concerned; but the reader is asked to hold her horses before rushing forward with objections to a political account of the rise of scientific philosophy in Poland along the lines suggested.
4. Safety in Numbers At the dawn of Polish independence in 1917, as part of a widespread campaign in favour of the conception of science as a laudable form of public service in the cause of the new Poland, the mathematician Zygmunt Janiszewski committed Polish mathematicians to a program designed to take advantage of the talents of the Polish mathematical community via systematic collaboration and concentration on specific
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problems and topics of research (see Janiszewski 1917). Janiszewski’s project, which proved to be of great success, is important for our present purposes for a number of distinct reasons: (i)
(ii)
(iii)
The topics chosen, above all in the area of set theory, were such as to lead to the possibility of fruitful collaboration between mathematicians and philosophers working in the area of logic. The foundations for such collaboration were laid already in 1894 when Twardowski began to teach philosophy at the university of Lvov; at that time Twardowski advised his students to study the science of mathematics in addition to philosophy, and some of his brightest students subsequently fell under the influence of the mathematician SierpiĔski, who taught in Lvov from 1910. Janiszewski was conscious of the comparative advantage possessed by smaller countries in those fields of scientific research not requiring significant expenditures on facilities and equipment. One can point, additionally, to a certain comparative advantage enjoyed by scholars in countries such as Poland in those fields – such as mathematics or music – where the issue of the native language of the scientist or artist is of secondary importance. (The achievements of Poland in the field of mathematics are matched, significantly, by similar achievements on the part of Hungary and Finland.) These comparative advantages of smaller nations on the world stage can be carried over also to other spheres, including philosophy, and especially to those areas of philosophy most remote from issues of politics and national culture. Mathematicians, and logicians and scientific philosophers, may also enjoy the advantages of relative personal and professional safety in turbulent political times, in a way which may not be possible for thinkers working in such fields as ethics or political theory or history. The relative superiority of work done in logic in Eastern as opposed to Western Germany is, I believe, to be explained in part in terms of this factor. On the other hand, however, given the role played by logical philosophers in the Solidarity movement and in the Polish underground university during the war, it is more difficult to gauge the significance of this factor in the case of Poland.
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5. Polish Philosophy Is Austrian Philosophy In his paper “Wittgenstein and Austrian Philosophy,” Rudolf Haller writes as follows: I wish [. . .] to defend two theses: first, that in the last 100 years there has taken place an independent development of a specifically Austrian philosophy, opposed to the philosophical currents of the remainder of the German-speaking world; and secondly that this development can sustain a genetic model which permits us to affirm an intrinsic homogeneity of Austrian philosophy up to the Vienna Circle and its descendants. (Haller 1981, p. 92)
The grain of truth in this passage can be seen already if we consider the degree to which the writings of such exemplary Austrians as Bolzano, Mach, Meinong, Twardowski, Popper and Gustav Bergmann, exhibit radical differences of style as compared to German philosophers such as Hegel, Heidegger, or Habermas who are standardly associated with Germany (see Smith 1991a; Mulligan 1993). Most simply put: the former employ a sober scientific style and shun pretensions. There are also associated differences pertaining to the differential role of science and logic, as opposed to that of politics in the two traditions differences which, as we shall see, serve to explain why it is (certain selected) German and not Austrian philosophers who have been taken up into the bosom of “Continental Philosophy” in North America. These are differences which are rooted deeply in history, and they do much to explain why Germany – in spite of the fact that it has brought forth such giants of mathematical logic as Frege, Hilbert and Gentzen – has taken so long to develop a community of analytic philosophers on its home territory and why not a few of those most centrally responsible for this development – above all Wolfgang Stegmüller – have hailed from Austria (or more precisely, in Stegmüller’s case, from the South Tyrol). I have sought elsewhere (see Smith 1994) to demonstrate the degree to which philosophy in Austria in the period from 1890 to the Anschluss was influenced by the thinking of Franz Brentano, and as the manifesto of the Vienna Circle points out, many of the characteristic concerns even of the logical positivist movement were foreshadowed in his writings: As a Catholic priest Brentano had an understanding for scholasticism; he started directly from the scholastic logic and from Leibniz’s endeavours to reform logic, while leaving aside Kant and the idealist systemphilosophers. Brentano and his students showed time and again their understanding of men like Bolzano and others who were working towards a rigorous new foundation of logic. (Neurath, Carnap and Hahn 1929, p. 302)
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In support of this contention as to the importance of Brentano, it is remarkable to consider the fact that the most important centers of scientific philosophy in Continental Europe – Vienna, Prague, Graz, Berlin, Göttingen and Lvov – were precisely those cities in which Brentano’s most distinguished students had held chairs in philosophy from the 1890s onwards. Brentano was not only sympathetic to the idea of a rigorously scientific method in philosophy; he also shared with the British empiricists and with the Vienna positivists an anti-metaphysical orientation, manifesting an especially forceful antipathy to the “mystical paraphilosophy” of the German idealists and stressing in all his work the unity of scientific method. Brentano’s writings involve the use of methods of language analysis similar in some respects to those developed later by philosophers in England. The thesis of an internally coherent tradition of Austrian philosophy is not, however, without its problems. Thus, while it seems that the works of Brentano, like those of Meinong and Husserl, were mentioned in discussions of the Vienna Circle, in the case of Brentano, at least, these writings were discussed primarily because Brentanian ethics was chosen by Schlick as a special object of scorn. Schlick himself was of course a German, as also were the three thinkers Carnap, Reichenbach and Hempel who are held by many to have made the most important contributions to philosophy of the logical positivist sort.
6. The Serendipitous Role of Twardowski “Austrian Philosophy” is, in any event, by no means as unified a phenomenon as some might like to believe. Perhaps, though, we can maintain a parallel thesis in regard to Poland, where the role of Brentanian ideas is more easy to gauge in light of the singular dominance, in the history of philosophy in Poland, of one man: Kazimierz Twardowski. The influence of Twardowski on modern philosophy in Poland is all-pervasive. Twardowski instilled in his students a passion for clarity and rigour and seriousness. He taught them to regard philosophy as a collaborative effort, a matter of disciplined discussion and argument, and he encouraged them to train themselves thoroughly in at least one extra-philosophical discipline and to work together with scientists from other fields, both inside Poland and internationally. This led above all, as we have seen, to collaborations with mathematicians, so that the Lvov school of philosophy would
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gradually evolve into the Warsaw school of logic, as Polish scientific philosophers availed themselves of the new techniques of formal philosophy developed by Frege and Russell. 3 Twardowski taught his students, too, to respect and to pursue serious research in the history of philosophy, an aspect of the tradition of philosophy on Polish territory which is illustrated in such disparate works as àukasiewicz’s groundbreaking monograph on the law of non-contradiction in Aristotle and Tatarkiewicz’s highly influential multi-volume histories of philosophy and aesthetics. In 1895, at the age of 29, Twardowski was appointed professor of philosophy in Lvov, still at that time an Austrian town. This meant that, like the Jagellonian University in Cracow, its university enjoyed a rather liberal and tolerant atmosphere. Thus Poles were allowed to study and to be taught by their own lecturers and professors, where “in the other parts of partitioned Poland they were engaged in a most savage struggle for national and economic survival” (Jordan 1945, p. 39). Twardowski taught at the university of Lvov until 1930 and continued to hold seminars until his death in 1938. His success in establishing a modern tradition of exact and rigorous philosophy in Poland can be seen in the fact that more than 30 of his Ph.D. students acquired professorships, and by the inter-war period his students held chairs in philosophy departments in all Polish universities with the single exception of the Catholic University in Lublin.4 As Tarski expressed it in a letter to Neurath of 1930: “almost all the researchers, who pursue the philosophy of exact sciences in Poland, are indirectly or directly the disciples of Twardowski” (Tarski 1992, p. 20). It has been suggested that Twardowski’s teaching was in some sense philosophically neutral, that the unity of his school was rooted in a common training in methods and habits of work, rather than in the handing down of any shared doctrines. Jordan, for example, asserts that the members of Twardowski’s school were not linked by any “common body of philosophical assumptions and beliefs.” Twardowski led his students, rather, “to undertake painstaking analysis of specific problems which were rich in conceptual and terminological distinctions, and
3
WoleĔski (1989) is now the standard history of the Lvov-Warsaw School. On Twardowski’s teaching see Skolimowski (1967, p. 26f ), who refers to Twardowski’s “Spartan drill.” On Twardowski’s intellectual development see Dąmbska (1978) and Twardowski (1991). 4 On Twardowski’s influence, see, again, WoleĔski (1989, Ch. 1, part 2), and also Skolimowski (1967, ch. II).
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directed rather to the clarification than to the solution of the problems involved” (Jordan 1963, pp. 7f ). While Twardowski held no truck with the system-building “philosophical” philosophies of the past, his work was nonetheless marked by a certain metaphysical attitude, which reveals itself in the work of those philosophers who came under his influence. This applies even to those – like Twardowski’s son-in-law Ajdukiewicz, also in other respects a noted Austrophile (see Giedymin 1982) – who were at certain times attracted by the positivism or reductionism of the Vienna Circle (see, e.g., Ajdukiewicz 1978, p. 348; Küng 1989). It applies to àukasiewicz, to KotarbiĔski, and to philosophers such as Drewnowski and Zawirski, who developed a conception of metaphysics as a hypothetical-deductive science to which the axiomatic method should be applied.5 The metaphysics to which Twardowski subscribed is that of Brentano (see Twardowski 1991),6 and Twardowski’s influence upon the content of modern philosophy in Poland can accordingly best be understood in terms of certain Brentanian ideas and attitudes which Twardowski conveyed to his Polish disciples. This influence reveals itself, more precisely, in the fact that modern philosophy in Poland is marked, on the one hand, by an attitude of metaphysical realism and, on the other hand, by a concern with the notion of truth as correspondence, both of which Twardowski had inherited – with some Bolzanian admixtures – from the early Brentano. Thus while Meinong’s theory of objects is a more widely known example of a generalized ontology built up on the basis of descriptive psychological analyses of the different kinds of mental acts, it was in fact Twardowski, of all the Brentanians, who was the first to develop a generalized ontology in this sense. As Ingarden puts it, Twardowski’s Content and Object (1894) is, “so far as I know, the first consistently constructed theory of objects manifesting a certain theoretical unity since the times of scholasticism and of the ‘ontology’ of Christian Wolff” (Ingarden 1938, p. 258, quoted in Schnelle 1982, p. 99). In some cases, a direct interest in Brentano and his school was inherited from Twardowski by his students. This is especially true of Ingarden; but it holds also of LeĞniewski, and àukasiewicz was subject to 5
See e.g. Jordan (1945, p. 38). A similar conception is represented in the work of contemporary Polish philosophers such as J. Perzanowski and many others. 6 As àuszczewska-Rohmanowa puts it, “Twardowski saw as his exclusive task the realization of the ideas of Brentano on Polish soil, ideas with which he himself in a way grew up and which he held to be indubitably correct” (àuszczewska-Rohmanowa 1967, p. 155, as quoted in Schnelle 1982, p. 90).
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the influence of Brentano’s ideas, too. He studied not only with Twardowski but also with Stumpf in Berlin and with Meinong in Graz, and among his earliest papers are a number of short reviews of works by Husserl, Höfler, Stumpf and Meinong. It would be wrong to suggest that specifically Brentanian doctrines were taken over whole by Twardowski’s students. Yet the implicit or explicit concern with metaphysics, and especially with realistic metaphysics and with truth as correspondence, is a constantly recurring feature of their work. Investigations in the ontology of truth, or of those relations between sentences and objects which are constitutive of truth, have been quite peculiarly prominent features of Polish philosophical writings from Twardowski to the present day, and they have coloured especially the Polish reception of the philosophy of Wittgenstein. 7 Even the early work of Tarski can illuminatingly be viewed in this light, though Tarski did not himself study with Twardowski (see Tarski 1956, p. 155, n. 2; WoleĔski and Simons 1989). At all events, though, it cannot be denied that an interest in the philosophy of truth has been a highly conspicuous moment of modern philosophy in Poland. The idea of realism, on the other hand, may initially be thought to have played a less prominent role. On closer inspection, however, we see that the realist attitude which Twardowski promulgated has in fact been taken for granted by Polish philosophers as something almost universally shared. Realism, even Aristotelian realism, is an unquestioned presupposition of LeĞniewski’s work and of that of his principal successors. It governs the work of Ingarden, dictating even the latter’s interest in the phenomena of aesthetics.8 It has been of repeated concern to Ajdukiewicz, and it has coloured also the work on epistemology of KotarbiĔski and his pupils (see Jordan 1945). And in each case, Twardowski has played a role in determining both the terminology and the thinking of the philosophers in question.
7. Scientific Philosophy and Catholicism Can we, then, accept an explanation of the rise and entrenchment of scientific philosophy in Poland in terms of the uniquely powerful influence of Twardowski? Before we move to answer this question, let us 7
From a wide selection of more recent works one might mention: Borkowski (1985), Perzanowski (1985), Suszko (1968), and Wolniewicz (1985). 8 See the Preface to his (1931); see also Ingarden’s critical writings on Husserl’s idealism, above all in his (1929).
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consider one further factor, which turns on the fact that Poland, like Austria, is a Catholic country. For some have offered religious explanations as to why scientific philosophy should have taken root in these countries – but not in (Protestant, Northern) Germany. Here again we may turn to Neurath, who writes as follows: Catholics accept a compact body of dogma and place it at the beginning of their reflections, [thus] they are sometimes able to devote themselves to systematic logical analysis, unburdened by any metaphysical details. [. . .] Once someone in the Catholic camp begins to have doubts about a dogma, he can free himself with particular ease from the whole set of dogmas and is then left a very effective logical instrument in his possession. Not so in the Lutheran camp, where [. . .] many philosophers and scholars from all disciplines, while avoiding a commitment to a clear body of dogma, have retained half-metaphysical or quarter-metaphysical turns of speech, the last remnants of a theology which has not yet been completely superseded [. . .]. This may explain why the linguistic analysis of unified science prevailed least in countries where the Lutheran faith had dealt the hardest blows to the Catholic Church, despite the fact that technology and the sciences that go along with it are highly developed in these countries. (Neurath [1933] 1987, p. 277)
Hence, Neurath claims, the “revolt against the metaphysical tradition is succeeding outside Lutheran countries in Calvinistic as well as in Catholic ones” and he notes with pride that there are in Austria “no such metaphysical autocrats as Heidegger, Rickert or others” (Neurath [1933] 1987).
8. A Copernican Shift Neurath is certainly onto something when he points to differential features of the history of Germany and Austria/Poland in this way. There are a number of severe problems with his specific thesis, however. Thus Heidegger himself was steeped rather in Catholic than in Lutheran metaphysics as a young man; and there are many Catholic countries, in other respects comparable to Poland, where logical empiricism and analytic philosophy have failed to take substantial root, just as there are Lutheran countries (Finland is here the most striking example), and of course countries of Anglican-Episcopalian filiation – not mentioned at all by Neurath – which have served as veritable bastions of the analytic tradition. Similar objections can be raised even more forcefully against our first (political) class of explanations of the rise of scientific philosophy in
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Central Europe (“‘scientific philosophy is the philosophy of the workers’ movement”). Not only is it the case that socialist movements in France or Spain or Italy, otherwise comparable to those in Poland and Austria, gave rise to no comparable movements in philosophy, but it is also the case that many of the most important thinkers associated with the Vienna circle and with the rise of scientific philosophy in Poland treated socialism with disdain (see Smith 1996). What, then, of explanations of the rise of scientific philosophy in Poland which stress the role of Austria in general and of Brentano and Twardowski in particular? Here again there are problems, not least as a result of the fact that the available explanations do little to explain why the ideas of Brentano and Twardowski were able to plant such firm and lasting roots precisely on Polish soil, where the contemporary influence of Brentanism in Austria itself, and in other parts of the former AustroHungarian Empire, is almost vanishingly weak. These problems become all the greater when one reflects on the tremendous difficulties faced by philosophers in Poland in keeping alive their philosophical traditions through the course of this country. It may, indeed, be possible to adjust and amend the offered explanations in order successfully to confront this and the remaining difficulties and thus to provide a reasonable explanation of the rise of scientific philosophy in Poland. I would like, however, to look at the matter from another, quite different perspective, and to raise instead the question: why did scientific philosophy not take root in, say, Bulgaria or Tadjikistan? The answer to these questions is I hope rather clear: scientific philosophy, or in other words a philosophy that respects the values of clarity, precision, seriousness, rigour and technical competence, is the product of an advanced intellectual culture and of the Western university. But why, then, did scientific philosophy to such a marked degree fail to take root in Germany? Recall, again, Neurath’s explanation of the metaphysical character of German philosophy in terms of the historical experience of the German people. We had occasion to reject this explanation when formulated in religious terms. What happens, however, if we recast the account in terms of the history of the Germans in the more narrow political sense? This manifests, from our present (certainly, radically over-simplified) point of view certain peculiar features as contrasted to the political history of the English or the Austrians. For philosophy has played a role in the history of the German state that is quite unique. Just as England has its National Theatre, and America has its Constitution and its Declaration of Independence, so Germany has its National Philosophy: Kant, Fichte,
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Hegel, Schlegel, etc. are national monuments of the German people, whose memory is held sacred not least because they were so closely involved in creating that unified national consciousness which made possible Germany itself as a unified nation state. Philosophical thinkers were made to play a role in the history of Germany that is analogous to the role of Mickiewicz in the history of Poland, of Homer in the history of Greece, or of Shakespeare in the history of the English. From this point of view, it is no accident that the most impressive German contributions to philosophical scholarship have consisted precisely in great critical editions of the classical German idealist philosophers. (For a consideration of the role of these editions in German culture, see Smith 1992.) The size and power of Germany in the twentieth century has furthermore ensured that the Germans have been able to keep alive their national philosophical tradition and to protect it in a way that would have been impossible for the smaller nations of Central and Eastern Europe. Certainly outside influences have occasionally been absorbed into the large central mass of post-Kantian German philosophising. Elements of the thinking of Searle, for example, have been absorbed into the work of Habermas and Apel; but they have thereby been transformed into something that is, from the perspective of the analytic tradition in which Searle’s thinking has its origins, scarcely recognisable. Attempts were made in the nineteenth century, in part under the inspiration of Fichte and the German model, to found a (“Messianistic”) national philosophy in Poland also: as the “Christ among the Nations” Poland has a quite special mission in the history of European Christianity. (Compare, in this respect, the work of such figures as Cieszkowski, Trentowski, Hoene-WroĔski; as discussed in Kuderowicz 1988.) Such attempts proved to be of little lasting influence, however, and were, in fact already in the 1870s overwhelmed by the more forwardlooking so-called “positivists” in Warsaw, who accused the nationalistic philosophers of being too naively idealistic in their goals and of thereby promoting national tragedies. The positivists advocated instead the virtues of “small” or “organic” work, which consisted not least in the promotion of science among the people in the spirit of Mill, Comte and Spencer (see Jadacki 1994). Now there is, of course, no important national philosophy in Britain or Austria, either: the imperial, multinational tradition seems for such purposes to be both too broad and too loose. There is also, and correspondingly, no particular concern for the purity or authenticity of the language of philosophy in England or Austria, for such issues there
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do not go hand in hand with issues of national-cultural integrity. And that Poland, as the mother of many nationalities, is to be seen as being allied to England and Austria in this respect manifests itself further in the fact that the Polish intellectuals, too from Twardowski, born in Vienna in 1866, to LeĞniewski, born in Petersburg in 1886 have often been multinational in their aspirations and have thus not shunned the use of Western languages in their work. How different is the case of Germany (and, by extension, France). The works of Kant, Fichte, Hegel, Heidegger are master texts of the German people, and like all such master texts, be they the master texts of a religion, a sect, a people or a culture, they manifest that type of density and obscurity which goes hand in hand with the tendency to spawn a commentary literature, with all that this implies by way of association with the commentary literatures on, for example, Aristotle, the Bible, or the writings of Marx and Engels (see Smith 1991b). German philosophers have in fact for centuries been schooled systematically in the habits of a philosophical culture in which the most important textual models are associated with a need for commentaries and with what one might call a hermeneutic intransigence. They grow up further in a philosophical culture which is sealed off by firm disciplinary boundaries from the empirical sciences and which places a high value not on consistency and clarity, but rather on “depth” and “authenticity.” Teamwork and the exercise of mutual criticism and persistent argument, international collaboration, and indeed the search for any sort of “truth” in philosophy, are from this perspective simply out of place (see Puntel 1991). Philosophy, rather, is seen as something that should come directly from the heart, as a direct expression of the author’s soul or “spirit.” Consider, in this context, the mind-deadeningly repetitive stream-of-consciousness rantings of Derrida who shows how, in this as in so much else, French philosophy (or more precisely, that part of French philosophy that has been approved as part of “Continental Philosophy”), has become little more than a parody of its German model (the result of applying to German philosophy a Nietzschean sceptical rejection of the very idea of seriousness). In the wider world, of course, it is not classical German idealism, with its national, textual and historical associations, but rather empirical, or at least scientifically oriented, philosophy that has come to constitute the contemporary mainstream. The latter is, for reasons not altogether accidental, a philosophy which values logic, argument and technical competence more highly than those literary, ideological and historical qualities which are at a premium in certain philosophical circles in
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Germany and France. Moreover, it seems likely to be the case that (whether for good or ill), as the discipline of philosophy becomes ever more a creature of the modern university, it will come to be marked to an increasing degree by the factor of professionalization, so that respect for technical competence and for the scientific method and the rejection of hagiography and the use of a mystificatory style will come increasingly to characterize the discipline of philosophy as a whole. The most prominent Polish philosophers have, when seen from this perspective, been speaking prose all along without knowing it.
9. Why Polish Philosophy Does Not Exist If, now, we return to our question as to how we are to explain the rise of scientific philosophy in Poland, then we can see that this question in fact needs no answer. In Poland, exactly as in Austria, and Scandinavia, and exactly as in England and the rest of the Anglosaxophone world, the rise of scientific philosophy is an inevitable concomitant of the simple process of modernization. Just as the term ‘Austrian Philosophy’ is a misnomer to the degree that it suggests that there is a corresponding national or regional or ethnic philosophy, or a special Austrian way of doing philosophy that is unavailable to those born (say) outside the borders of the former Habsburg Empire; and just as the term ‘women’s philosophy’ is a misnomer to the extent that it suggests that there is a special way of doing philosophy that is available only to those of feminine gender, so also the term ‘Polish philosophy’ is a misnomer and for just the same reasons. For Polish philosophy is philosophy per se, it is part and parcel of the mainstream of world philosophy – simply because, in contrast to French or German philosophy, it meets international standards of training, rigour, professionalism and specialization.
10. The Law of Conservation of Spread Why, then, is “Continental Philosophy” so popular in certain circles? Why do young philosophers in Poland in such large numbers choose to read – or rather buy – the newly made translations of the ghastly works of Derrida and his ilk? Why, more generally, should intelligent people come to hold that it is not necessary, in doing philosophy, to meet the normal standards of clarity and precision? Why, indeed, should some have found it attractive to reject the very goal of clarity in philosophy,
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and to praise, instead, the putative virtues of obscurity and depth? To answer these questions I should like, appealing to an analogy with the physicist’s law of conservation of matter, to advance a law of conservation of the various branches of intellectual concern which have traditionally, in the West, been grouped together under the heading “philosophy.” If one or other of these branches is in one way or another suppressed, or so I want to suggest, then it will somehow find a way to force itself through in some new and unexpected territory, or in some new and bastardized form. (If Marxist philosophy, broadly conceived, is no longer able to be taken seriously in the fields of economics or political theory, then it will rise again in the field of, say, “comparative literature” or “critical legal theory” or in the transzendentale Sprachpragmatik of Habermas and Apel.) Something like this, I suggest, has been the fate of many of the classical philosophical concerns now customarily dealt with by those pleased to call themselves “Continental Philosophers,” many of whom are grouped together in American universities in departments of comparative literature, of film studies, of “woman studies,” and so forth. For the best philosophical minds in the Anglo-Saxon world – and in Poland – have in recent decades turned primarily to logic and to the related branches of our discipline. To put it plainly: really existing logical or scientific philosophy, philosophy as concretely practiced in alliance with logic and science, has been overly narrow in the scope of the problems with which it has deigned to concern itself and has been too often associated with metaphysical standpoints (of nominalism, inscriptionalism, reism, eliminativist materialism, and so on) on the basis of which it is difficult, to say the least, to do justice to what we might call the phenomenological aspects of human existence. Those who have sought answers to the broader philosophical questions have thus fallen into the arms of those “Continental Philosophers” whose knavish tricks have been described above. Part of the blame for the excesses of the “Continental Philosophers” is, accordingly, to be laid at the door of Ryle and Quine and Carnap, who have played something like the same role, in the turning away from a unified adequatist metaphysics in our own day, as was played by Galileo (or the Galileo of Husserl’s Crisis) in an earlier period. (It is not for nothing that Quine, together with Heidegger and Derrida, is one of the heroes of Richard Rorty.) The problems of narrowness of scope and of metaphysical reductionism in philosophy were, perhaps, of lesser significance in Poland where Ingarden, above all, kept alive the flame of Grand Metaphysics, but even in Poland there were some influential members of the Lvov-Warsaw School who have
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muddied the waters by being less than wholly clear as to whether they were or were not engaged in “metaphysics.”
11. What Is to Be Done? How, now, should those – the contemporary heirs of Russell and àukasiewicz be they in Cracow or Canberra, in Pittsburgh or PoznaĔ – who believe in truth in philosophy, react to these developments? Should they simply ignore “Continental Philosophy” and the text- and commentary-based traditions of philosophizing in Germany and France from out of which it grew? Can they justifiably embrace the hope that they will all simply go away? Or is it not much rather the case that a fashion economy, when once established, manifests a quite remarkable resilience? Should they, as is now all too customary, allow the inhabitants of the C.P.-ghetto of Heideggerians, Derridians and Irigarians to perform their antics undisturbed, whether in the spirit of pluralistic tolerance or in that of scornful disdain? To react in this fashion would, I believe, be a great mistake. This is not because I believe that the proper reaction to the cynicisms, relativisms and irrationalisms which predominate in so many corners of our “postmodern” world would be to form a new “movement” charged with agitation on behalf of the scientific conception of philosophy. For as Schlick, however dimly, saw, the formation of a movement of “scientific philosophy” – to be ranked alongside “women’s philosophy,” “Australian regional philosophy,” and the like – can only contribute to the widespread confusion of supposing that there are different sorts of truth (see Smith 1996): scientific truth, women’s truth, aboriginal truth, proletarian truth, aryan truth, Tadjik truth, German truth, Jewish truth, and so on. Rather, we should orient ourselves more steadfastly around the idea that it is the proper business of philosophy to search for truth (for truth simpliciter), including truth in the various fields of the history of philosophy. This must imply also a search for truth even in relation to those byways of philosophical history and of philosophical concern that do not fit well into the customary and rather narrow picture of philosophical history which has been favoured by analytic philosophers hitherto. It must imply, indeed, a search for truth in the history of German and even of French philosophy in all its breadth. We should shine light, if one will, upon the dark places of our discipline and seek out the monsters that are breeding in its mists.
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It would be one incidental benefit of the study of the history of philosophy along these lines that it would help to make clear to philosophers and others that in former times, too, which is to say in previous dark ages of philosophical development, generations of philosophers have repeatedly been wont to declare themselves as constituting the “end,” or the “death,” of philosophy as we know it and have thereby engaged in competition with their predecessors in the wildness of the antics with which they have set out to support such claims. On the other hand, however, it will become clear also to the student of this catholic history of philosophy that such dark periods in philosophical history were in each case succeeded by new and healthier phases, in which truth and reason were once more, and with renewed vigour, given their due. 9
University at Buffalo Department of Philosophy 135 Park Hall Buffalo, NY 14260-1010, USA e-mail:
[email protected]
REFERENCES Ajdukiewicz, K. (1978). “The Scientific World-Perspective” and Other Essays. Dordrecht: D. Reidel. Ayer, A.J. (1977). Part of My Life. London: Collins. Borkowski, L. (1985). A Formulation of the Classical Definition of Truth. Studies in Logic and Theory of Knowledge 1, 33-44. Cackowski, Z., J. Kmita, and K. Szaniawski, eds. (1987). Filozofia a nauka: Zarys encyklopedyczny [Philosophy and Science. An Encyclopaedic Outline]. Warszawa: Ossolineum. Dąmbska, I. (1978). François Brentano et la pensée philosophique en Pologne: Casimir Twardowski et son ecole. In: R.M. Chisholm and R. Haller (eds.), Die Philosophie Franz Brentanos, pp. 117-130. Amsterdam: Rodopi. Derrida, J. (1978). Spurs: Nietzsche’s Styles. Translated by B. Harlow. Chicago & London: The University of Chicago Press. 9
I am grateful to Jacek Jadacki, Anna Kanik, Jerzy Perzanowski, Artur Rojszczak, Jan WoleĔski and to my esteemed translator, all of whom provided valuable help and inspiration during the preparation of this paper. Research for this publication was supported by a grant from the International Research and Exchanges Board, with funds provided by the US Department of State (Title VIII) and the National Endowment for the Humanities. None of these organizations is responsible for the views expressed.
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Dvorak, J. (1985). Wissenschaftliche Weltauffassung, Volkshochschule und Arbeiterbildung im Wien der Zwischenkriegszeit. Am Beispiel von Otto Neurath und Edgar Zilsel. In: H.J. Dahms (ed.), Philosophie, Wissenschaft, Aufklärung. Beiträge zur Geschichte und Wirkung des Wiener Kreises, pp. 129-143. Berlin & New York: Walter de Gruyter. Giedymin, J. (1982). Science and Convention: Essays on Henri Poincaré’s Philosophy of Science. Oxford: Pergamon Press. Haller, R. (1979). Studien zur österreichischen Philosophie. Amsterdam: Rodopi. Haller, R. ([1975] 1981). Wittgenstein and Austrian Philosophy. In: J.C. Nyíri, ed., (1986), pp. 91-112. Haller, R. (1986). Zur Historiographie der österreichischen Philosophie. In: J.C. Nyíri (ed.), (1986), pp. 41-53. Haller, R. (1986a). Fragen zu Wittgenstein und Aufsätze zur österreichischen Philosophie. Amsterdam: Rodopi. Haller, R. (1988). Questions on Wittgenstein. London: Routledge. Haller, R. (1993). Neopositivismus: Eine historische Einführung in die Philosophie des Wiener Kreises. Darmstadt: Wissenschaftliche Buchgesellschaft. Ingarden, R. (1929). Bemerkungen zum Problem Idealismus-Realismus. In: Festschrift Edmund Husserl zum 70. Geburtstag gewidmet (Jahrbuch für Philosophie und phänomenologische Forschung Ergänzungsband), pp. 159-190. Halle: Niemeyer. Ingarden, R. ([1931] 1973). Das literarische Kunstwerk. Halle: Niemeyer. English translation: The Literary Work of Art (Evanston: Northwestern University Press, 1973). Ingarden, R. (1938). DziaáalnoĞü naukowa Twardowskiego [Scientific Activity of Twardowski]. In: Kazimierz Twardowski: Nauczyciel – uczony – obywatel [Teacher Scholar Citizen], pp. 13-30. Lwów: PTF. Irigaray, L. (1985). Speculum of the Other Woman. Translated by G.C. Gill. Ithaca: Cornell University Press. Jadacki, J.J. (1994). Warsaw: The Rise and Decline of Modern Scientific Philosophy in the Capital City of Poland. Axiomathes 2-3, 225-241. Janiszewski, Z. (1917). O potrzebach matematyki w Polsce [On the Needs of Mathematics in Poland]. WiadomoĞci Matematyczne 7 (1963), 3-8. Jordan, Z. (1945). The Development of Mathematical Logic and of Logical Positivism in Poland between the Two Wars. Polish Science and Learning, vol. 6. Oxford: Oxford University Press. Partially reprinted in: McCall (1967), pp. 346-397. Jordan, Z. (1963). Philosophy and Ideology: The Development of Philosophy and Marxism-Leninism in Poland since the Second World War. Dordrecht: Reidel. Kuderowicz, Z. (1988). Das philosophische Ideengut Polens. Bonn: Bouvier. Küng, G. (1989). Ajdukiewicz’s Contribution to the Realism/Idealism Debate. In: Szaniawski, ed. (1989), pp. 67-85. àuszczewska-Rohmanowa, S. (1967). Program filozofii naukowej Kazimierza Twardowskiego [Kazimierza Twardowski’s Project of Scientific Philosophy]. Studia Filozoficzne 4, 154-168. McCall, S., ed. (1967). Polish Logic 1920–1939. Oxford: Clarendon Press. Mulligan, K. (1993). Post-Continental Philosophy: Nosological Notes. Stanford French Review 17, 133-150. Neurath, O., R. Carnap and H. Hahn (1929). Wissenschaftliche Weltauffassung: Der Wiener Kreis. Vienna: Wolf. English translation: The Scientific Conception of the World, in: O. Neurath (ed.), Empiricism and Sociology (Dordrecht: Reidel, 1973), pp. 299-318. (Page references are to the English translation.)
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Neurath, O. ([1933] 1987). Unified Science and Psychology. In: B. McGuinness (ed.), Unified Science (Dordrecht: Reidel), pp. 1-23, 274-278. (Page references are to the English translation.) Nyíri, J.C., ed. (1981). Studien zur Österreichischen Philosophie. Munich: Philosophia. Nyíri, J.C., ed. (1986). From Bolzano to Wittgenstein: The Tradition of Austrian Philosophy. Vienna: Hölder & Pichler-Tempsky. Perzanowski, J. (1985). Some Observations on Modal Logic and the Tractatus. In: R.M. Chisholm et al. (eds.), Philosophy of Mind – Philosophy of Psychology, pp. 544-550. Vienna: Hölder & Pichler-Tempsky. Puntel, L.B. (1991). The History of Philosophy in Contemporary Philosophy: The View from Germany. Topoi 10, 147-154. Schnelle, T. (1982). Ludwik Fleck – Leben und Denken: Zur Entstehung und Entwicklung des soziologischen Denkstils in der Wissenschaftsphilosophie. Freiburg i. Br.: Hochschulverlag. Skolimowski, H. (1978). Polish Analytic Philosophy: A Survey and a Comparison with British Analytic Philosophy. London: Routledge and Kegan Paul. Smith, B. (1991a). German Philosophy: Language and Style. Topoi 10, 155-161. Smith, B. (1991b). Textual Deference. American Philosophical Quarterly 28, 1-13. Smith, B. (1992). Thesen zur Nichtübersetzbarkeit der deutschen Philosophie. In: D. Papenfuss and O. Pöggeler (eds.), Zur philosophischen Aktualität Heideggers, vol. 3: Im Spiegel der Welt: Sprache, Übersetzung, Auseinandersetzung, pp. 125-147. Frankfurt: Klostermann. Smith, B. (1993). The New European Philosophy. In: B. Smith (ed.), Philosophy and Political Change in Eastern Europe, pp. 165-170, 191-192. La Salle: The Hegeler Institute. Smith, B. (1994). Austrian Philosophy: The Legacy of Franz Brentano. La Salle & Chicago: Open Court. Smith, B. (1996). Austria and the Rise of Scientific Philosophy: The Neurath-Haller Thesis. In: K. Lehrer and J.C. Marek (eds.), Austrian Philosophy Past and Present, pp. 1-20. Dordrecht: Kluwer. Smith, B., ed. (1994). European Philosophy and the American Academy. La Salle & Chicago: Open Court. Suszko, R. (1968). Ontology in the Tractatus of L. Wittgenstein. Notre Dame Journal of Formal Logic 9, 7-33. Szaniawski, K., ed. (1989). The Vienna Circle and the Lvov-Warsaw School. Dordrecht: Kluwer. Tarski, A. (1956). Logic, Semantics, Metamathematics. Oxford: Clarendon. Tarski, A. (1992). Drei Briefe an Otto Neurath. Grazer Philosophische Studien 43, 1-32. Twardowski, K. (1894). Zur Lehre vom Inhalt und Gegenstand der Vorstellungen: Eine psychologische Untersuchung. Vienna: Hölder. Reproduced: Munich & Vienna: Philosophia, 1982. English translation: On the Content and Object of Presentations, translated by by R. Grossmann (The Hague: Martinus Nijhoff, 1977). WoleĔski, J. (1989). Logic and Philosophy in the Lvov-Warsaw School. Dordrecht: Reidel. WoleĔski, J., P.M. Simons (1989). De Veritate: Austro-Polish Contributions to the Theory of Truth from Brentano to Tarski. In: Szaniawski, ed. (1989), pp. 391-442. Wolniewicz, B. (1985). Ontologia sytuacji: Podstawy i zastosowania [Ontology of Situations: Foundations and Applications]. Warszawa: PWN.
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Jacek Jadacki THE LVOV-WARSAW SCHOOL AND ITS INFLUENCE ON POLISH PHILOSOPHY OF THE SECOND HALF OF THE 20TH CENTURY
0. Thesis My thesis reads: Many factors influenced Polish philosophy of the second half of the 20th century; among those factors were philosophical traditions that had been present in Poland for a long time as well as traditions that appeared only after the Second World War with the influence of foreign ideas (mainly European and American analytical thought) and external political circumstances also playing a formative role. But it was the Lvov-Warsaw School whose influence proved decisive in any case upon what was of the greatest value in Polish philosophy of this period Firstly, the majority of the most respected philosophers were students of the School’s representatives and many of them also declared their membership of it. Secondly, the School determined the program of scientific philosophy that held good in Poland not without intervals of course – during the course of the entire 20th century. This was the program formulated by Twardowski at the beginning of his Lvov professorship and articulated emphatically by Jan àukasiewicz in Warsaw. In the second fifty-year period, the postulate of the scientific character of philosophy was strongly re-accentuated by Andrzej Grzegorczyk (1989). Thirdly, in the School two complementary methods of realising this program were present: the method of semantic analysis (Kazimierz Twardowski, Tadeusz CzeĪowski) and the method of formal reconstruction (Jan àukasiewicz, Stanisáaw LeĞniewski). Fourthly, problems which were exposed and elaborated by representatives of the first generation of the School have remained central in the research of their successors. Fifthly, proposals put forth by the main Polish
In: J.J. Jadacki and J. PaĞniczek (eds.), The Lvov-Warsaw School – The New Generation (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 89), pp. 41-83. Amsterdam/New York, NY: Rodopi, 2006.
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philosophers of the last fifty-year period usually referred to the results achieved in the School. They were either improvements of those results or counterproposals based on reliable criticisms of those results. I shall concentrate on the last two matters, because their importance is not only of a historical or local character. A systematic examination of the theoretical problems and results reached in contemporary Polish philosophy may be of use for many philosopher-specialists in their current research and may make the actual state of Polish and, in consequence, Euro-American philosophy easier for a philosopheramateur to comprehend (and who of us is not just an amateur in the majority of philosophical disciplines?!). With this in mind, I include a comparatively rich bibliographical guide, focusing especially on texts available in English. Before discussing the influence of the Lvov-Warsaw School on the Polish philosophy of the second half of the 20th century, I shall briefly describe the stages 20th-century Polish philosophy went through and its institutional and publishing basis.
1. Division into Periods From the perspective of the Lvov-Warsaw School, twentieth-century Polish philosophy began . . . in the 19th century (in 1895 to be precise) when Twardowski, the founder of the School, took the chair of philosophy at Lvov University. The century which has passed since that memorable year falls naturally into five twenty-year phases, preceded by the five-year prologue (1895-1900). 1.1. The Phase of Crystallisation During the first twenty years (1900-1920) let us call them the phase of crystallisation the process of forming the creative personalities of the main representatives of the first generation of Twardowski’s students took place; the majority of them having been born in the 1880s: Wáadysáaw Witwicki (b. 1878), Jan àukasiewicz (b. 1878), Bronisáaw Bandrowski (b. 1879), Marian Borowski (b. 1879), Zygmunt Zawirski (b. 1882), Kazimierz SoĞnicki (b. 1883), Stanisáaw LeĞniewski (b. 1886), Tadeusz KotarbiĔski (b. 1886), Wáadysáaw Tatarkiewicz (b. 1886), Stanisáaw Kaczorowski (b. 1888), Daniela Tennerówna-Gromska (b. 1889), Tadeusz CzeĪowski (b. 1889) and Kazimierz Ajdukiewicz (b. 1890). This was a generation to which Czesáaw Znamierowski (b. 1888), a philosopher and a jurist and Zygmunt Janiszewski (b. 1888),
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a mathematician, also belonged. Notwithstanding the fact that they studied abroad (Znamierowski with Cornelius and Janiszewski with Poincaré), both of them found themselves in the orbit of the influences of Twardowski’s School and played an important part in it. Janiszewski was one of the main initiators of the co-operation between mathematicians and philosophers, which resulted in the Warsaw Logical School. Znamierowski brought about a fusion of Leon PetraĪycki’s philosophy of law with the paradigm of Twardowski’s School. In the first five years of this period, the majority of the representatives of the second generation of the School came into the world: Alfred Tarski (b. 1901), Dina-Janina Sztejnbarg-KotarbiĔska (b. 1901), Edward PoznaĔski (b. 1901), Aleksander Wundheiler (b. 1902), Mordchaj Wajsberg (b. 1902), Józef Maria BocheĔski (b. 1902), Jan Salamucha (b. 1903), Izydora Dąmbska (b. 1904), Seweryna àuszczewska-Romahnowa (b. 1904), Jerzy Sáupecki (b. 1904), Henryk Mehlberg (b. 1904), Adolf Lindenbaum (b. 1904), MojĪesz Presburger (b. 1904), Maria KokoszyĔska-Lutmanowa (b. 1905), Leopold Blaustein (b. 1905), Stanisáaw JaĞkowski (b. 1906), Bolesáaw SobociĔski (b. 1906) and Stefan SwieĪawski (b. 1907). Józef Iwanicki (b. 1902) was born at the same time. His path was similar to that taken by Twardowski’s students, although he studied not in Lvov but in Strasbourg. All of them would join the group of their earlier-born colleagues: Antoni Korcik (b. 1892), Antoni PaĔski (b. 1894), Mieczysáaw Walfisz-Wallis (b. 1895), Maria NiedĨwiecka-Ossowska (b. 1896), Jan Franciszek Drewnowski (b. 1896), Stanisáaw Ossowski (b. 1897) and Janina Hosiasson-Lindenbaumowa (b. 1899). This period was ended by the premature death of two uncommonly talented scholars, Bandrowski (d. 1914) and Janiszewski (d. 1920) mentioned above, and by the outbreak of the First World War (waged in great part on Polish territories), accompanied – in Poland’s case by the Russian invasion (luckily victoriously repulsed), which interrupted normal scientific activities. 1.2. The Phase of Prosperity The second twenty-year period (1920-1940) was also closed by violent military and political events: in 1939, Poland was attacked by its allied neighbours Nazi Germany and Bolshevik Russia; this time, it was defeated and lost its independence for fifty years. In philosophy as well as in the whole Polish culture this second period was a phase of splendid creative prosperity: talents that crystallised during the former period bore fruit in the form of original scientific work ideas, conceptions and systems. At the same time, in the first part of the period,
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the future apostles and improvers of these results come into the world; they will belong to the third generation of the School: Jerzy àoĞ (b. 1920), Zygmunt ZiembiĔski (b. 1920), Leon GumaĔski (b. 1921), Halina Mortimer (b. 1921), Ija Lazari-Pawáowska (b. 1921), Jan Gregorowicz (b. 1921), Andrzej Grzegorczyk (b. 1922), Marian PrzeáĊcki (b. 1923), Tadeusz KubiĔski (b. 1923), Henryk Stonert (b. 1923), Jerzy Pelc (b. 1924), Tadeusz Pawáowski (b. 1924), Klemens Szaniawski (b. 1925), Jerzy Giedymin (b. 1925), Zdzisáaw Augustynek (b. 1925), Wojciech Pogorzelski (b. 1927), Bogusáaw Wolniewicz (b. 1927), Lech Dubikajtis (b. 1927), Zbigniew CzerwiĔski (b. 1927), Bogusáaw IwanuĞ (b. 1928), Leon Koj (b. 1929), Andrzej Malewski (b. 1929), Henryk Skolimowski (b. 1930), Tadeusz Kwiatkowski (b. 1930), Stanisáaw Surma (b. 1930), Ewa ĩarnecka-Biaáy (b. 1930), Witold Marciszewski (b. 1930), Zdzisáaw Ziemba (b. 1930) and, just after them, Ryszard Wójcicki (b. 1931), Jerzy Kmita (b. 1931) and Andrzej Siemianowski (b. 1932). They joined the people born in the previous ten years: Jordan (b. 1911), Czesáaw Lejewski (b. 1913), Andrzej Mostowski (b. 1913), Ludwik Borkowski (b. 1914), Stanisáaw Mazierski (b. 1915), Jerzy Kalinowski (b. 1916), Helena Rasiowa (b. 1917), Henryk HiĪ (b. 1917), Stanisáaw KamiĔski (b. 1919) and Roman Suszko (b. 1919). In his remarkable History of Philosophy, Tatarkiewicz characterised the situation of Polish philosophy at the threshold of the second half of our century: The second great war found it in blooming state [. . .]. It was destroyed by occupants between 1939 and 1944. The great part of the young generation perished in fights or was murdered in German [and Russian, let us add] camps. And the great part of scientific workshops, libraries and institutes, was devastated, robbed, razed to the ground. For Poland, much more than for other countries, these years closed an important and rampant, but short and unfinished epoch. (Tatarkiewicz 1981, p. 371)
1.3. The Phase of Destruction The external circumstances mentioned above meant that the third twenty years (1940-1960) deserve to be called the “phase of destruction.” Firstly, its beginning years witnessed the death of Twardowski (d. 1938), Borowski (d. 1938) and LeĞniewski (d. 1939). Then, the war devoured Wajsberg (d. 1939), Lindenbaum (d. 1941), PaĔski (d. 1942), HosiassonLindenbaumowa (d. 1942), Blaustein (d. 1944) and Salamucha (d. 1944). Soon after the war, Zawirski (d. 1948) and Witwicki (d. 1948) passed away. Afterwards, the country was exposed to the darkest five years of
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communist terror. Shortly after both àukasiewicz (d. 1956) and Wundheiler (d. 1957) died, both having emigrated earlier. It is hardly surprising that Polish analytical philosophy which was an object of special pressure of the ideologists of the regime went into the intellectual underground or, at best, was reduced to formal logic. At the time, this looked like the final destruction of the analytical tradition in Poland. Skolimowski, a historian of this tradition, wrote in 1967: The continuous development of the analytical movement [in Poland] led to its finest results in the late 1920s and in the 1930s. The war shattered this continuity. After the war, analytical philosophy never regained its previous strength; the 1950s saw its definitive decline. (Skolimowski 1967, p. 260) [In the early 1960s], the analytical movement become emasculated. [ . . .] Analytical philosophy is no longer a dominant trend in Poland; its strength has been diluted; its output drastically limited. (p. 235)
Skolimowski could not know, of course, that in this period the future representatives of the fourth generation of Twardowski’s successors were born and that they would give an analytical direction to Polish philosophy in the last ten years of the 20th century. Józef Herbut (b. 1933), Tadeusz Batóg (b. 1934), Barbara Stanosz (b. 1935), Stanisáaw MajdaĔski (b. 1935), Grzegorz Bryll (b. 1935), Zbigniew Zwinogrodzki (b. 1935), Stefan Zamecki (b. 1936), Adam Nowaczyk (b. 1936), Robert Leszko (b. 1937), Bohdan ChwedeĔczuk (b. 1938), Stanisáaw Kiczuk (b. 1938), Andrzej Bronk (b. 1938), ElĪbieta Pietruska-Madej (b. 1938), Edward NieznaĔski (b. 1938) and Tadeusz Prucnal (b. 1939) were born before the war. Then, successively: Krystyna Zamiara (b. 1940), Jan WoleĔski (b. 1940), Urszula Wybraniec-Skardowska (b. 1940), Eugeniusz ĩabski (b. 1940), ElĪbieta KaáuszyĔska (b. 1941), Mieczysáaw Omyáa (b. 1941), Zdzisáaw Kowalski (b. 1942), Leszek Nowak (b. 1943), Jerzy Perzanowski (b. 1943), Jacek Hoáówka (b. 1943), Ulrich Schrade (b. 1943), Joanna Górnicka-Kalinowska (b. 1943), Józef Wajszczyk (b. 1944), Teresa Hoáówka (b. 1944), Grzegorz Malinowski (b. 1945), Jan Zygmunt (b. 1945), Jacek Jadacki (b. 1946), Józef ĩyciĔski (b. 1948), Urszula ĩegleĔ (b. 1949), Wojciech Patryas (b. 1949), Adam Grobler (b. 1949), Roman Murawski (b. 1949), Witold StrawiĔski (b. 1949), Barbara TuchaĔska (b. 1949), Janusz Czelakowski (b. 1949), Michaá Krynicki (b. 1950), Kazimierz Jodkowski (b. 1950), Ryszard Kleszcz (b. 1950), Wojciech Buszkowski (b. 1950), Zbysáaw MuszyĔski (b. 1951), Marian Grabowski (b. 1951), Jacek PaĞniczek (b. 1951), Jerzy Pogonowski (b. 1951), Teresa Rzepa (b. 1952), Maágorzata Czarnocka
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(b. 1952), Wojciech Sady (b. 1952), Adam Jonkisz (b. 1953), Stanisáaw Judycki (b. 1954), Andrzej Pietruszczak (b. 1954), Cezary Gorzka (b. 1955), Marek Rosiak (b. 1956), Anna Jedynak (b. 1956), Jan Czerniawski (b. 1957), Tadeusz Szubka (b. 1958) and Andrzej WiĞniewski (b. 1958). 1.4. The Phase of Restoration The fourth twenty years (1960-1980) constitute a phase of the restoration of the Lvov-Warsaw School’s influence on Polish philosophy. This phenomenon occurred even though three important representatives of the first generation of Twardowski’s School passed away: Ajdukiewicz (d. 1963), SoĞnicki (d. 1971) and Tennerówna-Gromska (d. 1973), as well as Znamierowski (d. 1967). Also some members of the second generation died: Ossowski (d. 1963), JaĞkowski (d. 1965), Korcik (d. 1969), Kaczorowski (d. 1971), Ossowska (d. 1974), Drewnowski (d. 1978) and abroad PoznaĔski (d. 1974) and Jordan (d. 1977). It was especially poignant that three pillars of the third generation died: young Malewski (d. 1963) together with Mostowski (d. 1975) and Suszko (d. 1979), both in the prime of their creative life. On the other hand, within this period fall the dates of birth of the representatives of the fifth generation of successors of the School tradition: Tomasz Placek (b. 1960), Andrzej Biáat (b. 1960), Andrzej Rogalski (b. 1961), Marek Lechniak (b. 1962), Wojciech Krysztofiak (b. 1963), Tomasz Bigaj (b. 1964), Jacek Wojtysiak (b. 1967), Krzysztof Wójtowicz (b. 1967), Andrzej Rojszczak (b. 1968), Kazimierz Dudkiewicz (b. 1970), Joanna OdrowąĪ-Sypniewska (b. 1971) and Mieszko Taáasiewicz (b. 1973). 1.5. The Phase of Expansion In the period of the fifth twenty years (1980-2000) we witnessed the phase of expansion. True enough, the last representatives of the first generation of the School passed away: Tatarkiewicz (d. 1980), CzeĪowski (d. 1981) and KotarbiĔski (d. 1981). After the death of SobociĔski (d. 1980), KokoszyĔska-Lutmanowa (d. 1981), Dąmbska (d. 1983), Tarski (d. 1983), BocheĔski (d. 1995) and KotarbiĔska (d. 1997), SwieĪawski is the only active member of the second generation, being the unquestionable senior of the School. The third generation was decimated as well, for the following philosophers died: Mortimer (d. 1984), KamiĔski (d. 1986), Sáupecki (d. 1987), Szaniawski (d. 1990), Stonert (d. 1992), Mazierski (d. 1993), Giedymin (d. 1993), Borkowski (d. 1993), Rasiowa (d. 1994), Lazari-Pawáowska (d. 1994), IwanuĞ (d. 1995),
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Pawáowski (d. 1996), ZiembiĔski (d. 1996), Gregorowicz (d. 1998), Pszczoáowski (d. 1999) and Augustynek (d. 2001). At the same time, however, the activity of their students and the students of their students increased dramatically.
2. Institutional and Publishing Basis The theoretical efforts of the philosophers would not have been fruitful without the great organisational work of the environment of Twardowski’s students and their successors. Let me present the most important organisational enterprises. In the phase of restoration: the Department of Praxiology at the Polish Academy of Science (1965) was established on KotarbiĔski’s initiative (1965). At KotarbiĔski’s, Suszko’s and Pelc’s suggestion the Polish Semiotical Society (1967) was founded. The yearly Conferences on the History of Logic initiated at the beginning of this period (1959) by CzeĪowski became a customary phenomenon in Polish philosophical life. The conference on the analysis of the notion of justification (1961) organised by Ajdukiewicz and the Winter Formal Logic School inaugurated ten years later (1970) were of the utmost significance. The pressure on the political regime was so great that during the second Congress of Polish Science (1953) the communists were forced to put into their ideologists’ mouths a declaration of the reintroduction of logic teaching in universities and other academic schools. The quarterly Philosophical Movement founded by Twardowski (which appeared in 1911-1914, 19181939 and 1948-1950) then revived in 1958, and the annual Studia Logica founded by Ajdukiewicz in 1953 (a quarterly in English since 1974) were joined by further periodicals: Praxiology (Polish version) (1962), Methodological Studies (1965), Semiotical Studies (1970), Bulletin of the Section of Logic [PAS ] (in English) (1972), Reports of Mathematical Logic (in English) (1973), Philosophical Problems in Science (1978), Problems of the Science of Science (1978) and Reports on Philosophy (in English) (1977). Important series appeared: PoznaĔ Studies in the Philosophy of the Sciences and the Humanities (in English) (1975, Amsterdam: Rodopi the initiative came from Nowak) and PoznaĔ Studies in the Philosophy of Science (Polish version) (1976, PoznaĔ: UAM; since 1994 it appears as PoznaĔ Studies in the Philosophy of the Humanities). Small Encyclopaedia of Logic (1970) edited by Marciszewski and Small Encyclopaedia of Praxiology and the Theory of Organisation (1978) written by Pszczoáowski were published. Collected
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works of coryphaei of the Lvov-Warsaw School were published: KotarbiĔski’s writings, published during the previous period (1957), were joined by Ajdukiewicz’s writings (1960) as well as those of àukasiewicz (1961), Twardowski (1965), Ossowski (1966) and Tatarkiewicz (1971-1972). Their valuable handbooks were also re-edited: àukasiewicz’s Elements of Mathematical Logic (1958) and KotarbiĔski’s Elements of the Theory of Knowledge, Formal Logic and Methodology of Science (1961). The publications of Pawáowski’s anthology Logical Theory of Science (1966) and Pelc’s anthology Polish Semiotics 18941969 (1971) were important editorial events too. In the phase of expansion: the Polish Society of Logic and Methodology of Sciences (1993) was founded by Wójcicki and KabziĔski. Perzanowski inaugurated The Logical-Philosophical Workshops (1994). Conferences on the Application of Logic in Philosophy and Foundations of Mathematics started taking place. Wójcicki organised The Summer School for Theory of Knowledge (1998). During the sixth Polish Philosophical Congress (1995), Pelc contrasted literary philosophy with scientific philosophy and recognised only the latter as academic philosophy. Philosophical Quarterly (1990; it appeared in 1923-1938 and 1946-1950) and Philosophical Review (1992), founded by Weryho (it appeared in 1898-1939 and 1946-1949), were resumed. New periodicals were started: Studies in Logic, Grammar and Rhetoric (in English) (1982), Bulletin of the Commission of Logic, Warsaw Scientific Society (1991), Praxiology (English version) (1992) and Philosophy of Science (1993). Valuable series appeared: Realism Rationality Relativity (1984, Lublin: UMCS), Logic and Applications of Logic (1985, Warsaw: PWN), Studies in Logic and Theory of Knowledge (in English) (1985, Lublin: KUL), Sign Language Reality (1990, Warsaw: PTS), Logic and Logical Philosophy (in English) (1993, ToruĔ: UMK), Philosophy Logic Logical Philosophy (1995, ToruĔ: UMK), Dialogikon (1995, Kraków: UJ), Foundations of Science (in English) (1998, Dordrecht: Kluwer series edited by Wójcicki), Polish Analytical Philosophy (in English) (1999, Amsterdam: Rodopi subseries of PoznaĔ Studies in the Philosophy of the Sciences and the Humanities). Marciszewski edited the Dictionary of Logic as Applied in the Study of Language (English version) (1981) and Formal Logic: An Encyclopaedic Outline (Polish version) (1987); Cackowski, Kmita, Szaniawski and SmoczyĔski edited Philosophy and Science: An Encyclopaedic Outline (1987). The enterprise of publishing collected papers of the representatives of the first two generations of the Lvov-Warsaw School was continued: the writings of Ossowska (1983), CzeĪowski (1989), KamiĔski (1989-1998),
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KotarbiĔska (1990), KotarbiĔski (1990-2003), BocheĔski (1993), Tarski (1995), Drewnowski (1996), Salamucha (1997) and àukasiewicz (1998) saw the light of the day. Ajdukiewicz’s classic handbook Problems and Orientations of Philosophy (1983) and àukasiewicz’s famous monographs On the Principle of Non-Contradiction in Aristotle (1987) and Aristotle’s Syllogistic from the Standpoint of Contemporary Formal Logic (Polish version) (1988) were re-edited. It is worth adding that many representatives and sympathisers of the Lvov-Warsaw School (i.e. Dąmbska, Lazari-Pawáowska, KubiĔski, Szaniawski, IwanuĞ, Nowak, and Perzanowski) became involved in the Solidarity movement, though the slogan of non-intervention in political controversies belonged to the program of the School. The activity of Polish philosophers was accompanied by an increasing interest in Polish analytical philosophy abroad. At the beginning of the phase of expansion (1989), the yearly Philosophical Lectures devoted to Twardowski were inaugurated in Lvov (which since the Second World War has been within the borders of Ukraine). Then, conferences started: Stanisáaw LeĞniewski aujourd’hui (Grenoble 1992), The Lvov-Warsaw Philosophical School and Contemporary Philosophy (Lvov-Warsaw 1995), àukasiewicz in Dublin (Dublin 1996) and Alfred Tarski and the Vienna Circle (Vienna 1997). This growth in interest was certainly stimulated to a great extent by the promotional activities of the Poles themselves. Even before the war the state of Polish analytical philosophy was described in French by Zawirski (1935) and in German by KotarbiĔski (1933) and Ajdukiewicz (1935). After the war, new works were written: in English by Zbigniew Jordan (1945, 1973), Skolimowski (1967), Ingarden (1973), Pelc (1973), KamiĔski (1977). Szaniawski (1980), Jadacki (1980) and, most importantly, WoleĔski (1977); in French by BocheĔski (1947), KotarbiĔski (1958), Ostrowski (1971), and PrzeáĊcki and Jadacki (1993). Historical texts written by foreign analysts were also of great importance: in German by Franzke and Rautenberg (1972); in English by Simons (1992) and Smith (1996). Of course, publishing original texts in an English translation was crucial here. The fundamental works of KotarbiĔski (1966), àukasiewicz (1970), Tatarkiewicz (1970-1974, 1973, 1980), Twardowski (1977, 1999) and LeĞniewski (1992), CzeĪowski (2000), Salamucha (2003) as well as McCall’s (1967), Pelc’s (1979), Krajewski’s (1982, 2001), Szaniawski’s (1989), Coniglione, Poli and WoleĔski’s (1993), WoleĔski’s (1994), Kijania-Placek and WoleĔski’s (1998) and WoleĔski and Köhler’s (1999) anthologies began to appear.
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3. Formal Logic It is natural that the influence of the Lvov-Warsaw School on Polish philosophy of the second half of the 20th century manifests itself mainly in the domain of formal logic, which became a kind of international visiting card of the School as early as in the 1930s thanks to a great German thinker Scholz. 3.1. Sentential Calculus Sentential calculus, which had been an object of investigations under àukasiewicz’s leadership at Warsaw in the period of prosperity, in the next years continued to be studied mainly by logicians assembled around Sáupecki and Borkowski. Outside the group were GumaĔski (1981), who constructed equivalence (reversible) systems and Pietruszczak (1991), who was occupied with quantifierless calculi. Grzegorz Malinowski (1990) developed Chrisippian (two-valued), as well as non-Chrisippian (many-valued) logic initiated by àukasiewicz, including three-valued logic. Zawirski’s suggestions as to the possibility of using it in physics, have been taken up by Kiczuk (1995). But new ideas appeared as well. Firstly, àukasiewicz’s questioning Chrisippos’ principle of bivalence was followed by Suszko, who rejected Frege’s principle that the denotation of sentences is to be identified with their truth-value. Thus, the next non-classical logic – after the non-Chrisippian one – came into being: namely, a non-Fregean logic, which assumes that the denotation of sentences is to be identified with a corresponding situation. Omyáa (1986) systematised this new logic. Secondly, systems of nihilistic logic were constructed (ĩabski 1995). They were founded on a conception of truth, according to which a sentence of the form ‘The sentence p is true’ is synonymous with sentence p itself; such systems can be used to solve some antinomies. The genesis of research on «paradoxical» logics was analogous; they allow for a substitution of sentential variables with nonsensical (or sense-losing) expressions (Piróg-Rzepecka 1966, 1977, 1985). Thirdly, studies in logics which result from the weakening of classical logic by the elimination of some axioms (or rules of inference, respectively) were undertaken. Special attention, inspired by JaĞkowski, was devoted to intuitionistic logic, which rejects the principle tertium non datur and which was already an object of Zawirski’s interest, as well as to para-consistent logic, allowing for or rather ignoring contradiction by removing Duns Scotus’ law from among the axioms (JaĞkowski 1948; da Costa and Dubikajtis 1968, 1977).
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3.2. Nominal Calculus All three versions of the nominal calculus considered by Twardowski’s immediate students were pursued. Sáupecki (1955), Iwanicki (1965) and Kwiatkowski (1980) worked on an adequate interpretation of Aristotle’s syllogistic, NieznaĔski proposed his own axiomatisation for it and contrary to àukasiewicz’s standpoint IwanuĞ (1969) discussed the possibility of enriching it by introducing names that denote the empty and the full sets. In the area of functional calculus, codified by Borkowski (1958-1960), interesting results were obtained by the generalisation of the notion of quantifiers by taking into account ramified quantifiers and by the construction of systems containing such «bifurcational» quantifiers (Krynicki, Mostowski and Szczerba 1995). Extending functional calculus (of the first order) to «fictional» (Meinongian) logic pendant to the above mentioned enrichment of syllogistic made by PaĞniczek (1988, 1998) is even more interesting. LeĞniewski’s ontology also continued to be an object of interest (Sáupecki 1955; Lejewski 1958; IwanuĞ 1969, 1973, 1980; Borkowski 1970). Elementary nominal calculi, close to ontology, were built by KubiĔski (1971a), while Rogalski (1995) adjusted ontology to the needs of the reconstruction of mediaeval metaphysics. 3.3. Erotetics The genesis of contemporary erotetics in Poland can be found in Twardowski’s incidental remarks and in Ajdukiewicz’s theory of questions developing these remarks. Their ideas were taken up and completed by Giedymin (1964), KubiĔski (1971), Koj and WiĞniewski (1989), WiĞniewski (1990) and Jadacki (2003), as well as by Leszko (1980, 1983), who used the theory of graphs and matrices for that purpose. 3.4. Mereology Attempts at completing LeĞniewski’s mereology have not ceased. Lately, Pietruszczak (1996) studied it intensively and Gorzka (1999) on Tarski’s inspiration has extended it (by introducing the notion of the diameter of a region) with a view to constructing an ontology without points. At the same time, attempts at constructing an alternative mereology have started, using the notion of founding (Rosiak 1995, 1996).
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3.5. Metalogic Metalogical research went in two directions. The first (metamathematical) direction, determined by Tarski, contained a generalisation of his theory of deductive systems (Sáupecki and Borkowski 1963; Rasiowa 1963: Rasiowa and Sikorski 1968; Sáupecki and Bryll 1965), theory of logical calculi (Wójcicki 1988) and the theory of proof (consequence), in particular (Zygmunt 1984). The second direction aimed at a satisfactory reconstruction of the logic of induction (Hosiasson-Lindenbaumowa 1941; Mortimerowa 1982). 3.6. Semantics The model-theoretical semantics initiated by Tarski turned out to be the dominant semantics in Poland. Pelc (1971) contrasted with it functional semantics – and, broadly, semiotics as more suitable for the analysis of natural language. Starting from a similar motivation, Wybraniec-Skardowska (1985, 1991) chose categorial semantics (she constructed an original axiomatisation for it), while Pogonowski (1993) declared for combinatorial semantics. Moreover, specific semantics for languages of many-valued logics were examined (Lechniak 1999). Among particular semantic problems, the main attention was paid to the problem of empty, ambiguous and quotational subject terms as well as to self-referring expressions, probably because of their antinomiogeneity. After KotarbiĔski, semantic functions of empty names were discussed by Dąmbska (1949) and GumaĔski (1960, 1961) as well as by logicians interested in systems that allowed empty names in their vocabulary (IwanuĞ 1976; Wybraniec-Skardowska and Chuchro 1991). The problem of ambiguous names was analysed by KubiĔski (1958), by PrzeáĊcki (1964), who extended it to the problem of undetermined expressions and interpreted in the model-theoretical semantics, and by MuszyĔski (1988); recently, OdrowąĪ-Sypniewska has published a detailed monograph concerning this subject (2000). KubiĔski (1965) tried to find a remedy for the difficulties concerning the usage of quotational names, indicated already by LeĞniewski and Tarski. Indexical expressions were examined by Koj (1964). On self-evident grounds, semantic antinomies and paradoxes, which played such an important role in the logical research carried out by Twardowski’s students, also attracted a lot of interest. Among people who came back to them were: Suszko (1957), focusing on the liar antinomy (in àukasiewicz’s formulation); Koj (1963), linking semantic
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antinomies with the problem of transparency; Stanosz (1965), analysing the paradox of intensionality. 3.7. Pragmatics Two pragmatic relations were the main object of examination: asserting and understanding. The stimulus for examining the former came from Ajdukiewicz and for examining the latter from Dąmbska. Detailed reviews and systematisations of the problems of assertion were written by MajdaĔski (1974) and Patryas (1987). Koj (1969), Kmita (1971) and Jadacki (2003) analysed the nature and criteria of understanding (within the framework of the theory of interpretation).
4. Ontology In ontology as practised in Poland in the past fifty years, two (actually complementary) tendencies competed one with another: in the last ten years they have been emphatically articulated as Perzanowski’s formal ontology program (ontologic) (1996) and as Placek’s experimental ontology program (or metaphysics in general) (1997). Both programs refer to Augustynek’s ontological program. The program of experimental ontology is (consciously or not) a radicalisation of Augustynek’s postulate, which requires that an ontological system be compatible with contemporary physics (Augustynek and Jadacki 1993). 4.1. Theory of Being or Existence In the domain of the theory of being, two thematic spheres dominated: the analysis of the notion of existence and the program of unifying (the picture of) reality. It was Twardowski, LeĞniewski and Ajdukiewicz who initiated contemporary analysis of the notion of existence and non-existence in Poland. Then the subject was taken up by GumaĔski (1960), who formulated it in terms of existential assumptions, KubiĔski (1985a), Wojtysiak (2002), who drew subtle semantic distinctions in this area, Czarnocka (1986), who examined the nature and criteria of existence in the natural sciences, and PrzeáĊcki (1979, 1980), who focused on the ways of eliminating problems connected with sentences about non-being. The program of unifying reality took either the form of argumentation in favour of the structural unity of the world (Tempczyk 1978, 1981) or the form of realisation of the postulate of onto-categorial reduction.
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As far as reduction of ontic categories is concerned, the Lvov-Warsaw School entered the second half of the 20th century with KotarbiĔski’s reism seriously impaired by Borowski’s and Ajdukiewicz’s criticism. This criticism was continued by Szaniawski (1977), who indicated the unlikeliness of a satisfactory interpretation of the distributive notion of a set in this system, as well as by PrzeáĊcki (1984) and Wolniewicz (1990). However, reism also had its defenders (Czerniawski 1997). In the meantime, competitive conceptions have appeared. In those conceptions categories other than things were accepted as basic categories, namely: properties (attributivism), states of affairs/facts (situationism), events (eventism) and processes (processualism). ĩabski gave a formal shape to attributivism (1988) and Nowak developed the idea of a negative ontology opposed to (positivistic) attributivism (1998, 2004). Situationism was elaborated by Wolniewicz (1968, 1985) and Omyáa (1996). These attempts were accompanied by the analysis of the notion of a state of affairs covering negative (Kowalski, Krzysztofiak and Biáat 1998) and intentional (fictional) states of affairs (Pelc 1983; PaĞniczek 1991, 1998). The most perfect shape was given to eventism, considered by its authors (Augustynek and Jadacki 1993) as an ontology, which is compatible with relativistic physics. Processualism had its adherent in Tempczyk (1986). The structural basis for these new reductive formal ontologies and most certainly for eventism is set theory. Quite different namely combinatory character was given by Perzanowski (1995) to his refined ontological systems. 4.2. Theory of Necessity and Possibility The analysis of necessity and possibility has been carried out almost exclusively within the range of modal logic (see below). 4.3. Theory of Time and Space Augustynek has undertaken detailed studies on time referring to LeĞniewski’s and KotarbiĔski’s polemics, Ajdukiewicz’s conception and Zawirski’s and Dąmbska’s considerations concerning the logical status of sentences about the future. Firstly, Augustynek proposed a definition of time (1970) compatible with relativistic physics; secondly, he analysed various properties of time (topological and symmetric, in particular) (1975); thirdly, he introduced relational notions of the past, the present and the future (1979). Snihur (1990) was his opponent regarding this last issue.
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Perzanowski’s analyses concerning space (within the framework of a more capacious system of locative ontology) (1993) match in rigor and elegance Augustynek’s analyses of time. 4.4. Theory of Change and Motion Theory of change should solve two difficulties: how to get over the paradoxes of motion and becoming and how to reconcile changes with identity of changing objects. Regarding the first matter, Ajdukiewicz proved that it is possible to describe change without infringing on the principle of non-contradiction or the principle of excluded middle (1948). In this matter, Placek’s subtle analyses turned out to be decisive (1989, 1995). Regarding the second matter, CzeĪowski wrote a short paper (1951a), while Augustynek gave it more attention, proposing his own definition of gen-identity (1981). 4.5. Theory of Determination and Causality The notions of determination and causality, and determinism and causalism, respectively, so absorbing for àukasiewicz and (later on) for KotarbiĔska, were reconstructed precisely by Zbigniew Jordan (1963a), Mazierski (1961), Augustynek (1962) and TrzĊsicki (1989).
5. Epistemology Methodology Praxiology During the last fifty years traditional epistemology has in fact not been cultivated in the Lvov-Warsaw School. Ajdukiewicz’s standpoint was decisive here: according to him, epistemological problems could be studied only after a suitable semantic paraphrase and after such a paraphrase they became indistinguishable from respective methodological problems. However, some people saw the necessity of distinguishing epistemology from methodology (Zamiara 1974). On the other hand, methodology itself could be recognised either as a fragment of praxiology, constructed in the second half of our century, or on the ground of some assumptions as a fragment of a theory of behaviour (Malewski 1964), or, finally, as a fragment of the cognitive sciences (Bobryk 1988) and the theory of artificial intelligence (LubaĔski 1975). In the youngest generation there is a tendency to return to traditional problems of epistemology in their original form, but with contemporary methods, e.g. the realism-idealism controversy (Krysztofiak 1999).
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5.1. Programs In Polish philosophy of the last half a century, four main (usually competing) methodological programs have functioned: apragmatical and pragmatical, on the one side and descriptive and normative, on the other. Moreover, they have been realised either by means of semantic analysis or by means of formal reconstruction. A clear differentiation between the first two programs referring to the general distinction between acts and results made by Twardowski appeared thanks to Ajdukiewicz (1948a). Thus, it was realised that (apragmatical) meta-science should be carefully separated from psychology and sociology of knowledge. Sociology of knowledge with some elements of historiosophy became an object of greater interest only in the last phase of the twentieth-century Polish philosophy (Pietruska-Madej 1980; Jodkowski 1909; Jonkisz 1990, 1998). In this trend they analysed such matters as the question of continuity (paradigms) and changeability (revolutions) in science. The meta-scientific attitude was dominant (Wójcicki 1974, 1982). The psychological and sociological analyses provoked, at once, serious objections of «apragmatists» (KaáuszyĔska 1994a). Apart from apragmatical or pragmatical interest, methodologists were divided with respect to descriptive and normative approaches. Some of them (Giedymin 1961; Kmita 1971, 1976, 1980; Nowak 1971, 1973; Sady 1990) wanted to restrict themselves to logical reconstruction of real procedures used by scholars to obtain these results. Others (Koj 1998; Hoáówka 1998) thought that their main task is the formulation of norms that determine the methodological duties of scientists. All these programs were criticised by Misiek (1979). 5.2. Knowledge-Generating Procedures Within both the pragmatical and apragmatical programs the knowledgegenerating procedures and their results were the object of detailed study. Firstly, analyses concerned observation and evidence (Rojszczak 1994), in general, as well as experience (Kalinowski 1991; Czarnocka 1992) and measurement (KaáuszyĔska 1983), in particular. Measurement was subjected to a deep analysis by Ajdukiewicz in the final period of his life (1961). In the School, a broad understanding of empirical knowledge dominated, which included not only knowledge acquired by introspection but also by axiological intuition (CzeĪowski 1989; PrzeáĊcki 1996). Problems of observation were formulated, in general, in terms of observational sentences; in such a context, the problem of the analytical
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components of factual sentences corresponded to the problem of the theoretical components of scientific facts (Jodkowski 1983). It was usually connected with the problem of the status of theoretical terms (Borkowski 1966; PrzeáĊcki 1969, 1993; Nowaczyk 1985, 1990; KaáuszyĔska 1994). ĩytkow (1979) identifies those terms with sets of operational procedures. Secondly, studies in inferential procedures (ways of reasoning), begun already by Twardowski and àukasiewicz, were creatively continued. Polish philosophers analysed both infallible (deductive) and fallible (inductive) inferences. As far as infallible inferences are concerned, the work focussed on the problems of mathematical proof (Sáupecki and Pogorzelski 1962) and its algorithmisation (Oráowska 1973; Zwinogrodzki 1976; Rasiowa and Banachowski 1977; Marciszewski and Murawski 1995), on the one hand, and the problems of verification (CzeĪowski 1951), on the other. Ajdukiewicz began the studies on the problem of the logical reconstruction of fallible inferences; Mortimer (1982) took it up in its full generality and Oráowska and Pawlak (1984) interpreted this kind of reasoning as inferences in systems with incomplete information. Other philosophers examined particular fragments of the logic of induction: the theory of inference by analogy (Dąmbska 1962) and the possibility of its mechanisation (Zwinogrodzki 1982); the theory of «historical» inferences (i.e., inferences on the basis of testimony) and the question of the reliability of informants (Giedymin 1961); finally, the theory of probabilistic (CzeĪowski 1952) and statistical inferences, in the light of which it appeared that the majority of fallible methods of inference have no degree of infallibility (Szaniawski 1994). A separate study was devoted to the notion of certitude (Sady 1993). Problems of deduction were seen, more and more commonly, as problems of justification; moreover deductive justification was opposed to deductive inference (Borkowski 1966). Analogously, induction was tied with the context of discovery, which was logically reconstructed in the spirit of the School (Zamecki 1988; Pietruska-Madej 1990; Sady 1990). Prognostics (WoleĔski 1984) and explanation, as well as the notions of scientific law (Pelc, PrzeáĊcki and Szaniawski 1957; Mazierski 1993) and hypothesis (Herbut 1978) respectively, were engaging a good deal of attention. Thirdly, procedures of formulating problems were not neglected. The theory of questions took the shape of erotetic logic. Among particular matters, the notion of the essence of a problem was at the centre of investigations.
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Fourthly, mereology and set theory were used to describe procedures of partition, classification and ordering. In particular, the theory of classification was developed by CzeĪowski (1950), Batóg and àuszczewska-Romahnowa (1965) and Batóg (1994), to whom we owe its generalisation. Fifthly, Polish philosophers gave a considerable amount of thought to the verbalisation and the interpretation of theories. Twardowski’s followers have always remembered his postulate of clarity and, even if they did not accept officially its theoretical foundation, arguing that sometimes a clear thought cannot be expressed clearly (Gorzka 1990), they have in practise struggled to observe this postulate in the highest degree. In this area, studies culminated in the analysis of definition, inaugurated in Poland in the contemporary manner by LeĞniewski and Ajdukiewicz. Afterwards, many people were occupied with the theory of definition: KokoszyĔska-Lutmanowa (1971, 1973), who favoured the view that there is only one notion of definition, contrary to Ajdukiewicz (1958), Gregorowicz (1962), Stonert (1959) (in the deductive sciences) and Pawáowski (1978) (in the humanities). 5.3. Rationality In the domain of epistemologico-methodological problems, the main subjects of inquiry were definition, typology and criteria of rationality. Pre-war Dąmbska’s research on irrationalism (1937) before the war constituted a background for later attempts to deal with this question. Her research was connected directly or indirectly with the work of Grzegorczyk (1993, 1997), who finds in rationality a distinctive feature of the European civilisation, of PrzeáĊcki (1996), who extends the notion of rationality beyond the limits of scientific knowledge, of with Marciszewski (1991), who concentrates his considerations mainly on the rationality of discussion, of ĩyciĔski (1993), who struggles to find the place of rationality within the compass of religion, and, finally, of Grobler (1993), who analyses especially the notion of deferred rationality. Apart from these considerations, rationality has been approached in decision theory (Szaniawski 1994). Finally, Kleszcz (1998) presented a review of the results of investigations in this area, distinguishing seven types of rationality (conceptual, logical, ontological, epistemological, methodological, practical and axiological); he contrasted the rationality of beliefs with the rationality of acts; described the difference between rationality, on the one hand, and irrationality or non-rationality, on the other; drew up a list of criteria
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for rationality, introducing into it: verbal precision, application of logical laws, criticism and resolvability of entertained problems. StrawiĔski (1991) also added simplicity to them and devoted a special study to it. An original conception of rationality was constructed by Taáasiewicz (2002). 5.4. Truth The question of truth has not stopped being a object of deep inquiries since Twardowski presented a persuasive criticism of alethic relativism and Tarski developed the semantic (model-theoretical) version of the correspondence conception of truth. Nobody in this environment – especially after KokoszyĔska’s additional explications questioned alethic absolutism. Ajdukiewicz quickly retracted his radical conventionalism. On the other hand, Dąmbska (1962, 1975a) argued that radical conventionalism did not lead to alethic relativism because conventions do not have to be arbitrary. The acceptance of moderate conventionalism (Giedymin 1982; Siemianowski 1983, 1989) could be reconciled, a fortiori, with the absolutist conception of truth. Let us add that in general scepticism in this matter was not shared (WiĞniewski 1992). Similarly, the opinion that the correspondence conception of truth is correct, dominated. It was pointed out that both the coherentist and pragmatic conceptions are inadequate. This was done by either referring to common sense (ChwedeĔczuk 1984) or to philosophical interpretations of limiting theses (WoleĔski 1993). On the other hand, Grzegorczyk (1996) explicitly proved the accuracy of the correspondence conception. This does not mean, however, that the explanatory power of alternative conceptions of truth was not investigated. Thus, a «non-Fregean» version of the correspondence conception was constructed where states of affairs stated by sentences are considered to be extra-linguistic counterparts of sentences. Such a version was recognised as the most adequate interpretation of the classical (Aristotelian) solution (Borkowski 1995; NieznaĔski 1984; Biáat 1994, 1995; Jadacki 2003). Tomasz Jordan’s (1989) attempts tended in a similar direction approaching the intuitions of natural languages. On the other hand, Grobler (1993) not without sympathy presented a version of the pragmatic conception, namely the dynamic (approximative) version, in which the property of being true is replaced by the relation of being-closer-to-the-truth-than. Jacek Malinowski (1995) studied the illocutionary version of the pragmatic conception with efficiency as the equivalent of truth. The consensual version of the pragmatic conception was reconstructed lately by Kijania-Placek (2000). ĩabski (1995) built an original logic for the nihilistic conception.
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5.5. Praxiology Although the problem of distinguishing and analysing actions (versus products) was formulated by Twardowski, it was KotarbiĔski (1956, 1966b) who was the real creator of the theory of action i.e., praxiology. Afterwards, Podgórecki (1962), Pszczoáowski (1969) and ZiembiĔski (1972a) proposed important contributions and improved syntheses.
6. Philosophy of Science 6.1. Classification of the Sciences Twardowski made a penetrating analysis of the traditional classifications of sciences: the classification into a priori sciences and a posteriori sciences, in particular. The most universal inquiries into the notion of science and the classification of scientific disciplines – from various points of view – were undertaken by KamiĔski (1961). 6.2. Philosophy of Mathematics In philosophy of mathematics, Batóg (1996) and Murawski (1995, 1999) were active. In particular, the question of the philosophical significance of reverse mathematics held the attention of the latter. Now, two representatives of the younger generation have joined them; they have examined in great depth the arguments on account of mathematical realism (Bigaj 1997; Wójtowicz 1999) and intuitionism (Placek 1999). 6.3. Philosophy of Physics, Chemistry and Biology In philosophy of physics, the question of the philosophical interpretation of relativistic physics was continuously at issue (Czerniawski 1993). Lately, the theory of chaos and its implications for general philosophy have become an object of study (Tempczyk 1995, 1998). At the beginning of the period in question, Mehlberg (1951) considered the controversy between idealism and realism in contemporary physics; and at the end of it, Jodkowski (1996) studied the controversy between evolutionism and creationism in contemporary biology. Pietruska-Madej’s attention (1975) turned to the philosophy of chemistry.
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6.4. Philosophy of Psychology and Sociology Two philosophers from the circle of the Lvov-Warsaw School, Bobryk (1988) and Rzepa (2002), occupied themselves with the philosophical problems of psychology. 6.5. Philosophy of the Humanities: Linguistics, Jurisprudence and History The most serious results in the philosophy of linguistics were achieved by the program of formalising theoretical phonology, formulated and realised by Batóg (1967) and Pogonowski (1979, 1981). As a result, the reduction of the basic phonological categories was obtained (Batóg 1967). Relatively many philosophers worked creatively in the philosophy of law (ZiembiĔski 1963; Gregorowicz 1963; WoleĔski 1972, 1980, 1999; Nowak 1968, 1973). For instance, the status of juristic definitions (Gregorowicz 1962), modes of justifying juristic norms (ZiembiĔski 1972) and the relation between juristic and ethical norms (ZiembiĔski 1966) were investigated. Giedymin (1961, 1964), Nowak and Kmita (1968), and Kmita and Zamiara (1989) pursued the methodology of history – and the humanities, more broadly – concentrating their efforts especially on the reconstruction of interpretation procedures and also on the explaination of the status of theoretical terms in the theory of belles-lettres. 6.6. Reductionism and Holism The problem of integrating the sciences and the chances of reductionism in this field were investigated by StrawiĔski (1997) and Grobler (1993). Jedynak (1998) probed in detail the empiricist version of reductionism. She showed that it cannot be fully realised because of a disharmony of its particular components. Siemianowski (1988) indicated the consequences of radical empirism.
7. Axiology 7.1. Description, Estimation and Norm It was Twardowski’s Lvov lectures in ethics that proved to be the main impulse for inquiries in axiology (or, strictly speaking, ethics) among Polish philosophers influenced by the Lvov-Warsaw School. In these
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lectures, the founder of the School declared himself as a cognitivist and an axiologist regarding the question of the relations between description, estimation and norm. This standpoint mainly thanks to Znamierowski (1957), CzeĪowski (1989) and Ossowska (1947, 1963) has become the dominant paradigm in this context. Ethics as Ossowska emphatically stated could be a science and not just a set of moral norms, but it would have to be a real science of moral phenomena which would provide their scientific description and which would contain meta-ethics (1970) as well as psychology and sociology of morality (1963). Within the framework of the last of these, Ossowska, herself, reconstructed two examples of an ethos present in Polish society: the chivalry ethos (1973) and the middle-class ethos (1956). 7.2. Ontic Status and the Universality of Values In the controversy regarding the ontic status of values Twardowski and other representatives of the School after him (Tatarkiewicz 1919, 1938; PrzeáĊcki 1989) took the objectivist position: some objects are goods per se and not because somebody considers them as goods. The construction of a formal theory of goods has become a goal and it was CzeĪowski who gave the outline of such a theory first (1960). Objectivism was joined, in principle, with absolutism. At the same time, the analysis of scepticism (Dąmbska 1948) and relativism in relation to the question of the universality of values was engaging a good deal of attention. Lazari-Pawáowska (1975), following the slogan of the School clara et distincta contrasted axiological relativism with methodological, situational and cultural relativisms. Hoáówka presented a monograph on the problem (1981). 7.3. Motivation and Respecting Norms In the controversy regarding the sources of approval of moral norms, Twardowski and his followers were adherents of autonomism: moral norms do not need external justification, in general, and religious justification, in particular. For that reason, systems of independent ethics were developed (KotarbiĔski 1958a); they assumed the shape of atheistic Christianity (PrzeáĊcki 1989), i.e., hic et nunc catholic ethics but without theistic theses. Usually, autonomism was connected with intuitionism (CzeĪowski 1989). According to axiologism, good is what is commanded; and, what is good in individual situations is in the intuitionists’ opinion simply
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«visible». Thus, it is not surprising that the «organ» of moral cognition, conscience, was analysed in detail (Górnicka-Kalinowska 1992). Twardowski was rigorist as to respecting moral norms. None of his followers proclaimed (or respected) such a radical rigor and some people (KotarbiĔski 1966a; Lazari-Pawáowska 1992) tended rather towards a «soft» utilitarianism, whose praxiological version was presented by Pszczoáowski (1982). Anyway, philosophers referring to Twardowski’s program of scientific ethics offered deep analyses of the notions of responsibility and fault (Znamierowski 1957a), liberty (LazariPawáowska 1992) and justice (Ajdukiewicz 1939), including just distribution of goods (Szaniawski 1994). 7.4. Ethical Systems Separating, following Twardowski and Ossowska, ethical standpoints from the science of moral phenomena (as science ex definitione) Polish philosophers working under the sign of the Lvov-Warsaw School tried to put their own «unscientific» ethical views into the shape of possible, rationally reconstructed systems. Altruism, humanitarianism and perfectionism were stable reference points here. It is necessary (according to altruism) to take care not only of our own welfare but also and maybe first of all (PrzeáĊcki 1989) of others’ welfare. The dominant position was occupied by the ethics of favour towards others (Znamierowski 1957c), of good relations with others (Ossowska 1949) or at least of esteem in relation to others (Witwicki 1957). Fair life consists just of taking care of others’ welfare (KotarbiĔski 1966a). In connection with the altruistic attitude, semantic analyses of such notions as tolerance (Lazari-Pawáowska 1992) were put forth. In the controversy between maximalism and minimalism, the majority opinion was on the side of minimalism. Taking care of others’ welfare should manifest itself, in particular, in trying to minimalise the pains that others experience. This was the position of humanitarianism (LazariPawáowska 1992). As far as our own good is concerned, the perfectionistic-ascetic standpoint was dominant: we ought to perfect our virtues but the number of perfected virtues if the enterprise is to be successful should be radically limited to civic virtues in particular (Ossowska 1970). Hedonism was in fact only an object of theoretical interest. Tatarkiewicz (1947) offered a splendid analysis of the notion of happiness, separating the happiness of an ethical character from vital, psychological and dispositional happiness. One of the results of this analysis was a
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justification of the thesis that hedonist happiness cannot be a rational aim of human activity. 7.5. Aesthetics In aesthetics, studies were focused on the psychology of creation and perception of art (Tatarkiewicz 1951; Wallis 1968). Pawáowski (1989) initiated an inquiry into aesthetic values, trying to make use of Ockham’s razor also in this sphere.
8. Formalisation and Axiomatisation of Various Domains of Knowledge According to the paradigm of the Lvov-Warsaw School at least in the version which owes its shape to àukasiewicz (1927) and LeĞniewski (1927) the final form of philosophical disciplines should be their logical reconstruction and presentation in the shape of axiomatised formal systems. In the second half of our century, Poles constructed a few important systems of such «regional» logics, mainly of intensional character (Malinowski 1989). 8.1. Natural Deduction As far as a fragment of methodology is concerned, such a system was presented as early as 1934 by JaĞkowski as a system of natural deduction (assumptional logic). It was a realisation of àukasiewicz’s postulate (1927) to reconstruct the real modes of reasoning used in mathematics in logical terms. Afterwards, many philosophers worked on developing and perfecting this system: Iwanicki (1949), Sáupecki and Borkowski (1963), and lately Dudkiewicz (1988), who concentrated his efforts on using the method of semantic matrices. 8.2. Deontic Logic Deontic logic was a regional logic for ethics and jurisprudence. It was developed by Kalinowski (1965, 1972, 1996), GumaĔski (1980, 1981), Ziemba (1969, 1983), Ziemba and ĝwirydowicz (1988) and WoleĔski (1990).
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8.3. Diachronical Logic With historical inquiries in mind, Suszko (1957a) built a system of diachronic logic. 8.4. Relevant Logic and Categorial Grammar In the domain of natural languages, LeĞniewski’s and Ajdukiewicz’s ideas were developed; they were put into the mature form of categorial grammars (Suszko 1958-1960; Stanosz and Nowaczyk 1976; Buszkowski 1989). On the other hand, problems with using «normal» logic to examine natural languages signalised by Tarski resulted in the development of relevant logic (Tokarz 1993). 8.5. «Creational» Logic Praxiology «obtained» a «creational» logic, i.e., logic of action (efficiency) (KubiĔski 1985). 8.6. Doxastic (Epistemic) Logic It was àukasiewicz who set the framework for inquiries into the logic of convictions in Poland with his analysis of systems with functors of acceptance and rejection, written in connection with his reconstruction of Aristotle’s logic. àukasiewicz’s work concerning the logic of rejection was continued by Wybraniec-Skardowska and Bryll (1969), as well as by Sáupecki, Bryll and Wybraniec-Skardowska (1971-1972). Marciszewski devoted a monograph to the general theory of beliefs (1972). 8.7. Modal, Temporal, Transformational and Causal Logic Polish philosophers were also interested in the logical reconstruction of problems in the ontology of physics. Various modal systems for the notions of necessity and possibility were built (JaĞkowski 1951; ĩarnecka-Biaáy 1973; Perzanowski 1989). A review of various attitudes towards problems of modality in logic and philosophy was elaborated (ĩegleĔ 1990). Great efforts were made to construct a temporal, «transformational» logic that could help to avoid the problem of change, which threatened the principle of non-contradiction. Using àukasiewicz’s, Zawirski’s, Sáupecki’s and àoĞ’s ideas, Rogowski (1964), Kiczuk (1984a, 1991), and Wajszczyk (1989, 1995) engaged in research in this domain. Wajszczyk proposed detailed systems both for dichotomous (being non-being and vice versa) and continuous changes. In the case of causal
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logic, as in the case of modal and temporal logic, the impulse came from àukasiewicz and JaĞkowski (1951); later philosophers from a younger generation (Kiczuk 1984, 1995) have joined them. 8.8. «Theological» Logic The program of scientific philosophy, formulated by Twardowski (1921), was later extended by àukasiewicz, Drewnowski, BocheĔski and Salamucha to cover also theology. The extension was undertaken against the opinions of, e.g. Witwicki (1939), who claimed that theological problems (and religion in general) belonged to an irrational sphere. Witwicki’s view was endorsed by ChwedeĔczuk (1997, 2000) and it seems by the majority of the School’s sympathisers. Nevertheless, the opposite view has never lacked defenders (ĩyciĔski 1985-1986; Bronk 1996). The main efforts were put into the logical analysis of traditional justifications (proofs) of the basic theistic thesis that God exists (Salamucha 1934; BocheĔski 1965; NieznaĔski 1980).
9. Final Remark I end here my review of the theoretical problems and the results achieved by contemporary Polish philosophy that acknowledges its links with the Lvov-Warsaw tradition. To avoid possible misunderstandings, I must stress that my picture is necessarily of a sketchy character. One can hardly expect more than an introductory diagnosis, if one realises that now, in Poland, there are circa two thousand active philosophers and that two hundred of them are full titular professors!
Uniwersytet Warszawski Department of Philosophy ul. Krakowskie PrzedmieĞcie 3 00-047 Warszawa, Poland e-mail:
[email protected]
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REFERENCES Ajdukiewicz, K. (1935). Der logistische Antiirrationalismus in Polen. Erkenntnis 5, 151-164. Ajdukiewicz, K. (1939). O sprawiedliwoĞci [On Justice]. Reprinted in: Ajdukiewicz (1960-1965), vol. 1, pp. 365-376. Ajdukiewicz, K. (1948). Change and Contradiction. Reprinted in: Ajdukiewicz (1978), pp. 492-208. Ajdukiewicz, K. (1948a). Methodology and Metascience. Reprinted in: PrzeáĊcki and Szaniawski, eds. (1977), pp. 1-12. Ajdukiewicz, K. ([1948] 1983). Zagadnienia i kierunki filozofii: Teoria poznania, metafizyka [Problems and Orientations of Philosophy: Theory of Knowledge, Metaphysics]. Warszawa: Czytelnik. English version: Problems and Theories of Philosophy. Cambridge: Cambridge University Press, 1973. Ajdukiewicz, K. (1958). Three Concepts of Definition. Logique et Analyse 1, 3-4, 115-126. Ajdukiewicz, K. (1960-1965). JĊzyk i poznanie [Language and Cognition]. 2 vols. Warszawa: PWN. Ajdukiewicz, K. (1961). Pomiar [Measurement]. Reprinted in: Ajdukiewicz (1960-1965), vol. 2, pp. 356-364. Ajdukiewicz, K. ([1965] 1974). Pragmatic Logic. Warszawa & Dordrecht: PWN & D. Reidel. Ajdukiewicz, K. (1978). The Scientific World-Perspective and Other Essays (1931-1963). Edited by J. Giedymin. Dordrecht: Reidel. Augustynek, Z. (1962). Determinizm fizyczny [Physical Determinism]. Studia Filozoficzne 3, 3-65. Augustynek, Z. (1970). WáasnoĞci czasu [Properties of Time]. Warszawa: PWN. Augustynek, Z. (1975). Natura czasu [The Nature of Time]. Warszawa: PWN. Augustynek, Z. (1979). PrzeszáoĞü, teraĨniejszoĞü, przyszáoĞü [Past, Present, Future]. Warszawa: PWN. English version: Time: Past, Present, Future. Warszawa & Dordrecht: PWN & Kluwer, 1991. Augustynek, Z. (1981). Genidentity. Dialectics and Humanism 8, 1, 193-202. Augustynek, Z. (1997). CzasoprzestrzeĔ: Eseje filozoficzne [Space-time: Philosophical Essays]. Warszawa: WFiS UW. Augustynek, Z. and J.J. Jadacki (1993). Possible Ontologies. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 29. Amsterdam: Rodopi. Batóg, T. (1967). The Axiomatic Method in Phonology. London: Routledge and Kegan Paul. Batóg, T. (1986). Podstawy logiki [Foundations of Logic]. PoznaĔ: Wydawnictwo Naukowe UAM. Batóg, T. (1994). Studies in Axiomatic Foundations of Phonology. PoznaĔ: Wydawnictwo UAM. Batóg, T. (1996). Dwa paradygmaty: Studium z dziejów i filozofii matematyki [Two Paradigms: An Essay from the History and Philosophy of Mathematics]. PoznaĔ: Wydawnictwo Naukowe UAM Batóg, T. and S. àuszczewska-Romahnowa (1965). A Generalized Theory of Classifications, Part 1-2. Studia Logica 16, 53-73; 17, 7-24. Bigaj, T. (1997). Matematyka a Ğwiat realny [Mathematics and the Real World]. Warszawa: WFiS UW.
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Biáat, A. (1994). Prawda i stany rzeczy [Truth and States of Affairs]. Lublin: Wydawnictwo UMCS. Biáat, A. (1995). Spór o prawdĊ i stany rzeczy [Controversy about Truth and States of Affaires]. Ruch Filozoficzny 52, No. 2, 203-209. Bobryk, J (1988). The Classical Vision of the Mind and Contemporary Cognitive Psychology. Warszawa: Wydawnictwo UW. BocheĔski, J.M. (1947). La philosophie. In: J. Romer and J. Modzelewski (eds.), Pologne 1919-1939, vol. 3, pp. 229-260. Neuchâtel: Edition de la Baconnière. BocheĔski, J.M. (1965). Logic of Religion. New York: New York University Press. BocheĔski, J.M. (1993). Logika i filozofia: Wybór pism [Logic and Philosophy: Selected Works]. Edited by J. Parys. Warszawa: Wydawnictwo Naukowe PWN. Borkowski, L. (1958-1960). On Proper Quanitifiers. 2 parts. Studia Logica 8, 65-130; 10, 7-28. Borkowski, L. (1966). Deductive Foundation and Analytic Propositions, Studia Logica 19, 59-74 Borkowski, L. (1970). Logika formalna: Systemy logiczne: WstĊp do metalogiki [Formal Logic: Logical Systems: Introduction to Meta-Logic]. Warszawa: PWN. Borkowski, L. (1995). Pisma o prawdzie i stanach rzeczy [Works ond Truth and States of Affairs]. Lublin: Wydawnictwo UMCS. Bronk, A. (1996). Nauka wobec religii: Teoretyczne podstawy nauk o religii [Science and Religion: Theoretical Foundations of Sciences of Religion]. Lublin: TN KUL Buszkowski, W. (1989). Logiczne podstawy gramatyk kategorialnych AjdukiewiczaLambeka [Logical Foundations of Ajdukiewicz-Lambek’s Categorial Grammars]. Warszawa: PWN. Cackowski, Z., J. Kmita, P.J. SmoczyĔski and K. Szaniawski, eds. (1987). Filozofia a nauka: Zarys encyklopedyczny [Philosophy and Science: An Encyclopaedic Outline]. Wrocáaw: Ossolineum. ChwedeĔczuk, B. (1984). Spór o naturĊ prawdy [The Controversy about the Nature of Truth]. Warszawa: PIW. ChwedeĔczuk, B. (1997). “Trzeba w coĞ wierzyü?” i inne eseje z filozofii praktycznej [“Does One Need to Believe in Something?” and Other Essays in Practical Philosophy]. Warszawa: Aletheia. ChwedeĔczuk, B. (2000). Przekonania religijne [Religious Beliefs]. Warszawa: Aletheia. Coniglione, F., R. Poli and J. WoleĔski, eds. (1993). Polish Scientific Philosophy. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 28. Amsterdam: Rodopi. Costa, N.C.A. da and L. Dubikajtis (1968). Sur la logique discoursive de JaĞkowski. Bulletin Académie Polonaise des Sciences 15, 551-557. Costa, N.C.A. da and L. Dubikajtis (1977). On JaĞkowski’s Discurssive Logic. In: A.I. Arruda, N.C.A. da Costa and R Chuaqui (eds.), Non-Classical Logic, Model Theory and Computability, pp. 37-56. Amsterdam: North-Holland Publishing Company. Czarnocka, M. (1986). Kryteria istnienia w naukach przyrodniczych [Criteria of Existence in Physical Sciences]. Wrocáaw: Ossolineum. Czarnocka, M. (1992). DoĞwiadczenie w nauce: Analiza epistemologiczna [Experience in Science: Epistemological Analysis]. Warszawa: IFiS PAN. Czelakowski, J. (1980). Model-Theoretic Methods in the Methodology of Propositional Calculi. Warszawa: PAN. Czerniawski, J. (1993). Zrozumieü teoriĊ wzglĊdnoĞci [Understanding the Theory of Relativity]. Kraków: Tasso.
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Czerniawski, J. (1997). Jakiego reizmu Polacy potrzebują? [What Kind of Reism do the Poles Need?] Kwartalnik Filozoficzny 25, No. 3, 5-34. CzeĪowski, T. (1950). Klasyfikacja rozumowaĔ [Classification of Reasoning]. In: CzeĪowski (1958), pp. 186-196. CzeĪowski, T. (1951). De la vérification dans les sciences empiriques. Revue Internationale de la Philosophie 5, 347-366. CzeĪowski, T. (1951a). Identity and the Individual in Its Persistence. Reprinted in: CzeĪowski (2000), pp. 160-168. CzeĪowski, T. (1952) O rozumowaniu prawdopodobieĔstwowym [On Probabilistic Reasoning]. Sprawozdania Towarzystwa Naukowego w Toruniu 4 (1950), 83-88. CzeĪowski, T. (1956). On the Method of Analytic Description. Reprinted in: CzeĪowski (2000), pp. 42-51. CzeĪowski, T. (1958). Odczyty filozoficzne [Philosophical Lectures]. ToruĔ: Towarzystwo Naukowe w Toruniu. CzeĪowski, T. (1960). How to Construct the Logic of Goods. Reprinted in: CzeĪowski (2000), pp. 169-174. CzeĪowski, T. (1989). Pisma z etyki i teorii wartoĞci [Papers on Ethics and the Theory of Value]. Wrocáaw: Ossolineum. CzeĪowski, T. (2000). Knowledge, Science, and Values. Edited by L. GumaĔski. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 68. Amsterdam: Rodopi. Dąmbska, I. (1937). Irracjonalizm a poznanie naukowe [Irrationalism and Scientific Knowledge]. Kwartalnik Filozoficzny 14, No. 2, 83-118; 14, No. 3, 185-212. Dąmbska, I. (1948). O rodzajach sceptycyzmu [On Types of Scepticism]. Kwartalnik Filozoficzny 17, No. 1-2, 79-86. Dąmbska, I. (1949). Issues in the Philosophy of Proper Names. Reprinted in: Pelc, ed. (1977), pp. 131-143. Dąmbska, I. (1962). Dwa studia z teorii naukowego poznania [Two Essays in the Theory of Scientific Knowledge]. ToruĔ: Towarzystwo Naukowe w Toruniu. Dąmbska, I. (1967). O narzĊdziach i przedmiotach poznania [On Tools and Objects of Knowledge]. Warszawa: PWN. Dąmbska, I. (1975). Znaki i myĞli [Signs and Thoughts]. Warszawa: PWN. Dąmbska, I. (1975a). O konwencjach i konwencjonalizmie [On Conventions and Conventionalism]. Wrocáaw: Ossolineum Drewnowski, J.F. (1996). Filozofia i precyzja: “Zarys programu filozoficznego” i inne pisma [Philosophy and Precision: “An Outline of the Philosophical Program” and Other Works]. Lublin: TN KUL. Dudkiewicz, R. (1988). Z badaĔ nad metodą tablic semantycznych [Studies on the Method of Semantic Matrices]. Lublin: Redakcja Wydawnictw KUL. Franzke, N. and W. Rautenberg (1972). Zur Geschichte der Logik in Polen. In: H. Wessel (ed.), Quantoren, Modalitäten, Paradoxien, pp. 33-94. Berlin: Deutscher Verlag der Wissenschaften. Giedymin, J. (1961). Z problemów logicznych analizy historycznej [From Logical Problems of Historical Analysis ]. PoznaĔ: PTPN PWN. Giedymin, J. (1964). Problemy, ZaáoĪenia, RozstrzygniĊcia: Studia nad logicznymi podstawami nauk spoáecznych [Problems, Assumptions, Resolutions: Studies in Logical Foundations of Social Sciences]. PoznaĔ 1964: PWN. Giedymin, J. (1982). Science and Convention. Essays on Henri Poincaré’s Philosophy of Science and the Conventionalists Tradition. Oxford: Pergamon Press.
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Gorzka, C. (1990). Kazimierza Twardowskiego koncepcja jasnego stylu filozoficznego [Kazimierz Twardowski’s Conception of Clear Philosophical Style]. Ruch Filozoficzny 47, No. 3-4, 251-254. Gorzka, C. (1999). Ontologia bezpunktowa a mereologia [Ontology without Points and Mereology]. Ruch Filozoficzny 61, No. 1, 55-63. Górnicka-Kalinowska, J. (1992). Idea sumienia w filozofii moralnej [The Idea of Conscience in Moral Philosophy]. Warszawa: Wydawnictwa UW. Gregorowicz, J. (1962). Definicje w prawie i nauce prawa [Definitions in Law and Jurisprudence]. àódĨ: àTN. Gregorowicz, J. (1963). Z problemów logicznych stosowania prawa [Logical Problems in the Application of Law]. àódĨ: àTN. Grobler, A. (1993). Prawda i racjonalnoĞü naukowa [Truth and Scientific Rationality]. Kraków: Inter Esse. Grzegorczyk, A. (1989). Maáa propedeutyka filozofii naukowej [A Short Introduction to Scientific Philosophy]. Warszawa: Pax. Grzegorczyk, A. (1993). ĩycie jako wyzwanie: Wprowadzenie w filozofiĊ racjonalistyczną [Life as a Challenge: Introduction into Rationalistic Philosophy]. Warszawa: Wydawnictwo IFiS PAN. Grzegorczyk, A. (1996). Tarski’s Conception of Truth and Its Application to Natural Language. Dialogue and Universalism 1-2, 73-89. Grzegorczyk, A. (1997). Logic a Human Affair. Warszawa: Wydawnictwo Naukowe Scholar. GumaĔski, L. (1960). Logika klasyczna a zaáoĪenia egzystencjalne [Classical Logic and Existential Commitments]. Zeszyty Naukowe UMK. Nauki Humanistyczno-Spoáeczne. Filozofia 4, 3-64. GumaĔski, L. (1961). Elementy sądu a istnienie [Elements of Judgment and Existence]. ToruĔ: Towarzystwo Naukowe w Toruniu. GumaĔski, L. (1980). On Deontic Logic. Studia Logica 39, No. 1, 63-75. GumaĔski, L. (1981). Wprowadzenie w logikĊ wspólczesną [Introduction to Contemporary Logic]. ToruĔ: UMK. Herbut, J. (1978). Hipoteza w filozofii bytu [A Hypothesis in the Philosophy of Being]. Lublin: Wydawnictwa KUL. Hoáówka, J. (1981). Relatywizm etyczny [Ethical Relativism]. Warszawa: PWN. Hoáówka, T. (1998). BáĊdy, spory, argumenty: Szkice z logiki stosowanej [Errors, Controvercies, Arguments: Essays in Applied Logic]. Warszawa: WFiS UW. Hosiasson-Lindenbaumowa, J. (1941). Induction et analogie: comparaison de leur fondement. Mind 50 (200), 351-365. Ingarden, R. (1973). Gáówne kierunki w polskiej filozofii. Studia Filozoficzne 1, 3-15. English version: Main Directions of Polish Philosophy, Dialectics and Humanism 2 (1974), 91-103. Iwanicki, J. (1949). Dedukcja naturalna i logistyczna [Natural and Logistic Deduction]. Warszawa: Polskie Towarzystwo Teologiczne. Iwanicki, J. (1965). O sylogistyce Arystotelesa [On Aristotle’s Syllogistics]. Studia Philosophiae Christianae 2, 67-101. IwanuĞ, B. (1969). An Extension of the Traditional Logic Containing the Elementary Ontology and the Algebra of Classes. Studia Logica 25, 97-139. IwanuĞ, B. (1973). On LeĞniewski’s Elementary Ontology. Studia Logica 31, 73-125. IwanuĞ, B. (1976). W sprawie tzw. nazw pustych [On the Matter of the So-Called Empty Names]. Acta Universitatis Wratislaviensis 290 (Prace Filozoficzne 18), 73-90.
The Lvov-Warsaw School and Its Influence on Polish Philosophy
71
IwanuĞ, B. (1980). A Proof of Completeness of a Theory of Algebras of Sets. Acta Universitatis Wratislaviensis 546 (Prace Filozoficzne 25), 1-56. Jadacki, J.J. (1980). On the Sources of Contemporary Polish Logic. Dialectics and Humanism 7, No. 4, 163-183. Jadacki, J.J. (2003). From the Viewpoint of the Lvov-Warsaw School. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 78. Amsterdam: Rodopi. JaĞkowski, S. (1934). On the Rules of Suppositions in Formal Logic. Studia Logica 1, 5-32. JaĞkowski, S. (1951). On the Modal and Causal Functions in Symbolic Logic. Studia Philosophica 4, 71-92. JaĞkowski, S. (1948). Rachunek zdaĔ dla systemów dedukcyjnych sprzecznych [Propositional Calculus for Contradictory Deductive Systems]. Studia Societatis Scientiarum Toruniensis (Section A) 1, 55-77. English version: Propositional Calculus for Contradictory Deductive Systems, Studia Logica 24 (1969), 143-157. Jedynak, A. (1998). Empiryzm i znaczenie [Empricism and Meaning]. Warszawa: WFiS UW. Jodkowski, K. (1983). Problem uteoretyzowania faktów naukowych [The Problem of the Theoretical Nature of Facts]. Zagadnienia Naukoznawstwa 4, 419-435. Jodkowski, K. (1990). Wspólnoty uczonych, paradygmaty i rewolucje naukowe [Communities of Scholars, Paradigms and Scientific Revolutions]. Lublin: Wydawnictwo UMCS. Jodkowski, K. (1996). Metodologiczne aspekty kontrowersji ewolucjonizm-kreacjonizm [Methodological Aspects of the Evolutionism-Creationism Controversy]. Lublin: Wydawnictwo UMCS. Jonkisz, A. (1990). Struktura, zmiennoĞü i postĊp nauk: UjĊcie strukturalne [Structure, Changeability and the Progress of Sciences: A Structural Approach]. Lublin: UMCS. Jonkisz, A. (1998). CiągáoĞü teoretyczna wytworów nauki: UjĊcie strukturalne [Theoretical Continuity or Scientific Products: A Structural Approach]. Lublin: Wydawnictwo UMCS. Jordan, T. (1989). Aksjomatyczna definicja zdania prawdziwego w jĊzyku potocznym [Axiomatic Definition of a True Sentence in a Natural Language]. Studia Philosophiae Christianae 25, No. 2, 204-222. Jordan, Z. (1945). The Development of Mathematical Logic and of Logical Positivism in Poland between Two Wars. Oxford: Oxford Univeristy Press. Jordan, Z. (1963). Philosophy and Ideology. The Development of Philosophy and Marxism-Leninism in Poland since the Second World War. Dordrecht: Reidel Jordan, Z. (1963a). Logical Determinizm. Notre Dame Journal of Formal Logic 4, No. 1, 1-38. Kalinowski, J. (1965). Introduction à la logique juridique. Paris: T. Pchon et R. DurandAuzias. Kalinowski, J. (1972). Etudes de la logique deontique. Paris: Librairie Générale de Droit et de Jurisprudence. Kalinowski, J. (1991). Expérience et phenomenologie: Husserl, Ingarden, Scheler. Paris: Editions Univeristaires. Kalinowski, J. (1996). La logique déductive. Essai de présentation aux juristes. Paris: Presses Universitaires de France. KaáuszyĔska, E. (1983). WielkoĞü empiryczna i skale pomiarowe [Empirical Magnitude and Measurement Scales]. Wrocáaw: PWr. KaáuszyĔska, E. (1994). Modele teorii empirycznych [Models of Empirical Theories]. Warszawa: Wydawnictwo IFiS PAN.
72
Jacek Jadacki
KaáuszyĔska, E. (1994a). Styles of Thinking. In: W. Herfel, W. Krajewski, I. Niiniluoto and R. Wójcicki (eds.), Theories and Models in Scientific Processes (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 44), pp. 85-103. Amsterdam: Rodopi. KamiĔski, S. (1961). PojĊcie nauki i klasyfikacja nauk [The Notion of Science and the Classification of the Sciences]. Lublin: TN KUL. KamiĔski, S. (1977). The Development of Logic and the Philosophy of Science in Poland after the Second World War. Zeitschrift für allgemeine Wissenschaftentheorie 8, 163-171. KamiĔski, S. (1989-1998). Dzieáa zebrane [Collected Works]. 5 vols. Edited by A. Bronk, J. Herbut, T. Szubka, U. ĩegleĔ and M. Walczak. Lublin: TN KUL. Kiczuk, S. (1984). J. àukasiewicz’s Conception of the Causal Relation and Contemporary Causal Logic. Studies in Logic and Theory of Knowledge 1, 45-52. Kiczuk, S. (1984a). Problematyka wartoĞci poznawczej systemów logiki zmiany [Problems of Cognitive Value of Systems of the Logic of Change]. Lublin: Redakcja Wydawnictw KUL. Kiczuk, S. (1991). The System of the Logic of Change. Studies in Logic and Theory of Knowledge 2, 51-96. Kiczuk, S. (1995). Związek przyczynowy a logika przyczynowoĞci [Causal Relation and the Logic of Causality]. Lublin: Redakcja Wydawnictw KUL. Kijania-Placek (2000). Prawda i konsensus [Truth and Consensus]. Kraków: Wydawnictwo UJ. Kijania-Placek, K. and J. WoleĔski, eds. (1998). The Lvov-Warsaw School and Contemporary Philosophy. Dordrecht: Kluwer Academic Publishers. Kleszcz, R. (1998). O racjonalnoĞci: Studium epistemologiczno-metodologiczne [On Rationality: An Epistemological-Methodological Study]. àódĨ: Wydawnictwo Uà. Kmita, J. (1971). Z metodologicznych problemów interpretacji humanistycznej [Some Methodological Problems of Humanistic Interpretation]. Warszawa: PWN. Kmita, J. (1976). Szkice z teorii poznania naukowego [Essays on the Theory of Scientific Knowledge]. Warszawa: PWN. Kmita, J. ([1980] 1988). Problems in Historical Epistemology. Dordrecht & Warszawa: D. Reidel Publishing C. & PWN. Kmita, J. and K. Zamiara (1989). Visions of Culture and the Models of Cultural Science. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 15. Amsterdam: Rodopi. Koj, L. (1963). The Principle of Transparency and Semantic Antinomies. Reprinted in: Pelc, ed. (1979), pp. 376-406. Koj, L. (1964). O definiowaniu wyraĪeĔ okazjonalnych [On Defining Indexical Expressions]. Annales UMCS (Section F) 19, 27-55. Koj, L. (1969). Stosunek logiki do pragmatyki [The Relation between Logic and Pragmatics]. Lublin: UMCS. Koj, L. (1998). PowinnoĞci w nauce [Duties in Science], vol. 1: OkreĞlenie i poznawalnoĞü powinnoĞci [The Definition and Knowledge of Duties]. Lublin: Wydawnictwo UMCS. Koj, L. and A. WiĞniewski (1989). Inquiries into the Generating and Proper Use of Questions. Lublin: Wydawnictwo UMSC. KokoszyĔska-Lutmanowa, M. (1971). Trzy pojĊcia definicji czy jedno? [Three Notions or One Notion of Definition]? Ruch Filozoficzny 29, No. 1, 34-36. KokoszyĔska-Lutmanowa, M. (1973). Z teorii definicji [A Contribution to the Theory of Definition]. Ruch Filozoficzny 31, No. 1, 33-37.
The Lvov-Warsaw School and Its Influence on Polish Philosophy
73
KotarbiĔska, J. (1990). Z zagadnieĔ teorii nauki i teorii jĊzyka [Some Problems of the Theory of Science and the Theory of Language]. Warszawa: PWN. KotarbiĔski, T. ([1929] 1961). Elementy teorii poznania, logiki formalnej i metodologii nauk [Elements of the Theory of Knowledge, Formal Logic and Methodology of Science]. Wrocáaw: Ossolineum. English version: Gnosiology. Wrocáaw & Oxford: Ossolineum & Pergamon Press, 1966. KotarbiĔski, T. (1933). Grundlinien und Tendenzen der Philosophie in Polen. Slavische Rundschau 5, No. 4, 218-229. KotarbiĔski, T. (1956). SprawnoĞü i báąd [Skillfulness and Error]. Warszawa: PZWS. KotarbiĔski, T. (1957). Wybór pism [Selected Writings]. 2 vols. Warszawa: PWN. KotarbiĔski, T. (1958). La logique en Pologne. In: R. Klibansky (ed.), Philosophy in the Mid-Century, vol. 1: A Survey, pp. 234-241. Firenze: La Nuova Italia Editrice. KotarbiĔski, T. (1958a). Problèmes d’une éthique indépendante. Morale et Enseignement 7, No. 28, 1-14. KotarbiĔski, T. (1966a). Medytacje o Īyciu godziwym [Reflections on Fair Life]. Warszawa: Wiedza Powszechna. KotarbiĔski, T. (1966b). Traktat o dobrej robocie [Treatise on Good Work]. àódĨ: àTN. KotarbiĔski, T. (1990-2003). Dzieáa wszystkie [Collected Works]. 5 vols. Wrocáaw: Ossolineum. Kowalski, Z., W. Krysztofiak and A. Biáat (1998). Koncepcje negatywnych stanów rzeczy [Conceptions of Negative States of Affairs]. Lublin: UMCS. Krajewski, W., ed. (1982). Polish Essays in the Philosophy of the Natural Sciences. Dordrecht: Reidel. Krajewski, W., ed. (2001). Polish Philosophers of Science and Nature in the 20th Century. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 74. Amsterdam: Rodopi. Krynicki, M., M. Mostowski and L.W. Szczerba, eds. (1995). Quantifiers: Logics, Models and Computation. Vol. I: Survey. Vol. II: Contributions. Dordrecht: Kluwer Academic Publishers. Krysztofiak, W. (1999). Problem opozycji realizmu i idealizmu epistemologicznego [The Problem of Epistemological Realism-Idealism Opposition]. Lublin: UMCS. KubiĔski, T. (1958). Nazwy nieostre [Vague Names]. Studia Logica 7, 115-180. KubiĔski, T. (1965). Two Kinds of Quotation Mark Expressions in Formalized Languages. Studia Logica 17, 31-51. KubiĔski, T. (1971). WstĊp do logicznej teorii pytaĔ [Introduction to the Logical Theory of Questions]. Warszawa: PWN. English translation: An Outline of the Logical Theory of Questions. Berlin: Academie-Verlag, 1980. KubiĔski, T. (1971a). Trzy elementarne rachunki nazw [Three Elementary Calculi of Names]. Acta Universitatis Wratislaviensis 139 (Prace Filozoficzne 8), 9-24. KubiĔski, T. (1985). Teorie drugiego rzĊdu charakteryzujące pojĊcie sprawstwa [The Second-Order Theories Charaterizing the Notion of an Agent]. Ruch Filozoficzny 42, No. 1-2, 45-50. KubiĔski, T. (1985a). Sáów kilka o kilku znaczeniach sáowa “istnieje” [Some Remarks on Several Meanings of the Word ‘Exists’]. Ruch Filozoficzny 42, No. 3-4, 211-214. Kwiatkowski, T. (1980). Jan àukasiewicz a problem interpretacji logiki Arystotelesa [Jan àukasiewicz and the Problem of the Interpretation of Aristotle’s Logic]. Lublin: UMCS. Lazari-Pawáowska (1992). Etyka: Pisma zebrane [Ethics: Collected Writings]. Wrocáaw: Ossolineum. Lazari-Pawáowska, I., ed. (1975). Metaetyka [Meta-Ethics]. Warszawa: PWN.
74
Jacek Jadacki
Lechniak, M. (1999). Interpretacje wartoĞci matryc wielowartoĞciowych [The Interpretations of Values of Many-Valued Matrices]. Lublin: Redakcja Wydawnictw KUL. Lejewski, Cz. (1958). On LeĞniewski’s Ontology. Ratio 1, 150-176. Leszko, R. (1980). Wyznaczanie pewnych klas pytaĔ przez grafy i ich macierze [The Determination of Some Classes of Questions by Graphs and Their Matrices]. Zielona Góra: Wydawnictwo WSP. Leszko, R. (1983). Charakterystyka záoĪonych pytaĔ liczbowych przez grafy i macierze [A Characterization of Complex Numeral Questions by Graphs and Matrices]. Zielona Góra: Wydawnictwo WSP. LeĞniewski, S. (1927). On the Foundations of Mathematics. In: (1992), vol. 1, pp. 174-382. LeĞniewski, S. (1992). Collected Works. 2 vols. Edited by: S.J. Surma, J.T. Srzednicki, D.I. Barnett and V.F. Rickey. Warszawa & Dordrecht: PWN & Kluwer Academic Publishers. LubaĔski, M. (1975). Filozoficzne zagadnienia teorii informacji [Philosophical Problems of the Theory of Information]. Warszawa: ATK. àukasiewicz, J. ([1910] 1987). O zasadzie sprzecznoĞci u Arystotelesa [On the Principle of Contradiction in Aristotle]. Warszawa: PWN. àukasiewicz, J. (1927). O metodĊ w filozofii [For the Method in Philosophy]. Przegląd Filozoficzny 31, No. 1-2, 3-5. àukasiewicz, J. ([1929] 1958). Elementy logiki matematycznej [Elements of Mathematical Logic]. Warszawa: PWN. English version: Elements of Mathematical Logic. Warszawa & Oxford: PWN & Pergamon Press, 1966. àukasiewicz, J. ([1957] 1988). Sylogistyka Arystotelesa z punktu widzenia wspóáczesnej logiki formalnej [Aristotle’s Syllogistic form the Standpoint of Contemporary Formal Logic]. Warszawa: PWN. àukasiewicz, J. (1961). Z zagadnieĔ logiki i filozofii [Some Problems of Logic and Philosophy]. Edited by J. Sáupecki. Warszawa: PWN. àukasiewicz, J. (1970). Selected Works. Edited by L. Borkowski. Amsterdam & Warszawa: North-Holland & PWN. àukasiewicz, J. (1998). Logika i metafizyka [Logic and Metaphysics]. Miscellanea. Edited by J.J. Jadacki. Warszawa: WFiS UW. MajdaĔski, S. (1974). Problemy asercji zdaniowej: Szkice pragmatyczne [Problems of Propositional Assertion: Pragmatic Essays]. Lublin: TN KUL. Malewski, A. (1964). O zastosowaniach teorii zachowania [On the Applications of the Theory of Behaviour]. Warszawa: PWN. Malinowski, G. (1990). Logiki wielowartoĞciowe [Many-Valued Logics]. Warszawa: PWN. Malinowski, J. (1989). Equivalence in Intentional Logics. Warszawa: IFiS PAN. Malinowski, J. (1995). SkutecznoĞü a prawda: Logika illokucyjna Searla i Vanderveckena [Efficiency and Truth. Searle’s and Vandervecken’s Illocutionary Logic]. Warszawa: Oficyna Akademicka OAK. Marciszewski, W. (1972). Podstawy logicznej teorii przekonaĔ [Foundations of the Logical Theory of Beliefs]. Warszawa: PWN. Marciszewski, W. (1991). Logika z retorycznego punktu widzenia [Logic from a Rhetorical Point of View]. Warszawa: PTS. English version: Logic from a Rhetorical Point of View. Berlin: de Gruyter, 1994.
The Lvov-Warsaw School and Its Influence on Polish Philosophy
75
Marciszewski, W. and R. Murawski (1995). Mechanization of Reasoning in a Historical Perspective. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 43. Amsterdam: Rodopi. Marciszewski, W., ed. ([1970] 1988). Maáa encyklopedia logiki [Small Encyclopaedia of Logic]. Wrocáaw: Ossolineum. Marciszewski, W., ed. ([1981] 1987). Dictionary of Logic as Applied in the Study of Language. Dordrecht: Martinus Nijhoff, 1981. Polish version: Logika formalna: Zarys encyklopedyczny [Formal Logic: An Encyclopaedic Outline]. Warszawa: PWN. Mazierski, S. (1961). Determinizm i indeterminizm w aspekcie fizykalnym i filozoficznym [Physical and Philosophical Aspects of Determinism and Indeterminism]. Lublin: TN KUL. Mazierski, S. (1993). Prawa przyrody: Studium metodologiczne [Laws of Nature: A Methodological Study]. Lublin: Redakcja Wydawnictw KUL. McCall, S., ed. (1967). Polish Logic: 1920-1939. Oxford: Clarendon Press. Mehlberg, H. (1951). The Idealistic Interpretation of Atomic Physics. Studia Philosophica 4, 171-235. Misiek, J. (1979). Program metodologii nauk empirycznych [A Program for the Methodology of Empirical Science]. Kraków: UJ. Mortimer, H. (1982). Logika indukcji: Wybrane problemy [The Logic of Induction: Selected Problems]. Warszawa: PWN. English version: The Logic of Induction. Chicherster: EllisHorwood Lim, 1988. Murawski, R. (1995). Filozofia matematyki: Zarys dziejów [The Philosophy of Mathematics: An Outline of Its History]. Warszawa: Wydawnictwo Naukowe PWN. Murawski, R. (1999). Recursive Functions and Metamathematics. Dordrecht: Kluwer Academic Publishers. MuszyĔski, Z. (1988). O nieostroĞci [On Vagueness]. Lublin: UMCS. NieznaĔski, E. (1980). Formalizacyjne próby ustalenia logiko-formalnych podstaw stwierdzania pierwszych elementów relacji rozwaĪanych w tomistycznej teodycei [Formalistic Attempts of Determining Formal-Logical Foundations of Stating the First Elements of Relations Analyzed in the Thomistic Theodicy]. In: Miscellanea Logica 1, 7-194. NieznaĔski, E. (1984). O definiowaniu w semantyce logicznej klasycznego rozumienia prawdy [On Defining the Classical Conception of Truth in Formal Semantics]. Roczniki Filozoficzne 4, No. 1, 31-44. Nowaczyk, A. (1985). Logiczne podstawy nauk Ğcisáych [Logical Foundations of the Exact Sciences]. Warszawa: IFiS PAN. Nowaczyk, A. (1990). Wprowadzenie do logiki nauk Ğcislych [Introduction to the Logic of the Exact Sciences]. Warszawa: PWN. Nowak, L. (1968). Próba metodologicznej charakterystyki prawoznawstwa [An Attempt at a Methodological Characterization of Jurisprudence]. PoznaĔ: Wydawnictwo UAM. Nowak, L. (1973). Interpretacja prawnicza [Juristic Interpretation]. Warszawa: PWN. Nowak, L. (1998). Byt i myĞl: U podstaw negatywistycznj metafizyki unitarnej [Being and Thought: Foundations of Negativistic Unitarian Metaphysics], vol. 1: NicoĞü i istnienie [Nothingness and Existence]. PoznaĔ: Zysk i S-ka. Nowak, L. (2004). Byt i myĞl: U podstaw negatywistycznj metafizyki unitarnej [Being and Thought: Foundations of Negativistic Unitarian Metaphysics], vol. 2: WiecznoĞü i zmiana [Eternity and Change]. PoznaĔ: Zysk i S-ka. Nowak, L. and J. Kmita (1968). Studia nad teoretycznymi podstawami humanistyki [Studies in the Theoretical Foundations of Humanities]. PoznaĔ: Wydawnictwo UAM.
76
Jacek Jadacki
OdrowąĪ-Sypniewska, J. (2000). Zagadnienie nieostroĞci [The Problem of Vagueness]. Warszawa: WFiS UW. Omyáa, M. (1986). Zarys logiki niefregowskiej [An Outline of Non-Fregean Logic]. Warszawa: PWN. Omyáa, M. (1996). A Formal Ontology of Situations. In: R. Poli and P. Simons (eds.), Formal Ontology, pp. 173-187. Dordrecht: Kluwer Academic Publishers. Oráowska, E. (1973). Theorem Proving Systems. Dissertationes Mathematicae CIII. Warszawa: PWN. Oráowska, E. and Z. Pawlak (1984). Logical Foundations of Knowledge Representation. ICS PAS Reports 537. Ossowska, M. (1947). Podstawy nauki o moralnoĞci [Foundations of the Science of Morality]. Warszawa: Czytelnik. Ossowska, M. (1949). Motywy postĊpowania [Motives of Actions]. Warszawa: KiW. Ossowska, M. (1956). MoralnoĞü mieszczaĔska [Bourgeois Morality]. Wrocáaw: Ossolineum. Ossowska, M. (1963). Socjologia moralnoĞci: Zarys zagadnieĔ [The Sociology of Morality: An Outline of Problems]. Warszawa: PWN. Ossowska, M. (1970). Normy moralne: Próba systematyzacji [Moral Norms: An Attempt at a Systematization]. Warszawa: PWN. English version: Moral Norms. A Tentative Systematization. Warszawa: PWN, 1980. Ossowska, M. (1973). Etos rycerski [Chivalry’ Ethos]. Warszawa: PWN. Ossowska, M. (1983). O czáowieku, moralnoĞci i nauce [On Human, Morality, and Science]. Miscellanea. Warszawa: PWN. Ossowski, S. (1966-1970). Dzieáa [Works]. 6 vols. Warszawa: PWN. Ostrowski, J.-J. (1971). La philosophie analytique polonaise. Archives de Philosophie 34, No. 4, 673-676. PaĞniczek, J. (1988). Meinongowska wersja logiki klasycznej: jej związki z filozofią jĊzyka, poznania, bytu i fikcji [Meinongian Version of Classical Logic: Its Connections with the Philosophy of Language, Knowledge, Being and Fiction]. Lublin: UMCS PaĞniczek, J. (1998). The Logic of Intentional Objects. A Meinongian Version of Classical Logic. Dordrecht: Kluwer Academic Publishers. PaĞniczek, J., ed. (1991). Ontologia fikcji [Ontology of Fiction]. Warszawa: PTS. Patryas, W. (1987). Uznawanie zdaĔ [The Assertion of Sentences]. Warszawa: PWN. Pawáowski, T. (1978). Tworzenie pojĊü i definiowanie w naukach humanistycznych [Concept Formation and Definition in the Humanities]. Warszawa: PWN. English version: Concept Formation in the Humanities and the Social Sciences. Dordrecht: Reidel, 1980. Pawáowski, T. (1989). Aestethic Values. Dordrecht: Kluwer Academic Publishers. Pawáowski, T., ed. (1966). Logiczna teoria nauki [A Logical Theory of Science]. Warszawa: PWN. Pelc, J. (1971). O uĪyciu wyraĪeĔ [On the Use of Expressions]. Wrocáaw: Ossolineum. Pelc, J. (1973). The Development of Polish Semiotics in the Post-War Years. Dialectics and Humanism 1, 225-235. Pelc, J. (1983). O bytach fikcyjnych i tekstach fikcjonalnych [On Fictitious Beings and Fictional Texts]. Studia Semiotyczne 13, 179-224. Pelc, J., ed. ([1971] 1979). Semiotyka polska 1894-1969 [Polish Semiotics 1894-1969]. Warszawa: PWN. English version: Semiotics in Poland (1894-1969). Warszawa & Dordrecht: PWN & D. Reidel.
The Lvov-Warsaw School and Its Influence on Polish Philosophy
77
Pelc, J., M. PrzeáĊcki and K. Szaniawski (1957). Prawa nauki: Trzy studia z zakresu logiki [Laws of Science: Three Studies in Logic]. Warszawa: PWN. Perzanowski, J. (1989). Logiki modalne a filozofia [Modal Logics and Philosophy]. Kraków: UJ. Perzanowski, J. (1993). Locative Ontology. 3 parts. Logic and Logical Philosophy 1, 7-94. Perzanowski, J. (1996). A Way of Truth. In: R. Poli and P. Simons (eds.), Formal Ontology, pp. 61-130. Dordrecht: Kluwer Academic Publishers. Pietruska-Madej, E. (1975). Metodologiczne problemy rewolucji chemicznej [Methodological Problems of Chemical Revolution]. Warszawa: PWN. Pietruska-Madej, E. (1980). W poszukiwaniu praw rozwoju nauki [Search for the Laws of Scientific Development]. Warszawa: PWN. Pietruska-Madej, E. (1990). Odkrycie naukowe: Kontrowersje filozoficzne [Scientific Discovery: Philosophical Controversies]. Warszawa: PWN. Pietruszczak, A. (1991). Bezkwantyfikatorowy rachunek zdaĔ [Propositional Calculus without Quantifiers]. ToruĔ: Wydawnictwo Adam Marszaáek. Pietruszczak, A. (1996). Mereological Sets of Distributive Classes. Logic and Logical Philosophy 4, 105-122. Piróg-Rzepecka, K. (1966). Rachunek zdaĔ, w którym wyraĪenia tracą sens [A Propositional Calculus in Which Expressions Lose Their Sense]. Studia Logica 18, 139-164. Piróg-Rzepecka, K. (1977). Systemy nonsense-logics [Systems of Nonsense-Logics]. Warszawa: PWN. Piróg-Rzepecka, K. and A. Morawiec (1985). New Results in Logic of Formulas which Lose Sense. Bulletin of the Section of Logic [PAS] 14, No. 3, 114-121. Placek, T. (1989). Paradoksy ruchu Zenona z Elei a problem continuum: Dychotomia. [Zeno’s Paradoxes of Movement and the Problem of continuum: Dichotomy]. Studia Filozoficzne 4, 57-73. Placek, T. (1995). Paradoksy stawania siĊ: Whitehead kontra Zenon i Bell [Paradoxes of Becoming: Whitehead contra Zeno and Bell]. Ruch Filozoficzny 52, No. 3-4, 412-426. Placek, T. (1999). Mathematical Intuitionism and Intersubjectivity. Dordrecht: Kluwer Acedmic Publishers. Placek, T. (1997). Charting the Labyrinth of Bell-Type Theorems. Logic and Logical Philosophy 5, 93-120. Podgórecki, A. (1962). Charakterystyka nauk praktycznych [Characterization of Practical Sciences]. Warszawa: PWN. Pogonowski, J. (1979). Formal Methods in Linguistics. Buffalo Papers in Linguistics 1, No. 3, 31-83. Pogonowski, J. (1981). Tolerance Spaces with Applications to Linguistics. PoznaĔ: Wydawnictwo Naukowe UAM. Pogonowski, J. (1993). Combinatory Semantics. PoznaĔ: Wydawnictwo Naukowe UAM. Pogorzelski, W.A. (1969). Klasyczny rachunek zdaĔ: Zarys teorii [Classical Propositional Calculus: An Outline of the Theory]. Warszawa: PWN. PrzeáĊcki, M. (1964). The Semantics of Open Concepts. Reprinted in: Pelc (1979), pp. 284-317. PrzeáĊcki, M. (1969). The Logic of Empirical Theories. London: Routledge and Kegan Paul. Polish modified version: Logika teorii empirycznych. Warszawa: PWN, 1988. PrzeáĊcki, M. (1979). On What There Is Not. Dialectics and Humanism 8, No. 4 (1981), 123-129. PrzeáĊcki, M. (1980). There Is Nothing that does Not Exist.” Dialectics and Humanism 8, No. 4 (1981), 141-145.
78
Jacek Jadacki
PrzeáĊcki, M. (1984), Semantic Reasons for Ontological Statements. In: WoleĔski, ed. (1990), pp. 85-96. PrzeáĊcki, M. (1989). ChrzeĞcijaĔstwo niewierzących [The Christianity of Nonbelievers]. Warszawa: Czytelnik. PrzeáĊcki, M. (1993). Studia z metodologii formalnej [Studies in the Formal Methodology]. Special issue of the quarterly Filozofia Nauki. Warszawa: Uniwersytet Warszawski. PrzeáĊcki, M. (1996). Poza granicami nauki [Beyond Limits of Sciences]. Warszawa: PTS. PrzeáĊcki, M. and J.J. Jadacki (1993). [La philosophie en] Pologne. In: R. Klibansky and D. Pears (eds.), La philosophie en Europe, pp. 323-347. Paris: Gallimard. PrzeáĊcki, M. and R. Wójcicki, eds. (1977). Twenty-Five Years of Logical Methodology in Poland. Warszawa & Dordrecht: PWN & Reidel Publishing Company. Pszczoáowski, T. (1969). Prakseologiczne sposoby usprawniania pracy [Praxiological Methods of Rendering Work Efficient]. Warszawa: PWN. Pszczoáowski, T. (1978). Maáa encyklopedia prakseologii i teorii organizacji [Small Encyclopaedia of Praxiology and the Theory of Organization]. Wrocáaw: Ossolineum. Pszczoáowski, T. (1982). Dylematy sprawnego dziaáania [Dilemmas of Efficient Action]. Warszawa: Wiedza Powszechna. Rasiowa, H. (1968). WstĊp do matematyki wspóáczesnej [An Introduction to Contemporary Mathematics]. Warszawa: PWN. Rasiowa, H., L. Banachowski et al. (1977). An Introduction to Algorithmic Logic. Warszawa: PWN. Rasiowa, H. and R. Sikorski (1963). The Mathematics of Metamathematics. Warszawa: PWN. Rogalski, A.K. (1995). Z zastosowaĔ ontologii Stanisáawa LeĞniewskiego: Analiza ujĊcia Desmonda P. Henry’ego [Some Applications of Stanisáaw LeĞniewski’s Ontology: An Analysis of Desmond P. Henry’s Approach]. Lublin: Redakcja Wydawnictw KUL. Rogowski, L.S. (1964). Logika kierunkowa a Heglowska teza o sprzecznoĞci zmiany [The Directional Logic and Hegelian Thesis on the Contradiction of Change]. ToruĔ: Towarzystwo Naukowe w Toruniu. Rojszczak, A. (1994). Wahrheit und Urteilsevidenz bei F. Brentano. Brentano-Studien 5, 187-218. Rosiak, M. (1995). Ontologia ufundowania [The Ontology of Founding]. Filozofia Nauki 3, No. 1-2, 25-63. Rosiak, M. (1996). Formalizacja teorii czĊĞci i caáoĞci opartej na pojĊciu ufundowania [Formalization of the Theory of Part and Whole Grounded on the Notion of Foundation]. Filozofia Nauki 4, No. 1, 41-80. Rzepa, T. (2002). O interpretowaniu psychologicznym w krĊgu Szkoáy LwowskoWarszawskiej. Warszawa: PTS. Sady, W. (1990). Racjonalna rekonstrukcja odkryü naukowych [The Rational Reconstruction of Scientific Discoveries]. Lublin: UMCS. Sady, W. (1993). O pewnoĞci [On Certainty]. Warszawa: Aletheia. Salamucha, J. (1934). The Proof ex motu for the Existence of God. Reprinted in: Salamucha (2003), pp. 97-135. Salamucha, J. (1997). Wiedza i wiara: Wybrane pisma filozoficzne [Knowledge and Faith: Selected Philosophical Writings]. Edited by K. ĝwiĊtorzecka and J.J. Jadacki. Lublin: TN KUL.
The Lvov-Warsaw School and Its Influence on Polish Philosophy
79
Salamucha, J. (2003). Knowledge and Faith. Edited by K. ĝwiĊtorzecka and J.J. Jadacki. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 77. Amsterdam: Rodopi. Siemianowski, A. (1983). Fakty, prawa, decyzje. Rozprawy o konwencjonalistycznej filozofii nauki [Facts, Laws, Decisions. Dissertations on the Conventionalistic Philosophy of Science]. Prace Naukowe Akademii Ekonomicznej we Wrocáawiu 245, 1-103. Siemianowski, A. (1988). O pewnych konsekwencjach tezy radykalnego empiryzmu [On Some Consequences of the Thesis of Radical Empiricism]. Zagadnienia Naukoznawstwa 3-4, 513-526. Siemianowski, A. (1989). Zasady konwencjonalistycznej filozofii nauki [The Principles of the Conventionalist Philosophy of Science]. Warszawa: PWN. Simons, P. (1992). Philosophy and Logic in Central Europe from Bolzano to Tarski: Selected Essays. Dordrecht: Kluwer Academic Publishers. Skolimowski, H. (1967). Polish Analytical Philosophy. London: Routledge and Kegan Paul. Skolimowski, H. (1968). Logic in Poland. In: R. Klibansky (ed.), Contemporary Philosophy: A Survey, vol. 1: Logic and Foundations of Mathematics, pp. 190-201. Firenze: La Nuova Italia Editrice. Sáupecki, J. (1955). St. LeĞniewski’s Calculus of Names. Studia Logica 3, 7-76. Sáupecki, J. and W.A. Pogorzelski (1962). O dowodzie matematycznym [On a Mathematical Proof]. Warszawa: PZWS. Sáupecki, J. and L. Borkowski ([1963] 1967). Elements of Mathematical Logic and Set Theory. Oxford & Warszawa: Pergamon Press & PWN. Sáupecki, J. and G. Bryll (1975). Przyczynki do ogólnej teorii systemów dedukcyjnych [Contributions to the General Theory of Deductive Systems]. Zeszyty Naukowe WSP w Opolu: Matematyka 15, 53-62. Sáupecki, J., G. Bryll and U. Wybraniec-Skardowska (1971-1972). Theory of Rejected Propositions. Parts 1-2. Studia Logica 29, 75-123; 30, 97-145. Snihur, S. (1990). Czas i przemijanie. Studium filozoficzne [Time and Passing. Philosophical Essay]. Warszawa: Wydawnictwo SGGW-AR. Stanosz, B. (1965). Znaczenie i oznaczanie a paradoks intensjonalnoĞci [Meaning and Designation versus the Paradox of Intensionality]. Studia Filozoficzne 2, 19-48. Stanosz, B. and A. Nowaczyk (1976). Logiczne podstawy jĊzyka [Logical Foundations of Language]. Wrocáaw: Ossolineum. Stonert, H. (1959). Definicje w naukach dedukcyjnych [Definitions in Deductive Sciences]. Wrocáaw: Ossolineum. StrawiĔski, W. (1991). Prostota, redukcja, jednoĞü nauki: studium z zakresu filozofii nauki [Simplicity, Reduction, Unity of Science: An Essay in the Philosophy of Science]. Warszawa: Wydawnictwo FEA. StrawiĔski, W. (1997). JednoĞü nauki, redukcja, emergencja: Z metodologicznych i ontologicznych problemów integracji wiedzy [Unity of Science, Reduction, Emergence: Some Methodological and Ontological Problems of the Integration of Knowledge]. Warszawa: Aletheia. Suszko, R. (1957). Zarys elementarnej skáadni logicznej: W sprawie antynomii káamcy i semantyki jĊzyka naturalnego [An Outline of the Elementary Logical Syntax: On the Liar’s Paradox and the Natural Language Semantics]. Warszawa: PWN. Suszko, T. (1957a). Logika formalna a niektóre zagadnienia teorii poznania: Diachroniczna logika formalna [Formal Logic and Some Problems of the Theory of Knowledge: Diachronic Formal Logic]. MyĞl Filozoficzna 2, 27-45; 3, 34-67.
80
Jacek Jadacki
Suszko, T. (1958-1960). Syntactic Structure and Semantical Reference. Part 1-2. Studia Logica 8, 213-244; 9, 63-91. Suszko, R. (1965). Wykáady z logiki formalnej [Lectures on Formal Logic]. Part I: WstĊp do zagadnieĔ logiki: Elementy teorii mnogoĞci. [Introduction to the Problems of Logic: Elements of Set Theory]. Warszawa: PWN. Szaniawski, K. (1977). Philosophy of the Concrete. Dialectics and Humanism 5, 67-72. Szaniawski, K. (1980). Philosophy of Science in Poland. In: J. Barr (ed.), Handbook of World Philosophy, pp. 281-295. Westport: Greenwood Press. Szaniawski, K. ([1994] 1998). O nauce, rozumowaniach i wartoĞciach: Pisma wybrane [On Science, Reasoning and Values: Selected Works]. Warszawa: PWN. English version: On Science, Inference, Information and Decision Making: Selected Essays in the Philosophy of Science. Dordrecht: Kluwer Academic Publishers. Szaniawski, K., ed. (1989). The Vienna Circle and the Lvov-Warsaw School. Dordrecht: Kluwer Academic Publishers. Taáasiewicz, M. (2002). The Concept of Rationality of Empirical Science. In: Taáasiewicz, ed. (2002), pp. 165-169. Taáasiewicz, M., ed. (2002). Logic, Methodology and Philosophy of Science at Warsaw University. Warszawa: Semper. Tarski, A. (1995). Pisma logiczno-filozoficzne [Logical and Philosophical Writings]. 2 vols. Edited by J. Zygmunt. Warszawa: PWN. Tatarkiewicz, W. (1919). O bezwzglĊdnoĞci dobra [On the Absoluteness of Goodness]. Warszawa: Gebethner i Wolff. Tatarkiewicz, W. (1938). Dobra, których nie trzeba wybieraü [Goods that do Not Need to Be Chosen]. Reprinted in: Tatarkiewicz (1971), pp. 312-320. Tatarkiewicz, W. (1947). Analysis of Happiness. Warszawa & The Hague: PWN & M. Nijhoff, 1976. Tatarkiewicz, W. ([1948-1950] 1981). Historia filozofii [History of Philosophy]. 3 vols. Warszawa: PWN. English version of vol. 3: Twentieth Century Philosophy, Part 1-2. Belmont: Wadsworth, 1973. Tatarkiewicz, W. (1951). Skupienie i marzenie [Concentration and Dream]. Kraków: M. Kot. Tatarkiewicz, W. (1960-1967). History of Aesthetics. 3 vols. Warszawa & The Hague: PWN & Mouton, 1970-1974. Tatarkiewicz, W. (1971-1972). Pisma zebrane. [Collected Papers]. Vol. 1: Droga do filozofii [A Path towards Philosophy]. Vol. 2: Droga przez estetykĊ [A Path through Esthetics].Warszawa: PWN. Tatarkiewicz, W. ([1975] 1980). A History of Six Ideas: An Essay in Aesthetics. Warszawa & The Hague: PWN & M. Nijhoff. Tempczyk, M. (1978). Strukturalizm w fizyce wspóáczesnej [Structuralism in Contemporary Physics]. Warszawa: Wydawnictwa UW. Tempczyk, M. (1981). Strukturalna jednoĞü Ğwiata [Structural Unity of the World]. Warszawa: PWN. Tempczyk, M. (1986). Fizyka a Ğwiat realny: Elementy filozofii fizyki [Physics and the Real World: Elements of the Philosophy of Physics]. Warszawa: PWN. Tempczyk, M. (1995). ĝwiat harmonii i chaosu [The World of Harmony and Chaos]. Warszawa: PIW. Tempczyk, M. (1998). Teoria chaosu a filozofia [The Theory of Chaos and the Philosophy]. Warszawa: Wydawnictwo CIS. Tokarz, M. (1993). Elementy pragmatyki logicznej [Elements of the Logical Pragmatics]. Warszawa: PWN.
The Lvov-Warsaw School and Its Influence on Polish Philosophy
81
TrzĊsicki, K. (1989). àukasiewiczian Logic of Tenses and the Problem of Determinism. In: Szaniawski, ed. (1989), pp. 293-312. Twardowski, K. ([1894] 1977). On the Content and Object of Presentations. A Psychological Investigation. The Hague: Nijhoff. Twardowski, K. (1921). Symbolomania and Pragmatophobia. In: Pelc, ed. (1979), pp. 3-6. Twardowski, K. (1965). Wybrane pisma filozoficzne [Selected Philosophical Writings]. Warszawa: PWN. Twardowski, K. (1999). On Actions, Products and Other Topics in Philosophy. Edited by J.L. Brandl and J. WoleĔski. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 67. Amsterdam: Rodopi. Wajszczyk, J. (1989). Zmiana a sprzecznoĞü logiczna [Change and Logical Contradiction]. Prakseologia 1-2, 101-117. Wajszczyk, J. (1995). Logika a czas i zmiana [Logic versus Time and Change]. Olsztyn: WSP. Wallis, M. (1968). PrzeĪycie i wartoĞü [Experience and Value]. Kraków: Wydawnictwo Literackie. WiĞniewski, A. (1990). Stawianie pytaĔ. Logika i racjonalnoĞü [Posing Questions. Logic and Rationality]. Lublin: UMCS. WiĞniewski, A. (1992). Sceptycyzm a kryterium prawdy [Scepticism and the Criterion of Truth]. PoznaĔskie Studia z Filozofii Nauki 12, 173-190. Witwicki, W. (1939). La foi des éclairés. Paris: Libraire Félix Alcan. Witwicki, W. (1957). Pogadanki obyczajowe [Taks on Mores]. Warszawa: PWN. Wojtysiak, J. (2002). Istnienie: Podstawowe koncepcje [Existence: The Main Conceptions]. In: A.B. StĊpieĔ and J. Wojtysiak, eds. (2002), Studia metafilozoficzne [Metaphilosophical Studies], vol. 2, pp. 215-262. Lublin: TN KUL. WoleĔski, J. (1972). Logiczne problemy wykáadni prawa [Logical Problems in Law]. Kraków: PWN. WoleĔski, J. (1980). Z zagadnieĔ analitycznej filozofii prawa [Some Problems of the Analytical Philosophy of Law]. Kraków: PWN. WoleĔski, J. (1984). Przewidywania i ich klasyfikacja [Prognoses and Their Classification]. Wrocáaw: Wydawnictwo PWr. WoleĔski, J. (1985). Filozoficzna Szkoáa Lwowsko-Warszawska [The Lvov-Warsaw Philosophical School].Warszawa: PWN. English version: Logic and Philosophy in the Lvov-Warsaw School. Dordrecht: Kluwer, 1989. WoleĔski, J. (1990). Deontic Logic and Possible Worlds Semantics: A Historical Sketch. Studia Logica 59, No. 2, 273-282. WoleĔski, J., ed. (1990a). KotarbiĔski: Logic, Semantics and Ontology. Dordrecht: Kluwer Academic Publishers. WoleĔski, J. (1993). Metamatematyka a epistemologia [Metamathematics and Epistemology]. Warszawa: PWN. WoleĔski, J. (1999). Okolice filozofii prawa [Around the Philosophy of Law]. Kraków: Universitas. WoleĔski, J., ed. (1994). Philosophical Logic in Poland. Dordrecht: Kluwer Academic Publishers. WoleĔski, J. and F. Köhler, eds. (1999). Alfred Tarski and the Vienna Circle: AustroPolish Connection in Logical Empiricism. Dordrecht: Kluwer Academic Publishers. Wolniewicz, B. (1985). Ontologia sytuacji [The Ontology of Situations]. Warszawa: PWN. Wolniewicz, B. (1990). Concerning Reism. In: WoleĔski, ed. (1990), pp. 199-204.
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Wójcicki, R. (1974). Metodologia formalna nauk empirycznych [Formal Methodology of Empirical Sciences]. Wrocáaw: Ossolineum. Modified English version: Topics in Formal Methodology of Empirical Sciences. Dordrecht: D. Reidel, 1979. Wójcicki, R. (1982). Wykáady z metodologii nauki [Lectures on the Methodology of Science]. Warszawa: PWN. Wójcicki, R. (1988). Theory of Logical Calculi. Dordrecht: Kluwer. Wójcicki, R. (1991). Teorie w nauce: WstĊp do logiki, metodologii i filozofii nauki [Theories in Science: Introduction to Logic, Methodology and Philosophy of Science], part. 1. Warszawa: IFiS PAN. Wójtowicz, K. (1999). Realizm mnogoĞciowy [Set-Theoretical Realism]. Warszawa: Wydawnictwo WFiS UW. Wybraniec-Skardowska, U. (1985). Teorie jĊzyków syntaktycznie kategorialnych [Theories of Syntactically Categorial Languages]. Warszawa: PWN. Enlarged English version: Theory of Language Syntax: Categorial Approach. Dordrecht: Kluwer Academic Publishers, 1991. Wybraniec-Skardowska, U. and G. Bryll (1969). Z badaĔ nad teorią zdaĔ odrzuconych [Some Inquiries Concerning the Theory of Rejected Sentences]. Opole: WSP. Wybraniec-Skardowska, U. and M. Chuchro (1991). O nazwach pustych i nazwach wáasnych w Ğwietle semiotyki i filozofii [On Empty Names and Proper Names in the Light of Semiotics and Philosophy]. Ruch Filozoficzny 48, No. 2, 128-136. Zamecki, S. (1988). PojĊcie odkrycia naukowego a historia dziedziny nauki [The Notion of Scientific Discovery and the History of Science]. Wrocáaw: Ossolineum. Zamiara, K. (1974). Metodologiczne znaczenie sporu o status poznawczy teorii [The Methodological Sense of the Controversy concerning the Cognitive Status of Theories]. Warszawa: PWN. Zawirski, Z. (1935). Les tendances actuelles de la philosophie polonaise. Revue de Syntese 10, 129-143. Ziemba, Z. (1969). Logika deontyczna jako formalizacja rozumowaĔ normatywnych [Deontic Logic as a Formalization of Normative Reasoning]. Warszawa: PWN. Ziemba, Z. (1983). Analityczna teoria obowiązku: Studium z logiki deontycznej [The Analytical Theory of Duty: An Essay in Deontic Logic]. Warszawa: PWN. Ziemba, Z. and K. ĝwirydowicz (1988). On Deontic Calculi with Contradictory Duties. Semantical Independence Proofs for Selected Formulae of Deontic Logic. Warszawa: Wydawnictwa UW. ZiembiĔski, Z. (1963). Normy moralne a normy prawne: Zarys problematyki [Moral Norms and Juridical Norms. An Outline of Problems]. PoznaĔ: Wydawnictwo UAM. ZiembiĔski, Z. (1966). Logiczne podstawy prawoznawstwa [Logical Foundations of Jurisprudence]. Warszawa: Wydawnictwo Prawnicze. ZiembiĔski, Z. (1972). Etyczne problemy prawoznawstwa [Ethical Problems of Jurisprudence]. Wrocáaw: Ossolineum. ZiembiĔski, Z. (1972a). Analiza pojĊcia czynu [An Analysis of the Notion of Action]. Warszawa: Wiedza Powszechna. Znamierowski, Cz. (1957). Oceny i normy [Value Judgements and Norms]. Warszawa: PWN. Znamierowski, Cz. (1957a). Wina i odpowiedzialnoĞü [Guilt and Responsibility]. Warszawa: PWN. Znamierowski, Cz. (1957b). Zasady i kierunki etyki [Principles and Directions of Ethics]. Warszawa: PWN. Zwinogrodzki, Z. (1976). Automatyczne dowodzenie twierdzeĔ [Automated Proofs of Theses]. Part I. Kraków: AG-H.
The Lvov-Warsaw School and Its Influence on Polish Philosophy
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Zwinogrodzki, Z. (1982). Automated Deduction by Analogy. Kraków: AG-H. Zygmunt, J. (1984). An Essay in Matrix Semantics for Consequence Relations. Wrocáaw: UWr. ĩabski, E. (1988). Cecha i istnienie: Formalizacja fragmentu ontologii [Property and Existence: A Formalization of a Fragment of Ontology]. Acta Universitas Wratislaviensis: Prace Filozoficzne 57, 93-101. ĩabski, E. (1995). Logiki nihilistyczne: Zarys problematyki [Nihilistic Logics: An Outline of Problems]. Warszawa: Oficyna Akademicka. ĩarnecka-Biaáy, E. (1973). Funktory modalne i ich definiowalnoĞü w systemach rachunku zdaĔ [Modal Functors and Their Definability in Systems of Propositional Calculus]. Reports on Mathematical Logic 1, 69-98. ĩegleĔ, U.M. (1990). ModalnoĞü w logice i w filozofii: Podstawy ontyczne [Modality in Logic and Philosophy: Ontic Foundations]. Warszawa: PTS. ĩyciĔski, J. (1983). JĊzyk i metoda [Language and Method]. Kraków: Znak. ĩyciĔski, J. (1985-1986). Teizm i filozofia analityczna [Theism and Analytical Philosophy]. 2 vols. Kraków: Znak. ĩyciĔski, J. (1993). Granice racjonalnoĞci: Eseje z filozofii nauki [The Limits of Rationality: Essays in the Philosophy of Science]. Warszawa: PWN. ĩytkow, J. (1979). Spójny zbiór procedur operacyjnych jako interpretacja terminu empirycznego [A Consistent Set of Operational Procedures as an Interpretation of an Empirical Term]. Studia Filozoficzne 6, 95-112; 7, 25-38.
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PART II OBJECTS AND PROPERTIES
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John T. Kearns AN ELEMENTARY SYSTEM OF ONTOLOGY
1. Ontology According to SobociĔski (1949), the Polish logician Stanisáaw LeĞniewski devised his logical system Ontology in order to capture or express the notion of a distributive class. However, it isn’t clear to me that Ontology involves any sort of classes. I think LeĞniewski’s system is best understood as a theory concerned with some features of common nouns – in contrast to first-order theories, which focus on referring expressions and predicates of individuals. In this paper I will explain my understanding by developing elementary systems of Ontology in which the semantic account makes no provision for distributive classes. After developing these systems of Ontology, I will discuss collections, which I think are close to what LeĞniewski understood distributive classes to be. As it turns out, the elementary systems of Ontology are not suited for making statements about collections. I will finish by sketching changes in one system of elementary Ontology which allow it to incorporate statements about collections. In order to understand how logical systems can shed light on natural languages, I adopt a speech act approach to language and logic. I won’t try to defend this here (I have made such an attempt in Kearns 1996), but will simply state certain principles and use them to motivate my analyses. On my view, the primary linguistic reality is constituted by the linguistic skills and the language acts of human beings. A language act, or speech act, is a meaningful act performed with an expression. Such an act can be performed by speaking out loud, or writing, or (merely) thinking. And it isn’t just persons producing expressions who perform language acts. The person who listens with understanding, or who reads, is using the expressions she hears or reads to perform language acts. It is language acts, not expressions, which are the primary bearers of meaning. These acts have the meanings that the language user intends.
In: J.J. Jadacki and J. PaĞniczek (eds.), The Lvov-Warsaw School – The New Generation (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 89), pp. 87-112. Amsterdam/New York, NY: Rodopi, 2006.
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But various expressions are conventionally used to perform acts with specified meanings, and it is customary for a person to intend a meaning conventionally associated with the expression she uses. From this perspective, there is a sharp distinction that must be drawn between syntax and semantics. Syntactic features characterize expressions. Indeed, expressions can be considered to be syntactic objects. But expressions don’t have semantic features; these features are instantiated by linguistic acts. To illustrate, consider the situation where Eileen looks at the vase on her desk, and says “That flower is a carnation.” We can analyze her statement as follows: (1)
(2)
The phrase ‘That flower’ is used to direct her attention to a particular flower, or to express her attending if she was already looking at the flower. The referring act “sets up” Eileen’s act of using ‘is a carnation’ to acknowledge the flower to be a carnation.
The referring act, the acknowledging act, and the enabling relation between these acts constitute Eileen’s statement. Her statement has both a syntactic character and a semantic structure. The syntactic character is supplied by the expressions used, their syntactic categories, and the order in which the expressions occur. The semantic structure of the statement is independent of the expressions used. We give semantic structure by indicating the kinds of component acts performed and the way in which they are organized. The analysis above of Eileen’s statement presents the semantic structure of her statement. The artificial languages of modern logic are not used by people to perform language acts. No one speaks these languages, or uses them for thinking. We might regard the logical languages as languages that can, in principle, be used to perform speech acts, even though we don’t actually speak or write these languages. I find it more useful to consider the sentences of artificial languages as representations. They are representations of language acts, ordinarily of propositional acts. (A propositional act is one that can appropriately be evaluated in terms of truth and falsity.) However, instead of describing logical-language sentences as representations of propositional acts, I will more often speak of the sentences as representing natural-language statements. The syntactic account for an artificial language gives rules for constructing sentences of the artificial language. These rules need have no relation to principles governing expressions in natural languages. But the truth conditions for logical-language sentences are the conditions of
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the statements these represent. Deductive systems codify artificiallanguage expressions. 2. The Language L LeĞniewski’s system Ontology, which is described in Luschei (1962), is formulated in a very different way than are standard systems of firstorder and higher-order logic. The practice now is to completely specify an artificial language by indicating all of its basic symbols and the manner in which these are combined to constitute formulas or sentences. In an intuitive sense, these artificial languages are “finished products.” In contrast, LeĞniewski conceived of Ontology as a “growing” system. Whatever symbols the artificial language possesses at a given time can always be augmented by the introduction of new symbols. It is also always possible to augment the language as it is at a time with new syntactic categories. In LeĞniewski’s formulation, there are rules for adding definitions to Ontology, which definitions introduce both new symbols and new categories. According to Lejewski (1995), LeĞniewski regarded creative definitions as a philosophically important feature of his systems, but the unfinished character of Ontology is a drawback for some purposes. And this character isn’t really essential for carrying out the normal types of logical investigation. The language L of Elementary Ontology will be specified at the start. The fundamental category of expressions in L is common nouns, or noun constants: A, B, C, A1 , . . . A noun constant is used to represent some acts performed with common nouns or noun phrases in natural languages. A noun constant will label zero, one, or more than one individuals (like ‘square circle’, ‘capital of New York State’, and ‘dog’). Capital letters from the end of the alphabet are used as noun variables: X, Y, Z, X1 , . . . The language L contains one sentence-forming functor ‘H’ for noun constants; it takes two noun constants as arguments. An atomic sentence of L is written: [A H B]
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which means that the one and only A is a B. It is unfortunate that epsilon is also commonly used for set membership, because LeĞniewski’s epsilon is intended to capture a common use of ‘is’. I will follow Simons (1987) in employing two styles of epsilon. The epsilon ‘’ is for set membership, while ‘H’ is used in Ontology. A sentence: [A H B] is true if, and only if (from now on: iff), there is exactly one A and this A is also a B. It is characteristic of what I am calling elementary Ontology that there is only this one functor which combines with common nouns to yield sentences. Other sentence-forming functors can be introduced by definitions, but defined expressions are regarded as mere abbreviations. Elementary Ontology does not contain variables in the categories of sentence-forming functors for noun constant arguments. It isn’t clear whether LeĞniewski failed to recognize that proper names and other referring expressions belong to a different syntactic category than common nouns, or whether he simply thought the distinction between singular terms and common nouns is of no great importance. Some terms label no individuals, some label exactly one, and some label more than one, but all these terms are adequately accommodated by a single category of Ontological expressions. Given LeĞniewski’s perspective, a good reading for the functor of elementary Ontology might be ‘is a’. Although it makes sense to have a sentence: [B H C] where B labels many individuals (e.g. ‘Dog is an animal’), the sentences are only true when the subject labels exactly one individual. LeĞniewski’s attitude toward singular terms and common nouns appears to be endorsed in Simons (1987), but this attitude/understanding is incompatible with the present speech-act approach to language. Referring acts are the fundamental linguistic acts by which language users “pick out” objects in the world, and so “fasten” their statements to the world. Referring acts are fundamentally different from characteristic acts performed with common nouns, and it is quite misleading for expressions in a single logical-language category to be used to represent both referring acts and common-noun acts. In the present paper, noun constants are not referring expressions. As a reading for a sentence ‘[A H B]’, we could say “There is exactly one A, and it is a B” or “The one and only A is a B,” but these are both cumbersome. I prefer to treat noun constants as plural nouns, and will
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provide a reading that is grammatically appropriate for this treatment. I propose to introduce a new, quasi-technical, use for ‘singly’, and to read ‘[A H B]’ as “A’s are, singly, B’s.” A’s are, singly, B’s just in case there is exactly one A, and this A is a B. It is understood that the plural reading carries no indication of a plurality of objects. The language L contains the connectives ‘~’ and ‘’, and the universal quantifier ‘’. The connectives ‘&’, ‘’, and ‘{’ are defined in standard ways. The quantifier ‘’ is combined with a noun variable D to constitute a quantified phrase (D). The particular quantifier ‘’ is defined in a standard way. The language L does not permit vacuous quantification. The connectives have the standard, truth-table, truth conditions. (They are used to represent statements having these truth conditions.) But the quantifiers are not understood in the standard way. The quantified phrase ‘(X)’ doesn’t mean for every individual X, because ‘X ’ isn’t an individual variable. To make use of quantifiers and make sense of quantification in L , we are forced to construe quantifiers substitutionally. To understand how to do this, let us notice that common nouns in English can be used in different ways. A common noun can be predicated of an individual that has been identified by a referring act, as in: Mary is a gymnast. Common nouns can be used nonpredicatively as subjects of sentences: Gymnasts are athletes. The use as a predicate of individuals seems to be prior to the second use, for in order to speak meaningfully of gymnasts, one need to know what it is to be a gymnast. But to use common nouns predicatively, we must have referring devices for picking out particular individuals. The language L contains no referring expressions (no syntactically-signalled singular terms). However, we shall construe noun constants of L as expressions that can in other circumstances be predicated of individuals. A natural language predicate like ‘(is a) dog’ can be conceived as expressing a function from objects in the world to truth and falsity. So to interpret L , we begin with an empty or nonempty domain E of individuals. An interpreting function f of L for a nonempty E takes each common noun D to a truth-valued function on E . So, for example, if U is an individual in E , then f (A) applied to U – f (A)(U) – yields the value truth or the value falsity. When E is empty, an interpreting function f of
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L for E will take each common noun D to a truth-valued function on some other, nonempty, domain. The “idea” for the universal quantifier is that a sentence: (X)M should be true if M becomes true no matter which common noun is substituted for the free occurrences of ‘X ’ in M. But there is a problem here. We want a universally quantified sentence (the statement represented by such a sentence) to have a truly “unlimited” force. But a particular interpreting function f might assign values to the common nouns of L in such a way that M becomes true for all the interpreted nouns that happen to be in L , but there is some noun that might have been in L for which M would be false. For example, consider the domain of human beings, and let all noun constants in L be assigned the truth-valued function which yields truth for females and falsity for everyone else. Then if we understand the quantified phrase with respect to (interpreted) noun constants of L , the sentence: (X)~[X H A] which says that no noun constant can replace ‘X ’ in ‘[X H A]’ to yield a true sentence, is true. But there are lots of females in our domain. If we had the right nouns in L , we would have true sentences of that form. (All we need is a noun which labels exactly one female human being.) To overcome this difficulty, we don’t understand universally quantified phrases just with respect to nouns as interpreted by one function f. We consider them with respect to nouns as interpreted by f and all “alternatives” to f which differ from f in their treatment of some one noun constant. That way a sentence (D)M is true if M becomes true no matter what noun is substituted for D in M, including nouns found in extensions of L . A sentence (D)M does not make (represent) a statement about all objects in the domain E . For among the nouns “covered” by the universally quantified phrase will be nouns which are true of nothing (nouns like ‘square circle’). To make a statement about all objects in the domain, we need something like this: (X)[[X H X] . . . X . . . ] LeĞniewski didn’t regard sentences of Ontology as representations of ordinary statements, for that construal of artificial-language sentences depends on a speech-act/language-act perspective. But LeĞniewski may
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have thought that Ontology is adequate for analyzing ordinary statements, and that Ontology “captures” ordinary language in the sense that Ontology possesses the resources for giving faithful translations of ordinary statements (once Ontology is supplied with a suitable vocabulary). However, the use of nouns for talking about all the objects that the noun labels presupposes the use of nouns as predicates of individuals picked out by using referring expressions. An adequate language must contain expressions for referring to single individuals, and predicate (and relational) expressions which can be combined with referring expressions to characterize the objects referred to. LeĞniewski’s system Ontology fails to provide a category of singular referring terms (a category of singular terms for representing referring acts). We have construed noun constants as predicates of individuals, but Ontology provides no “place” for sentences predicating these constants of individuals. With respect to the goal of representing and investigating naturallanguage statements, Ontology is inadequate in the sense that it is incomplete. Singular terms are not, as LeĞniewski may have thought, just general terms that happen to apply to a single object. A statement made with this sentence: Denver is a large city. is not claiming that Denvers are, singly, large cities. The statement identifies the city Denver, and acknowledges this to be a large city. Ontology, especially a system which goes beyond elementary Ontology, possesses the resources to represent some natural-language statements, but many ordinary statements can be represented only after Ontology is supplemented with a category of referring expressions. Although a statement which characterizes Denver as a large city is not adequately represented by a sentence: [D H C] this Ontological sentence is a kind of “counterpart” to the naturallanguage statement. For every genuine singular term like ‘Denver’, we can introduce a corresponding common noun, say ‘denver’, which is true of exactly the object associated with the singular term. And whenever we have a true statement made with a sentence like ‘Denver is a large city’, we can make a corresponding true statement to the effect that denvers are, singly, large cities.
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3. A Careful Formulation of Elementary Ontology The well-formed formulas (wffs) of L are given by: (1) (2) (3) (4)
If D, E are noun constants or noun variables of L , then [D H E ] is a wff, an atomic wff of L . If M, N are wffs of L then so are ~M, [M N ]. If M is a wff containing free occurrences of noun variable D, then (D)M is a wff. All wffs of L are obtained by (1)-(3).
Let E be a nonempty domain of individuals. A function I on L is a truthvalued function iff for each U in E , I(U) = t or I(U) = f, where t and f are the truth values. Let E be a domain of individuals. If E z , an interpreting function f of L for E assigns a truth-valued function on E to each noun constant of L . If E = , then an interpreting function f of L for E assigns a truthvalued function on an arbitrarily selected nonempty domain to each noun constant of L . Let f be an interpreting function of L for E . Let E be a noun constant of L . Then an interpreting function f * of L for E is a E-variant of f iff f * agrees with f on the value assigned to every noun constant with the possible exception of E. Let f be an interpreting function of L for a domain E . The valuation of L determined by f is as follows: (1)
(2) (3)
An atomic sentence [D H E ] is true iff f (D) is a function which is true for exactly one individual U in E , and f (E )(U) = t. The sentence is false otherwise. Sentences ~M, [M N ] have values determined by the truth-tables for ‘~’ and ‘’. Let (D)M be a sentence of L , and let E be the first noun constant in alphabetical order not occurring in M. Then (D)M is true for the valuation determined by f iff the result of replacing all free occurrences of D in M by E is true for every E-variant of f.
The deductive system EO is a natural deduction system which uses tree proofs to establish that argument sequences M1 , . . . , Mr / N (r t 0) are theorems. Here, the Mi are premisses and N is the conclusion. In tree proofs of EO, only sentences occur as steps. For the propositional part of EO, the elementary rules are:
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Contradiction Elimination M ~M N
The following proof establishes the logical validity of argument sequence ‘M, ~[M N] / ~M ’: M I ~ [M N ] [M N ] CE ~M A nonelementary rule of inference cancels, or discharges, one or more of the hypotheses used to reach premisses for the rule. In illustrating nonelementary rules, the hypotheses that are cancelled are enclosed in braces. Elimination {M }{M } [M N ] P P P
~ Elimination {~ M} M M
The following proof establishes ‘~[M N] / ~M ’ to be a theorem: x
x
~~M ~M CE M ~ E , canceled ~ M M I ~ [M N ] [M N ] CE ~M ~ E , canceled ~ ~ M ~M Hypotheses which are cancelled have an ‘x’ placed above them. The rule for establishing theorems of EO is as follows: An argument sequence M1 , . . . , Mr / N is a theorem of EO iff there is a tree proof whose uncancelled hypotheses are among M1 , . . . , Mr and whose conclusion is N. ~ To illustrate the rules for the universal quantifier, I will use ‘ S ’ to designate the result of substitution. If M is a wff, D is a noun variable, E is a noun variable or a noun constant, then
~D S M/ E
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is the result of replacing all free occurrences of D in M by E. The quantifier rules for EO are the following: Elimination Introduction (D) M ȕ is a noun constant which ȕ is a noun ~ D S M/ does not occur in M or in any constant ~D E S M/ other uncancelled hypothesis E (D) M leading to the occurrence of ~D S M/ E
The rules for ‘H’ are as follows: RX [D H E] [D H D ]
SY [D H E][E H E] [E H D]
TR [D H E][E H J ] [D H J ]
H Introduction [G H J ] (D)(E)[[[D H J ] & [E H J ]] [D H E]] [J H J] Given a domain E of individuals, an argument sequence M1, . . . , Mr / N of L is logically valid with respect to E iff there is no interpreting function f of L for E such that each of M1, . . . , Mr is true for the valuation determined by f , but N is false for this valuation. (If N is true for the valuation determined by f , we indicate this: f (N ) = t.) An argument sequence M1, . . . , Mr / N is logically valid iff it is logically valid with respect to every domain of individuals. It is fairly obvious that EO is sound i.e., that every argument sequence which is a theorem of EO is logically valid. I will sketch a proof of this result without filling in the details, for the argument is entirely straightforward. An inference figure is a “move” in a tree proof, an instance of one of the rules of EO. The rank of a tree proof * is the number of inference figures in *. The minimum rank is 0; a sentence M standing alone is a tree proof having rank 0 this proof establishes the argument sequence M / M. LEMMA. Let * be a tree proof of EO having uncancelled hypotheses M1, . . . , Mr and conclusion N. Let E be a domain of individuals and f be an interpreting function of L for E such that f (M1 ) = . . . = f (Mr) = t. Then f (N ) = t.
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This is proved by induction on the rank of *. THEOREM 1. Every theorem of EO is a logically valid argument sequence. This is an easy consequence of the lemma. We cannot prove that EO is complete. For given a domain E of individuals, an interpreting function f of L for E , a universally quantified sentence (D)M is true if M is true for every subset ] of E as value of D. (This amounts to the same as saying that ~D S M/ E is true for every E-variant of f.) If E is denumerable, then it has nondenumerably many subsets. We can establish a version of Gödel’s Incompleteness Theorem for the system EO. Elementary Ontology is stronger in expressive power than first-order logic, for first-order logic is complete, while elementary ontology is not. It is an advantage of standard logic as compared to Ontology that firstorder logic is a “natural” subsystem of higher-order logic, one which is sound and complete. Elementary Ontology is a natural subsystem of Ontology, but it is sound without being complete.
4. First-Order Ontology
We shall characterize a subsystem of Elementary Ontology which is fairly natural, and which is sound and complete. First-order Ontology is obtained from Elementary Ontology by dropping the quantifier ‘’, and replacing it by the restricted quantifier ‘i’. A sentence (iD)M has the significance of: (D)[[D H D] M]. And the (defined) existential quantifier ‘i’ gives sentences (iD)M which have the significance: (iD)[[D H D] & M]]. The language L i is obtained from L by replacing the (unrestricted) quantifier ‘’ by ‘i’. The restricted quantifier ‘i’ is defined: (iD)M = (def ) ~(iD) ~M. Given a domain E and an interpreting function f of L i (or L ) for E , the value of the restricted quantifier is determined as follows: Let (D)M be a sentence of L , and let E be the first noun constant in alphabetical order not occurring in M. Then (iD)M is true for the valuation determined by f iff the result of replacing all free occurrences of D in M by E is true for every E-variant of f in which E is assigned a truth-valued
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function which yields the value true for exactly one individual in E . If E = , the sentence (iD)M is (vacuously) true. The deductive system 1O has the same rules for connectives as EO. The rules for the restricted quantifiers are the following: i Elimination ( i D) M [E H E] ~D S M/ E
i Introduction ȕ is a noun constant which {[E H E]} does not occur in M or in any ~D uncancelled hypothesis other S M/ than the one in braces in the E proof of ( i D) M ~D S M/ E
The rules for ‘H’ are the same for 1O as for EO except for the rule H Introduction: H Introduction [G H J ] ( i D)( i E)[[[D H J ] & [E H J ]] [D H E]] [J H J] It is a straightforward matter to prove the following: THEOREM 2. Every theorem of 1O is logically valid. Let X be a set of sentences of L i and let M be a sentence of L i. Then M is a logical consequence of X, and X logically implies M (X ş M) iff there are no domain of individuals E and interpreting function f of L i for E such that each member of X has value t for (the valuation determined by) f , but f (M) = f. Let X be a set of sentences of L i and let N be a sentence of L i. Then N is deducible from X (X Ō N) in 1O iff there are sentences M1, . . . , Mr which are members of X such that M1, . . . , Mr / N is a theorem of 1O. Let X be a set of sentences of L i. Then X is consistent with respect to 1O iff there is no sentence N of L i such that both X Ō N and X Ō ~N. Let X be a set of sentences of L i. Then X is maximal consistent with respect to 1O iff X is consistent with respect to 1O, and for every sentence M of L i, either M is a member of X or X {M} is not consistent. Let X be a set of sentences of L i. Then X is instantially sufficient iff for every sentence ~(iD)M of L , if ~(iD)M is a member of X, then for some noun constant E,
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~D [[E H E]& ~ S M /] E is a member of X. LEMMA. Let X be a maximal consistent, instantially sufficient set of sentences of L i. Then (1) ~M X iff M X; (2) [M N] X iff M X or N X; (3) (iD )M X iff for every noun constant E, ~D [[E H E]& ~ S M /] E is a member of X. THEOREM 3. Let X be a maximal consistent, instantially sufficient set of sentences of L i. Then there is a domain of individuals E and an interpreting function f of L i for E such that for every sentence M of L i, f (M) = t iff M X. Proof. Let E be a noun constant of L i such that [E H E ] X. Then C(E ) = {J _ J is a noun constant of L i such that [J H E ] X }. Let E = {C(E ) _ E is a noun constant such that [E H E ] X }. If E z , then let f be the function defined on the noun constants of L i such that if J is a noun constant, then f (J ) is the function I such that I[C(E )] = t iff [E H J ] X, and I[C(E )] = f otherwise. If E = , then f(J ) is a function on some arbitrarily selected non-empty domain (say {1, 2, 3, 4}) that is true for 0 or more elements and false for the rest. Now we can establish the theorem by arguing by induction on the length of M. Let L i+ be the extension of L i obtained by adding the following noun constants: D, D1, . . . LEMMA 1. Let X be a consistent set of sentences of L i. Then X can be extended to a maximal consistent set of sentences of L i. LEMMA 2. A maximal consistent set of sentences of L i can be extended to a maximal consistent, instantially sufficient set of sentences of L i+. THEOREM 4. Let X be a consistent set of sentences of L i. Then there is a domain of individuals E and an interpreting function f of L i for E such that each member of X has value t for the valuation determined by f . THEOREM 5. Let X be a set of sentences of L i and M be a sentence of L i such that X ş M. Then X Ō M.
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5. Referring
In the following sections we will consider Elementary Ontology. It is straightforward to adapt our remarks to the system First-order Ontology. Before I consider collections of objects, and determine whether sentences of L are suited to represent statements about collections, I will discuss referring. Referring takes place when a person uses an expression to direct her attention to a particular object, and there really is an object of her attention. A person can use a name to refer: Napoleon was poisoned. Several of our friends live in Paris. But she can also refer with other expressions: That girl is quite tall. The author of Paradise Lost was English. A person who uses an expression to direct her attention to a genuine object has identified the object; referring is a kind of identifying. If someone is to use an expression to refer to an object, she must be connected to the object in some way that she knows about. If she experiences or has experienced the object, she has a direct connection to the object (so long as she doesn’t forget). If she merely learns about the object, she is connected to the object via her sources of information and their connections to the object. But there are other connections that a person can exploit in referring to an object. For example, I have never been to El Salvador, but I have read and heard about El Salvador. I know (roughly) how I am situated with respect to El Salvador, and I know how to get there from where I am now. In referring to El Salvador, I intend the country to which I have this geographical connection. To refer to an object in the unqualified sense, there must really be an object, and I must succeed in identifying it. But we also talk and think about fictional characters. Different people can discuss the same fictional character. It is useful to recognize fictional forms of identifying and referring so that we can accommodate talk about Sherlock Holmes or Lady Macbeth. I follow Searle (1974) in holding that the person who tells a story is pretending to refer to characters and make assertions about them. But the storyteller creates an objective situation which provides targets for fictional referring acts. It doesn’t very often happen that a person directs her attention, intending to refer to an object, when there is no object. Even when a person uses an expression which is inappropriate or incorrect for an object, she can successfully refer to the object. The target of the referring
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act is determined by the language user’s intentions, not by the expression she uses. But if it should happen that an attempted referring act has no target, then any characterization of the “referent” will be incorrect. Suppose that in Mary’s statement: The man who did this is inconsiderate. the act performed with the subject expression has no referent. Then her statement isn’t correct, no matter whether or not we decide to call it false. But while we can deny her statement, Mary can’t do this herself by saying something like: It isn’t true that the man who did this is inconsiderate. For Mary’s use of the referring expression marks a commitment to acknowledge the object of attention to exist. This is a presupposition of her statement, even when she uses a negative prefix. I have discussed referring acts, because I want to compare our talk about collections to referring acts. Sentences of Ontology, of Elementary Ontology, and of First-order Ontology do not represent referring acts. But perhaps such sentences (or their components) do represent acts of talking about collections.
6. Collections
When a speaker says something like: George is smarter than he looks. she uses the word ‘George’ to identify the person George. In a similar way, I think, the person who says: Dogs make better pets than cats. is using the word ‘dogs’ to direct her attention to something. That something is the collection of dogs. Unlike the words ‘set’ and ‘class’, the word ‘collection’ has not got an established technical use. So I am pressing this word into service for my own ends. My use of ‘collection’ has features in common with ordinary uses of this word, but I am not trying to capture ordinary usage. My collections are just what I say they are. However, I do intend by my use of ‘collection’ to “pick out” entities that play an important role with respect to thought and language.
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A collection of objects is an aggregate of those objects. It is made up of those objects, considered together. The collection has no internal structure, but is unified by being the object of someone’s attention. A real collection, as opposed to a fictional one, contains only existing real objects. There is no collection at present which contains the city Troy, or Carthage. A collection can gain and lose members. The collection of dogs at one time contained Rin Tin Tin, but no longer does, since the Rin Tin Tin of the movies no longer exists. The collection of dogs will have new members next year, and will have lost some of its current members. However, we can also consider the collection of exactly those dogs alive at this moment. That collection will not gain new members, and will cease to exist once one of those dogs dies. There are also collections which go out of existence, and are later reconstituted. The collection of Farmer Jones’ sheep will go out of existence if that farmer sells them all, and be reborn when he subsequently buys new sheep. A collection is constituted by its members; there is no empty collection. When the members of a collection cease to exist, so does the collection. And a collection of a single object consists of that object. On my analysis of linguistic acts, collections are important in connection with some uses of plural nouns. A single sentence can be used (on different occasions) to perform acts with different semantic structures, but a speaker would commonly use these sentences: All dogs are animals. No dogs are birds. Some dogs are collies. Some dogs are not collies. to direct her attention to the collection of dogs, and to acknowledge the collection to all be animals, never be birds, etc. The statements made might be concerned only with the collection of dogs at present, but in making the universal statements, it would be natural to intend the collection of dogs at all times. As customarily used, the first word of each categorical sentence qualifies the acknowledging act. The dogs are all animals, in no case birds, sometimes collies, etc. The common use of the categorical sentences is different in this respect from common uses of sentences like these: Every dog is a mammal. Some dog has rabies.
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Characteristic acts of using these last sentences involve the quantificational use of noun phrases, and will not pick out the collection of dogs. A collection must be distinguished from what I will call a group. A group is a structured whole of objects. Its internal structure is what unifies the elements making up the group. A group is also a concrete object, while a collection is slightly abstract, for the collection is constituted by its elements considered apart (in abstraction) from any relations they might have to one another. (But collections are not abstract entities of the sort that numbers, concepts, and propositions have traditionally been thought to be.) A wolf pack is a group as opposed to a collection. The pack is constituted by its component wolves linked by “kinship” and hierarchical relations. The collection of wolves in that pack is just the wolves, and not the relations. If the relations between wolves in the pack changes, the group/pack is changed, but the collection will not be affected. The Solar System is a group in my sense, constituted by the Sun and its planets (and their moons, and smaller bodies, etc.). When someone uses an expression to direct her attention to a particular real object, she has referred to/identified that object. In referring, she makes use of (exploits) relations that she knows about linking her to the object. She is situated by these relations with respect to the object, so that the object has a location prior to and independent of her referring act. Groups are concrete objects found in the world, and are qualified to be the objects of referring acts. However, collections are not. Someone who uses an expression to direct her attention to a collection has not referred to that collection. For collections do not have an independent “standing” apart from acts of attending to (thinking of) them. There are no antecedent relations linking language users to collections that the language users can know about so as to intend the object reached by the relations. Although a collection is not suited to be the object of someone’s referring act, a language user can direct her attention to a collection. How does she do this? The language user attends to a collection with respect to a linguistic practice. If there is a predicate I which is used to acknowledge objects to be \, then there are criteria associated with the predicate. The language user employs these criteria to correctly acknowledge an object to be \. In using the predicate to attend to the collection of \’s, the language user is attending to whatever objects satisfy I’s criteria. This collection does not constitute an object apart from the language user’s linguistic practice and her attending act. Given
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the linguistic practice, the collection is merely potential until someone actually attends to it. A collection which is constituted by someone’s attending to it is not a unified whole. It hasn’t got sufficient unity to be an indivisible element of a further collection unless it is a collection consisting of a single object. So if X is a collection and Y is a collection, the collection of X and Y is no different from the collection of X ’s and Y ’s. Using a set theoretic analogy, if X and Y are collections, we can consider the collection X Y but there is no collection {X, Y} alternatively, we might have it that the collection {X, Y} “reduces” to X Y.
7. Sets and Collections
Collections are, according to me, genuine elements of the world, though they depend for their existence on being the objects of people’s attention. One common reason for attending to a collection is to predicate something of its members. There is affirmative universal (distributive) predication: All cats are felines. And negative universal predication: No tigers make good pets. And “typical” distributive predication: Birds fly. Dogs bark. We also attend to collections to provide targets for collective predication: Dinosaurs are extinct. Bats are numerous. Collections are important for many of the things we say (and think) about the world. In contrast to collections, sets are not important for our ordinary linguistic practice. Sets do play important roles in mathematics and mathematically-related disciplines, but the ontological status of sets has been controversial since Cantor founded set theory a century ago. It is my opinion that logicians and philosophers who regard sets as fictions are correct. Although no one can refer in the unqualified sense to a set, fictional-referring to sets is possible. The set-theoretic story is consistent
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and coherent, though not yet complete, and this story can profitably be investigated and developed. In giving the truth conditions of sentences of L and L i, and in proving soundness results for EO and 1O and a completeness result for 1O, I have made free use of set-theoretic concepts and techniques. This is entirely appropriate, for set-theoretic models are legitimate devices to use to investigate theories of various kinds. That we can use set-theoretic techniques to establish the strong completeness of 1O is convincing evidence that 1O is adequate to the arguments made with sentences of L i (made with statements represented by those sentences). Our proofs are probably the best we can do by way of supporting the adequacy of 1O. However, the sentences of L and L i are intended to represent statements of kinds that people might actually make. A set-theoretic interpreting function is merely an abstract model of what I will call a fully specific interpretation of a logical language. A fully-specific interpretation ties logical-language expressions to specific kinds of linguistic acts, performed with specified expressions. A fully-specific interpretation of either L or a first-order language wouldn’t be based on a domain of individuals which is a set, but would instead have a domain which is a collection given by using a noun or noun phrase. A genuine collection is nonempty, but we could also use some expression like ‘square circle’ or ‘healthful cigarette’ to specify an empty domain. Since all collections have members, it is a façon de parler to speak of an empty domain. A fully specific interpretation determines which kinds of acts are represented by the various expressions. For a first-order language, one might do this by saying something like: Let ‘F(x)’ mean x is a fox Let ‘P(x, y)’ mean x is a parent of y Etc. For Ontology, we might have this: Let ‘A’ be a noun constant for anteaters Let ‘B’ be a noun constant for bananas Etc. The interpreting functions we have employed above assign truth-valued functions to noun constants. Such functions are extensional mathematical counterparts to predicative acts, but they don’t “do justice” to these acts. For one function might correspond to different predicates (predicative
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acts). And the function can only capture the extension of the predicate at some particular moment.
8. Capturing Talk about Collections
If someone attempts to refer to an object and, further, say something about the object, when there is no object perhaps with this sentence: The person who did this is deranged. then her statement is not correct. I prefer to classify such statements as false rather than making a special category for them. These false statements have an existential presupposition that might also characterize a speaker’s denial of the statement. If both of these statements: The person who did this is deranged. It isn’t true that the person who did this is deranged. presuppose that there is a person who did whatever this is, and no person did it, then both statements are false. (Even someone who holds out for calling them neither true nor false must admit that neither is correct.) I think it is also the case that the person who directs his attention to a collection, and goes on to say something about this collection, presupposes the existence of the collection his attending act commits him to acknowledge the collection to exist, which “amounts” to acknowledging the collection to have members. A person who, by mistake, directs his attention to a nonexistent collection, and goes on to make a statement “about” this collection, has said something false (incorrect) no matter how he characterizes the collection. For the “success” and correctness of his statement depends on his attentiondirecting act having a genuine target. (But we can say true things about collections, like the collection of dinosaurs, that once existed and no longer do.) If there are no I’s, then someone who uses these sentences: All I’s are \ No I’s are 4 to claim that the (collection of) I’s are all \, and never 4, has made false statements. But if she uses these sentences: It is false that all I’s are \ It is false that no I’s are 4
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and still directs her attention to the collection of I’s, her statements are still false. When someone uses a predicate or noun I to direct her attention to the collection of I’s, she has used the expression directedly. The directed use of the expression involves an existential commitment (or presupposition). But when the same (or a derivative) expression is predicated of an object, there is no existential presupposition. The speaker who uses a sentence: D is a I to claim that D is a I is making/reflecting a commitment to accept statements to the effect that something is a I and that I’s exist. But if she denies the statement, using one of these: D is not a I It is false that D is a I she is not committed by what she says to accept a statement that I’s exist. The predicative use of an expression is not characterized/ constituted by existential commitment. As the language L (and also L i) has been developed to this point, no noun constants are used directedly. A statement represented by: [D H I] to the effect that D’s are, singly, I’s is false if either there are no D’s or no I’s. (It is also false if there are D’s and I’s, but either there is more than one D or the single D is not I.) And if this statement is false, then the following will represent a true statement: ~[D H I] The language L does not contain a category of referring expressions, so in L there are no sentences which predicate a noun constant of an individual picked out by a referring expression. But we think of L as a fragment of a larger language in which the noun constants are predicated of individuals (in which the noun constants represent acts predicating something of individuals). However, an expression can be used predicatively without being predicated (or denied) of an individual. What is characteristic of the predicative use of a predicate expression is the absence of existential commitment/presupposition. (I am stipulating my own usage here, not reporting conventions governing the use of English.) A sentence: [D H I]
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has the sense: Exactly one thing is D, and that thing is I. In this sentence (phrase) I have used to give the sense, both ‘D ’ and ‘I ’ have been used as predicates. If Ontology is intended to capture or represent statements about collections, then it is unsuccessful. Ontology captures instead (some) predicative uses of common nouns. I will expand the language L to L which contains expressions for collections (expressions representing acts of using words to direct one’s attention to collections). In L , noun constants which have underlining are used to represent the directed use of nouns. A plain noun constant is one of: A, B, C, A1 , . . . A directed noun constant is obtained by underlining a plain noun constant. The wffs of L are wffs of L . In addition, we have: If M is a wff of L , and contains occurrences of plain noun constant D, then the result of replacing some or all occurrences of D by D in M is a wff of L . As for truth conditions, we treat a sentence M containing directed constants D1 , . . . , Dn (and no others) as if it were the conjunction: M* & (X)[X H D1 ] & . . . & (X)[X H Dn ] where M* is obtained from M by replacing all occurrences of directed noun constants by their plain counterparts. So, for example, both a sentence: [A H B] and: ~[A H B] imply that something is a B. If there are no B’s, then both of the sentences are false. A single English sentence can be used (on different occasions) to make statements having different semantic structures. But someone making a statement with this sentence: All dogs are animals. would be very unlikely to use ‘dogs’ predicatively. In sentences of L , any place that can be occupied by a constant D can also be occupied by the plain version D, and conversely. However, while sentences of L and L (and also L i) represent statements which someone can make, not all of the artificial-language sentences represent kinds of statements that are common.
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To provide a completely adequate deductive system for L , it would be necessary to make use of elements of illocutionary logic, as explained in Kearns (1997, 2000, and 2002). But doing this would make the present paper much too long. I will briefly sketch the deductive system EO, and won’t prove results about the system. EO is obtained from EO by adding rules for directed constants. To illustrate these rules, if M is a wff and D is a directed constant, I will write ‘MD ’ to indicate that M contains one or more occurrences of D. To understand the significance of the new rules of EO, we must regard the system as being used with respect to some established body of knowledge. We use proofs/arguments in the deductive system to establish consequences of this knowledge. If M is a sentence representing a statement of what is known, M can be the top node of a branch in a tree proof without being a hypothesis of the proof. In such a case, M is an initial assertion of the tree proof. A tree proof from initial assertions M1, . . . , Mr and hypotheses N1, . . . , Ns to conclusion P establishes that the argument sequence N1, . . . , Ns / P is correct or valid with respect to the body of knowledge K. In EO, the restrictions on the constant generalized by the rule Introduction require that this constant occur in neither an initial assertion nor a hypothesis leading to the sentence which is the premiss for Introduction. No hypothesis in a tree proof of EO can contain occurrences of a directed constant D. The additional rules of EO are the following: Directed Introduction [ D H E] [ D H E]
Directed Transmission MD N ND
The premiss is the conclusion of a tree proof with no uncancelled hypotheses; thus it is an addition to the body of knowledge.
N contains occurrences of the plain constant D, and some or all of these are replaced by D in ND.
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Directed Elimination MD M
Some or all occurrences of D in MD are replaced by D in the conclusion.
It is clear that there are no logical truths of L which contain directed constants. It should also be noted that an argument sequence: [D H E ] / [D H E ] is not inferentially correct in the sense that an inference from its premiss to its conclusion is unconditionally legitimate. Whenever the premiss is true, so is the conclusion. Asserting the premiss commits a person to asserting/accepting the conclusion. But supposing the premiss does not commit a person to a supposition of the conclusion. (If we suppose some statements to be true, and then derive a conclusion from these statements, our conclusion has the force of a supposition even though we don’t prefix the conclusion with the word ‘suppose’.) The directed use of a noun constant has the force of an assertion, so that supposing: [D H E ] is like saying: I assert that E ’s exist, and I will suppose that the D ’s are, singly, E ’s.
9. Some Conclusions
The plain system Elementary Ontology consists of the language L , the account of truth conditions for sentences of L , and the deductive system EO. This system is a truncated version of LeĞniewski’s system Ontology. The system Elementary Ontology isn’t exactly like LeĞniewski’s system, for it doesn’t have the “growing” character of LeĞniewski’s system, and it contains a semantic account which LeĞniewski did not provide. However, the open character of LeĞniewski’s system isn’t essential, and the account of truth conditions seems pretty much what LeĞniewski must have had in mind, except for the fact that noun constants are construed as predicates of individuals. The system First-order Ontology is a restricted version of Elementary Ontology in which the only quantifier is restricted to one-individual noun constants. This makes a sentence ‘( iD)M ’ equivalent to a sentence about all individuals in the domain. The system 1 O is sound and
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complete. LeĞniewski himself probably wouldn’t have had any use for First-order Ontology, but I think it is useful to call attention to a fundamental system of Ontology which is complete as well as sound. LeĞniewski failed to appreciate the essential difference between referring expressions and common nouns, for, according to SobociĔski (in his classroom lectures), LeĞniewski thought that a statement to the effect that Socrates is a human being is captured by an Ontological sentence like this: [Socrates H human being] This failure kept LeĞniewski from recognizing that Ontology provides an inadequate analysis for the whole of a natural language. But Ontology is suited for analyzing some uses of common nouns. However, Ontology isn’t suited for analyzing statements about collections (as I understand them), and I think that collections are those entities which are genuinely distributive classes. We say things about these collections in order to predicate properties of each of their members. The directed system Elementary Ontology, which consists of L , its semantic account, and EO, does allow us to analyze statements about collections. However, the directed system would be more satisfactory if it incorporated principles and notation proper to illocutionary logic, for the notation characteristic of directed constants marks a force analogous to illocutionary force, and would be more conveniently treated in a system with symbols for illocutionary force.1
University at Buffalo Department of Philosophy 607 Baldy Hall Buffalo, NY 14260-1010, USA email:
[email protected]
REFERENCES Kearns, J.T. (1996). Reconceiving Experience: A Solution to a Problem Inherited from Descartes. Albany/New York: State University of New York Press.
1
In writing and revising this paper, I have received many helpful suggestions from my colleague John Corcoran. They have substantially improved the paper in both style and substance. Comments from Barry Smith were also extremely useful.
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Kearns, J.T. (1997). Propositional Logic of Supposition and Assertion. Notre Dame Journal of Formal Logic 38, 325-349. Kearns, J.T. (2000). An Illocutionary Logical Explanation of the Surprise Execution. History and Philosophy of Logic 20, 195-214. Kearns, J.T. (2002). Logic Is the Study of a Human Activity. In: T. Childers and O. Majer (eds.), The Logica Yearbook 2001, pp. 101-110. Prague: Filosofia. Lejewski, Cz. (1995). Remembering Stanisáaw LeĞniewski. In: D. Miéville and D. Vernant (eds.), Stanisáaw LeĞniewski Aujourd’hui, pp. 25-66. Paris, Grenoble & Neuchatel: Groupe de Recherches sur la philosophie et le langage & Centre de Recherches Sémiologiques. LeĞniewski, S. (1927). O podstawach matematyki [On Foundations of Mathematics]. Przegląd Filozoficzny 30, 164-206; 31, 261-291; 32, 60-101; 33, 77-105; 34, 142-170. LeĞniewski, S. (1929). Grunzüge eines neuen Systems der Grundlagen der Mathematik. Fundamenta Mathematicae 14, 1-81. LeĞniewski, S. (1930). Über die Grundlagen der Ontologie. Sprawozdania z posiedzeĔ Towarzystwa Naukowego Warszawskiego, Wydziaá III (Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III) 23, 111-132. LeĞniewski, S. (1932). Über Definitionen in der sogenannten Theorie der Deduktion. Sprawozdania z posiedzeĔ Towarzystwa Naukowego Warszawskiego, Wydziaá III (Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III) 24, 289-309. Luschei, E.C. (1962). The Logical Systems of LeĞniewski. Amsterdam: North Holland. Searle, J.R. (1974). The Logical Status of Fictional Discourse. New Literary History 6, 319-322. Reprinted in: Expression and Meaning (Cambridge: Cambridge University Press, 1979), pp. 58-75. Simons, P. (1987). Parts: A Study in Ontology. Oxford: Oxford University Press. SobociĔski, B. (1949). L’Analyse de l’Antinomie russellienne par LeĞniewski. Methodos 1, 94-107, 220-228, 308-316; 2, 237-257.
Jacek PaĞniczek DO WE NEED COMPLEX PROPERTIES IN OUR ONTOLOGY?
In discussing ontological issues philosophers sometimes mention complex properties. However, they usually dismiss the concept as theoretically useless and even dangerous (see Grossmann 1972). Only some of them try to argue in favour of complex properties and even then their arguments are not sufficiently convincing to give rise to more serious consideration of this concept (see, for example, Meixner 1991). In the present paper, we aim to show the ontological usefulness of complex properties and to suggest that these properties can be treated as a formal-ontological means of categorial differentiation of objects. The main idea is that objects may differ not only with respect to simple properties but also with respect to complex properties. In particular, two objects may possess the same simple properties and differ in complex ones. We believe, however, that the configuration of simple and complex properties is neither accidental nor arbitrary but that it is amenable to certain general ontological rules. We adopt here a liberal ontological approach and do not restrict our considerations to any particular category of objects (like individuals, for example). The problem of complex properties is very often considered parallel to the problem of complex predicates (the latter is discussed usually by logicians or linguists) and the two problems are in fact inseparable (see especially: Swoyer 1997, 1998). Quite often acceptance of complex properties is motivated by linguistic reasons. In semantic analyses of language, we need complex predicates and these should be equipped with interpretations. Here we will prefer the “ontological” approach but, for obvious reasons, we will talk, explicitly or implicitly, also about complex predicates.
In: J.J. Jadacki and J. PaĞniczek (eds.), The Lvov-Warsaw School – The New Generation (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 89), pp. 113-128. Amsterdam/New York, NY: Rodopi, 2006.
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1. Introducing Complex Properties: A Formal Theory of Complex Properties What can be considered a complex property? Given any (simple) properties P and Q, we talk about the negation (or: complement) of P: ¬P, the conjunction of P and Q: (P Q), or the disjunction of P and Q: (P Q). One can take into account kinds of complex properties other than those built up by means of connectives such as ¬, , , for example properties built up by means of modal operators or relations (the socalled relational properties). Here we focus only on complex properties composed of simple properties and connectives. 1 The problem whether complex properties exist somehow apart from simple properties belongs to metaphysics. However, this problem, when considered exclusively within a metaphysics of properties, is not particularly interesting and we are not going to discuss it in this paper. Our concern is primarily ontological. This means that we consider various categories of entities in order to discover dependencies between simple and complex properties, as if they were existent, alongside dependencies between properties and objects. We then consider various categories of objects relative to these dependencies. Any discussion of properties should, of course, be accompanied by a discussion of objects qua subjects of predication. Only in this context may we reasonably investigate ontological relations between simple and complex properties by asking whether the predication that involves complex properties implies, is implied by, or is equivalent to, the predication that involves respective simple properties (e.g. whether the fact of possessing P is equivalent to the fact of not possessing P). This possibility would make the concept of complex properties ontologically relevant. Let a represent an object and aP express the predication: a possesses P. We may here distinguish the following principles of dependency between simple and complex predication, i.e., between possessing simple properties and possessing complex properties. P1. P2. P3. P3.* P4. P5. 1
a¬P ¬aP (consistency) ¬aP a¬P (completeness) a(P Q) aP aQ ¬a(P ¬P) (a(P Q) aP aQ) aP aQ a(P Q) (closeness under conjunction) aP aQ a(P Q)
The case of relational properties is more complicated from a formal point of view but at the same time it is not much more interesting from a philosophical point of view.
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P6. P7.
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a(P Q) aP aQ a(P Q) (aP aQ)
We assume that connectives are mutually definable in the usual way when they are applied to properties: R1.
If Į { ȕ is an instance of a tautology expressed by means of property variables then for every object a: aĮ { aȕ holds.
E.g. an object a possesses a complex property (¬P Q) iff it possesses the property (P Q). Additionally, we will consider the following two rules: R2.
If Į is an instance of a tautology expressed by means of property variables then for every object a: aĮ holds (R2ƍ: ¬a¬Į holds also).
If R2 is assumed then every object possesses the property (P P) in particular. R3.
If Į ȕ is an instance of a tautology expressed by means of property variables then for every object a: aĮ aȕ holds.
According to R3 objects are closed with respect to logical entailment, i.e. logically closed. E.g. if a(P Q) then aP and aQ as well. Obviously, R3 is stronger than R1, i.e. R1 follows from R3. It should also be noticed that if we additionally assume, and this seems quite reasonable, that every object possesses at least one property then R2 will also follow from R3.2 Let us indicate some other logical interdependencies between P1-P7 and R2, R3 if R1 is assumed. When all principles and rules listed above hold, this situation will be called individuality. FACT FACT FACT FACT FACT FACT FACT FACT
2
1. 2. 3. 4. 5. 6. 7. 8.
P1-P7 are independent from each other. P1-P4 entail R2 and R3. R3 entails P3. P7 and R2 entail R3. P2 and P4 entail P3*; P2, P4, and R2ƍ entail P3. R2 and P7 entail P4. P3 and P4 entail P7. The following groups of principles and rules are equivalent and each of them entails individuality: (a) P1-P4; (b) P1, P2, P5, P6; (c) P1, P2, P7, R2; (d) P1, P2, P4, R2ƍ; (e) P1, P2, P4, R3.
Suppose that D is a tautological property and that for some E, aE. In this case E D is also a tautological property and, according to R3, aE aD and hence aD.
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FACT 9. P1 and P2 do not entail any of P3-P7.3 Since R1 is assumed we may model (interpret) our basic ontology of properties in a Boolean algebra: P =
, where P is a set of properties, , are distributive lattice operations of join and meet respectively, * is the operation of complement, 0 and 1 are the minimum and maximum elements respectively.4 This modelling is also treated as a semantics for a language in which we talk about complex properties by means of predicate variables and connectives (the language can be successively enriched). Thus, let I be an interpretation function which assigns to P, Q, etc. the elements of P and assigns to complex properties their Boolean counterparts: I(¬P) = I(P)*, I(P Q) = I(P) I(Q), I(P Q) = I(P) I(Q), I(P Q) = I(P)* I(Q). Thus, I(P ¬P) = 1 and I(P ¬P) = 0. Let I assign to object variables a, b, . . . subsets of the power set of P, i.e. sets of properties. We then say that these sets constitute respective objects and that the proposition aP is true if and only if I(P) I(a). Thus, objects in this semantics are represented by sets of properties which they are supposed to possess. Yet, this is just a representation which does not commit us to a bundle theory of objects. As can be expected, R1 holds in the algebra P but neither R2 nor R3 does.5 Also, none of P1-P7 are valid in this semantics. In order to be able to express all facts about the properties in P, we obviously need a much richer formal language than the one adopted above. Most ontologists would presumably agree that all principles P1-P7, R1, R2, R3 are true. As, certainly, would all philosophers who admit individuals as the only category of entities (this motivates our choice of the term individuality in this context). The truth of these principles means two things. First, it means that complex predication is always reducible to simple predication (complex predicates can then be viewed as merely a trivial notational variant of the simple predicates). Second, we can accept an ontology of complex properties and treat P1-P4 as the metaphysical theses stating jointly that there exist only individuals, i.e., objects insensible to a distinction between simple and complex properties. However, even if we do not admit entities other than individuals, the concept of complex properties and its related principles allow us to gain an insight into the ontological nature of individuals. Generally, when we 3
We omit the proofs of theorems included in this paper. Most of those proofs are quite elementary or they follow from well-known facts concerning Boolean algebras. 4 A reader not acquainted with Boolean algebras may consult any elementary textbook on this topic. 5 Essentially the same ontological framework for semantics of natural language is adopted in Keenan and Faltz (1985).
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choose some of the principles P1-P7 and R1, R2, R3 as the axioms of our theory, this decision is metaphysical and means that there only exist objects that obey these principles. Yet, if we discuss objects that fulfil some of these principles then this is merely an ontological approach, which does not entail any metaphysical theses.6
2. Ontological Interdependencies between Objects and Properties If we assume that properties are more basic entities than objects then the ontology of properties can induce an interesting ontology of objects (but not a metaphysics thereof). If we assume the converse ontological dependence then the possible relations between properties such as entailment and possible operations on them such as negation, conjunction, etc., can be entirely determined by the ontology of objects. The second ontological view is certainly much more popular among philosophers. The extensional approach to properties is a paradigmatic example of this view. 7 We simply conceive of properties as sets of individuals and the relations between those sets determine all the possible relations between properties. The relations in question are usually established, especially in formal ontologies, by identity and definition axioms (for properties and objects, respectively): IdPR IdOB
a (aP { aQ) P = Q P (aP { bP) a = b
IdPR states that coextensive properties are identical and this is the most straightforward formulation of extensionalism. IdOB is the strong version of Leibniz’s principle. Although in these axioms we quantify over objects and properties, respectively, the axioms carry no metaphysical
6
Here we distinguish between the meaning of ‘ontological’ and ‘metaphysical’. By the latter term we mean those theses that state or entail the existence of such and such objects or objects of a such and such kind. Ontological theses also involve existence but they state dependencies between different categories of entities, forms of entities, structures of predication, etc. and basically they do not entail any existential theses. I say ‘basically’ since the issue depends on what criterion of ontological commitment we accept. The ‘ontological-metaphysical’ distinction has been precisely defined by a Polish phenomenologist, Roman Ingarden (see Ingarden 1964). 7 Given a set of individuals D, the structure is a Boolean algebra with inclusion as its ordering. See section 5.
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commitments in the sense of entailing the existence of objects and properties.8 DfPR DfOB
P a (aP { Į), where P does not appear in Į. a P (aP { Į), where a does not appear in Į.
These two definition axioms are strictly metaphysical – they explicitly state the existence of properties and objects. Of course, since the content of the formula Į determines a particular property or a particular object, the ontology of properties and objects directly hinges on the expressive power of the language in which Į is phrased. It is possible to assume both DfPR and DfOB, i.e., to allow mutual ontological definability of objects and properties. However, one should be aware that this gives rise to a circularity which may result in a contradiction. According to our approach properties are ontologically basic. This seems to make objects depend on properties since objects are constituted by properties. However, such an interpretation is only partially correct, for although objects that possess the same properties are indistinguishable, nothing guarantees that there exists an object that possesses such and such properties (including complex ones). Even if we introduce the definition axiom DfOB into our theory it will have no significant creative power. We will be able to define new objects only relative to those already present. In particular, we may define the negation, the inversion, the conjunction, and the disjunction of objects: [¬a]P { ¬aP, [~a]P { ¬a¬P, [a b]P { aP bP, [a b]P { aP bP.9 Yet, the axiom DfOB, as it stands, does not allow us to “create” objects from any arbitrary properties. This goal of “creativity” can be at least partially achieved if we introduce the symbol of identity into the language of our ontology. We can then define (bring into existence) every object constituted by a finite number of selected properties, e.g. a P (aP { P = Q1 P = Q2 . . . P = Qn ) states the existence of an object constituted by properties: Q1 , Q2 , . . . , Qn . Of course, the cardinality of objects that can be defined depends strictly on the number of properties in P. It should be stressed that we cannot adopt DfPR instead of introducing complex properties in the way we have done. If we did that, complex properties would be dependent on objects. In particular, the only 8 According to Quine’s criterion, they do in the sense that there must exist at least one object or one property when quantification is based on classical logic. 9 Notice that when we use a tautology or contradiction for Į, we may define the object that possesses every property or the object that possesses no property. These are certainly very bizarre objects and hardly anyone can accept them.
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way of defining the negation of a property is: P a (a¬P { ¬aP). If we insisted on the uniqueness of P then this would force us to treat this property extensionally – for every two coextensive but distinct properties their negations would be identical. 10 As such, the algebra of properties does not bring into being any object. All we can say is that objects may be represented by sets of properties and this fixes the upper boundary of the class of all objects that could be. We may adopt the Meinongian approach and allow every set of properties to represent an object, perhaps with the exception of the empty set (see below). We can distinguish many categories of objects (although clearly a finite number of them) which fulfil various combinatorically possible systems of principles and rules listed above. However, as we already noticed, this does not mean that we are ontologically committed to the existence of those objects, i.e., that we must accept some metaphysical theses. Moreover, from an ontological point of view, most of those categories seem quite uninteresting and one could hardly imagine objects that exemplify them.
3. Negation and Conjunction of Properties. Completeness, Consistency and the Conjunctive Closure of Objects Perhaps the negation (or the complement) of a property is the most often mentioned type of complex property. In a natural language, we usually refer to the negation of a property by means of prefix like non- or not inserted in front of the respective predicate expression, e.g. ‘non-human’, ‘not a cat’, etc. Two properties are called contradictory if one is the negation of the other. The concept of negation enables us to express two formal-ontological features of objects – their consistency and completeness. An object a is said to be consistent if and only if P1 holds for all properties, i.e., an object cannot possess contradictory properties.11 An object is said to be complete if and only if P2 holds for every property, i.e., an object possesses at least one of every two contradictory properties. Usually consistency and completeness – if considered by traditional philosophers 10 This is the problem of every intensional theory of properties in which DfPR appears as a theorem. The problem can, to a certain extent, be evaded only in theories with two modes of predication (see Zalta 1983 and 1988). 11 There is a weaker concept of contradictory properties according to which being round and being a square are contradictory, see below.
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at all are attributed to all individuals or to all objects. But then these two concepts turn out to be universal in the domain of objects and so not ontologically relevant. On the other hand, they are quite trivial if one does not acknowledge complex properties or treat those properties as reducible to simple ones. Thus, all objects turn out to be ex definitione complete and consistent. Let us emphasize that consistency and completeness have a formal-ontological character and as such the notions do not need to entail any metaphysical existential theses, in particular, they do not need to entail any theses about the existence of inconsistent or incomplete objects. However, there are some metaphysical theories that allow for inconsistent and incomplete objects. Here we should mention perhaps the most characteristic theory of this kind, i.e. the Meinongian theory of objects. The Meinongian ontology comprises, apart from existing objects which are consistent and complete, also non-existing objects which are inconsistent or incomplete (an example is the non-round circle). It is worth mentioning that, in this theory, the concepts of consistency and completeness play an essential role in distinguishing new ontological categories of objects different from existing individuals. Since consistency and completeness are independent neither entails the other their intersection gives rise to four categories of entities: consistent and complete, inconsistent and complete, consistent and incomplete, inconsistent and incomplete. It is a commonly shared view that existing objects (individuals) are consistent and complete, although not every consistent and complete object must exist. 12 There is also another notion of inconsistency, different from the one given above. Let us call it impossibility. An object is said to be impossible if it possesses a contradictory property, e.g. a(P ¬P). R2ƍ states that every object is possible (is not impossible). If P3 or R3 is assumed then every impossible object is inconsistent; if P4 is assumed then every inconsistent object is impossible. The conjunction of properties is still another kind of complex property frequently discussed. Some philosophers accept conjunctions of properties as the only sort of complex properties.13 However, there seem to be no good reasons for rejecting either P3 or P4 as a principle true for all objects and properties. In particular, one can treat a conjunction P Q as a property “stronger” than P and Q alone in the sense that generally, i.e., P3 holds for every object while P4 does not need to hold for every 12
It is easy to construe a counterexample (to this view) on the ground of Boolean algebra. Armstrong admits the conjunction of properties to be a property but he deprives of this status the negation and disjunction of properties (see Armstrong 1997). 13
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object. Let us notice here that, in a certain sense, P3 is in fact weaker than P4. For, on the one hand, P3 follows from the logical closure expressed by R3 (which is a very natural condition supposed to be obeyed by all objects as explained below); on the other hand, P3 follows from P4 for complete objects that do not possess the empty property (see FACT 4). We see also that complete, consistent, possible objects that are closed under conjunction are individuals (see FACT 7d). It is worth considering another class of objects that embraces the class of individuals, viz. the class of consistent objects, i.e. objects that fulfil P1. Of course, consistent objects do not need to be incomplete but the category of incomplete and consistent objects is particularly interesting. Intuitively, objects that are referred to by definite descriptions such as the wooden table, the black cat, the rectangle with equal sides are consistent but not complete objects. In particular, the wooden table is supposed to be wooden and to be a table but neither to be square nor to be round (non-square). Another example of this kind of incomplete entity is provided by fictional objects. Those objects are to a large degree undetermined with respect to their properties. E.g. Sherlock Holmes is neither an orphan nor a non-orphan. This underdetermination follows from the obvious fact that it is impossible to invent a complete object, i.e., for every property to ascribe that property or its complement to a fictional object. It is worth noting that incomplete objects play an important role in the Meinongian ontology as entities that mediate intentional relation or reference to complete, in particular, to existent objects. Incomplete objects as determined merely by P1 can be subjected to further ontological refinement. Let us consider the rectangle with equal sides. This object can be thought of as constituted by two properties: being a rectangle and being a geometrical figure with equal sides. As such the rectangle with equal sides is a rectangle and it is a geometrical figure with equal sides but that object does not possess the conjunction of the two properties, i.e., it is not a rectangle with equal sides. This certainly may be seen as a counterintuitive result: why is the rectangle with equal sides not a rectangle with equal sides? This will not be the case if objects distribute the conjunction of properties, i.e. if they obey P4. Such incomplete objects closed under conjunction of properties can be called general objects.14 14
One is not supposed to associate any special meaning with this term. However, it may be mentioned that this meaning of “general objects” is close to the notion of a general object assumed by some philosophers of the Lvov-Warsaw School (see àukasiewicz 1987, ch. XVIII; KotarbiĔski 1920; LeĞniewski 1992).
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Let us now assume that the rhomb with equal diagonals is constituted of the following properties: being a rhomb, being a figure with equal diagonals, being a rhomb with equal diagonals. Intuitively the rectangle with equal sides is the same as the rhomb with equal diagonals and the square (constituted of a single property: being a square). So how can one render formally the fact that, in one sense, these objects are identical while, on the other hand, they are different because they are constituted by different properties? The following solution to this question may be suggested. First, we need to assume that complex properties: being a rectangle with equal sides and being a rhomb with equal diagonals are identical as well as identical with the simple property of being a square. The three objects mentioned above turn out then to have the same infimum: the property of being a square. This feature may be taken generally as a mark of a special sense of object identity, say virtual identity: two objects are virtually identical if and only if they have the same infimum. In this sense the rectangle with equal sides, the rhomb with equal diagonals, and the square are virtually identical; analogously the Polish Pope, the Cardinal born in Wadowice, John Paul II are virtually identical objects (although they do not need be strongly identical).15 Notice, that for objects which are logically closed (R3) and closed under conjunction virtual identity implies strong identity.
4. Property Entailment. Objects Closed under Entailment An important problem connected with properties is whether there is any entailment between them.16 It seems to be true that redness entails colouredness, roundness entails non-squareness. One could simply answer that a property P entails a property Q if and only if (necessarily) every object that possesses P possesses (or possesses necessarily) Q as well, i.e. a (aP aQ) or: a (aP aQ). However, this answer would mean that property entailment is basically dependent on actually existing objects (the range of individual variables) or merely possible objects and in this sense the entailment is accidental from a metaphysical point of view. Of course, we do not want to adopt such a view of property entailment at the outset, for this would basically result in the extensional view of properties. However, there can be notions of property entailment 15
For they are constituted by the following sets of properties: {being a Pole, being a Pope}, {being a Cardinal, being born in Wadowice}, {being John Paul II}, respectively. 16 Some authors prefer to talk about the part-whole relation holding between properties instead of talking about entailment between properties.
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independent of what objects exist or may exist. In particular, property entailment is that which mimics propositional entailment in classical logic and which is expressed in the rule R3: a property Į entails a property ȕ if and only if Į ȕ is an instance of a tautology expressed by means of property variables. Yet, this definition is purely formal and as such does not capture cases like redness entailing colouredness; and, being based on classical material implication, it inherits its counterintuitive features (in particular, self-contradictory or empty properties entail all other properties). The concept of property entailment should presumably be treated as primitive, in contradistinction to the concept of metaphysical entailment, rendering analytic or synthetic a priori truths. And R3 should be understood only as a sufficient condition for this entailment.17 We may understand property entailment as determined by the ordering d of a particular Boolean algebra of properties in the sense that P entails Q iff I(P) d I(Q). Certainly, in this sense redness may entail colouredness in a particular Boolean algebra of properties. The empty and full properties still, however, remain indistinguishable in this algebra. Yet, given the concept of property entailment , whatever it could be, one may adopt another definition of contradictory properties: properties P and Q are contradictory if and only if P entails the negation of Q (P ¬Q). In this sense the round square, i.e., an object which is round and is a square turns out to be inconsistent. As we noticed earlier, not all combinatorically possible categories, i.e., categories that result from combinations of some independent conditions P1-P7 and R1-R3, deserve to be studied. However, some categories of objects that lack certain features of individuality nevertheless exemplify a sort of regularity worth considering. In particular, one may distinguish a category of closed objects, objects closed under some sort of entailment (ontological move), or one may also accept a metaphysical thesis that all objects are closed. There is some evidence that every intentional object, i.e., an object we are conscious of, is somehow closed, although the issue of what kind of closure we are dealing with is a matter of logical and phenomenological discussions. Thus, not only the ordinary existing individuals we encounter in the real world, but also objects of imagination and dreams, theoretical and fictional objects, etc. are closed. If we think of the rectangle with equal sides or even of the round square we think of these “objects” as geometrical figures. When we read Arthur C. Doyle’s stories we have no 17
Even this view may, however, be questioned on the basis of the paradoxes of material implication (for example: does roundness entail roundness or brightness?)
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doubts that Sherlock Holmes is a European even if this is not explicitly stated in any story. Let us take into account objects closed under property entailment generated by the ordering of algebra P and consider now objects that fulfil the following condition, which we call the condition of monotonicity: P8
P d Q (aP aQ)
Assuming P8, let 4 be an object interpreted in P by {1} and let 5be interpreted by P(P)-{0}. Then 4 and 5 can be understood as the universal and particular quantifier objects, respectively. One should here notice that when sets and {} are precluded from representing any objects 18 the following formulas are valid for objects closed in the sense of P8:
(*)
4P aP aP 5P 4P { ¬5¬P 4(P Q) (aP aQ) R2
This means that closed objects generate a simple version of classical quantifier logic where quantifiers 4 and 5 are treated as categorematic expressions referring to what is sometimes called quantifier objects.19 Notice that P8 is equivalent to (*). The closure of objects can also be expressed by P7. The meaning of this notion of closure is in a sense close to the meaning of the notion of closure under conjunction (see FACT 5 and FACT 6).
5. Extending an Ontology of Properties Should some additional assumptions be imposed on the algebra of properties? In particular, should we assume that P is a complete Boolean algebra (completeness means here that for every subset of P there exists an infimum and a supremum). One can point out to an interesting correlation between individuals and properties in complete P. Let us consider an object a. In complete P the infimum a (the meet of all 18 We do not want to say that something that possesses no properties or something that possesses all properties is an object. 19 A logic of this kind is developed in PaĞniczek (1998).
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elements of a) and supremum a (the join of all elements of a) exist. The following formula will then hold: (*)
if a z 0 and a is an individual then a a and a is an atom in P.20
An element of Boolean algebra is an atom if there are no smaller elements other than 0. If a is an individual then a can be treated as its haecceity since a directly identifies a in the sense that aP if and only if a d P. Notice that there may be an object constituted by haecceity as its only property. Although such an object possesses the property a which could be read: being identical with a, it does not possesses other properties of a. This may suggest another argument in favour of the closure of objects under the property entailment induced by d: if an object possesses an atom-haecceity then why should it not possess all properties entailed by the haecceities? Clearly, not every object a contains a; in other words, the assumption that a must be an individual is necessary here. Another question is whether the algebra of properties should be atomic. In atomic algebras every element is entirely identified by atoms in the sense that it is a union of atoms (two properties that contain the same atoms are equal). Consequently, the atomicity of the algebra of properties results in a kind of extensional view of properties. But this is not a bona fide extensionalism as long as we do not acknowledge a oneto-one correspondence between atom-haeceities and individuals. That correspondence does not need to be obligatory from an ontological point of view. Maybe there are haeceities that are exemplified by no existent or even possible individual or and this is perhaps a less conceivable possibility there are individuals that are correlated with no haecceity at all. We are not going to discuss these ontological issues here.21 Let us here notice, however, that if there were unexemplified haecceities then we would escape classical extensionalism: there could be two properties with the same extension consisting of individuals but with a different “extension” consisting of atoms-haecceities. It is an interesting question whether abandoning the assumption about the atomicity of the algebra of properties would not open another 20
a is an individual if and only if a is an ultrafilter in the algebra of properties generated by a. 21 The first possibility can be understood in such a way that some individuals do not exist or even cannot exist in a given possible “extension” of the real worlds. As we stressed before, we are not committed to all objects that can be constituted by properties that belong to P (which are correlated with the subsets of P).
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possibility of the intensional approach to properties. However, a nonatomic algebra can hardly be interpreted as non-extensional, i.e., as an intensional model of properties. For atomicity seems to be strictly connected with the cardinality of a given Boolean algebra (it is a wellknown point that every finite Boolean algebra is atomic).22 The extensional approach to properties certainly has flaws of its own. Still, it makes many issues connected with structural features of properties, identity, quantification (also generalized quantification), cardinality, etc. much more natural and straightforward than does the intensional approach.23 So let us assume that the algebra of properties P is atomic with D as the set of atoms and that there is a one-to-one correspondence between the set of atoms as haecceities and the respective set of individuals D. So let us assume that D is a non-empty domain of individuals and I is a function assigning to P, Q, etc. subsets of D and assigning to complex properties their Boolean counterparts: I(¬P) = D I(P), I(P Q) = I(P) I(Q), etc. Let I assign subsets of P(D) to a, b, etc. As before, we will then say that the proposition aP is true if and only if I(P) I(a). What is important, individuals, i.e., members of D, can be embedded in the domain of objects, i.e., can be identified with some subsets of P(D) in the following way: d D o {X D: d X}. Clearly, for any property P, d I(P) if and only if I(P) {X D: d X}. In what follows, we will indicate another consequence of the assumption that the algebra of properties is atomic. The problem of complex properties can still be considered in a more general ontological framework. Properties are usually treated as a kind of relation, i.e., one-argument relations. Consequently, singular (oneargument) predication can be treated as a special case of plural (manyargument) predication. The structural complexity of relations far exceeds the complexity of properties and a much more sophisticated algebraic description is needed than that based on the Boolean algebra. One may also achieve a more general approach to complex properties by admitting 22 Theoretically, it can happen that two different properties “consist” of the same set of atoms. 23 Keenan and Faltz motivate the adoption of atomic Boolean algebra for the semantics of natural language differently. They need atoms to provide denotations for some proper names and descriptions. Consequently, they treat a property: a vegetarian who is John as an atom. But if this property is an atom of a Boolean algebra then it is the same property as a student who is John, a philosopher who is John or simply John. Thus, their argument is mistaken. Notice, that our approach enables us to distinguish the object a vegetarian who is John from the objects a student who is John, a philosopher who is John or simply John since they are constituted by the following sets of properties: {vegetarian, John}, {student, John}, {philosopher, John}, {John}, respectively.
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other kinds of complex properties. So far we have considered only complex properties built out of simpler ones by means of Boolean operations. But we can also take into account relational properties like “is loved by someone,” “loves Mary” built out of relations by means of several special operations which do not exist in ordinary Boolean algebra (like universalisation, conversion, reflection, plugging, etc. (see in particular: Bealer 1982; Menzel 1986; Zalta 1983, 1989; Swoyer 1997). One can ponder whether possessing a relational property is or should be always tantamount to bearing a respective relation to something. Also, in particular, one can ponder whether John possessing the relational property “loves Mary” is tantamount to Mary possessing the property “is loved by John.” Certainly, when a very general ontological setting is adopted then any singular predication does not need to be equivalent to plural predication (and the active form of predication does not need to be equivalent to the passive form of predication).24 In such cases we could further differentiate objects with respect to their category if we found sufficient reasons (evidence) to do so. However, we are not going to explore here this new ontological perspective for it would first require the introduction of a quite complicated formal syntax. We only point to an interesting fact. If an atomic algebra of properties is assumed, i.e., properties are treated extensionally and every relational property is represented in that algebra then P1-P7 turn out to be the only formal characteristics that may be used in distinguishing categories of objects. For instance, if an object a is consistent and closed under conjunction (i.e., if it fulfils P1 and P4) then, if a bears a relation to itself then a possesses the property of bearing the relation to itself. Thus, the ontological categorization of objects based on the Boolean algebra of properties is maximal if that algebra is atomic.
Uniwersytet im. M. Curie-Skáodowskiej Department of Philosophy 20-031 Lublin, Poland email: [email protected]
24 Considering complex properties in the framework of complex relations is not, of course, strictly equivalent to considering complex properties as relational properties. These are two different approaches to the nature of predication (and, as a matter of fact, to the nature of the subject of predication). However, these two approaches are basically equivalent when properties and relations are treated extensionally.
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REFERENCES Armstrong, D.M. (1997). A World of States of Affairs. Cambridge: University Press. Bealer, G. (1982). Quality and Concept. Oxford: Oxford University Press. Grossmann, R. (1972). Russell’s Paradox and Complex Properties. Noûs 6, 153-164. Ingarden, R. (1964). Der Streit um der Existenz der Welt. Tübingen: Max Niemeyer Verlag. Keenan, E.L. and L.M. Faltz (1985). Boolean Semantics For Natural Language. Dordrecht: Reidel Publishing Company. KotarbiĔski, T. (1920). Sprawa istnienia przedmiotów idealnych [The Problem of the Existence of Ideal Objects]. Przegląd Filozoficzny 23, 149-170. LeĞniewski, S. (1911). The Critique of the Logical Principle of Excluded Middle. In: S. LeĞniewski, Collected Papers, edited by S.J. Surma, J.T. Srzednicki, D.I. Barnett and V.F. Rickey, vol. 1, pp. 47-85. Dordrecht: Kluwer Academic Publishers. àukasiewicz, J. (1987). O zasadzie sprzecznoĞci u Arystotelesa [On the Priciple of Contradiction in Aristotle]. Warszawa: PWN. Meixner, U. (1991). On Negative and Disjunctive Properties. In: K. Mulligan (ed.), Language, Truth and Ontology, pp. 28-36. Dordrecht: Kluwer Academic Publishers. Menzel, Ch. (1986). A Complete, Type-Free Second Order Logic of Properties, Relations, and Propositions. Center for the Study of Language and Information, Stanford University. Technical Report #CSLI-86-40. PaĞniczek, J. (1998). The Logic of Intentional Objects. A Meinongian Version of Classical Logic. Dordrecht: Kluwer Academic Publishers. Swoyer, Ch. (1997). Complex Predicates and Conversion Principles. Philosophical Studies 87, 1-32. Swoyer, Ch. (1998). Complex Predicates and Logics for Properties and Relations. Journal of Philosophical Logic 27, 295-325. Zalta, E. (1983). Abstract Objects: An Introduction to Axiomatic Metaphysics. Dordrecht: Reidel. Zalta, E. (1988). Intensional Logic and the Metaphysics of Intentionality. Cambridge, MA: The MIT Press.
Andrzej Biáat OBJECTS, PROPERTIES AND RUSSELL’S PARADOX
1. “To be an object” means “to have properties.” Thus, any object has at least one property. A good formalization of this simple conclusion is a thesis of second-order logic: (1)
x P (Px)
This formalization is based on two assumptions: (a) object variables range over the universe of objects; and (b) one-place predicate variables range over the universe of properties. Thesis (1) does not exhaust the ontological content of these assumptions. For example, it does not exclude the existence of properties which themselves have properties and are therefore objects but which are not values of object variables. This may give rise to a question how to formalize the following rule in an object language: (2)
Each property that is an object is a value of object variables.
Methods for formalizing this type of statements are given by secondorder type-free systems in which predicates can be arguments of predicates. Especially, for a proper expression of thesis (2) one needs to use a “generalized” identity functor which can take expressions belonging to various syntactical categories as its arguments. (3)
P (Q (Q(P)) o x (P = x))
The traditional definition of an object as the subject of properties gives rise to further questions, the formalization of which requires the use of a “generalized” identity relation, as it is in the case of a hypothesis concerning the existence of objects that are not properties: (4)
x P ¬(P = x)
In: J.J. Jadacki and J. PaĞniczek (eds.), The Lvov-Warsaw School – The New Generation (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 89), pp. 129-142. Amsterdam/New York, NY: Rodopi, 2006.
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Another example of a typical formula of type-free systems is the following proposition: (5)
P x ¬(P = x)
The last formula expresses the main thesis of this paper: there are properties which are not objects. This postulate is also assumed (although only in the metalanguage) in standard second-order logic. In contrast to this logic, however, here we do not exclude the existence of properties which are objects. Our defence of the main thesis of this paper is at the same time an attempt at generalizing the ontology that constitutes the foundation of standard second-order logic.
2. Various type-free systems (first- or second-order), which have recently appeared in great numbers, are in fact developed theories of properties, relations and propositions. In those systems, various theses regarding the quantification over objects of higher “logical types” (such as properties of properties, properties of propositions or relations between objects and properties, etc.) are expressed. However, in contrast to higher-order logic, this type of hierarchy of entities is not fully reflected in the syntax of those theories. A type-free approach gives a more comfortable tool for logicophilosophical analysis in comparison to higher-order logic.1 Moreover, this approach is not as philosophically committed as the latter, which from the start accepts the existence of a hierarchy of properties (one or another, finite or infinite) and excludes the existence of properties belonging to themselves (contrary to the intuition that such properties exist: being cognisable, untouchable, different from Immanuel Kant, being a property, etc.). In spite of the fact that second-order type-free systems are substantially richer than analogical first-order theories (for at least two kinds of variables objects and predicates are there distinguished), they are simpler in certain respects. They do not require discerning extra1
The advocates of the type-free approach formulate various arguments for this view. For example, S. Feferman defended the need to use a type-free theory for explaining some crucial aspect of mathematics. N. Cocchiarella and G. Bealer employ their own systems (very different from each other) for reconstructing logicism. G. Chierchia and R. Turner are developing Montague semantics in a type-free manner and argue that it helps in explaining important linguistic phenomena.
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logical constants (such as “exemplify,” “is a property,” etc.) necessary in first-order theories. This, in turn, allows us to treat those systems as rich and convenient conceptions of philosophical logic. 2 The assumption that all properties are objects (i.e., are values of object variables, although not necessary only of them) is very characteristic for the type-free approach, at least in its contemporary forms. By using a “generalized” identity functor, the thesis that the class of properties and relations (the class P) is included in the class of objects (the class O) can be expressed as follows: (a)
Q x (x = Q)
(inclusion of P in O)
Typical examples of other possible relations between extensions of two non-empty classes P and O are described by the following formulas: (b) (c) (d) (e)
Q x (x = Q) x Q (x = Q) (equivalence) x Q (x = Q) (inclusion of O in P) x Q ¬(x = Q) x Q (x = Q) x Q ¬(x = Q) (intersection) x Q ¬(x = Q) (disjointness)
Some of these possibilities were in fact expressed in certain conceptions of logic; some other correspond to notions of object developed in philosophy. For example, in standard logic the disjointness of these two classes (e) is assumed. Type-free systems usually adopt variant (a). Inclusion of O in P (c) corresponds to the idea of Meinongian logic and of the so-called bundle conception of object (where objects are identified with appropriate classes or bundles of properties; O is included in P if and only if those bundles are conceived as complex properties). Variant (b) is adopted in Zalta’s system. It is difficult to indicate a system that would represent the relation of intersection of the classes P and O. This case seems, however, to be the most interesting, for it gives the richest partition of the considered universe: objects that are not properties (class A), objects that are properties (class B) and properties that are not objects (class C).
2
One example of relatively simple systems of second-order type-free logic is presented by T.N. Cocchiarella in “Whither Russell’s Paradox of Predication?” This system results from extending classical second-order logic with atomic formulas in which predicates can occupy the place of arguments (so such formulas as P 1 (R 2 ), R 2 (x, P 1 ), P 1 (P 1 ) are meaningful) and adding a scheme: xD o PD (x/P) (where the formula D (x/P) results from substituting the variable x with a predicate variable P).
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3. The main thesis of this paper says that class C is not empty. Thus, we allow only three of the five presented possibilities: inclusion (c), intersection (d), and disjointness (e). Variant (a), usually adopted in typefree logic, is rejected here. We shall now attempt to show that its acceptance gives rise to certain problems of a logical nature. We shall first define the Russellian property (being a property that does not belong to itself) and then indicate difficulties connected with taking it to be a value of an object and of a predicate variable at the same time. Let us consider the standard second-order language extended to formulas of the form: x = P and P = x. Let us call this language “L*.” Apart from the standard logical laws, we accept the following principle of extentionality for identity: (i)
x P (x = P o (D l D(x // P)))
where D(x // P) is a formula of language L*, which is the result of a legitimate substitution of the object variable x with the predicate variable P in D. Such substitution is legitimate when: (a) it does not lead beyond the set of formulas, i.e., its result is a correctly built formula; and (b) the predicate variable P is free wherever variable x is free in D. Let us also accept the standard comprehension principle for properties: (ii)
P x (Px l D)
where D is a formula in which variable x is free and variable P is not free. On the basis of (i) and (ii), we will show that there exists at least one property that is not an object. In other words, we will prove the following thesis: The set of all formulas of language L* that are instances of schemata (i) and (ii) is inconsistent on ground of standard logical laws and of the postulate: (iii)
P x (P = x)
In the proof, we will use a definition of the Russellian property R, which is an instance of the comprehension principle (ii): 3 3
Strictly speaking, the schema (ii) does not prove that R is one and only one: one needs also a suitable principle of property identification. This fact, however, plays no significant role at this moment since constant R is introduced here only for the purpose of the proof.
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(R) x (Rx l P (x = P ¬Px)) (R is a property that belongs to all and only those objects which are properties that do not belong to themselves.) Taking the issue in a somewhat simplified way (which assumes the correctness of atomic formulas in which predicates take the place of logical subjects): if the property P were an object (i.e., the value of an object variable), then it would be allowed to substitute variable x with constant R by universal quantifier elimination in (R). This would produce the sentence: R(R) l P (R = P ¬P(R)), from which, on the basis of the principle of extensionality for identity, follows the counter-tautological equivalence R(R) l ¬R(R). Thus, we obtain a particular form of Russell’s antinomy for properties (the paradox of predication). The detailed proof proceeds in the following way: (a) R=r (iii), assumption (b) Rr l Q (r = Q ¬Qr) from (R) (c) Q ((r = Q ¬Qr) o Rr) from (b) (d) (r = R ¬Rr) o Rr from (c) (e) ¬Rr o Rr from (d), (a) (f) Rr from (e) (g) Q (r = Q ¬Qr) from (f), (b) (h) R = Q0 ¬Q0 r from (g), (a), (i) (i) ¬Rr from (h), (i) Contradiction.
4. Premises (i), (ii) and (iii) are essential in this argument. One could, therefore, avoid Russell’s antinomy either by rejecting or modifying one of them or by altering the standard logical principles. In similar forms of Russell’s antinomy, one usually restricts premise (ii) – the general comprehension principle for properties. Premise (i) is sometimes rejected and sometimes logic is radically changed (for example, if àukasiewicz’s or Kleene’s three-value logic is employed). However, as far as the author knows, the view that would reject premise (iii) is absent from the literature. The laws of classical logic and the principle of extensionality for identity (i) build the framework of our considerations. We cannot here evaluate the appropriateness of the framework’s choice. Let us, however, make some comments on typical conceptions that accept certain
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restrictions on the general form of the comprehension principle for properties and which could be then used for modifying schema (ii). Restrictions modelled upon Zermello’s or Neumann’s conceptions of set theory (which consist in substituting formula D in (ii) either with a conjunction of Qx D, in a Zermellian manner or with a formula Q (Qx) D, in a Neumannian manner)4 lead to some quite surprising consequences. Either the universal property of being an object does not exist (in the Neumannian sense) or there exist objects that have no properties. Moreover, both versions of the comprehension principle introduce the existence of relevant properties only conditionally and that requires the acceptance of further – as a matter of fact extra-logical – axioms that define which properties exist unconditionally.5 Another way of restricting premise (ii) consists in restricting the range of possible forms of formula D. Cocchiarella’s late suggestions, which restrict that range to formulas stratifiable in Quine’s sense, are among the best known.6 The soundness of this solution has been questioned,7 however, especially since it lacks a satisfactory ontological justification. This answer, moreover, does not give any basis for introducing non-paradoxical properties, for example “being a property exemplified by itself.”8 Those solutions which limit quantification over predicates in formula D are even more restrictive: in Menzel’s (1986) conception, one is not allowed to quantify over predicate variables that 4
G. Bealer in (1982, pp. 96-100) considers Zermellian and Neumannian variants of the comprehension principle for properties. The author of this paper also accepted a certain Neumannian restriction (expressed in a first-order modal theory of classes and properties) “Do Negative States of Affairs Exist?” (in Polish, 1998). 5 The analogy between this conception and set theory is sufficient to allow the former to be considered simply as a version of the latter properly interpreted. This has been done (in a first-order theory) by M. Jubien (1989). 6 Probably the earliest of those propositions was formulated in Cocchiarella’s (1975). His even-earlier attempt at a solution of Russell’s paradox for properties was expressed in system T* (see footnote 3, above). This attempt consists in rejecting the antinomial schema PQ(P(a) l D) (for any formula D of language T* which does not contain a free variable P and contains a free variable Q) with retaining the comprehension principle (ii). Since thesis (iii) is observed in system T*, many essential difficulties occur when the predicate of identity is added to this system. Those difficulties led Cocchiarella to reject this solution and to accept the idea of restricting the comprehension principle with a condition of the stratifiability of formulas. In our considerations we attempt another solution: retaining schema (ii) and rejecting thesis (iii). 7 See, for example, Bealer (1982, p. 14, postulate 14) and H.-N. Castañeda (1976, p. 73). 8 This objection is formulated by Castañeda (1976). Castañeda sees the essence of Russell’s paradox in an over-liberal use of negation. In a schema he proposes, no predicate can be placed within the scope of sentence-negation (although it can be placed within the scope of predicate-negation; see 1976, pp. 79-80).
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stand in the place of the subject9; in Zalta’s (1993) conception, one is not allowed to quantify over predicate variables in D at all. Two general objections against such modifications of schema (ii) can be formulated. First, those modifications eliminate the possibility of defining such properties as R, and this is rather counterintuitive. In those conceptions one assumes that R does not exist. This, however, goes against the intuition that most properties do not belong to themselves (being green, being an even number, etc.). An assumption that there exists such a property which belongs to these properties and only to them, is very natural if we accept any version of the comprehension principle for properties at all. It is then permitted to maintain that the Russellian property exists and is non-empty. Second, those modifications do not sufficiently protect against the possibility of rendering Russell’s antinomy. For in each type-free system one can introduce a predicate of exemplification E that fulfils the following condition: (a)
x (E(P, x) l Px)
Thus, the following postulate would be a special case of the schema of comprehension: (b)
P x (Px l ¬E(x, x))
On the basis of (a) this postulate is equivalent to: (c)
P x (E(P, x) l ¬E(x, x))
If a given system fulfils principle (iii), then on the basis of (c) we obtain: (d)
y x (E(y, x) l ¬E(x, x))
From this, a contradiction follows in a well-known way: (e)
E(y0 , y 0 ) l ¬E(y 0 , y 0 )
To sum up: the conclusion that takes postulate (iii) as the source of Russell’s antinomy for properties seems to dominate over alternative views.
9
This restriction follows from Menzel’s more general assumption that there exist only such complex properties that can be constructed from simpler ones by means of certain specified logical operations. Those operations, however, do not give a basis just for constructing the Russellian property but also for such properties as “being a non-empty property.” An attempt at a modification of Menzel’s system is contained in Orilia’s work (1991).
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5. A similar conclusion may also be arrived at in the case of multi-argument properties. In particular, one can render an antinomy for Russellian relations on the basis of two premises: P2 x (P2 = x) P2 x y (P2 xy l Q2 (x = Q2 ¬Q2 xy)) Similarly, this can be done for multi-term relations. In each case, it leads to the conclusion that was formulated in the case of properties. Given these conclusions, we assume that Russellian properties and relations are not objects. Any property or relation that is not an object will be called a “quasi-object.” Thus, we divide the totality of entities (i.e. the totality of what exists in the most general sense of that term) into objects and quasi-objects. From the accepted definition of an object as the subject of properties, it follows that each quasi-object is a entity of a special kind: it possesses no properties. This consequence, although at first glance counterintuitive, yields a simple explanation of a certain logical asymmetry between standard and type-free (with predicates in the position of subject in propositions) formulas. This explanation consists in the fact that for the latter the schema of comprehension (analogical to (ii)) is not valid: (*)
P Q (P(Q) l D)
where P is not free in D while Q is free in D.10 The principle that properties belong solely to objects explains why certain instances of schema (*) must lead to contradiction: one attempts to define complex properties that are exemplified by beings which possess no properties. This explanation gives at the same time a general diagnosis concerning Russell’s antinomy for properties. In this solution, the analysis of typical examples of quasi-objects, i.e., properties and relations of the Russellian type, suggests that these are properties (relations), which either (1) possess “overly broad scopes” of application which, in turn, makes it impossible to predicate properties of those properties (in this case it is natural to assume that those broad scopes of applications are proper classes, i.e., classes which are not elements of any class) or (2) are “maximal” in one of two meanings of this term: (a) are properties (relations) of the highest order (in this sense 10 This schemata cannot be accepted under the threat of rendering an ordinary Russell’s paradox for properties: (a) Q (R 0 (Q) l ¬Q(Q)) [from (*)], (b) R 0 (R 0 ) l ¬R 0 (R 0 ) [from (a)], (c) contradiction [from (b)].
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similar to higher-order complete logic) or (b) are not elements of any class (similarly to proper classes).11 One should not assume, however, that the interpretation of quasiobjects as ontologically “naked” beings is the only possible explanation of the mentioned asymmetry. Another possible explanation is given by an interpretation of quasi-objects based on a semantic conception of an object. Within this conception, an object is anything that can be designated by an argument of any predicate in a given language. That is, it is anything of which any property can be predicated in that language. In accordance with the argumentation accepted here, one must then recognize that there are properties, such as the Russellian one, that are not objects in the object language of logic (they are then quasi-objects in the semantic sense). It follows that it is not the case that in a given language one can predicate any property of all properties (although any property can be meaningfully predicated of any object even if that property does not belong to it). Whereas in the “naive” schema of comprehension (*), it is assumed that all properties generated by its substitution can be meaningfully predicated of all properties contrary to the fact that some propositional forms (for example ¬Q(Q)) yield properties that do not fulfil this requirement.12
6. On the ontological conception of object assumed in this paper (in which all and only objects possess properties), no extension of the language of logic to formulas in which predicates are arguments of any predicates is needed. For the formula P(Q) can be interpreted here only in the following way: the property Q is an object that possesses the property P. This can in turn be defined by means of identity: (7)
P(Q) = df x (x = Q Px)
11 A solution of the latter type was presented by the author (1998) within a framework of a certain elementary theory of classes and properties. 12 It seems that a proper understanding of the expression “to predicate meaningfully” is possible on the basis of a semantics in which properties are interpreted as propositional functions (in the sense coming from Frege’s thought, although not necessarily in a strictly Fregean sense, where the values of propositional functions are only zero and one), total or partial in the ontological universe. The expression “a property is meaningfully predicable of a given element of that universe” would then mean that a given propositional function is specified on that element.
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It is now easy to verify that postulate (3) from section 1 follows from (7). This can also be done for relations by, for example, accepting the following definition13: (8)
R(x, P) = df y (y = P 4 Rxy)14
It seems also that there are no special difficulties in using formulas of the type x = P (as well as P = Q). In order to demonstrate this fact, we will define a consistent calculus – a system of logic of objects, properties and relations in accordance with the conclusions formulated above – in which such formulas play an essential role. We will call the language of that system “L.” Its vocabulary accords with the vocabulary of ordinary logic and the predicate of identity. The full list of primitive symbols is as follows: (1) (2) (3) (4) (5) (6)
object variables: x1 , x 2 , x 3 , . . (we will also use: x, y, z, . . . ) predicate variables: P1 , Q1 , . . . ,P2 , Q2 , . . . , the identity symbol: = propositional connectives: ¬, , , o, l, quantifiers: , , parentheses: (, ).
The elementary categories of expression in language L are object variables, predicate variables and propositional formulas. The concept of a formula is defined inductively:
13
These definitions have a certain explanatory power: they explain the only logically (in our sense of “logic”) acceptable sense in which a predicate can be used in the position of the subject. In particular, they explain the ambiguity of propositions of the form ¬P(Q): (a) ¬x = Q(Px) (there does not exist an object Q that possesses property P), and (b) x = Q(¬Px) (there exists an object Q that does not possess property P). They also explain the truth of some propositions which are alleged substitutions of negation of the law of excluded middle: ¬P(P(R) ¬P(R)) (R is here the Russellian property). 14 Within a semantic conception of object (according to which one can meaningfully predicate any properties of all objects in, but only in, the object language) the mentioned extension of language would in turn introduce logically undetermined propositions (for example R(R)) which do not fall under the law of excluded middle. Let us also note that in this conception one does not exclude the possibility of using any predicates as arguments of the identity functor. For from the fact that predicates denoting quasi-objects cannot be arguments of any predicate, it does not follow that predicates which can take any predicates as arguments do not exist. On the contrary, it is reasonable to think that there is at least one such predicate, namely the symbol of identity. This would correspond to a semantic assumption that the propositional function of identity (which takes the value 1 when its arguments are identical and 0 in all other cases) is an element of any model (more precisely, of a class of propositional functions in any model).
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if t 1 , . . . , t n are object variables and P is an n-argument predicate variable for n t 1, then Pt 1 . . . t n is an (atomic) formula; if u, w are (object or predicate) variables then u = w is an (atomic) formula; if D, E are formulas and u is a variable, then ¬D, (D E), (D E), (D o E), (D l E), u D, u D are formulas. no other sequence of symbols is a formula.
Two expressions (of elementary categories) belong to the same category if and only if they are either object variables or n-argument predicate symbols, for n t 1, or formulas. As usual, language L is identified with the set of all formulas. We retain the convention that values of metavariables u, w are (object or predicate) variables. The schema D(u / w) signifies an expression obtained from formula D by substituting all free occurrences of variable u with variable w in D. This substitution is legitimate if it does not lead beyond the set of formulas (i.e., its result is a correctly built formula) and w is free in D(u / w) wherever variable u is free in D. The schema D(u // w) signifies any formula obtained from formula D by substituting all or some occurrences of variable u that are not bound variables in D with variable w. This substitution is legitimate if it does not lead beyond the set of formulas and w is free in D(u // w) wherever u is free in D.
7. The axiomatisation of the logic of objects, properties and relations is determined by the following schemata: (PC) D, if D is an instance of a thesis of classical propositional logic. (Q1) u D o D(u / w), if that substitution D(u / w) is legitimate and u, w belong to the same category. (Q2) u (D o E) o (D o uE), if variable u is not free in D (Q3) u D l ¬u ¬D (I1) u = u, where u is either an object variable or a predicate variable (I2) u = w o (D o D(u // w)), where D is any formula, the substitution D(u // w) is legitimate and u, w are variables of the same or different categories. (CP) Pn x 1 . . . x n (Pn x 1 . . . x n l D), for n t 1, where D is any propositional formula in which object variables x1 , . . . , x n are free and the predicate variable Pn is not free.
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The rules of inference are: modus ponens (MP) and the rule of generalization (Gen) (formulated jointly for first- and second-order quantification): (MP) D o E, D / E (Gen) D / u D Two things are characteristic for this axiomatisation: (1) a condition imposed on (Q1), according to which expressions in substitution must not belong to different categories, and (2) a generalization of the principle of extensionality for identity, expressed by (I2), where substitution expressions can belong to different categories. This generalization expresses a more liberal understanding than does a standard theory of identity. The constraint imposed on (Q1) is, in turn, given a more restrictive understanding than that given by type-free second-order systems. The system defined in this way fits in the middle between standard logic and type-free second-order logic. The constrain imposed on (Q1) impedes the possibility of generating antinomial properties and relations by means of schema (CP). Consistency of the formulated axiomatisation can be ascertained by interpreting it in a standard way in any non-empty model (the logical value of any equivalence of the form Pn = x and x = Pn is equal to 0). From (I2) and (Q1), two schemata characteristic of this logic follow: (8) (9) (10)
x (P = x) o (x D o D(x / P)), if the substitution D(x / P) is legitimate.15 P (x = P) o (P D o D(P / x)), if the substitution D(P / x) is legitimate. u (w = u) o (u D o D(u / w)), for all variables u, w (which belong to the same or to different categories), if the substitution D(u / w) is legitimate.
Russell’s antinomial reasoning may be used in an indirect proof of another schema characteristic of this logic: (11)
Pn ¬x (Pn = x)
under which thesis (5) formulated in section 1, among others, fails. Special cases of (CP) are the various theses that state the existence of properties and relations, for example: (12) 15
P x (Px l Q(x = Q y Qy))
This is a formula analogical x (a = x) o (x D o D(x / a)).
to
a
characteristic
thesis
of
free
logic:
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(there exists a property of being an object which is a non-empty property). (13)
P x (Px l Q (Q = x Qx))
(there exists a property of being an object exemplified by itself). (14)
R x y (Rxy l P (y = P Px)
(there exists a relation of exemplifying properties, which are objects). 16 On the basis of the comprehension principle (CP) and of the law of identity (I1), it is possible to infer the condition of object identity: (15)
P (Px l Py) o x = y 17
from which by (I2), we obtain the Russell-Leibniz principle of identity and the “condition of individualization” of objects: (16) (17)
x = y l P (Px l Py) x z y l P (Px ¬Py)
As usual, by using the law of identity for objects and the schemata (CP) one can prove the existence of non-empty universal properties (which belong to all and only objects) and of empty properties (which belong no objects): (18) (19)
P x (Px) P ¬x (Px)
By transposing the quantifiers in (18) we obtain postulate (1). Translated from Polish by Agnieszka Lekka-Kowalik
Uniwersytet im. M. Curie-Skáodowskiej Zakáad Logiki i Metodologii Nauk pl. Marii Curie-Skáodowskiej 4 20-031 Lublin, Poland email: [email protected] 16 It is worth stressing that these examples of existential theses are not “metaphysical” in the sense that they do not assume the non-emptiness of properties and relations whose existence they postulate. 17 The proof: 1) P (Px l Py) [the premise]; 2) P x (Px l x = y) [from (CP)], 3) P y x l x = y [from 2], 4) P y x l P y y [from 1], 5) P y y l y = y [from 2], 6) P y y [from 5, (I1)], 7) P y x [from 6, 4], 8) x = y [from 7, 3]. Compare with the proof given in Sáupecki and Borkowski (1963, pp. 117-118).
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REFERENCES Bealer, G. (1982). Quality and Concept. Oxford: Clarendon Press. Biáat, A. (1998). Czy istnieją negatywne stany rzeczy [Do Negative States of Affairs Exist]? In: Z. Kowalski, W. Krysztofiak and A. Biáat (eds.), Koncepcje negatywnych stanów rzeczy [Conceptions of Negative States of Affairs], pp. 105-130. Lublin: UMCS. Castañeda, H.-N. (1976) Ontology and Grammar: I. Russell’s Paradox and the General Theory of Properties in Natural Language. Theoria 42, 43-92. Chierchia, G., R. Turner (1988). Semantics and Property Theory. Linguistics and Philosophy 11, 261-302. Cocchiarella, N. (1973). Whither Russell’s Paradox of Predication? In: M. Munitz (ed.), Logic and Ontology, pp. 133-158. New York: New York University Press. Cocchiarella, N. (1975). Second-order Theories of Predication: Old and New Foundations. Noûs 9, 33-53. Feferman, S. (1984). Toward Useful Type-Free Theories: Part I. The Journal of Symbolic Logic 49, No. 1, 75-111. Jubien, M. (1989). On Properties and Property Theory. In: G. Chierchia, B. Partee and R. Turner (eds.), Properties, Types and Meanings, pp. 159-175. Dordrecht: Kluwer Academic Publisher. Menzel, C. (1986). A Complete, Type-Free, “Second Order” Logic and Its Philosophical Foundations. Center for the Study of Language and Information, Stanford University. Technical Report #CSLI-86-40. Orilia, F. (1991). Type-Free Property Theory, Exemplification and Russell’s Paradox. Notre Dame Journal of Formal Logic 32, No. 3, 432-447. Sáupecki, J. and L. Borkowski (1963). Elementy logiki matematycznej i teorii mnogoĞci [Elements of Mathematical Logic and Set Theory]. Warszawa: PWN. Zalta, E. (1993). Twenty-Five Basic Theorems in Situation and World Theory. Journal of Philosophical Logic 22, 385-428.
Joanna OdrowąĪ-Sypniewska
ON THE NOTION OF IDENTITY 1
1. Introduction The notion of identity has been a source of much controversy for a long time. Its origin and ontological status remain unclear. It is difficult to imagine, it has been observed, that the notion of identity comes from the perception of a single object (this perception gives us the notion of unity); but it is also hard to conclude that the perception of a few objects is its source (this perception gives us the notion of multitude). If, in the sentence ‘That object is the same as itself’, the words ‘object’ and ‘itself ’ denoted the same notion then this proposition would be a tautology (Hume 1898, p. 489). “Once one object is supposed to exist, we must either suppose another to exist also; in which case we have the idea of number [i.e. multitude]: or we must suppose it not to exist; in which case the first object remains the same” (Hume 1898, p. 489). Perhaps, then, we should refer to the notion of time. When, at different times, we perceive the same object, which lasts through time and is unchangeable, we acquire first the notion of multitude (because we perceive this object at different moments) and then the notion of unity (because we always perceive the same object). These notions are inconsistent, and from this inconsistency ari