Alfred Tarski: Philosophy of Language and Logic

by Patterson, Douglas

• ISBN13: 9780230221215
• ISBN10: 0230221211
• Format: Hardcover
• Copyright: 2012-03-15
• Publisher: Palgrave Macmillan

Summary

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.

Author Biography

Douglas Patterson is Visiting Scholar, University of Pittsburgh, Pittsburgh, USA. His publications include a collection of essays on Alfred Tarski, edited volumes on Inconsistency Theories of Understanding and on whether understanding language is a kind of knowledge. He has also published numerous articles on the philosophy of language and philosophical logic.

Table of Contents

Series Editor's Foreword	p. viii
Introduction	p. 1
Expressive and representational semantics	p. 1
The received view	p. 4
Themes	p. 7
Intuitionistic Formalism	p. 12
What was Intuitionistic Formalism?	p. 12
A puzzle about concepts and definitions	p. 12
Tarski, Lesniewski and Intuitionistic Formalism	p. 16
Formalism	p. 19
Lesniewski	p. 20
Lesniewski's early work	p. 20
Lesniewski's later work	p. 25
Kotarbinski	p. 31
Tarski in context	p. 37
The axiomatic method	p. 37
Monism vs tolerance	p. 41
Five doctrines	p. 43
Tarski's project	p. 49
Tarski as Intuitionistic Formalist	p. 53
The early metamathematical works	p. 53
Axiomatizing consequence	p. 53
Relativization to a deductive science	p. 55
Explicit definition	p. 62
Defining definition	p. 63
Two conceptions of definition	p. 65
Padoa's method	p. 67
Categoricity and completeness of terms	p. 70
Provable monotransformability	p. 70
Absolute monotransformability	p. 76
Theory and concept	p. 80
Semantics	p. 84
Philosophical resistance	p. 85
The quantifier	p. 86
Paradox	p. 89
Mathematical acceptance	p. 91
Intuitionistic Formalism in "On Definable Sets"	p. 94
The intuitive notion of definability	p. 95
Defining definable sets vs defining "Defines"	p. 100
Truth	p. 108
Convention T	p. 109
Terminological notes	p. 109
Truth in the Lvov-Warsaw school	p. 111
Semantic concepts in a mathematical theory	p. 114
T-sentences	p. 117
Tarski's definitions	p. 122
Truth for the language of the calculus of classes	p. 122
Higher order and polyadicity	p. 124
Domain relativization and consequence	p. 128
Evaluating Tarski's account	p. 129
Familiar questions	p. 129
Tarskian definitions and Tarski's "theory"	p. 133
Reduction and physicalism	p. 138
Correspondence and deflationism	p. 140
Indefinability and Inconsistency	p. 144
Indefinability	p. 145
Indefinability before 1931	p. 145
Theorem I: textual issues	p. 147
Theorem I and Intuitionistic Formalism	p. 155
Axiomatic semantics	p. 158
Inconsistency in everyday language	p. 160
Inconsistent Kotarbinskian conventions	p. 162
Tarski after Kotarbinski	p. 166
Transitions: 1933-1935	p. 169
The 1935 postscript	p. 170
Carnap on analyticity and truth	p. 174
The establishment of scientific semantics	p. 179
Logical Consequence	p. 181
Tarski's definition	p. 182
Synopsis	p. 182
Objections to Tarski's account	p. 185
Consequence in Logical Syntax	p. 187
L-consequence and condition F	p. 187
Tractarianism in the Vienna circle	p. 191
The overgeneration problem and domain variation	p. 194
Domain variation	p. 194
Consequence in Gödel's completeness theorem	p. 198
Tarski's fixed domain	p. 201
The modality problem and "Tarski's Fallacy"	p. 203
Modalities	p. 204
Consequence and truth	p. 206
Tarski's "must"	p. 208
The formality problem and the logical constants	p. 209
Constant and consequence	p. 209
Anachronistic readings	p. 211
Carnap on formality	p. 213
The ¿-rule and Gödel sentences	p. 214
Antitractarianism and the nature of logic	p. 215
Evaluating Tarski's account	p. 219
The analytic problem	p. 219
Eliminating transformation rules	p. 221
Epistemic and generality conceptions of logic	p. 223
Conclusion	p. 227
Paris 1935 and the reception of semantics	p. 227
Final remarks	p. 232
Notes	p. 234
Bibliography	p. 249
Index	p. 260
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