Elektrotechnika Teoretyczna Borkowski Pdf Merger

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
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.
8
Jacek Jadacki and Jacek PaĞniczek
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,
The Lvov-Warsaw School
9
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.
10
Jacek Jadacki and Jacek PaĞniczek
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.
The Lvov-Warsaw School
11
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
12
Jacek Jadacki and Jacek PaĞniczek
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.
The Lvov-Warsaw School
13
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
14
Jacek Jadacki and Jacek PaĞniczek
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)
The Lvov-Warsaw School
15
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
This page intentionally left blank
PART I THE SCHOOL: ITS ORIGINS AND SIGNIFICANCE
This page intentionally left blank
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.
20
Barry Smith
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 0010 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 0010 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 0010 in certain circles 0010 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
Why Polish Philosophy Does Not Exist
21
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 0010 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 0010 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.
22
Barry Smith
Inside Plato’s 0010 or Socrates’ 0010 cave, an artificial wall curtain 0010 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 0010 and sewing up 0010 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)?
Why Polish Philosophy Does Not Exist
23
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
24
Barry Smith
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.
Why Polish Philosophy Does Not Exist
25
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 0010 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)
26
Barry Smith
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 0010 Carnap, Reichenbach and Hempel 0010 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
Why Polish Philosophy Does Not Exist
27
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).
28
Barry Smith
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).
Why Polish Philosophy Does Not Exist
29
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).
30
Barry Smith
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
Why Polish Philosophy Does Not Exist
31
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,
32
Barry Smith
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
Why Polish Philosophy Does Not Exist
33
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 0010 from Twardowski, born in Vienna in 1866, to LeĞniewski, born in Petersburg in 1886 0010 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
34
Barry Smith
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 0010 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,
Why Polish Philosophy Does Not Exist
35
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 0010 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
36
Barry Smith
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 0010 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.
Why Polish Philosophy Does Not Exist
37
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.
38
Barry Smith
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 0010 Scholar 0010 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.)
Why Polish Philosophy Does Not Exist
39
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.
This page intentionally left blank
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 0010 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 0010 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.
42
Jacek Jadacki
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) 0010 let us call them the phase of crystallisation 0010 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),
The Lvov-Warsaw School and Its Influence on Polish Philosophy
43
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 0010 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 0010 Nazi Germany and Bolshevik Russia; this time, it was defeated and lost its independence for fifty years. In philosophy 0010 as well as in the whole Polish culture 0010 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 0010 ideas, conceptions and systems. At the same time, in the first part of the period,
44
Jacek Jadacki
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
The Lvov-Warsaw School and Its Influence on Polish Philosophy
45
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 0010 which was an object of special pressure of the ideologists of the regime 0010 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
46
Jacek Jadacki
(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 0010 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),
The Lvov-Warsaw School and Its Influence on Polish Philosophy
47
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 0010 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
48
Jacek Jadacki
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 0010 Rationality 0010 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 0010 Language 0010 Reality (1990, Warsaw: PTS), Logic and Logical Philosophy (in English) (1993, ToruĔ: UMK), Philosophy 0010 Logic 0010 Logical Philosophy (1995, ToruĔ: UMK), Dialogikon (1995, Kraków: UJ), Foundations of Science (in English) (1998, Dordrecht: Kluwer 0010 series edited by Wójcicki), Polish Analytical Philosophy (in English) (1999, Amsterdam: Rodopi 0010 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),
The Lvov-Warsaw School and Its Influence on Polish Philosophy
49
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.
50
Jacek Jadacki
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 0010 thanks to a great German thinker 0010 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 0010 or rather ignoring 0010 contradiction by removing Duns Scotus’ law from among the axioms (JaĞkowski 1948; da Costa and Dubikajtis 1968, 1977).
The Lvov-Warsaw School and Its Influence on Polish Philosophy
51
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 0010 contrary to àukasiewicz’s standpoint 0010 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 0010 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 0010 pendant to the above mentioned enrichment of syllogistic 0010 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) 0010 on Tarski’s inspiration 0010 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).
52
Jacek Jadacki
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 0010 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
The Lvov-Warsaw School and Its Influence on Polish Philosophy
53
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.
54
Jacek Jadacki
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 0010 and most certainly for eventism 0010 is set theory. Quite different 0010 namely combinatory 0010 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 0010 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.
The Lvov-Warsaw School and Its Influence on Polish Philosophy
55
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 0010 Methodology 0010 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 0010 on the ground of some assumptions 0010 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).
56
Jacek Jadacki
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 0010 referring to the general distinction between acts and results made by Twardowski 0010 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 0010 with some elements of historiosophy 0010 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
The Lvov-Warsaw School and Its Influence on Polish Philosophy
57
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.
58
Jacek Jadacki
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
The Lvov-Warsaw School and Its Influence on Polish Philosophy
59
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 0010 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 0010 approaching the intuitions of natural languages. On the other hand, Grobler (1993) 0010 not without sympathy 0010 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.
60
Jacek Jadacki
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 0010 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.
The Lvov-Warsaw School and Its Influence on Polish Philosophy
61
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
62
Jacek Jadacki
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 0010 mainly thanks to Znamierowski (1957), CzeĪowski (1989) and Ossowska (1947, 1963) 0010 has become the dominant paradigm in this context. Ethics 0010 as Ossowska emphatically stated 0010 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 0010 and other representatives of the School after him (Tatarkiewicz 1919, 1938; PrzeáĊcki 1989) 0010 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 0010 clara et distincta 0010 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 0010 in the intuitionists’ opinion 0010 simply
The Lvov-Warsaw School and Its Influence on Polish Philosophy
63
«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 0010 and maybe first of all (PrzeáĊcki 1989) 0010 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 0010 if the enterprise is to be successful 0010 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
64
Jacek Jadacki
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 0010 at least in the version which owes its shape to àukasiewicz (1927) and LeĞniewski (1927) 0010 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).
The Lvov-Warsaw School and Its Influence on Polish Philosophy
65
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 0010 signalised by Tarski 0010 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 0010 non-being and vice versa) and continuous changes. In the case of causal
66
Jacek Jadacki
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 0010 by àukasiewicz, Drewnowski, BocheĔski and Salamucha 0010 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 0010 it seems 0010 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]
The Lvov-Warsaw School and Its Influence on Polish Philosophy
67
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.
68
Jacek Jadacki
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.
The Lvov-Warsaw School and Its Influence on Polish Philosophy
69
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 0010 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.
70
Jacek Jadacki
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 0010 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.
82
Jacek Jadacki
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
83
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.
This page intentionally left blank
PART II OBJECTS AND PROPERTIES
This page intentionally left blank
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.
88
John T. Kearns
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
An Elementary System of Ontology
89
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]
90
John T. Kearns
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
An Elementary System of Ontology
91
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 ‘0005’. The connectives ‘&’, ‘Š’, and ‘{’ are defined in standard ways. The quantifier ‘0005’ is combined with a noun variable D to constitute a quantified phrase (0005D). The particular quantifier ‘0007’ 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 ‘(0005X)’ 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
92
John T. Kearns
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: (0005X)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: (0005X)~[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 (0005D)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 (0005D)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: (0005X)[[X H X] Š . . . 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
An Elementary System of Ontology
93
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.
94
John T. Kearns
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 (0005D)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 (0005D)M be a sentence of L , and let E be the first noun constant in alphabetical order not occurring in M. Then (0005D)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:
An Elementary System of Ontology
› Introduction M N [M › N ] [M › N ]
95
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
96
John T. Kearns
is the result of replacing all free occurrences of D in M by E. The quantifier rules for EO are the following: 0005 Elimination 0005 Introduction (0005D) 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 (0005D) 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 ] (0005D)(0005E)[[[D H J ] & [E H J ]] Š [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 0010 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 0010 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.
An Elementary System of Ontology
97
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 (0005D)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 ‘0005’, and replacing it by the restricted quantifier ‘0005i’. A sentence (0005iD)M has the significance of: (0005D)[[D H D] Š M]. And the (defined) existential quantifier ‘0007i’ gives sentences (0007iD)M which have the significance: (0007iD)[[D H D] & M]]. The language L i is obtained from L by replacing the (unrestricted) quantifier ‘0005’ by ‘0005i’. The restricted quantifier ‘0007i’ is defined: (0007iD)M = (def ) ~(0005iD) ~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 (0005D)M be a sentence of L , and let E be the first noun constant in alphabetical order not occurring in M. Then (0005iD)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
98
John T. Kearns
function which yields the value true for exactly one individual in E . If E = ‡, the sentence (0005iD)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: 0005i Elimination (0005 i D) M [E H E] ~D S M/ E
0005i 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 (0005 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 ] (0005 i D)(0005 i E)[[[D H J ] & [E H J ]] Š [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 ~(0005iD)M of L , if ~(0005iD)M is a member of X, then for some noun constant E,
An Elementary System of Ontology
99
~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) (0005iD )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.
100
John T. Kearns
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
An Elementary System of Ontology
101
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.
102
John T. Kearns
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.
An Elementary System of Ontology
103
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
104
John T. Kearns
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 0010 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} 0010 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
An Elementary System of Ontology
105
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
106
John T. Kearns
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 0010 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 0010 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
An Elementary System of Ontology
107
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]
108
John T. Kearns
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* & (0007X)[X H D1 ] & . . . & (0007X)[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.
An Elementary System of Ontology
109
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 0005 Introduction require that this constant occur in neither an initial assertion nor a hypothesis leading to the sentence which is the premiss for 0005 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.
110
John T. Kearns
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 0010 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 ‘( 0005iD)M ’ equivalent to a sentence about all individuals in the domain. The system 1 O is sound and
An Elementary System of Ontology
111
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.
112
John T. Kearns
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.
114
Jacek PaĞniczek
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 š 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 ¬, š, ›, 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 Š ¬aP (consistency) ¬aP Š a¬P (completeness) a(P š Q) Š aP š aQ ¬a(P š ¬P) Š (a(P š Q) Š aP š aQ) aP š aQ Š a(P š Q) (closeness under conjunction) aP › aQ Š 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.
Do We Need Complex Properties in Our Ontology?
P6. P7.
115
a(P › Q) Š aP › aQ a(P Š Q) Š (aP Š 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 Š 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 Š P) in particular. R3.
If Į Š ȕ is an instance of a tautology expressed by means of property variables then for every object a: aĮ Š aȕ holds.
According to R3 objects are closed with respect to logical entailment, i.e. logically closed. E.g. if a(P š 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 Š D is also a tautological property and, according to R3, aE Š aD and hence aD.
116
Jacek PaĞniczek
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 U is a nonempty set (the universe) and f is the interpretation function defined on the set of non-logical and non-erotetic constants of L (that is, predicates, individual constants and 0010 if there are any 0010 function symbols) in the standard way. Of course, there are many interpretations of L . If I is an interpretation, then by a I-valuation we mean an infinite sequence of the elements of the universe of I. The concepts of value of a term under a I-valuation and of satisfaction of a d-wff in an interpretation I by a I-valuation are defined in the standard manner. A d-wff A is said to be true in an interpretation I if and only if A is satisfied in I by all I-valuations; by a model of a set of d-wffs we mean an interpretation in which all the d-wffs of this set are true. Note that the concept of truth does not apply to questions of L . In the case of questions, however, we use the concept of soundness. A question Q is said to be sound in an interpretation I if and only if at least one direct answer to Q is true in I. The further semantical concepts pertaining to L are defined by means of the concept of normal interpretation of L . Yet, the language L was characterized only in a schematic manner and in fact there are many languages which fulfil the conditions specified so far. For that reason we 4
Some logical theories of questions (for example, Belnap’s theory or KubiĔski’s theory) allow questions of formalized languages which have only one direct answer, but it seems that this step is motivated rather by the pursuit of generality than other reasons.
Reducibility of Safe Questions to Sets of Atomic Yes-No Questions
223
only assume that the class of interpretations of L includes a non-empty subclass (not necessarily a proper subclass) of normal interpretations, but we do not decide what the normal interpretations are in each particular case. If the declarative part of L is an applied first-order language, normal interpretations can be defined as those in which some meaning postulates and/or axioms are true. Normal interpretations can also be defined for purely erotetic reasons. If L contains questions about objects satisfying some conditions, it would be natural to define normal interpretations as those in which all the objects called for have names (are values of some closed term(s)): by doing so we would avoid the paradoxical consequence that there are objects which satisfy the appropriate conditions, but nevertheless the corresponding questions have no true answers. There are also other possibilities of defining normal interpretations (for more information, see WiĞniewski 1995, pp. 104-105). We do not even exclude that the class of normal interpretations of some language of the considered kind is equal to the class of all interpretations of this language. Yet, for the purposes of this analysis the assumption about the existence of a non-empty class of normal interpretations is sufficient. By means of normal interpretations we shall define the relevant concepts of entailment in L . We will introduce two concepts of entailment: multiple-conclusion entailment being a relation between sets of d-wffs and (single-conclusion) entailment understood as a relation between sets of d-wffs and single d-wffs. DEFINITION 1. A set of d-wffs X of L multiple-conclusion entails (mc-entails for short) in L a set of d-wffs Y of L iff the following condition holds: (#) for each normal interpretation I of L : if all the d-wffs in X are true in I, then at least one d-wff in Y is true in I. DEFINITION 2. A set of d-wffs X of L entails in L a d-wff A of L iff A is true in each normal interpretation of L in which all the d-wffs in X are true. Note that the above concepts are defined in terms of truth and not of satisfaction. Note also that in the general case mc-entailment cannot be defined in terms of (single-conclusion) entailment. For instance, assume that the declarative part of L is the language of Classical Predicate Calculus and that each interpretation of L is a normal one. Then the singleton set {A › B}, where A, B are atomic sentences, mc-entails the set {A, B}, but neither A nor B is entailed by the set {A › B}. On the other
224
Andrzej WiĞniewski
hand, entailment can be defined in terms of mc-entailment as multipleconclusion entailment of a singleton set. The concept of multiple-conclusion entailment proved it usefulness in the logic of questions in many ways. (For the properties of mc-entailment, see Shoesmith & Smiley 1978; see also WiĞniewski 1995, pp. 107-113.) Since the concept of normal interpretation was left unspecified, the same pertains to the above concepts of entailment. But since the class of normal interpretations was assumed to be a subclass of the class of all interpretations, logical entailment (defined in the manner similar to that of Definition 2, but with respect to any interpretation) is a special case of entailment in L . We may also say that, in particular, any disjunction of sentences (or, to be more precise, a singleton set containing this disjunction) mc-entails in L the set made up of the appropriate disjuncts. In what follows the specification “in L ” will normally be omitted. We shall use the symbol š for mc-entailment in L and the symbol ş for entailment in L . We shall write Aš Y instead of {A}š Y. The relation š is said to be compact if and only if for any sets of d wffs X, Y such that Xš Y there exist a finite subset X1 of X and a finite subset Y1 of Y such that X1 š Y1 . In the case of ş the concept of compactness is understood in the standard way. It may be proved that mc-entailment in a language is compact if and only if entailment in this language is compact. However, we neither claim nor deny that entailment in L and mc-entailment in L are compact. Compactness of entailment in a language depends on the conditions imposed on the class of normal interpretations of the language and there are languages of the considered kind in which entailment is compact and languages in which it is not. We are now ready to define the concept of reducibility of questions. DEFINITION 3. A question Q is reducible to a non-empty set of questions ) iff for each direct answer A to Q, for each question Qi of ): A mc-entails the set of direct answers to Qi, and (ii) each set made up of direct answers to the questions of ) which contains exactly one direct answer to each question of ) entails some direct answer to Q, and (iii) no question in ) has more direct answers than Q. (i)
For conciseness, the non-emptiness clause will be omitted in the sequel. Also for the sake of brevity we shall introduce the notion of a P())-set. Let ) be a non-empty set of questions. By a P())-set we mean a set made up of direct answers to the questions of ) which contains
Reducibility of Safe Questions to Sets of Atomic Yes-No Questions
225
exactly one direct answer to each question of ). By means of this concept the second clause of Definition 3 can be expressed as follows: each P())-set entails some direct answer to Q. When saying that no question in ) has more direct answer than Q we mean that the cardinality of the set of direct answers to any question of ) is not greater than the cardinality of the set of direct answers to Q. Let us finally clarify the erotetic concepts of safety and riskiness. A question Q of L is said to be safe if and only if Q is sound (has a true direct answer) in each normal interpretation of L ; otherwise Q is said to be risky. (It is easy to observe that safety can be also defined in terms of mc-entailment: a question Q is safe iff the set of direct answers to Q is mc-entailed by the empty set.) Note that a question can be safe although no direct answer to it is valid (i.e. is true in each normal interpretation of the language)! Of course, each simple yes-no question is safe, but there are also safe questions which are not simple yes-no questions. In what follows we will be frequently speaking of simple yes-no questions, so, to simplify matters, we need a temporary notation for them. We shall write them down as ? {A, ¬A}. Under this notational convention the signs ?, {, } belong to the (erotetic part of the) objectlanguage5. Yet, we might have adopted some other notational convention for simple yes-no questions as well. The advantage of this one is that it makes explicit what the direct answers to a simple yes-no question are: these are the sentences enclosed in { }. Let us finally recall that an atomic yes-no question is a simple yes-no question whose affirmative direct answer is an atomic sentence (i.e., a sentence built up of a predicate and closed term(s)) and whose negative direct answer is the negation of this atomic sentence. In other words, an atomic yes-no question has the form ? {B, ¬B}, where B is an atomic sentence.
4. The Quantifier-Free Case It can be shown that in the case of quantifier-free safe questions the reduction to homogenous sets of atomic yes-no questions is always possible. By a quantifier-free question we mean a question whose direct answers contain no occurrence of a quantifier. Let us prove 5
Of course, the brackets { } also occur in the metalanguage in their normal roles.
226
Andrzej WiĞniewski
LEMMA 1: Let A be a quantifier-free sentence. Then the simple yes-no question ? {A, ¬A} is reducible to some finite set of atomic yes-no questions. PROOF: Let us observe that the clauses (i) and (iii) of the definition of reducibility are fulfilled by each set made up of atomic yes-no questions with respect to any “initial” question. The clause (i) is fulfilled because the set of direct answers to an atomic yes-no question is mc-entailed by any d-wff; the clause (iii) is satisfied since each question has at least two direct answers and an atomic yes-no question has exactly two direct answers. So it remains to be shown that for each quantifierfree sentence A there exists a finite set of atomic yes-no questions ) such that for each P())-set Y, Y entails the sentence A or the sentence ¬A. The proof goes on by induction on the structure of A. (1)
(2)
(3)
Assume that A is an atomic sentence. Let Q = ? {A, ¬A}. So {Q} is a finite set made up of atomic yes no-questions. On the other hand, it is obvious that {A} ş A and {¬A} ş ¬ A. Assume that A is of the form ¬B. By induction hypothesis there exists a finite set ) of atomic yes-no questions such that for each P())-set Y we have Y ş B or Y ş ¬B. But B ş ¬A and ¬B ş A. So each P())-set entails A or entails ¬A. Assume that A is of the form B & C. By induction hypothesis there are a finite set ) 1 of atomic yes-no questions and a finite set )2 of atomic yes-no questions such that for each P()1 )-set Y we have Y ş B or Y ş ¬B, and for each P()2 )-set Z we have Z ş C or Z ş ¬C. On the other hand, the following hold: (a) (b) (c) (d)
{B, C} ş A, {B, ¬C} ş ¬A, {¬B, C} ş ¬A, {¬B, ¬C} ş ¬A.
Let ) = )1 ‰ )2 . Each P())-set equals to a union of a P()1 )-set and a P()2 )-set. But each P()1 )-set entails B or entails ¬B, and each P() 2 )-set entails C or entails ¬C. So by the conditions (a) – (d) each P())-set entails A or entails ¬A. It is obvious that ) is a finite set made up of atomic yes-no questions. (4)
Assume that A is of the form A › B. We proceed as above by means of the following facts: (e) (f)
{B, C} ş A, {B, ¬C} ş A,
Reducibility of Safe Questions to Sets of Atomic Yes-No Questions
(g) (h) (5)
{¬B, C} ş A, {¬B, ¬C} ş ¬A.
Assume that A is of the form B Š C. We proceed analogously as above by using the following: (i) (j) (k) (l)
(6)
227
{B, C} ş A, {B, ¬C} ş ¬A, {¬B, C} ş A, {¬B, ¬C} ş A.
Assume finally that A is of the form B { C. We use the following: (m) (n) (o) (p)
{B, C} ş A, {B, ¬C} ş ¬A, {¬B, C} ş ¬A, {¬B, ¬C} ş A. Ŷ
Lemma 1 yields THEOREM 1. Each quantifier-free simple yes-no question is reducible to some finite set of atomic yes-no questions. Thus quantifier-free simple yes-no questions are reducible to sets of logically prior questions, that is, atomic yes-no questions. Let us now consider the possibility of reduction of any quantifier-free safe question to a homogenous set of atomic yes-no questions. We shall first prove THEOREM 2. If Q is a quantifier-free safe question, then Q is reducible to some set of quantifier-free simple yes-no questions; if moreover Q has a finite number of direct answers or entailment in the language is compact, then Q is reducible to some finite set of quantifier-free simple yes-no questions. PROOF: Let Q be a quantifier-free safe question. Direct answers are sentences and the set of direct answers to each question is at most countable. Let s = A1 , A2 , . . . be a fixed sequence without repetitions of direct answers to Q such that each direct answer to Q is an element of s. Let us then define the following set of simple yes-no questions: ) = {Q*: Q* is of the form ? {Ai, ¬Ai}, where i > 1} In other words, ) consists of the simple yes-no questions based on the elements of the sequence s with the exception of the simple yes-no
228
Andrzej WiĞniewski
question based on the first element of s. It is clear that the clauses (i) and (iii) of Definition 3 are fulfilled by ) with respect to Q. Let Y be a P())set. There are two possibilities: (a) the set Y contains some affirmative direct answer(s) to the questions of ), (b) the set Y is made up of the negative direct answers to the questions of ). If the possibility (a) holds, then – since the affirmative direct answers to the questions of ) are also direct answers to Q – the P())-set Y entails some direct answer(s) to Q. Suppose that the possibility (b) takes place. Since Q is a safe question, then ‡ š dQ. It follows that Y ş A1 . So there is a direct answer to Q which is entailed by Y. But Y was an arbitrary P())-set. Therefore Q is reducible to ). It is obvious that the set ) constructed in the above manner consists of quantifier-free simple yes-no questions. Moreover, it is also clearly visible that if Q has a finite number of direct answers, then – since each question has at least two direct answers – the set ) constructed according to the above pattern is finite and nonempty. Let us now assume that entailment in L is compact and that Q is an arbitrary but fixed quantifier-free safe question. If entailment is compact, so is mc-entailment. So there is an at least two-element subset Z of the set of direct answers to Q such that ‡ š Z (if ‡ entails some direct answer to Q, it also mc-entails each at least two-element subset of dQ which contains this answer; if ‡ does not entail any single direct answer to Q, then by compactness there is an at least two-element finite subset of dQ which is mc-entailed by ‡). We fix some at least two-element finite subset of the set of direct answers to Q which is mc-entailed by the empty set and then proceed as above; as the outcome we obtain a finite set of quantifier-free simple yes-no questions such that Q is reducible to this set. Ŷ We can now prove THEOREM 3. Each quantifier-free safe question Q is reducible to some set of atomic yes-no questions; if moreover Q has a finite number of direct answers or entailment in the language is compact, then Q is reducible to a finite set of atomic yes-no questions. PROOF: Assume that Q is a quantifier-free safe question. According to Theorem 2, Q is reducible to some set of quantifier-free simple yes-no questions (a finite set if Q has a finite number of direct answers or entailment in L is compact). Let ) be a fixed set of quantifier-free simple yes-no questions such that Q is reducible to ); if Q has a finite
Reducibility of Safe Questions to Sets of Atomic Yes-No Questions
229
number of direct answers or entailment in the language is compact, ) is supposed to be a finite set. By Theorem 1 each question in ) is reducible to some finite set of atomic yes-no questions. We associate each question in ) with exactly one finite set of atomic yes-no questions such that the considered question of ) is reducible to this set. Let < be the union of sets of atomic yes-no questions associated with the questions of ) in the above manner. The set < is a homogenous set of atomic yes-no questions. It is clear that the clauses (i) and (iii) of Definition 3 are met by < with respect to Q. Let Y be a P(<)-set. It is easily seen that Y entails some direct answer to each question of ). So there exists a P())-set, say, X, such that each normal interpretation which is a model of Y is also a model of X. But since Q is reducible to ), the P())-set X entails some direct answer to Q. Therefore the P(<)-set Y entails some direct answer to Q. But since Y was an arbitrary P(<)-set, it follows that the clause (ii) of Definition 3 is also fulfilled by < with respect to Q. Therefore Q is reducible to <, where < is a set of atomic yes-no questions. It is clear that if Q has a finite number of direct answers or entailment in the language is compact, then < is a finite set. Ŷ Theorem 3 shows that in the case of quantifier-free safe questions the reduction to sets of atomic yes-no questions is always possible; moreover, it shows that in some cases the reduction to finite sets of atomic yes-no questions is possible as well. Note that no assumptions concerning the particular form of the semantics of L have been used in the proofs of the above theorems; it follows that the reducibility of quantifier-free safe questions to sets of atomic yes-no questions takes place in every language of the considered kind.
5. The General Case So far we have restricted ourselves to quantifier-free safe questions. But what happens if the initial question is not quantifier-free? Sometimes the initial safe question Q is not quantifier-free, but nevertheless it is reducible to some set of quantifier-free simple yes-no questions. One can easily prove THEOREM 4. Let Q be a safe question. If Q is reducible to some set of quantifier-free simple yes-no questions, then Q is reducible to some set of atomic yes-no questions; if moreover Q is reducible
230
Andrzej WiĞniewski
to some finite set of quantifier-free simple yes-no questions, then Q is reducible to some finite set of atomic yes-no questions. PROOF: Similar to that of Theorem 3. It is obvious that if Q is reducible to a finite set of quantifier-free simple yes-no questions, then the resultant set < is finite. Ŷ Yet, there is no guarantee that each safe question is reducible to a set of quantifier-free simple yes-no questions (although, as we shall see, there is a guarantee that each safe question is reducible to some set of simple yes-no questions). Moreover, there are examples which show that Theorem 3 cannot be generalized to any safe question with respect to any language of the considered kind. Here is a very simple example: assume that the declarative part of L is the language of Monadic Classical Predicate Calculus and that each interpretation of L is a normal one. Let us then consider a simple yes-no question of the form ? {0005P(x), ¬0005P(x)}, where P is a predicate. At first sight it may look as if the above question is reducible to the set made up of atomic yes-no questions of the form ? {P(t), ¬P(t)}, where t is a closed term. Yet, the set which contains only the affirmative direct answers to the above questions does not entail any direct answer to the initial question. The reason is that there may exist some “unnamed” elements of the domain which do not satisfy the sentential function P(x). The above example not only shows that the reducibility to sets of atomic yes-no questions does not always hold, but also suggests a certain sufficient condition whose satisfaction enables reducibility of any safe question to a set of atomic yes-no questions. Let Ax be a sentential function with exactly one free variable. Let us designate by S(Ax) the set of sentences which result from the sentential function Ax by proper substitution of a closed term for the variable which occurs free in Ax (i.e. the set of sentences which have the form A(x/t), where t is a closed term). Let us now consider the following condition: (Z) for each sentential function Ax with exactly one free variable, 0007 x Ax š S(Ax). The condition (Z) says that for each sentential function with exactly one free variable, the existential generalization of this sentential function multiple-conclusion entails the set of sentences which are instantiations
Reducibility of Safe Questions to Sets of Atomic Yes-No Questions
231
of this sentential function.6 In other words, the condition (Z) requires that for each normal interpretation of the language the truth of the existential generalization of a sentential function with exactly one free variable guarantees that at least one sentence which results from this sentential function by proper substitution of a closed term for the free variable is true. It follows that the set of normal interpretations of the considered language must be a proper subclass of the class of all interpretations of it: as a matter of fact the normal interpretations are those, in which all the elements of the universe have names (to be more precise, the condition (Z) is fulfilled if for each element y of the universe there exists a closed term t such that for any valuation s, y is the value of t under s). It is clear that the condition (Z) is met only by some languages of the considered kind. But we may prove that if the condition (Z) does hold in the case of some language, each simple yes-no question of this language is reducible to a set of atomic yes-no questions. In order to continue we need the concept of prenex normal form of a d-wff: this concept is understood here in the standard sense. It is a well-known fact that for each d-wff there exists a logically equivalent d-wff in prenex normal form which contains the same free variables as the initial d-wff. Since logical entailment yields entailment in a language, then for each sentence A there exists a sentence B in prenex normal form such that A ş B and B ş A. One can easily prove LEMMA 2. If A is a sentence and B is a sentence in prenex normal form such that A ş B and B ş A, then the question ? {A, ¬A} is reducible to a set of questions ) iff the question ? {B, ¬B} is reducible to the set ). Now we shall prove LEMMA 3. If the following condition holds: (Z) for each sentential function Ax with exactly one free variable, 0007x Axš S(Ax) then for each sentence B in prenex normal form, the simple yes-no question ? {B, ¬B} is reducible to some set of atomic yes-no questions. PROOF: Let B be a sentence in prenex normal form. As above, let us observe that the clauses (i) and (iii) of the definition of reducibility are Let us recall here, however, that the set of closed terms of L need not be (but of course can be) infinite – we only imposed the non-emptiness condition on it. 6
232
Andrzej WiĞniewski
fulfilled by any set of atomic yes-no questions with respect to the question ? {B, ¬B}. So it remains to be proved that for each sentence B in prenex normal form there exists a set of atomic yes-no questions ) such that for each P())-set Y, Y entails the sentence B or the sentence ¬B. The proof will go on by induction on the number of layers of quantifiers in the prefix of B. Assume that the sentence B contains no layers of quantifiers. Since B is in prenex normal form, it follows that B is a quantifier-free sentence. So by Lemma 1 the question ? {B, ¬B} is reducible to some set ) of atomic yes-no questions and thus for each P())-set Y, Y entails the sentence B or the sentence ¬B. Assume now that B contains n layers of quantifiers in its prefix, where n > 0. By induction hypothesis for each sentence C in prenex normal form that contains n-1 layers of quantifiers in its prefix there exists a set of atomic yes-no questions 6 such that for each P(6)-set X, X entails C or entails ¬C. We have four possibilities: (a) (b) (c)
(d)
B is of the form 0005xD, where D is in prenex normal form, contains n-1 layers of quantifiers in its prefix and x is not free in D, (b) B is of the form 0005xD, where D is in prenex normal form, contains n-1 layers of quantifiers in its prefix and x is free in D, (c) B is of the form 0007xD, where D is in prenex normal form, contains n-1 layers of quantifiers in its prefix and x is not free in D, (d) B is of the form 0007xD, where D is in prenex normal form, contains n-1 layers of quantifiers in its prefix and x is free in D.
If the possibility (a) holds, then – since B is a sentence – D is also a sentence; moreover, we have D ş B as well as B ş D and thus ¬D ş ¬B. The sentence D contains exactly n-1 layers of quantifiers and is in prenex normal form. Thus, by induction hypothesis there exists a set of of atomic yes-no questions, say, ), such that for each P())-set Y, Y entails the sentence D or the sentence ¬D. Therefore for each P())-set Y, Y entails the sentence B or the sentence ¬B Suppose that the possibility (b) takes place. Now D is a sentential function with x as the only free variable; let us designate it by Dx. Let us now introduce the set S(Dx), i.e., the set of sentences of the form D(x/t), where t is a closed term. Since the set of closed terms is nonempty, so is the set S(Dx); moreover, this set is made up of sentences in prenex normal form which contain exactly n-1 layers of quantifiers in their prefixes. So by induction hypothesis for each sentence C in the set S(Dx)
Reducibility of Safe Questions to Sets of Atomic Yes-No Questions
233
there exists a set < of atomic yes-no questions such that each P(<)-set entails the sentence C or the sentence ¬C. Let us now consider a union of such sets of questions; to be more precise, for each C  S(Dx) choose exactly one set of atomic yes-no questions which fulfill the inductive hypothesis and consider the set, say, ), which is the union of these sets. Let Y be a P())-set. There are two possibilities: (1) the set Y entails each sentence from the set S(Dx), i.e., each sentence of the form D(x/t), where t is a closed term; (2) the set Y entails some sentence of the form ¬D(x/t). In the case of (2) Y entails the sentence ¬B. Let us now consider the case (1). Suppose that Y does not entail the sentence B, i.e., the sentence 0005x Dx. So there is a normal interpretation I such that I is a model of Y and the sentence 0007x ¬Dx is true in I. By assumption we have 0007x ¬Dx š S(¬Dx). So at least one sentence of the form ¬D(x/t) is true in I. But Y entails each sentence of the form D(x/t). Therefore each such sentence is true in I. We arrive at a contradiction. So Y entails the sentence B. Thus we may say that each P())-set entails the sentence B or the sentence ¬B. If the possibility (c) holds, we proceed as in the case of (a). Suppose finally that the possibility (d) takes place. Again, D is now a sentential function with x as the only free variable. We designate it by Dx. Then we construct the set ) as in the case of (b). Let Y be a P())-set. There are two possibilities: (1) the set Y entails some sentence from the set S(Dx), i.e., some sentence of the form D(x/t), where t is a closed term; (2) the set Y entails each sentence of the form ¬D(x/t). In the case of (1) Y entails the sentence B. Let us now consider the case (2). Suppose that Y does not entail the sentence ¬0007x Dx. So there is a normal interpretation I such that I is a model of Y and the sentence 0007x Dx is true in I. By assumption we have 0007xDx š S(Dx). So at least one sentence of the form D(x/t) is true in I. But Y entails each sentence of the form ¬D(x/t). Therefore each such sentence is true in I. We arrive at a contradiction. So Y entails the sentence ¬0007x Dx. This sentence, however, is equal to ¬B. Thus we may say that each P())-set entails the sentence B or the sentence ¬B. Ŷ Next we shall prove THEOREM 5. If the following condition holds: (0007) for each sentential function Ax with exactly one free variable, 0007x Ax š S(Ax)
234
Andrzej WiĞniewski
then each simple yes-no question is reducible to some set of atomic yes-no questions. PROOF: Let ? {A, ¬A} be a simple yes-no question. It is obvious that there exists a simple yes-no question ? {B, ¬B} such that B is in prenex normal form and A ş B as well as B ş A. By Lemma 3 the question ? {B, ¬B} is reducible to some set of atomic yes-no questions; so by Lemma 2 the question ? {A, ¬A} is reducible to some set of atomic yes-no questions. Ŷ Now we need the following THEOREM 6. Each safe question is reducible to some set of questions made up of simple yes-no questions. The proof of Theorem 6 is similar to that of Theorem 2. For details, see WiĞniewski (1994). By means of Theorem 5 and Theorem 6 we can prove THEOREM 7. If the following condition holds: (Z) for each sentential function Ax with exactly one free variable, 0007x Axš S(Ax) then each safe question is reducible to some set of atomic yes-no questions. PROOF: Let Q be a safe question. By Theorem 6 Q is reducible to some set of simple yes-no questions. Let ) be an arbitrary but fixed set of simple yes-no questions such that Q is reducible to ). By Theorem 5 each question in ) is reducible to some set of atomic yes-no questions. Let us then pair each question in ) with exactly one (arbitrary but fixed) set of atomic yes-no questions to which the considered question in ) is reducible. Let < be the union of sets of atomic yes-no questions associated with the questions of ) in the above manner. The set < is a homogenous set of atomic yes-no questions. Then we proceed as in the proof of Theorem 3. Ŷ Thus, if the condition (Z) holds, then each safe question is reducible to some set of atomic yes-no questions. But it is not the case that the condition (Z) holds for any language of the considered kind. So designing the semantics in such a way that the condition (Z) would be met is the price which, if paid, gives us the unrestricted reducibility of
Reducibility of Safe Questions to Sets of Atomic Yes-No Questions
235
safe questions to homogenous sets of atomic yes-no questions. And it may be a high price: as a by-product we may obtain the lack of compactness of entailment as well as of mc-entailment.7
Adam Mickiewicz University Section of Logic and Cognitive Science Department of Psychology ul. Szamarzewskiego 89a 60-568 PoznaĔ, Poland e-mail: [email protected]
REFERENCES Åqvist, L. (1965). A New Approach to the Logical Theory of Interrogatives. Uppsala: Almqvist & Wiksell. Belnap, N.D. (1969). Questions, Their Presuppositions and How They Can Fail to Arise. In: K. Lambert (ed.), The Logical Way of Doing Things, pp. 23-37. New Haven, CT: Yale University Press. Belnap, N.D. and T.B. Steel (1976). The Logic of Questions and Answers. New Haven, CT: Yale University Press. Hajièová, E. (1983). On Some Aspects of Presuppositions of Questions. In: F. Kiefer (ed.), Questions and Answers, pp. 85-96. Dordrecht: D. Reidel. Harrah, D. (2002). The Logic of Questions. In: D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 8, 2nd ed., pp. 1-60. Dordrecht: Kluwer. Hintikka, J. (1985). A Spectrum of Logics of Questioning. Philosophica 35, 135-150. Kiefer, F. (1980). Yes-No Questions as Why-Questions. In: J.R. Searle, F. Kiefer and M. Bierwisch (eds.), Speech Act Theory and Pragmatics, pp. 97-119. Dordrecht: Reidel. Kiefer, F. (1988). On the Pragmatics of Answers. In: M. Meyer, F. Kiefer and M. Bierwisch (eds.), Questions and Questioning, pp. 255-279. Berlin: Walter de Gruyter. Koj, L. (1972). Analiza pytaĔ II: RozwaĪania nad strukturą pytaĔ. Studia Semiotyczne 4, 23-39. English translation: Inquiry into the Structure of Questions, in: L. Koj and A.WiĞniewski (eds.), Inquiries into the Generating and Proper Use of Questions (Lublin: Wydawnictwo Naukowe UMCS, 1989), pp. 33-60. KubiĔski, T. (1973). Twierdzenia o relacjach sprowadzalnoĞci operatorów pytajnych [Theorems about the reducibility of interrogative operators]. Ruch Filozoficzny 31, 313-320. KubiĔski, T. (1980). An Outline of the Logical Theory of Questions. Berlin: Akademie Verlag. 7
I am grateful to the Netherlands Institute for Advanced Study in the Humanities and Social Sciences, and to the Foundation for Polish Science for their support.
236
Andrzej WiĞniewski
LeĞniewski, P. (1997). Zagadnienie sprowadzalnoĞci w antyredukcjonistycznych teoriach pytaĔ [The problem of reducibility in anti-reductionistic theories of questions]. PoznaĔ: Wydawnictwo Instytutu Filozofii UAM. Shoesmith, D.J. and T.J. Smiley (1978). Multiple-Conclusion Logic. Cambridge: Cambridge University Press. WiĞniewski, A. (1994). On the Reducibility of Questions. Erkenntnis 40, 265-284. WiĞniewski, A. (1995). The Posing of Questions: Logical Foundations of Erotetic Inferences. Dordrecht: Kluwer.
PART IV CATEGORIAL GRAMMAR
This page intentionally left blank
Peter Simons LANGUAGES WITH VARIABLE-BINDING OPERATORS: CATEGORIAL SYNTAX AND COMBINATORIAL SEMANTICS The analysis of an expression that contains an operator, e.g. the general proposition ‘(3x).fx’, into functors and arguments with appropriate semantic categories, seems to meet with insuperable difficulties. Kazimierz Ajdukiewicz, “Syntactic Connexion” (1967), pp. 220-221.
Artur Rojszczak in memoriam
1. Introduction Many who have come across categorial grammar (CG), whether in the original paper by Ajdukiewicz (see Ajdukiewicz 1935) or elsewhere, were probably, like myself, initially captivated by its elegance, only later to grow disillusioned in the face of the complications and shortcomings of the available theories. Although CG has revived healthily in recent years,1 one problem has resisted solution: CG as it stands cannot cope adequately with variable-binding operators. To the extent that natural languages manage without variable binding they are not affected by this problem, and CGs, especially the more flexible versions developed since Ajdukiewicz’s time, have many virtues in the description of natural languages. As the opening quotation shows, Ajdukiewicz was himself acutely aware of the difficulty posed by variable-binding operators, devoting a good part of his famous paper to it, but failing to solve the problem. One 1
Signs of this revival are Buszkowski et al. (1986) and Oehrle et. al., eds. (1988).
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. 239-268. Amsterdam/New York, NY: Rodopi, 2006.
240
Peter Simons
reason for the problem’s intransigency lies in the mixed ancestry of CG. Ajdukiewicz was building on the work of more than one thinker, and there is a tension between two ways of regarding functors. On the one hand, they may be considered as quotable expressions, detachable unitary pieces of a syntactical whole. This line of thought informs the work of LeĞniewski, who was the first to consciously formulate a symbolic language along categorial lines. On the other hand, functors may be considered as non-detachable moments or aspects of a whole. The latter view stems from Frege, and tends to push one in the direction of seeing variables as a merely superficial device, rather like parentheses, not present in the “deep structure” of a language, so that functors and operators are only superficially different in kind. Although attractive, this view avoids the problem, which is that of providing a syntactic and semantic analysis of languages which actually contain variables, rather than “explaining them away.” The structure of the rest of this paper is as follows. §2 gives notation and principles for strict or inflexible CGs, §3 for more flexible CGs. In neither case are operators included. §4 reviews the problems involved in describing operator/variable languages using plain CG. §5 shows how to give a syntax for such languages. It includes a new analysis of the nature of variable binding, which distinguishes the roles of place marking and place filling. I call the resulting kind of theory “extended categorial grammar” (ECG), since while it goes beyond the functor/argument scheme, the notation and principles governing operators are recognizably similar to those of CG. One of the principal attractions of CG is the close connection it establishes between syntax and semantics. As an alternative to more usual function- or set-theoretic semantics, in §6 I present the outlines of combinatorial semantics for languages without operators, and in §7 the semantics is extended to languages with operators.
2. Syntax for Strict Categorial Languages Ajdukiewicz’s first and major success was the application of his notation for CG to the simple case of propositional logic notated in the style of àukasiewicz. I shall use a slightly different notation for the categorial indices from Ajdukiewicz, and generalize the analysis to a wider but essentially similar class of possible languages. I shall be brief, as much of this is very familiar (for a more detailed account, see Simons 1989, §2).
Languages with Variable-Binding Operators
241
2.1. Categorial Notation There are a finite number of basic category symbols, each standing for a basic category. Each basic category symbol is a category symbol. If a, b 1 , . . . , b n are category symbols (n • 1), then the symbol a is a functor category symbol, standing for the functor category with input (argument) categories b 1 . . . b n in order and output (value) category a. Nothing is a category symbol which is not a basic or functor category symbol so formed. Let ‘s’ be the category symbol for the basic category SENTENCE. Then the category symbols for the categories of one-place and two-place connectives are respectively ‘s<s>’ and ‘s<ss>’. If ‘n’ is the category symbol for the basic category NAME , then s is the category of three-placed verbs,2 n is the category of two-placed function symbols, while s<s> is a category of functors taking one-place verbs to sentences, a category often assigned to determiners in CGs. We assume that if category symbols are different, they denote distinct categories. This distinguishes multi-place functors from multi-link functors – as in LeĞniewski.3 2.2. Categorial Languages Suppose we have a system of categories based on a finite set of basic categories as above. A categorial language (CL) describable by this system of categories is one which fulfils the following conditions: (CL1) There are a number of indecomposable or simple expressions of the language, which we follow LeĞniewski in calling “words” (they need not coincide with words in the everyday sense). Each word belongs to exactly one category of the system generated by the basic categories, and no word can be construed as a complex expression compounded of other simple signs, where a simple sign is either a word or some other indecomposable syncategorematic symbol (one which is not a word, such as a bracket) which the language might possess. 2 The distinction between verbs and predicates is a special case of that between functors as pieces of an expression and hence themselves expressions (here: verbs) and functors as undetachable moments of expressions (here: predicates). See Simons (1981, 1983), for further details. 3 A multi-link functor is one whose output is a functor. For example, s is a category of multi-link functor distinct from multi-place functors of category s. For a clear account of multi-link functors, see Lejewski (1967), pp. 73-75.
242
Peter Simons
(CL2) If X, Y1 , . . . , Yn , are any expressions belonging to the categories a, b 1 , . . . , b n respectively, then X(Y1 , . . . , Yn ) is a wfe of category a. (WF3) Nothing is a wfe except in virtue of WF1 and WF2. This covers a multitude of possibilities of realization in actual concrete expressions. For example, the various ways in which classical propositional calculus may be notated should all conform to it. Nevertheless the bracketless àukasiewicz notation is particularly simple, because the complex expression X(Y1 , . . . , Yn ) is written simply as the string ‘XY1 , . . . , Yn ’. The mere concatenation of a functor with its arguments in linear order takes care of both the order of arguments and the application of functor to arguments. Any string of simple expressions can be automatically checked for well-formedness, and if it is well-formed, it can be so in only one way.
Languages with Variable-Binding Operators
243
3. Greater Flexibility Natural languages do not display the tidy categorial behaviour outlined in the previous section. For one thing, different tokens of one type expression may belong to different categories. A clear example is provided by the conjunction ‘and’, which can conjoin any pair of expressions of like category. For example, in the logicians’ complex connective ‘if and only if ’, the ‘and’ has effective category s<ss> <s<ss> s<ss>>. In languages with linear structure where binary functors have mediate position between their arguments, it is natural to view not only the whole string Arg + Funct + Arg as having a ternary structure, but also to regard the two partial strings Arg + Funct and (more usually) Funct + Arg as being well-formed syntactic units, so we can analyse such strings as having an extra level: (Arg + Funct) + Arg, or Arg + (Funct + Arg). The view that an expression may be analysed in more than one way for logical purposes goes back (at least) to Frege. What it means for CG is that for certain purposes we do not or cannot distinguish between categories a, a, and a. For Frege at any rate there can be no distinction between multi-link and multi-place functors, or, to put the same point procedurally, simultaneous complete saturation and successive partial saturations yield the same result. For LeĞniewski, by contrast, there is a syntactic difference. There is system to the categories a single expression type may adopt in different contexts, and this system is recognized in CGs which admit what are called “type-change” rules. Of these, the best-known and most widely accepted is Geach’s Rule. 4 A special instance is If an expression can have category a, it can have category a< />>. Expressed in the quotient notation of Ajdukiewicz, this corresponds to “cancelling out”: a / b = (a/c) / (b / c). More generally we might have GR If an expression can have category a, it can have category a . . . c mnm >> 4
The source of Geach’s Rule is Geach (1971).
. . . b m
244
Peter Simons
Another rule which has been found occasionally useful is one which allows the roles of (single) argument and functor to be switched: it is known as Montague’s Rule: 5 MR An expression of category a may also be of category b4. Problems One of the prices of linearization is that no element can be contiguous with more than two elements, so any functor with more than two arguments or any two-argument prefixed functor will be separated from one or other of its arguments, and iteration of infixed binary functors will lead to structural ambiguity unless bracketing is introduced. Both separation and bracketing involve the idea of separated components of the linear realization being structurally connected across others, or syntactic connection at a distance. Brackets may of course be arbitrarily widely separated from their partners in symbolic languages with infix notation, but the same phenomenon is observable in ordinary language, 5
The source is Montague (1973), which “lifts” proper names from the category n to the category s<s>. A more systematic account of admissible type-changes based on the analogy between type-derivation and inference goes back earlier to Lambek (1958). For a survey, see van Benthem (1988). 6 Frege’s two-dimensional notation for implication and negation is effectively constituency trees turned on their side. Since implication is the only binary connective he uses, there is no need to notate it separately from the structural lines themselves, and because of the configuration of these lines, it is not necessary to retain the standard order of writing (antecedent below consequent). Pivoting the constituents freely about their joins does not alter the constituent structure; the propositions could be realized physically as three-dimensional mobiles where no linearity, only hierarchy remains.
Languages with Variable-Binding Operators
245
for instance in the word pairs both/and and either/or which are functional units sometimes separated by long stretches of text. Also well known are German separable verbs, as in Wir stellten die Suche bei Dämmerung ein where ein and stellten (‘discontinued’) belong together despite the two intervening phrases. Any attempt to take account of these facts using CG must either be reconciled to the idea of structure-crossing or disconnected constituents, which are not well-loved in syntax, or else may consider the idea of movement transformations which shift arguments originally found next to their functors to other final positions. In neither case do we remain within the bounds of CG alone in giving an account of the resulting linear structure. If on the other hand the linear string itself is taken as the object on which our syntactic theories are to work directly, then to what category are brackets to be assigned? Although a piece in a string, a bracket without its mate or even a pair of mated brackets is not of any category, and is not (usually) regarded as a functional part at all. But clearly it is (again, usually) doing the job of delimiting or scope marking, or it would not be there. I do not see how this job can be explained in purely CG terms.7 So those versions of CG which simply ignore brackets are not giving a complete description of the syntactic phenomena. There is another aspect of the syntax of many artificial languages which is like brackets and other separable units in that it also involves “action at a distance,” but which throws up more fundamental problems for CG. This is the use of bound variables and the operators which bind them. Consider for example the universal quantifier. Frege interpreted this quite naturally as a function of higher order. In Everything flows the quantifier everything of category s<s> is saturated by the verb flows of category s to yield a sentence. Frege of course used not the words of an ordinary language but a symbolic notation with variables to say this: we have simply 0005x(x flows). Superficially, we do not seem to have changed anything essential. A closer look however shows that there is a notable difference between the natural language expression ‘everything’ and the quantifier-variable notation. The latter allows quantifiers to bind variables in expressions of arbitrary complexity, and quantifiers may also 7 In fact brackets may do more than one job. The usual one is structural grouping, but they can contribute to determining the category of an expression, as in LeĞniewski’s formal languages. See Luschei (1962), p. 97.
246
Peter Simons
be embedded to any depth. For instance, the classic definition of continuity of a function F at number a is 8 0005H{H > 0 o 0007G{G > 0 & 0005x{|x – a| < G o |F(x) – F(a)| < H}}} and here each of the variables H, G, x occurs more than once within the scope of its quantifier. Because of the embedding of the quantifiers, each quantifier must be assigned a different effective category: the innermost scope contains three variables (assuming ‘F’ and ‘a’ are constants) so the innermost quantifier has effective category s <s>, the middle quantifier has effective category s <s> and only the outermost one has category s<s>. Of course, given Geach’s Rule, we can accept this categorial flexibility, just as we have to accept it in natural languages. But the difference is that whereas in natural language we have a connected expression, e.g. everything, some dog, most heads of state as the quantifier, here we cannot take the mere symbol ‘0005’ as the quantifier, because if we did, an expression like ‘0005(x = x)’ would be well-formed, which it is not. So we must add the variable to the symbol ‘0005’. But the expressions ‘0005H’, ‘0005G’ and ‘0005x’ are not the quantifiers either, because in an expression like ‘0005H(a = b)’ the quantifier does not close any gaps, as it should do if it is a functor. If a and b are constants, a = b is a sentence, and the combination s<s> + s is not syntactically connected. Ajdukiewicz gave this account of variable binders (see Ajdukiewicz 1935, § II), but it fails to account for the difference between vacuous and non-vacuous quantification. Many logical languages allow vacuous quantification, treating it as a harmless by-product of the symbolism, but logicians with a more finely developed sense of propriety, such as Frege and LeĞniewski, did not allow vacuous quantification. Indeed for Frege the scope of the quantifier cannot be a chunk of language, that is, a separable, quotable expression, but must be a pattern. If we choose to see variable-binding operators together with their variables as functors, we shall have to assign functor and argument status to something other than quotable expressions as has generally happened hitherto. The variables of such languages then turn out to be much more like brackets than they appeared to be at first sight: they come in groups which function only together, they have no meaning on their own, and they may be widely separated from their associates. But they differ from brackets in being associated with a category and being able to stand where and only where constant expressions of this category stand, excepting only their tag position alongside the operator symbol. 8
The braces are operator scope markers. See Ajdukiewicz (1935), § II.
Languages with Variable-Binding Operators
247
It might be objected that, just as brackets are dispensable, provided a suitable àukasiewicz-type notation is chosen, so we can manage without variables, provided we choose a suitable notation. This would show that at a deeper level than that found in the superficial syntax of such languages, the principles of CG indeed apply, the difference being then one of realization, as in the case of propositional calculi. And indeed variables are dispensable. Given a suitable supply of combinators, variables of a categorially-based language can be eliminated, and the resulting language is adequately describable by CG (see Simons 1989). However, there are problems arising from this. Do the combinators merely constitute a different kind of notation from the operator/variable notation, there being some “deep structure” they share, or do we not in fact have languages with completely different syntactic structure? On the face of it, the second view is more plausible. In any case, no matter how “deep” the supposed structures are which may be postulated to lie beneath all the variants, their postulation does not help us to give a syntactic description of the sign systems we see in front of us when we read them, brackets, dots, bound variables, left-right ordering, suffixes, primes, commas, and all. Here I think we must concede that CG rarely, if ever, tells more than a part of the story. The most extensive use of CG is found among those logicians who have developed model-theoretic semantics in the wake of Richard Montague. The syntax and semantics in such languages are of course designed to mesh as closely as possible, but to take account of variable binding again it is usual to go beyond pure CG and introduce lambda abstraction (see, for example, Cresswell 1973, pp. 80 ff).
5. Extended Categorial Grammar: Accommodating Operators If we are to find an account of something like CG which can cope with variable-binding operators as they stand, rather than postulating a deep structure where they are no longer needed, we shall need to take account of the fact that operators can bind variables which are embedded to any finite depth in a (finitely) complex structure. The operators can penetrate as many levels of structure as we like and still operate in the same way. This alone makes them different from functors, which simply add a further layer of structure but do not reach inside their arguments. But operators are like functors in having a scope and determinate categories of input and output.
248
Peter Simons
To provide a notation for operators adequate to cope with all of these facts, we must signalise more than just scope, output category, and input categories, as we do with functors. We need to know which categories of variables the operator binds. For complete generality we cannot confine ourselves to operators binding a single variable, nor need all variables bound be of the same category. Let us call the categories of variables bound marker categories, for reasons which will become apparent later. So we need to signify in addition (1) (2) (3)
Marker categories Full syntactic structure (not just category!) of the expression to which the operator is applied Indication of the places within this structure where variables of the relevant marker categories are bound.
To achieve all this at one go we need to substantially extend the notation of CG. We can represent the full syntactic structure of a complex expression even for CG without considering variable binding. The categories are written as in §2, and the schematic notation a(b 1 . . . b n ) is now used to signify the structure (however concretely realized) of a complex expression where a functor of category a is applied to arguments of category b 1 , . . . , b n . The resulting complex is then enclosed in square brackets and its category written to the left. Thus the structure of a sentence consisting of the application of a binary predicate to two names is signified s[s(nn)] while that of the predicate logical expression ~F(a) › G(bc) is s[s<ss>(s[s<s>(s[s(n)])]s{s(nn)])] The notation to date is redundant, in that we do not need to have the square brackets or the symbol for the output category to the left of them. We can leave these off in the context of a rigid CG of the type considered in §3. The structure of the last example would then be represented compactly by s<ss>(s<s>(s(n))s(nn)). Bracketed linear notations of this sort are compact but difficult to survey, and for many purposes we may resort to the familiar sort of constituency trees, which however we omit in this paper for economy and simplicity. We stipulate that functors in principle always appear to the left of their
Languages with Variable-Binding Operators
249
argument(s) though in giving concrete examples we often resort to the most usual infix notation. If we wish to allow for categorial flexibility as illustrated by Geach’s Rule, and the partial filling of slots, then this part of the notation can be turned to good use and is no longer redundant. We do not need to alter the category of a functor according to its context, but can let the context partially determine the category of the outcome. For example, a functor of the category a (or a, this amounting to the same thing for our purposes) can be partially filled by an expression of, say, category b<de>. We may notate the complex arising as a <de>[a(b<de>)]. the unfilled slots being carried across and retained in the “denominator” of the result. This context-dependence of outcome is much more akin to the way we actually determine effective category of expressions than one which assigns them a potential infinity of categories and bids us pick the right one for the context. Returning to the case of a strict CG without type-changes, we now have a way to notate the full syntactic structure of the expression or expressions to which the operator is applied. To obtain the category symbol for the operator we add to its output category and input categories written in the usual way a list of its marker categories. We place these in a new kind of bracket, here written with left- and rightslanted slashes and / and place this between the input and output symbols. The marker category of a quantifier of first-order predicate logic being n, the notation for such a quantifier’s category is sn/<s>. Now to mark the effect of the operator on its operand expression we enclose the full syntactic description of the operand again in new brackets, this time braces { and }, which thus show the operator’s scope.9 All we need to do now is to indicate which of the marker slots inside the operand are filled by variables belonging to which place in the operator’s list of marker categories. There are various ways to do this. We could connect the appropriate slots with operator places by linking lines, for instance (see Quine 1951, p. 70). We choose instead to show the links using subscripts, for which we use lower case Greek letters. A Greek letter subscript next to a place in the structure pairs up with one next to a letter in the operator’s marker category list and shows that the operator binds with this category into this place in the structure. Of course the marker category and the category of the place(s) bound must match, and 9
LeĞniewski used lower corners around variables to signify the universal quantifier: we have used inward slanting brackets. LeĞniewski used upper corners as we use braces to mark operator scope. See Luschei (1962), pp. 194 ff.
250
Peter Simons
the letters must be chosen with the usual regard to avoiding ambiguities due to overlapping scope. So for example the following simple sentence of predicate logic 0005x{F(x) & G(x)} has the structural analysis s[sn D /<s>{ss<ss>(s[s(n D )]s[s(n D )])}] or in the more economical notation sn D /<s>{ss<ss>((s(n D ))s(n D ))}. Note that the more economical notation allows us to replace each symbol of the syntactic description by an expression of the language according to obvious replacement rules. Here is another example: a definite description operator in a simple sentence: G(the x{F(x)}) This has structure (in the compact notation) s(nn D /<s>{s(n D )}) A more complex example is provided by the Cauchy definition of continuity mentioned above. The resulting sentence has structure sn H/<s>{s<ss>(s(n Hn)sn G/<s>{s<ss>(s(n Gn)sn D /<s> {s<ss>(s(n(n(nn D ))n G)s(n(n (n(n)n(n D )))n H))})})} The final example is a binary operator. What in English is said with There are more Fs than Gs can be rendered in predicate logic with a binary quantifier as more x {F(x), G(x)} which has structure sn D /<ss>{s(n D ) s(n D )}. The kind of categorial grammar obtained by adding notation and principles of syntactic connection for operators I call extended categorial grammar (ECG). This designation is warranted by the facts that CG provides the basis for the grammar and the extension is made on recognizably similar lines. I shall consider below the extension of CGs with type-changes to more flexible ECGs. However in the more restricted
Languages with Variable-Binding Operators
251
and therefore more perspicuous context of a strict ECG without typechanges the main features of operators and variable binding can be brought out more clearly. We must consider a possible objection which threatens to undermine the whole enterprise of ECG. We are trying to explain how variable-binding operators work and yet in our notation we use precisely such a device in the form of Greek suffixes, or, if we did not have them, we should have to resort to some obvious equivalent, such as Quine’s connecting lines. How can variable binding be satisfactorily explained by variable binding? There are two things to be said in answer. Firstly, since variable binding has proved resistant to incorporation within the functor/argument pattern of ordinary CG, it is not very surprising that its like shows up in our metalanguage. This is just evidence that variable binding is a syntactic phenomenon sui generis. Secondly, there is an importance difference between the variables of object languages such as predicate logic and the Greek suffix letters we use in the metalanguage when describing the syntactic structure of complex expressions containing operators. The Greek suffix letters are not variables bound by an operator: they are place-markers showing which places in a structure are linked with which operator. They cannot be variables of the usual kind because they neither have, nor are invariably associated with, a particular syntactic category. The very same Greek letters serve the very same purpose no matter which category symbol they suffix. Bound variables on the other hand are divided into categories in just the same way as simple constants. Our Greek letters mark places but do not fill them. Places in object language expressions are filled by variables, whereas places in the metalinguistic descriptions are filled by category designations. In the object language, a bound variable both marks and fills a place. It is crucial to distinguish these two functions. That they can be not only distinguished but also separated may be seen by considering a wider range of formal devices than those usually employed. Place marker suffixes occur alongside normal bound variables in the object language of one (and, to my knowledge, only one) system of modern logic, but one whose historical importance is unsurpassed: it is the system of Frege’s Begriffsschrift (1879). Alongside the universal quantifier and other operators Frege introduces operators yielding the proper and improper ancestrals of a relation. To signify the holding of the ancestral of a relation F between two objects, Frege places the symbol for the ancestral before a sentence in which the sign for the relation F occurs, with the
252
Peter Simons
names of the two objects in the appropriate places. A relation is signified in Frege’s logic not by an expression as such but by an expression function, a sentence in which two classes of places are marked as variable. The places may themselves be occupied by constants, variables or functional expressions, provided these are categorially suitable, but in a sentence in which the places are filled we do not know which places are relevant unless they are marked in some way, and for this Frege uses Greek suffixes, putting copies of the relevant Greek letters next to the sign for the ancestral operator. An example shows how the idea works. To express that the number a is a multiple of the number d Frege uses the (improper) ancestral: a is obtained by adding d to 0 some finite number of times (possibly zero). Using ‘Anc’ for this operator and letting its Greek suffix place-markers follow it, instead of using Frege’s awkward sign, we can write this then as 10 AncEJ/{0 J + d = a E} Frege’s invention did not survive into his later logical system (Grundgesetze, 1893–1903) and it appears that even he was not fully aware of its nature. At all events it has found no imitators. ECG copes with Frege’s operators as effortlessly as it copes with normal variable-binders. The above sentence has the syntactic structure sn En J/<s>{s(n(n Jn)n E)} How then are we to interpret the difference between operators with mere place-markers, like these ancestral operators of Frege, and the more familiar operators whose variables both mark and fill their places? The difference is, I suggest, merely one of notational convenience. We could easily manage without bound variables in a formal language, provided we have place-marker suffixes instead. For instance, the predicate-logical sentence 0007F{0005x{0007y{F(x) & F(y) & x z y}}} could be replaced by a notation such as 0007 ss I/{0007 n n D /{0007 n n E/{PI(ND ) & PI(NE) & Na z NE}}} where ‘N ’ is a constant name and ‘P’ a dummy constant one-place predicate and the category of variable the quantifiers bind is shown by appending the category symbols to the quantifier symbols. Here the roles of place-marking and place-filling are separated. It is in this case quite 10
See Frege’s Begriffsschrift, §26, §29. For a commentary, see Simons (1988).
Languages with Variable-Binding Operators
253
irrelevant to the meaning of the result which expressions we use to fill the appropriate places in the structure. As the example shows, any meaning of ‘N ’ as a proper name plays no role in determining the meaning and truth-value of the result. We could replace ‘N ’ either uniformly or non-uniformly by any other simple or complex name or names and the meaning of the whole would be unaffected, and the same goes for the predicate place occupied by ‘P’. This is what is peculiar about the places marked by such operators as distinct from those marked by the ancestral operator. So we could instead adopt meaningless dummy expressions (name, predicate, etc.) to fill the relevant places, and the system would not suffer at all if we had only one dummy expression per category. The pattern of binding would still be shown by the Greek suffixes. Normal bound variables simply fulfil both of these roles. Rather than having a single meaningless dummy expression of each category we have arbitrarily many, and we leave it to their typographical equiformity and difference to connote the binding pattern. The Greek suffixes are then redundant in normal variable-binding languages, which is why neither they nor anything like them need occur. The effect of Frege’s place-marking operators may alternatively be achieved using lambda abstraction, and in that case we can use ordinary bound variables. It is instructive to see why. Lambda operators, rather like ‘and’, can appear in many different categorial guises. We could let the single categorially ambiguous lambda be replaced by a sheaf of fixed-category lambdas to conform with the strict ECG we are considering. Any such lambda operator has a category of the form a {b 1 . . . b n } Consider the special case s <s> { n } as found in the lambda abstract Ox{F(x) & G(x)} with syntactic structure sn D /<s>{s<ss>(s(n D ) s(n D ))} We can then, as Ajdukiewicz realised, leave all the variable binding to be done by abstractors (see Ajdukiewicz 1935, § III), since they replace marker categories by argument gaps in functor categories and leave a unified functor expression which may be applied as it stands to arguments and to which further functors may be applied. Any other variable-binder can be expressed as the product of a functor and a lambda abstractor. In this case we may add a universal functor of category s<s> and obtain the same result as the universally quantified sentence
254
Peter Simons
given earlier. This works for Frege’s non-binding operators too, which can be seen as compressing into one notation the three steps of lambda abstraction, application of a functor to the abstract so formed, and then application of the modified functor to suitable arguments. This flexibility of lambda abstraction is another reason for the neglect of Frege’s device, since it shows we can manage well enough without it. For instance, the ancestral can be represented by a functor ANC of category s <s>, and we can express the sentence for which Frege used his ancestral operator by ANC(Oxy{x + d = y})(0, a). We can extend our analysis of operators to the case of a more flexible CG involving type-changes. One thing we can do with this more flexible ECG is to explain something which everyone does without being able to justify it syntactically, namely defining one quantifier in terms of another.11 It is common to define 0007 as ~ 0005 ~, but this is not covered by the usual principles of definition for functors, since it is not a functor. If however we extend Geach’s Rule in the obvious way to operators, we have sn D /<s> + s<s> = sn D /<s> and s<s> + sn D /<s> = sn D /<s> so s<s> + sn D /<s> + s<s> = sn D /<s> and hence the sequence ~ + 0005 + ~ is a syntactic unit of the right operator category. This is just a case of a more general phenomenon, namely the extension of Boolean functors like conjunction and negation to apply to operators. We are familiar in natural language with such complex quantifiers as some but not all so we can not only define a complex quantifier 11
See Quine (1951), p. 102: “The parts of ‘~(x)~’ do not, of course, hang together as a unit [. . .]. But the configuration of prefixes ‘~(x) ~’ figures so prominently in subsequent developments that it is convenient to adopt a condensed notation for it.” This is a fudge by Quine’s own high standards. Others were more scrupulous: Frege never defined the dual to the universal quantifier, LeĞniewski never used it in his “official” logical language. Perhaps just such reservations hindered them as are expressed by Quine. The price of scruple is inconvenience, so our demonstration of the acceptability by the highest standards of the combination justifies usual practice.
Languages with Variable-Binding Operators
(0007 & ~0005)x {A} =
Def.
255
0007x {A} & ~0005x {A}
in context like this, but we can do so with a clear syntactic conscience and out of context, assuming we know what & and ~ mean, because & has effective category s<s>n D /<s<s>n D / s<s>n D /> and the whole complex (0007 & ~0005) then has the structure s n D /<s> [s n D /<s>< s n D /<s> s n D /<s> > (s n D /<s> s n D /<s> [s<s>(s n D /<s>)])]. We might even go so far as to allow variables to take the place of operator symbols and introduce operators which bind operator variables. But how this would go in practice and what benefits it might bring are something I have not gone into. We can now see why quantifiers appear to hover uncertainly between the categories s<s> and s<s>. In their effect they are closely akin to functors of category s<s>, and in simple cases where the variable occurs only once in the matrix they can be replaced by such functors. On the other hand, disregarding their marker categories, they look like ordinary s<s> functors, and indeed this is the way they are effectively treated by those logicians who allow vacuous quantification as well-formed. We can now see that there is nothing syntactically objectionable in this. On the other hand the meaning of quantifiers makes it understandable why Frege and LeĞniewski should have disallowed vacuous quantification, insisting that some marker categories be connected to places within any quantifier’s scope. Both alternatives can be accommodated within ECG, though of course the more usual grammar allowing vacuous quantification is simpler. The Frege/LeĞniewski syntax places restrictions not only on the overall category of the operand but also on its admissible structure: it must contain at least one place of relevant marker category and this place must be linked to that in the operator’s marker category list. Now that we see that variable-binding quantifiers are not in fact of category s<s>, we do not need to explain why they also appear to be of category s<s>, s<s> etc. So although with Geach’s Rule such flexibility is already explicable within ordinary CG, that is here irrelevant, and our account works also for strict ECGs where Geach’s Rule does not hold.
256
Peter Simons
6. Combinatorial Semantics ECG is a kind of syntax, and tells us nothing about the semantics of formal languages. However, the close parallels between syntax and model-theoretic semantics have been one factor encouraging the widespread use of CGs, so it is important to consider how such methods may be extended to accommodate operators as conceived in ECG. The next two sections present a new kind of semantics for a range of formal languages. The approach, which I call combinatorial semantics, was initially developed to provide a theory of extensional meaning for LeĞniewski’s Ontology (see Simons 1985). The motivation there was to avoid obvious ontological commitment to abstract entities, which as a nominalist LeĞniewski could not accept. Combinatorial semantics appears on the face of things also to be Platonistic. The question whether this appearance is deceptive will be here left aside: independently of the ontological issue the approach has a naturalness which recommends it for itself. In my previous paper I considered a language, that of LeĞniewski’s Ontology, containing only one variable-binding operator, a categorially flexible universal quantifier (so flexible that LeĞniewski regarded it as syncategorematic). So although the general methods of combinatorial semantics there developed do not accommodate such operators, the single exception could be coped with ad hoc. Semantics for formal languages is usually done in pursuit of an account of logical truth and validity, soundness and completeness for a particular logic. This is not what is at stake here, where, except for some remarks on logical constants, we are concerned not with logic as such but with investigating the connections between syntactic and semantic combination. The goal is to present a pattern of what Kaplan calls a “logically perfect language” (see Kaplan 1970, p. 283), that is, one in which syntactic and semantic combination and evaluation are in perfect harmony. Such a language may, but need not, be suitable as a basis for a logical system. 6.1. Ways of Meaning Basic to the theory is the unanalysed concept of an (extensional) way of meaning. This choice of primitive embodies rejection of the idea that being meaningful always or usually involves being assigned some kind of object as meaning (extension). This kind of denotational semantics, which we find in embryo in Frege, and which is continued in Carnap and the model-theoretic tradition, treats all expressions as names, the
Languages with Variable-Binding Operators
257
differences amongst them being only in what they name. The most common kind of semantics assigns each categorematic expression some object from a set-theoretic hierarchy. This not only couples us from the start with a Platonistic ontology, it also underrates the semantic differences between categories of expressions. Thus I say not that an expression has this or that object as its meaning, but rather that it means in this way or that, thus or so. Nominalizing these “thuses,” one may then speak of ways of meaning. However, having made this point, I shall also now allow myself to speak simply of meanings. Ways of meaning come in kinds, called modes of meaning. By design, there is one mode per syntactic category. So there is one mode for sentences, another one for names, another for intransitive verbs, and so on. We might alternatively call modes of meaning semantic categories. The mode of meaning of a functor expression (and hence of its category) is determined uniquely by the modes of its inputs in order and of its output. So the modes of functor categories are constructed recursively in parallel to the categories. For most formal languages we need only consider the two basic categories of sentence and name. Since we are concerned only with extensional semantics, the mode of sentences is to have a truth-value, or, as one might say, be truth-valued. The mode of meaning of names is to designate. Coextensional expressions mean in the same way (this is an extensional semantics), so for sentences to be coextensional is for them to be materially equivalent, while for names to be coextensional is for them to designate the same object(s), and coextensionality for functor categories is defined in terms of coextensionality for their simpler input and output categories. If we assume given a fixed supply of meanings for each basic category, then the meanings deriving from these for functor categories are given as follows. Assuming given meanings for the categories a, b 1 , . . . , b n , we obtain a meaning for category a by specifying for each possible combination of input meanings of categories b 1 , . . . , b n in order, which meaning of category a is obtained as output. For example, the meanings for category s<ss> may be represented by the usual truth-value tables, since these precisely tell us which truth-value we obtain as output for each combination of truth-values as inputs. Combinatorial semantics simply generalizes this idea. Where meanings for functor categories may be tabulated, we may speak in general of semantic tables. If there are M(a) meanings of category a and M(b i) meanings for category b i, 1 d i d n, then there are altogether M(a) M(b 1 )x . . . xM(b n )
258
Peter Simons
meanings of category a. To take a familiar example: if we have just two truth-values, then there are 22x2 = 16 ways of meaning for binary sentential connectives. 6.2. Categorial Languages Interpreted A language is (fully) interpreted iff each of its categorematic words means in some way appropriate to its category. We require an interpretation to be unambiguous, that is, no expression may mean in more than one way at once on this interpretation. We do not consider partial interpretations, where some words are left meaningless. However, by allowing as a way of meaning for names that of designating no individuals, and as a way of meaning for sentences that of having no truth-value, we are able to accommodate reference gaps and truth-value gaps. This is an advantage of considering ways of meaning rather than entities meant. The ways of meaning actually available for expressions depend, as we have seen, on those available for the basic categories. In most cases we have to consider, we need worry only about the truth-values and the domain of individuals. A bivalent interpretation, on which sentences may only be true or false, offers fewer possibilities for sentences and functors derived using s than multi-valued interpretations and/or those admitting truth-value gaps. Likewise if we consider two domains of individuals, one properly containing the other, then the larger offers a wider range of ways of meaning for names and functors derived using n than the smaller. We may also restrict interpretations to a subset of the ways of meaning which are available. For instance, we might deliberately restrict ways of meaning for sentences to being true and being false, even though others are available. Or we might restrict names to designating exactly one individual, as in standard predicate logic, or to designating not more than one individual, as in certain free logics, or to designating at least one but not all individuals, as in Aristotle’s syllogistic. Given a larger number of truth-values or a larger domain, we can always simulate the effect of having available only a smaller number of truth-values or a smaller domain by restricting interpretations in this manner. The ways of meaning interpretations allow among those available are the admissible ways of meaning. When no restrictions are made, the admissible ways are all those available. On a given interpretation the meaning of a complex expressions is jointly determined by the meanings of its words and its syntactic structure. Thus if expression X, Y1 , . . . , Yn of categories a, b 1 , . . . , b n have meanings, then the meaning of X(Y1 , . . . , Yn ) is the
Languages with Variable-Binding Operators
259
output meaning of X for the input meanings of Y1 , . . . , Yn in that order. By induction, every expression we can form in the language has a unique meaning on the interpretation, and the meaning of the whole is evaluated in terms of the meanings of its parts in the same order in which the whole expression is syntactically constructed of its parts. In these respects combinatorial semantics resembles the more familiar semantics of functions. We must distinguish the two kinds of semantic simplicity: the simplicity of meanings of expressions in basic categories and the simplicity of words. A word simply has its meaning (means in its peculiar way) without further ado, but a word may be of any category and there is no necessity that a CL have words in all of its basic categories. The meanings in the basic modes are simple in that they do not involve other meanings, whereas the meanings of a functor mode are defined in terms of those of its inputs and outputs. It will be noted that no expression is variable in meaning within a given interpretation, and any expression can be given a different meaning on another interpretation. This may seem strange if we are accustomed to distinguishing as special those expressions whose meaning is the same on all interpretations, such as the logical constants. That certain symbols are given the same meaning on all interpretations is however dictated in the semantics of logical systems by the need to distinguish between logical and non-logical expressions for the purposes of defining logical truth and validity. It would not be to the purpose if for example the sign ‘&’ sometimes meant conjunction, sometimes disjunction, sometimes material implication etc. But of course there is nothing inherently forbidden about assigning signs for connectives different meanings. 6.3. Logical Constants Within the present framework we can nevertheless make a natural distinction between logical and non-logical meanings, which can then be used to define the concept of a logical constant for expressions of extensional categorial languages based on the categories s and n. Given that logic is about truth-preservation of arguments, the truth-values are logical meanings, so any sentential word is a simple logical constant, as is any word of a purely propositive category, that is, a category whose index contains no letters other than s’s. Suppose we have a fixed domain of individuals for interpreting names. A permutation of the domain is a one-one correspondence of the domain with itself. Permutations of the domain induce in a well-defined way permutations on the meanings of those categories which are not purely propositive, that is, those whose
260
Peter Simons
index contains an n. For instance, if i is an individual in the domain, then designating i is a way of meaning for names, and if a permutation P carries i to j = P(i) then it carries the way of meaning of designating i to that of designating j. Similarly if c is a class of individuals then one way of meaning for one-place predicates is to yield truth as output for designating a member of c as input and falsehood otherwise (i.e. having c as its extension). The permutation P sends c to another class d, so it sends the predicate meaning to that for which d is the extension. And so on. Those meanings which are invariant under all permutations of the domain (such as designating nothing, or all individuals, or the meaning of the identity predicate) are logically constant with respect to the domain in question, and any word which has one of them as its meaning is a simple logical constant with respect to the domain. The most obvious example is the identity sign ‘=’. We may then define further complex logical constants in terms of those obtained hitherto (e.g. difference as non-identity). This idea is due to Tarski (see Tarski 1986), and it can be used in conjunction with Bolzano’s procedure of variation to explicate the concepts of logical constant, logical truth and validity for a range of bivalent extensional languages (see Simons 1987). However this characterization of logical constants will not suffice as it stands to exhibit as logical such operators as the usual quantifiers or Russell’s description operator, because we have yet to cover their semantics. To this we now turn.
7. The Same, Extended An integrated linguistic theory of operator/variable languages has to provide both a syntax and a semantics adequate to account for them. The formal semantics of logical languages have usually managed to cope well enough with variable-binders because these have been kept to a small number (typically a few quantifiers and abstraction operators) which are reckoned among the logical constants, so their semantic effect can be given in each case ad hoc by special clauses. On the other hand a general semantics for variable-binders has not been forthcoming. Variable-binders do not have to be logical constants. We now extend the combinatorial semantics of the last section to accommodate operators of both kinds mentioned earlier: the variable-binding and the place-marking, in such a way that the semantics as far as possible respects and mirrors the syntax, as for unextended CGs.
Languages with Variable-Binding Operators
261
7.1. Meanings for Operators Despite the differences between functors and operators, it is worth always bearing in mind the close connections between them. Variable-binding operators would be unnecessary if we only ever bound one occurrence of each variable in the outermost level of structure: instead of the quantifiers of category s n/ <s> we could use the associated functors of category s<s>, for instance. Reflecting on this similarity helps us to see how operators work. Taking the universal functor everything as our example, we see that it yields truth as output for the universal s functor as input, and falsehood as output for all other inputs. The universal s functor is the one which yields truth for every singular nominal input. We know that a sentence of standard predicate logic of the form 0005x{A(x)} is evaluated as true iff no matter what singular designating meaning we give to ‘x’, the truth-value of the result of evaluating the open sentence ‘A(x)’ with this meaning of ‘x’ is truth. So the effect of the universal quantifier can be pictured in the following procedural terms: the quantifier as it were successively inputs “messenger” values of ‘x’ to all the relevant positions in the formula within its scope, evaluates the resultant truth-value and stores it next to the value of ‘x’ input. Call this procedure tabulation. When tabulation is complete for all admissible values of ‘x’, the quantifier then delivers its own output: truth if all the resultant values are truth, falsehood otherwise. We can then predict that if the open sentence has the same outputs for inputs as the universal s functor, the quantifier will output truth, otherwise falsehood. In contrast to the functor however, the operator carries with it in the form of its marker variable the means to penetrate to arbitrary depths of structure within its scope. The procedure is the same no matter how complex the structure of the scope is, only the evaluation is more or less involved. The nesting of operators is also no problem: the results issuing from inner operators are passed on in the tabulations carried out for those lying further out, the values for bound variables issuing from outside the scope of the operator currently being evaluated being temporarily held fixed in the course of the inner variations. We have variations within variations. Consider a second example: a definite description operator, taken as a genuine nominal operator of category n n/ <s>. The complex term (name) is Lx{A(x)} for some suitable open sentence A(x) and we assume L inputs as “messengers” to its matrix singular designating nominal meanings. If on
262
Peter Simons
tabulation exactly one such meaning input yields the resultant truth, the operator outputs this nominal meaning; otherwise it outputs a suitable “default” value, which may vary according to the description theory. The alternatives will be considered more fully below. For the last example we take a Fregean-style place-marking operator, one which could be used in mathematics. Consider how we may write the value of the derivative of a function at a point, say the function sin(x) + cos(S/3) for the argument S/3 (the value is 0.5). It would not do to write d/dx(sin(S/3) + cos(S/3)) because it is not clear which function it is which is being differentiated. A better notation, which says all we need and is widely used, is d/dx[(sin(x) + cos(S/3))] x = S/3 However, if we indicate the arguments of the function with respect to which we are differentiating by means of a Greek suffix to a differential operator D, and mark their places within the scope using the same Greek letters as suffixes, then we can insert the argument expression ‘S/3’ at this very place, thus: DĮ/ {sin((S/3)Į ) + cos(S/3)} and we have achieved the same result in a more compact way. The subscript enables us to distinguish the two places where ‘S/3’ occurs, the first as being bound into, the second as not. The meaning of ‘D’ then works as follows. For each possible meaning of any expression which can occupy the places marked with its Greek letter, it evaluates the result of combining this meaning at the places marked by the Greek letter with the others meant by the expressions within the operator’s scope, as directed by the structure of the matrix. It tabulates the resulting output meanings against the input meanings and so arrives at the resultant meaning of its matrix (which will be of category n, a monadic function). In our case it will “recognize” by its table the function sin(x) + cos(S/3). Then the differential operator will operate on this function, yielding another function, in this case the derivative cos(x). To complete the process the meaning of the expression in the place(s) marked by the Greek letter is fed into the derivative and its value obtained. We get cos(S/3) = 0.5. This is then finally output as the result of the operation.
Languages with Variable-Binding Operators
263
All of this sounds very long-winded and time-consuming. We have expressed the action of the operator in procedural terms, but of course the stages are not run through temporally. However, the order of the three stages is essential and cannot be changed: (1) tabulate the operand, (2) operate on it, (3) apply the result to the value(s). This is exactly the sequence carried out if we use lambda-abstraction to extract a function, modify it with a functor and then apply it. It is an indication that our intuitive view of Fregean operators as telescoping three distinguishable moves is correct. 7.2. Application: Some Logical Operators We noted above that Tarski’s idea of the permutation of the domain of individuals can be used to provide necessary and sufficient conditions for an expression to mean a logical constant. This may be extended to variable-binding operators. We shall show that the meanings of the universal quantifier binding individual variables (category s n/ <s>) and some (but not all) definite description operators (category n n/ <s>) are logical constants. Recall that meanings in a simple CG are logical iff they are invariant under permutations of the domain of individuals. That is, if M is a meaning and P a variable ranging over permutations extended to all meanings, M is logical iff for all P, P(M) is coextensional with M. Coextensionality for sentences is material equivalence, for names is denoting the same individual(s), and for a functor category two meanings are coextensional (coex) iff they always give coextensional output for coextensional inputs. The effect of a permutation P on a meaning M of functor category a is given by for all B1 in b 1 , . . . , Bn in b n : P(M)(B1 . . . Bn ) coex P(M(P–1 (B1 ) . . . P–1 (Bn )). Now we need to say how permutations affect operators. Again it is instructive to recall how operators of category a de . . . / c<de . . . > . . . >. The effect of P on a functor F of category a. The effect of P on it in context, where we have an expression of the form Q DE . . . / {B(D, E, . . . ), C(D, E, . . . ) . . . }
264
Peter Simons
where ‘B(D, E, . . . )’ and ‘C(D, E, . . . )’ stand for possibly complex contexts of categories b and c, in which variables of categories d, e, . . . may occur, is given by P(Q)DE . . . / {B(D, E, . . . ), C(D, E, . . . ) . . . } coex P(QDE . . . / {P–1 (B(D, E, . . . ), P–1 (C(D, E, . . . ), . . . }) Since the output of Q is of category a it is clear how the first P works, but we must say what is meant by P–1 (B(D, E, . . . ) etc. It cannot mean just the result of applying P–1 to the complete expressions of categories b, c, etc. For if this were so, all operators of the category sn/<s> for instance would be logical because the truth-values are logical constants. But not all quantifiers of this category are logical. Consider the quantifier ‘Eng’ defined by Eng x/ {A(x)} = Def. for all x, if x lives in England, then A(x). Clearly this is not logical, since one permutation switches England and France and nothing else, and it is certain that the attributes shared by all inhabitants of England are not the same as those shared by all inhabitants of France (‘x lives in England’ for instance) . So the effect of the internal P–1 s must take account of the fact that the matrix expressions contain bound variables. The effect is this: the outputs for inputs are tabulated for each matrix as usual. The categories of the resulting meanings are indeed b<de . . . >, c<de . . . > etc. We then apply P–1 to these meanings in the usual fashion of functor expressions. The resulting meanings are likewise of the categories b<de . . . >, c<de . . . > etc. It is on them that the meaning of Q acts, and then the result is acted on by P. So let us consider the universal quantifier 0005, of category s n/ <s>, and write the variable now in inward slanting brackets because we shall be operating on the ‘0005’ part of the symbol. We need only consider the case where the matrix A(x) contains no other bound variables than x, because in any other cases, where other operators whose scope includes the quantifier expression 0005 x/ {A(x)} and other bound variables occur in the matrix, whenever the meaning of this quantifier takes effect, all other variables are being held constant in the course of compiling meaning tables for the outer operators. We assume bivalence. The meaning of 0005 is that it yields truth if the matrix yields truth for all nominal meaning inputs confined in standard fashion to the designating of a single existing individual. Otherwise, we get falsehood. We suppose given an arbitrary domain D and a permutation P of D. The case of the empty domain is trivial so suppose D non-empty. The effect of P on 0005 is
Languages with Variable-Binding Operators
265
P(0005) x/ {A(x)} l P(0005 x/ {P–1 (A(x))}) (coextensionality for category s is material equivalence). The effect of P on truth-values is nil, so we have P(0005) x/ {A(x)} l 0005 x/ {P–1 (A(x))} What then is the effect of P–1 on the matrix A(x)? The effective category of this matrix is s and the effect of P–1 on functor meanings F of category s is given by for all x: P–1 (F)(x) l P–1 (F(P(x)) since (P–1 ) –1 = P. But P–1 for category s has again no effect, so for all x: P–1 (F)(x) l F(P(x)) The extension of P–1 (F) is the class of all individuals which P sends into the extension of F, i.e. it is the image of the extension of F under the inverse of P, as we should expect. So ‘0005 x/{P–1 (A(x))}’ is true if and only if matrix P–1 (A(x)) yields truth for all singular nominal meaning inputs. But this is so if and only if A(x) yields truth for all such inputs, since permuting the individuals then makes no difference. Hence 0005 x/ {P–1 (A(x))} l 0005 x/ {A(x)} whence P(0005) x/ {A(x)} l 0005 x/ {A(x)} so the meaning of ‘0005’ is invariant, which was to be shown. Hence ‘0005’, being a simple expression, is a simple logical constant. Consider now a definite description operator L of category nn/<s> whose effect on any sentential matrix A(x) is as follows: if the matrix yields the output truth for exactly one singular nominal input, this nominal input is the output of the operator. Otherwise, the output is the null nominal meaning, that of designating no individuals. We have then P(L) x/ {A(x)} = P(L x/ {P–1 (A(x))}) where ‘=’ here expresses coextensionality for (non-plural) names: designating the same individual or both designating no individuals. Take the two possible kinds of case. Suppose the matrix A(x) is not uniquely satisfied. Then neither is P–1 (A(x)), since permutations preserve cardinality. So the effect of L on P–1 (A(x)) is to output the null nominal
266
Peter Simons
meaning, and P, which permutes individuals, leaves this alone. Again, since permutations preserve cardinality, P–1 (A(x)) is uniquely satisfied iff A(x) is, and the output is the image of the output of A(x) under P–1 . If the individual a is the unique satisfier of A(x) and N(a) is the nominal meaning of designating precisely a, then the nominal meaning designating the unique satisfier of P–1 (A(x)) is N(P–1 (a)). This is then output by L and the effect of P on it is of course just to take us back to N(a) again. Hence L is invariant under P, which was to be shown. There are other definite description operators which differ from this on their default values, i.e., in their action for improper descriptions. 12 One sort assigns improper descriptions as output in effect the class of individuals satisfying the matrix. Since we are not guaranteed to have classes here we must consider plural nominal meanings, those of designating more than one individual. It can easily be seen that this sort of description operator is a logical constant too. Another sort makes the default value that of designating the whole domain. Since permutations trivially leave the domain unaltered this too is a logical constant. Another kind is the selected object theory, in which all improper descriptions are assigned the same nominal meaning of designating a selected individual. This sort of description operator is, interestingly, not a logical constant, for having assigned the improper description P-1 (A(x)) the selected object *, P acts on *, and for many permutations P, P(*) z * (* is not a fixed point of the permutation). Some description theories insist that * be outside the domain. As a piece of trickery, this solves the problem, but it is arbitrary: it amounts to saying that some individual is not “really” an individual. So logicians should disapprove of selected object description operators: they are not logical constants. In similar fashion we can show that other familiar variable-binders such as numerical quantifiers, the binary quantifier more from §5, and the lambda abstractors, are all logical constants. These are not surprising results, but it is reassuring to have support for one’s intuitions and prove what one previously assumed. On the other hand the set abstraction operators are not logical constants if sets are construed as (abstract) individuals subject to the permutations of the domain.13 It is not clear that this is how sets are to be construed, but that is an issue best left for another occasion.14 12 Both classical and free logics have offered several theories of descriptions. For a survey of the possibilities in free logics, see Bencivenga (1986), pp. 415-421. 13 As in Scott (1967). 14 Tarski (1986, pp. 151-153) notes that if sets are construed as individuals and set-membership as an undefined primitive, it is not a logical relation, whereas if
Languages with Variable-Binding Operators
267
University of Leeds School of Philosophy Leeds, LS2 9JT, UK e-mail: [email protected]
REFERENCES Ajdukiewicz, K. (1935). Die syntaktische Konnexität. Studia Philosophica 1, 1-27. Reprinted in: D. Pearce and J. WoleĔski (eds.), Logischer Rationalismus (Frankfurt am Main: Athenäum, 1988), pp. 207-226. English translation: Syntactic Connexion, in: S. McCall (ed.), Polish Logic 1920-1939 (Oxford: Clarendon Press, 1967), pp. 207-231. Bencivenga, E. (1986). Free Logics. In: D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, vol. III, pp. 373-426. Dordrecht: Reidel. Benthem, J. van (1988). The Lambek Calculus. In: Oehrle et. al., eds. (1988), pp. 35-68. Buszkowski, W., W. Marciszewski and J. van Benthem, eds. (1986). Categorial Grammars. Amsterdam: Benjamin. Cresswell, M.C. (1973). Logics and Languages. London: Methuen. Geach, P.T. (1971). A Program for Syntax. Synthese 22, 3-17. Reprinted in: D. Davidson and G. Harman (eds.), Semantics of Natural Language (Dordrecht: Reidel, 1972), pp. 483-497. Kaplan, D. (1970). What is Russell’s Theory of Descriptions?. In: W. Yourgrau and A.D. Breck (eds.), Physics, Logic and History, pp. 277-285. New York: Plenum. Lambek, J. (1958). The Mathematics of Sentence Structure. American Mathematical Monthly 65, 154-169. Lejewski, C. (1967). A Theory of Non-Reflexive Identity and Its Ontological Ramifications. In: P. Weingartner (ed.), Grundfragen der Wissenschaften und ihre Wurzeln in der Metaphysik, pp. 65-102. Salzburg: Pustet. Luschei, E.C. (1962). The Logical Systems of LeĞniewski. Amsteram: North-Holland. Montague, R. (1973). The Proper Treatment of Quantification in Ordinary English. In: J. Hintikka, J. Moravcsik and P. Suppes (eds.), Approaches to Natural Language, pp. 221-242. Dordrecht: Reidel. Reprinted in: R. Montague, Formal Philosophy (New Haven, CT: Yale University Press, 1974), pp. 247-270. Oehrle, R.T., E. Bach and D. Wheeler, eds. (1988). Categorial Grammars and Natural Language Structures. Dordrecht: Reidel. Quine, W.V.O. ([1940] 1951). Mathematical Logic. Revised edition. Cambridge, MA: Harvard University Press. Scott, D. (1967). Existence and Description in Formal Logic. In: R. Schoenman (ed.), Bertrand Russell, Philosopher of the Century, pp. 181-200. London: Allen & Unwin. Simons, P.M. (1981). Unsaturatedness. Grazer Philosophische Studien 14, 73-96. Simons, P.M. (1983). Function and Predicate. Conceptus 17, 75-90. Simons, P.M. (1985). A Semantics for Ontology. Dialectica 39, 193-216. Simons, P.M. (1987). Bolzano, Tarski, and the Limits of Logic. Philosophia Naturalis 24, 378-405. set-membership is construed as a kind of relation crossing adjacent logical types in the sense of Russell, then all such relations (there are many) are logical.
268
Peter Simons
Simons, P.M. (1988). Functional Operations in Frege’s Begriffsschrift. History and Philosophy of Logic 9, 35-42. Simons, P.M. (1989). Combinators and Categorial Grammar. Notre Dame Journal of Formal Logic 30, 241-261. Suszko, R. (1958). Syntactic Structure and Semantical Reference I. Studia Logica 5, 213-244. Tarski, A. (1986). What Are Logical Notions? History and Philosophy of Logic 7, 143-154.
Urszula Wybraniec-Skardowska ON THE FORMALIZATION OF CLASSICAL CATEGORIAL GRAMMAR
1. Ajdukiewicz’s Assumptions The languages of formal logic and mathematics are most often built according to the basic principles of the theory of syntactic categories. The theory, which was constructed by LeĞniewski (1929, 1930) for symbolic languages of systems of protethetics and ontology, was improved upon by Ajdukiewicz (1935) and made use of in the general description of language, including fragments of natural language. When considering Ajdukiewicz, and to some extent also Bar-Hillel (1953), in characterizing language and the categorial grammar that generates it, several interrelated syntactic factors must be taken into consideration. We shall discuss them below, explicating them for the needs of formalization. 1.1. Categorisation Every word in the vocabulary of a given language is taken as belonging to a definite syntactic category. Everyone of the compound expressions formed from the words in the vocabulary – that is the simple words of the language – is assigned exactly one syntactic category. Syntactic categories of expressions are distinguished with respect to the syntactic role which the expressions perform. They are divided into the basic and other functorial ones. Functorial categories create a branched hierarchy similar to that of Russell’s types. They are used for showing the general principles of the concatenation of words in syntactic entities.
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. 269-288. Amsterdam/New York, NY: Rodopi, 2006.
270
Urszula Wybraniec-Skardowska
1.2. Functorialibility Every well-formed compound expression of language has a functorargument structure: one may distinguish in it one constituent called the main functor and other constituents, called arguments of the functor, with which it forms the expression as a linguistic entity. Also, every constituent of a given expression which is not a simple word has a functor-argument construction. Well-formed compound expressions of language are functorial in this sense. In the “functorial analysis” of a given expression each of its functors is an operation, a function which together with other expressions of the language yields the new, more compounded expression. The value of every such function-functor of a given expression for arguments which are its constituents, is always a constituent of the given expression (the expression itself may be a constituent of the given expression). The “functorial analysis” of every concatenation of the words in the vocabulary leads, in Ajdukiewicz’s framework, to examining whether a function-argument recording corresponds to the concatenation: all the functors precede their arguments as appropriate (here in parentheses). Let us consider, for instance, compound expressions of the language of arithmetic: a. 4 > 2 0010 1,
b. 2 0010 1 > 00101,
c. (5 > 2) = 1.
The parenthetical recordings aƍ, bƍ, cƍ and diagrams of trees meant to explicate them, Ta, Tb, Tc, show a natural, phrasal “functorial analysis” of these expressions. The dotted lines show functors. Ta. 4 > 2 0010 1
4
>
200101
2
0010
aƍ. (4) > ((2) 0010 (1))
Tc. (5 > 2) = 1
Tb. 2 0010 1 > 00101
1
2
200101
>
00101
0010
1
0010
1
bƍ. ((2) 0010 (1)) > (0010 (1))
5
5>2
=
>
2
1
cƍ. ((5) > (2)) = (1)
Appropriate function-argument recordings a f, b f, c f and diagrams of trees: Ta f, Tb f, Tc f show “functional analysis” of expressions a, b, c in Ajdukiewicz’s prefix notation.
271
On the Formalization of Classical Categorial Grammar
Ta f. 4 > 2 0010 1
>
4
200101
0010
2
a f. > (4, 0010 (2, 1))
Tc f. (5 > 2) = 1
Tb f. 2 0010 1 > 00101
1
>
200101
00101
0010
2
1 0010
b f. > (0010 (2, 1), 0010 (1))
1
=
5>2
1
>
5
2
c f. = (> (5, 2), 1)
The “functorial analysis” of expressions a, b, c leads to the statement that they are functorial expressions of the language of arithmetic. The functorial expressions of a language may (though they need not) be its well-formed expressions, in short wfes. a and b are such expressions, while c is not. Let us note here that the structurally ambiguous expression 5 > 2 = 1 is not a functorial expression as it is impossible to distinguish the main functor in it. It is also easy to check that, e.g. the expression 5 > (= 2) is not a functorial expression. Let us note that the “functorial analysis” of a, b, c given here is unambiguously determined due to the semantic functions of the signs ‘>’, ‘=’ and ‘0010’: the first two are signs of two-argument relations between numbers, the third one in a denotes a two-argument number operation, while in b it also denotes a oneargument operation. The mentioned signs, as functors, and thus as functions on signs of numbers, have as many arguments as their semantic correlates have. Unambiguous “functorial analysis” is a feature of the languages of formal sciences. In relation to natural languages the analysis depends on linguistic intuition and often allows for a variety of possibilities (see e.g. Marciszewski 1988b). Traditional phrasal linguistic analysis, formalized by Chomsky (1957) in his grammars of phrasal structures, takes into consideration grammatical phrasal analysis. It imposes in particular the “functorial analysis” of sentence a which is shown in parenthetical recordings Ɨƍ and a f and suitable trees TƗƍ and TƗ f. Expressions Ɨƍ and Ɨf indicate that a is treated here as the functorial expression in which the sign ‘>’ is not the main functor. It is here a functor-forming functor whose only argument is the term ‘2 0010 1’.
272
Urszula Wybraniec-Skardowska
TƗƍ. 4 > 2 0010 1
4
TƗ f. 4 > 2 0010 1
>200101
>
>
200101
2
0010
4
>200101
1
200101
0010
Ɨƍ. (4) ( > ((2) 0010 (1)))
2
1
Ɨ f. ( > (0010 (2, 1))) (4)
The two different “functorial analyses” of sentence a given above are equipollent from the point of view of the syntax of logic. In first-order predicate calculus two logical forms, R(x, y) and P(x), correspond to sentence a. In Ajdukiewicz’s conception categorization does not lead, however, to maintaining the view that “functorial analysis” of a linguistic expression must be determined unambiguously but to the statement that the categorization refers to expressions of a determined functor-argument structure. 1.3. Assigning Indices The method of categorizing functorial expressions by assigning them categorial indices that determine whether they belong to a given syntactic category was introduced by Ajdukiewicz (1935) and is a fundamental idea of categorial grammar. Every categorial index is here a kind of metalanguage variable symbol whose scope is an established syntactic category. The index of an expression of a basic category is a single letter, e.g. ‘s’ stands for expressions of sentential category, ‘n’ for the category of nominal expressions. In Ajdukiewicz’s conception indices of functors of functorial categories have a fractional notation, which is quasi-arithmetical: the index of the expression which is formed by a functor and its argument is placed above the line, indices of its subsequent arguments are placed below the line. Categorial indices permit description of the categorial structure of every functorial expression. This is so because to every simple word which is part of the expression there corresponds exactly one index appropriate to its form and functorial indices determine indices of its compound constituents. Indices of simple words which are parts of the expression determine its
273
On the Formalization of Classical Categorial Grammar
indexing term, which originates from its function-argument notation (possibly from a parenthetic notation complying with the natural order of simple words) by substituting in it corresponding indices for all its simple words. The indexing term thus has not only a structure wholly corresponding to its functorial structure but also determines its categorial structure (both internal and external). This makes possible determining the syntactic categories (indices) of all the compound constituents of the expression (including the expression itself) by means of the syntactic categories (indices) of their main functors, and, more precisely, of the syntactic categories (indices) of the expressions formed by them, according to the following principle of reduction of indexing terms to simple indices: (p)
If f is an index of the main functor, whose arguments have indices y x 1 , . . . , x n and if f takes the shape of , then z1 , . . . , z n
f (x1 , . . . , xn ) = y (or (x1 , . . . , xk) f (xk+1 , . . . , x n ) = y). Let us consider, for example, indexing terms i(b f), i(bƍ), i(cf), i(Ɨƍ) of expressions b, c, a in notations b f, bƍ, cf and Ɨƍ, respectively. The “categorial analyses” of expressions b, c, a in this notation are explicated by diagrams of trees of categorial indices Ti(b f), Ti(b), Ti(cf), Ti(Ɨƍ) formed from diagrams of trees Tb f, Tb, Tcf, TƗƍ by substituting for each expression its categorial index. For fractional indices we use here slash signs instead of horizontal lines. s
Ti(b f)
s/nn
n
n/nn
n
s
Ti(b)
n
n n/n
i(b f) s/nn (n/nn (n, n), n/n (n))
n
n
n
n/nn
s/nn
n
n
n/n
n
i(bƍ) ((n) n/nn (n)) s/nn (n/n (n))
274
Urszula Wybraniec-Skardowska
s
Ti(cf)
s
Ti(Ɨƍ)
s/nn
s
n
s/nn
n
n
i(cf) s/nn (s/nn (n, n), n)
n
s/n
s/n//n
n
n
n/nn
n
(Ɨƍ) (n)(s/n//n ((n) n/nn (n)))
It is clear that “moving” in the diagrams of trees of categorial indices from the bottom to the top in order to determine the indices of compound constituents of defined expressions makes use of principle (p). Ordinary transformations of functional formulas are made use of here according to the principle. For i(b f) and i(cf) we obtain: (1) (2)
s/nn (n/nn (n, n) n/n (n)) = s/nn (n, n/n (n)) = s/nn (n, n) = s, s/nn (s/nn (n, n), n) = s/nn (s, n) = s.
For i(bƍ) and i(Ɨƍ) we have: (3) (4)
((n) n/nn (n)) s/nn (n/n (n)) = (n) s/nn (n/n (n)) = (n) s/nn (n) = s, (n (s/n//n ((n) n/nn (n))) = (n) (s/n//n (n)) = (n) s/n = s.
Let us note that the symbol ‘0010 ’ in the “functorial-categorial analyses” of expressions b f and bƍ given here is assigned two different syntactic categories; likewise, the symbol ‘>’ in the analyses of expressions c f and Ɨƍ. Each of these symbols performs here not only two different syntactic functions but also two semantic functions, which allows each one to be treated as two distinct simple words of the language of arithmetic. Similarly we distinguish between homonyms as structurally ambiguous expressions in natural languages. Many equiform or indiscernible expressions may be assigned more than one categorial index. We differentiate them, e.g. by investing them with some additional signs and assign exactly one categorial index to them according to their form. Let us note that the analysed expressions a, b, c belong to the category of sentences. This does not, however, mean that they are all sentences of the language of arithmetic. The functorial expression c is not a sentence.
On the Formalization of Classical Categorial Grammar
275
1.4. Syntactic Connection Whether a given functorial expression with a set index is a well-formed expression of the language (wfe), i.e. whether it is syntactically connected, and whether it is, in particular, a sentence of the language, depends on whether each of its constituents is well-formed, i.e. it is a simple word or functorial expression which satisfies the following grammatical rule establishing the relation between the index of the main functor of the given expression and the indices of this expression and of the subsequent arguments of the functor: (r)
If f (x1, . . . , x2 ) = y (or (x1 , . . . , xk) f (xk+1 , . . . , xn ) = y), then y f= x1 , . . . , x n
Rule (r) may be called the rule of syntactic connection. It states that the index of the main functor of any functorial expression is the functorial index whose numerator is the index of expression that the functor forms and the indices of the subsequent argument of the functor are the denominator. It may be seen that expression c is not a wfe: one constituents of c does not satisfy rule (r) (formula s/nn (s, n) = s, holds here, see Tcf and (2), and s/nn  s/sn). On the other hand, all the constituents of expressions bf, bƍ and Ɨƍ satisfy rule (r) (cf. (1), (3), (4) and Tb f, Tb, TƗƍ) and accordingly, expression b as well as a, according to the “functorial analysis” Ɨƍ, are wfes. The algorithm for the examination of the syntactic connection of expressions, similar to the procedure used by Ajdukiewicz, amounts to checking whether functional formulas whose starting point is the indexing term of the expression are transformed successively according to principle (p) and yield a single index according to rule (r). We do not obtain, in particular, a single index by applying rule (r) for the indexing term of expression c (cf. (2)). We have only: s/nn (s/nn (n, n), n) = s/nn (s, n). Let us note that the converse implication to (r) holds for any constituent of functorial expression in virtue of (p) (r 1 )
If f =
y , then f (x1 , . . . , xn ) = y x1 , . . . , x n (or (x1 , . . . , x k) f (xk+1 , . . . , xn ) = y).
276
Urszula Wybraniec-Skardowska
When a functorial expression of the language is syntactically connected, rule (r1 ) may be strengthened to an equivalence. That rule (r1 ), which we will call the rule of syntactic connection in Ajdukiewicz’s sense, should hold for any constituent of a functorial expression is a necessary but not sufficient condition for its syntactic connection: rule (r) does not follow from rule (r1 ) ((r1 ) is true when its antecedent is false). Rule (r1 ) corresponds to the following formulas of index transforming: y (x1 , . . . , xn ) = y, x1 , . . . , x n y (x1 , . . . , xk) (xk+1 , . . . , xn ) = y, x1 , . . . , x k x k 000e1 , . . . , x n which in non-parenthetic recording of indexing terms corresponds to the laws of index reduction: y x1 , . . . , xn o y, x1 , . . . , x n y x1, . . . , xk x k+1 , . . . , xn o y. x1 , . . . , x k x k 000e1 , . . . , x n The first was applied by Ajdukiewicz in his procedure for checking syntactic connection, the other derives from Bar-Hillel (1953). 1.5. Substitutability The categorization of the expressions of language in LeĞniewski’s and Ajdukiewicz’s conceptions is based on the views of pure grammar furnished by Husserl (1900-1901), and, especially, on the notion of semantic (syntactic) category as a class of mutually substitutable expressions in contexts possessing uniform meaning. These contexts in a LeĞniewski-Ajdukiewicz’s framework are sentential contexts or, more generally, well-formed ones. The definition of a syntactic category given by Ajdukiewicz may be comprised under the scheme: D Ÿ ( E œ J ),
where D, E , J denote the following expressions: D. E. J.
Expression S(B) is formed from expression S(A) by substituting its for its constituent A the constituent B, A, B are expressions of the syntactic category of sentences. S(A), S(B) are expressions of the syntactic category of sentences.
On the Formalization of Classical Categorial Grammar
277
Introducing syntactic categories in this way causes some difficulties. The definition given above refers to the concept of substitutability and that of a sentence or, more generally, to the notion of a well-formed expression, wfe. These concepts, however, hadn’t been defined earlier. Distinguishing the category of sentences and, generally, the class of wfes determines the language. The concept of a sentence or, more generally, the notion of a wfe of a given language must, therefore, be defined and in such a way as to make it possible to use the algorithm for checking syntactic connection that was given by Ajdukiewicz and discussed in Section 1.4.
2. The Aims of Formalization and the Principles of Their Realization
The concept of categorial grammar introduced by Bar-Hillel, Gaifman and Shamir (1960) for describing and revealing the syntactic structures of language by means of indices (types) has already had its own history (see Marciszewski 1988a, van Benthem 1988). It has also seen the development and elaboration of its formal bases (see Buszkowski 1988, 1989; Wybraniec-Skardowska 1989, 1991). Concentrating here on the formalization of so-called classical categorial grammars we focus upon the axiomatic theory whose assumptions have been described in Section 1 and whose construction is a realization of the aims given in the points (1)-(5) below. The overriding aim of such a formalization, as was stressed in the end of Section 1.5, is: (1)
to provide an exact but, at the same time, general definition of wfe which would support the “functorial-categorial analysis” of its syntactic connection.
Such an analysis, in Ajdukiewicz’s framework, is a set of psychophysical activities, has a functional character, depends on pragmatic conditioning and on treating language expressions as well as indices (which expose their functorial-categorial construction in syntactic analysis) as linguistic concreta, i.e., physical, temporal objects, the socalled object-tokens. This approach pays regard to: (2)
elaborating a concretistic conception of language, as accepted by LeĞniewski, which is based on a primitive metalinguistic characterization of language solely by means of object-tokens and the relations between them.
278
Urszula Wybraniec-Skardowska
At the basis of a formalized theory of language (or grammar) lies: (3)
the striving for a general functorial-categorial characterization of language.
The universal set T of all tokens and the concatenation relation c, which in practice entails connecting tokens either linearly (from left to right, e.g. in European languages, right to left, e.g. in Hebrew or Semitic languages) or non-linearly (e.g. in hieroglyphs and various mathematical formulas), are then the starting point of the formalization. The following two initial vocabularies: the vocabulary V0 1 of a language and its auxiliary vocabulary V0 2 are singled out from set T. Both may include structural symbols, e.g. parentheses, punctuation marks. The first includes the vocabulary V1 of a language, consisting of its simple words, the second its auxiliary vocabulary V2 , consisting of the basic indices that belong to the metalanguage. By means of the concatenation relation c it is possible to generate from the initial vocabularies the set W1 of all the words of the language and the set W2 of all its auxiliary words, respectively. Then, we single out, from W1 , the set E1 of all its expressions, which is the sum of V1 and the set Ec1 of all its compound expressions. On the other hand, the set E2 of all categorial indices, i.e. the sum of V2 and Ec2 of all functorial indices is distinguished from W2 . In a general syntactic characterization of a language, determining the set S of all wfes can not depend on the number or on the shape of simple words, it also can not depend on symbolism, parenthetic or nonparenthetic notation, or the chosen method of connecting words through concatenation. In a general functorial-categorial characterization of the type Ajdukiewicz would approve of, the generation of compound wfes of the set S V1 can depend neither on their specific construction nor on their specific notation and the internal structure of categorial indices which allows one to determine their categorial structure (apart from the notation of functorial indices deriving from Ajdukiewicz, various other ones, e.g. quasi-fractional or parenthetic, are also known; see Marciszewski 1981). We assume with respect to the compound expressions of Ec1 and the functorial indices of Ec2 that they belong to the counterdomains of the relation r1 forming compound expressions and, respectively, the relation r2 forming functorial indices. Relation r1 replaces any rule for obtaining expressions of functor-argument structure as defined by concatenations built up from the main functor and its arguments. The relation r 2 replaces, on the other hand, any rules for forming functorial indices from basic indices.
On the Formalization of Classical Categorial Grammar
279
The relation r 1 is defined on all finite sequences of words possessing categorial indices. Assigning indices (typisation) of these words is carried out by means of the relation i which indicates the indices of words and which consists in assigning only one index to defined words, in particular to all the simple words of vocabulary V1 according to their form, or even better, to their indiscernibility. Assigning indices also concerns compound expressions which belong to the counterdomain of relation r1 . It allows every expression of the language which has the same index (with respect to indiscernibility) to be placed in a determinate syntactic category and examines if it is a wfe. The set S is distinguished from the set E of all functorial expressions of set E1 . The set E is the sum of the vocabulary V1 and the set of compound expressions each of whose constituents belongs to E 1 . Syntactic connection of functorial expressions of E is obtained in virtue of the rule of syntactic connection (r) holding for all of their constituents (see Sec. 1.4): (r)
the index of the main functor of a given functorial expression is formed from the index of the expression and the indices of the consecutive arguments of this functor. The set S of all wfes may then be generated by the following system: G = VOLUME 68 (2000) Tadeusz CzeĪowski KNOWLEDGE, SCIENCE AND VALUES A PROGRAM FOR SCIENTIFIC PHILOSOPHY
(Edited by L. GumaĔski) L. GumaĔski, Introduction. PART 1: LOGIC, METHODOLOGY AND THEORY OF SCIENCE — Some Ancient Problems in Modern Form; On the Humanities; On the Method of Analytical Description; On the Problem of Induction; On Discussion and Discussing; On Logical Culture; On Hypotheses; On the Classification of Sentences and Propositional Functions; Proof; On Traditional Distinctions between Definitions; Deictic Definitions; Induction and Reasoning by Analogy; The Classification of Reasonings and its Consequences in the Theory of Science; On the so-called Direct Justification and Self-evidence; On the Unity of Science; Scientific Description.. PART 2: THE WORLD OF HUMAN VALUES AND NORMS — On Happiness; How to Understand 'the Meaning of Life' ?; How to Construct the Logic of Goods?; The Meaning and the Value of Life; Conflicts in Ethics; What are Values?; Ethics, Psychology and Logic.. PART 3: REALITY-KNOWLEDGE-WORLD — Three Attitudes towards the World; On Two Views of the World; A Few Remarks on Rationalism and Empiricism; Identity and the Individual in Its Persistence; Sensory Cognition and Reality; Philosophy at the Crossroads; On Individuals and Existence; J.J. Jadacki, Trouble with Ontic Categories or Some Remarks on Tadeusz CzeĪowski's Philosophical Views; W. Mincer, The Bibliography of Tadeusz CzeĪowski.
VOLUME 74 (2000) POLISH PHILOSOPHERS OF SCIENCE AND NATURE IN THE 20TH CENTURY (Edited by Wáadysáaw Krajewski) W. Krajewski, Introduction. I. PHILOSOPHERS — J. Wolenski, Tadeusz KotarbiĔski – Reism and Science; A. Jedynak, Kazimierz Ajdukiewicz – From Radical Conventionalism to Radical Empiricism; L. GumaĔski, Tadeusz CzeĪowski – Our Knowledge though Uncertain is Probable; M. Taáasiewicz, Jan àukasiewicz – The Quest for the Form of Science; I. Szumilewicz-Lachman, Zygmunt Zawirski – The Notion of Time; A. Jedynak, Janina Hosiasson-Lindenbaumowa – The Logic of Induction; T. Bigaj, Joachim Metallmann – Causality, Determinism and Science; J. WoleĔski, Izydora Dąmbska – Between Conventionalism and Realism; A. Koterski, Henryk Mehlberg – The Reach of Science; I. Nowakowa, Adam Wiegner’s Nonstandard Empiricism; W. Krajewski, Janina KotarbiĔska – Logical Methodology and Semantic; M. Taáasiewicz, Maria KokoszyĔska-Lutmanowa – Methodology, Semantics, Truth; T. Batóg, Seweryna àuszczewska-Romahnowa – Logic and Philosophy of Science; M. Omyáa, Roman Suszko – From Diachronic Logic to Non-Fregean Logic; J. WoleĔski, Klemens Szaniawski – Rationality and
Statistical Methods; A. Jedynak, Halina Mortimer – The Logic of Induction; K. Zamiara, Jerzy Giedymin – From the Logic of Science to the Theoretical History of Science; J.M. Dolega, B. J. Gawecki – A Philosopher of the Natural Sciences; A. Bronk, Stanisáaw KamiĔski – A Philosopher and Historian of Science; Z. Hajduk, Stanisáaw Mazierski – A Theorist of Natural Lawfulness. II. SCIENTISTS — W. Krajewski, Marian Smoluchowski – A Forerunner of the Chaos Theory; A. Motycka, Czesáaw Biaáobrzeski’s Conception of Science; M. Tempczyk, Leopold Infeld – The Problem of Matter and Field; M. Czarnocka, Grzegorz Biaákowski – Science and Its Subject; J. Plazowski, Jerzy Rayski – Physicist and Philosopher of Physics; J. Misiek, Zygmunt ChyliĔski – Physics, Philosophy, Music; W. Sady, Ludwik Fleck – Thought Collectives and Thought Styles. III. GENERAL SURVEYS — K. Ajdukiewicz, Logicist AntiIrrationalism in Poland; K. Szaniawski, Philosophy of Science in Poland; I. Nowakowa, Main Orientations in the Contemporary Polish Philosophy of Science.
VOLUME 77 (2003) KNOWLEDGE AND FAITH (Edited by J. Jadacki and K. ĝwiĊtorzecka) Editorial Note; J.J. Jadacki, K. ĝwiĊtorzecka, On Jan Salamucha’s Life and Work. PART I: LOGIC AND THEOLOGY — On the «Mechanization» of Thinking; On the Possibilities of a Strict Formalization of the Domain of Analogical Notion; The Proof ex motu for the Existence of God. Logical Analysis of St. Thomas Aquinas’ Arguments. PART II: HISTORY OF LOGIC — The Propositional Logic in William Ockham; The Appearance of Antinomial Problems within Medieval Logic; From the History of Medieval Nominalism. PART III: METAPHYSICS AND ETHICS — From the History of One Word (‘Essence’); The Structure of the Material World; Faith; The Relativity and Absoluteness of Catholic Ethics; The Problem of Force in Social Life; A Vision of Love. COMMENTS AND DISCUSSIONS — J.M. BocheĔski, J. Salamucha, 'The Proof ex motu for the Existence of God. Logical Analysis of St. Thomas Aquinas' Arguments'; J.F. Drewnowski, The Mathematical Logic and the Metaphysics; H. Scholz, J. Salamucha, 'The Appearance of Antinomial Problems within Medieval Logic'; J. Bendiek, On the Logical Structure of Proofs for the Existence of God; K. Policki, On the Formalization of the Proof ex motu for Existence of God; J. Herbut, Jan Salamucha's Efforts Towards the Methodological Modernization of Theistic Metaphysics; F. Vandamme, Logic, Pragmatics and Religion; E. NieznaĔski, Logical Analysis of Thomism. The Polish Program that Originated in 1930s; Bibliography.
VOLUME 87 (2005) Adam Wiegner OBSERVATION, HYPOTHESIS, INTROSPECTION (Edited by Izabella Nowakowa) I. Nowakowa, Introduction: Adam Wiegner's Nonstandard Empiricism. Adam Wiegner, OBSERVATION, HYPOTHESIS, INTROSPECTION — Translator's Note; List of Translational Decisions. HOLISTIC EMPIRICISM — A Note on Holistic Empiricism (1964); The Problem of Knowledge in light of L. Nelson's Critical Philosophy (1925); The 'Proton Pseudos' in Wundt's Criticism of R. Avenarius' Philosophy (1963); Philosophical Significance of Gestalt Theory (1948); The Idea of a Logic of Knowledge (1934). OTHER EPISTEMOLOGICAL AND METHODOLOGICAL CONTRIBUTIONS — Remarks on Indeterminism in Physics (1932); A Note on the Concept of Relative Truth (1964); On the so-called 'Relative Truth' (1963); On Abstraction and Concretization (1960). PHILOSOPHY OF MIND AND PHILOSOPHY OF PSYCHOLOGY — On the Nature of Mental Phenomena (1933); On the Debate about Imaginative Ideas (1932); On the Subjective and Objective Clarity in Thought and Word (1959); References; Original Sources; J. Kmita, Wiegner's Conception of Holistic Empiricism.