Alfred Tarski: Philosophy of Language and Logic (History of Analytic Philosophy)

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence. Cover......Page 1 Title......Page 4 Copyright......Page 5 Contents......Page 6 Series Editor’s Foreword......Page 9 0.1 Expressive and representational semantics......Page 12 0.2 The received view......Page 15 0.3 Themes......Page 18 1.1.1 A puzzle about concepts and definitions......Page 23 1.1.2 Tarski, Le ́sniewski and Intuitionistic Formalism......Page 27 1.1.3 Formalism......Page 30 1.2.1 Le ́sniewski’s early work......Page 31 1.2.2 Le ́sniewski’s later work......Page 36 1.3 Kotarbi ́ nski......Page 42 1.4.1 The axiomatic method......Page 48 1.4.2 Monism vs tolerance......Page 52 1.4.3 Five doctrines......Page 54 1.4.4 Tarski’s project......Page 60 2.1.1 Axiomatizing consequence......Page 64 2.1.2 Relativization to a deductive science......Page 66 2.2 Explicit definition......Page 73 2.2.1 Defining definition......Page 74 2.2.2 Two conceptions of definition......Page 76 2.2.3 Padoa’s method......Page 78 2.3.1 Provable monotransformability......Page 81 2.3.2 Absolute monotransformability......Page 87 2.4 Theory and concept......Page 91 3 Semantics......Page 95 3.1 Philosophical resistance......Page 96 3.1.1 The quantifier......Page 97 3.1.2 Paradox......Page 100 3.2 Mathematical acceptance......Page 102 3.3 Intuitionistic Formalism in “On Definable Sets”......Page 105 3.3.1 The intuitive notion of definability......Page 106 3.3.2 Defining definable sets vs defining “Defines”......Page 111 4 Truth......Page 119 4.1.1 Terminological notes......Page 120 4.1.2 Truth in the Lvov–Warsaw school......Page 122 4.1.3 Semantic concepts in a mathematical theory......Page 125 4.1.4 T-sentences......Page 128 4.2.1 Truth for the language of the calculus of classes......Page 133 4.2.2 Higher order and polyadicity......Page 135 4.2.3 Domain relativization and consequence......Page 139 4.3.1 Familiar questions......Page 140 4.3.2 Tarskian definitions and Tarski’s “theory”......Page 144 4.3.3 Reduction and physicalism......Page 149 4.3.4 Correspondence and deflationism......Page 151 5 Indefinability and Inconsistency......Page 155 5.1.1 Indefinability before 1931......Page 156 5.1.2 Theorem I: textual issues......Page 158 5.1.3 Theorem I and Intuitionistic Formalism......Page 166 5.1.4 Axiomatic semantics......Page 169 5.2 Inconsistency in everyday language......Page 171 5.2.1 Inconsistent Kotarbi ́ nskian conventions......Page 173 5.2.2 Tarski after Kotarbi ́ nski......Page 177 6 Transitions: 1933–1935......Page 180 6.1 The 1935 postscript......Page 181 6.2 Carnap on analyticity and truth......Page 185 6.3 The establishment of scientific semantics......Page 190 7 Logical Consequence......Page 192 7.1.1 Synopsis......Page 193 7.1.2 Objections to Tarski’s account......Page 196 7.2.1 L-consequence and condition F......Page 198 7.2.2 Tractarianism in the Vienna circle......Page 202 7.3.1 Domain variation......Page 205 7.3.2 Consequence in Gödel’s completeness theorem......Page 209 7.3.3 Tarski’s fixed domain......Page 212 7.4 The modality problem and “Tarski’s Fallacy”......Page 214 7.4.1 Modalities......Page 215 7.4.2 Consequence and truth......Page 217 7.4.3 Tarski’s “must”......Page 219 7.5.1 Constant and consequence......Page 220 7.5.2 Anachronistic readings......Page 222 7.5.3 Carnap on formality......Page 224 7.5.4 The ?-rule and Gödel sentences......Page 225 7.5.5 Antitractarianism and the nature of logic......Page 226 7.6.1 The analytic problem......Page 230 7.6.2 Eliminating transformation rules......Page 232 7.6.3 Epistemic and generality conceptions of logic......Page 234 8.1 Paris 1935 and the reception of semantics......Page 238 8.2 Final remarks......Page 243 Notes......Page 245 Bibliography......Page 260 Index......Page 271 Alfred Tarski is known as the founder of the rigorous study of semantics, but little is known about the views he held at the time other than that at one point he calls his position 'Intuitionistic Formalism'. Alfred Tarski: Philosophy of Language and Logic sets out a detailed account of these views, in particular by looking to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski. Both subscribed to an account of language on which meaning was a matter of the expression of a thought through symbols governed by conventional rules. In particular Lesniewski held that they best way to express thought was in the form of a rigorously crafted deductive theory. Tarski accepted these views and made it his project to express metatheoretic thought -thought about formal systems themselves - to intuitionistic formalist standards. He began with simple theories of the relation of logical consequence, conceived of in terms of a fixed set of primitively valid rules. Tarski next turned his attention to the semantic concepts that figured in the work of Skolem and G̲del, as well a group known as the American Postulate Theorists. The result of his study here was his now famous method for the definition of truth by recursion on satisfaction. In light of the reading of Tarski developed in the early chapters of the book the major topics concerning Tarski's semantics are covered: the significance of the T-sentences, the meaning and purpose of the famous Convention T, and questions about whether or not Tarski held that each language is covered by its own peculiar concept of truth. This work done, within a few years Tarski realized that the semantics he had developed could actually replace the intuitionistic formalist conception of meaning. His famous work on logical consequence is read in this light and the shift in his thinking is discussed in detail Intuitionistic Formalism -- Tarski As Intuitionistic Formalist -- Semantics -- Truth -- Indefinability And Inconsistency -- Transitions: 1933-1935 -- Logical Consequence -- Conclusion. Douglas Patterson. Includes Bibliographical References And Index.