Alfred Tarski: Philosophy of Language and Logic
MathematicsâPhilosophy Logic Linguistics Social sciencesâPhilosophy Modern philosophy Philosophy of Mathematics Science, Humanities and Social Sciences, multidisciplinary Linguistics, general Social Philosophy
Imprint: Palgrave Macmillan
2012
1st ed. 2012.
EISBN 1283440210
Cover; Title; Copyright; Contents; Series Editor's Foreword; 0 Introduction; 0.1 Expressive and representational semantics; 0.2 The received view; 0.3 Themes; 1 Intuitionistic Formalism; 1.1 What was Intuitionistic Formalism?; 1.1.1 A puzzle about concepts and definitions; 1.1.2 Tarski, Le Ìsniewski and Intuitionistic Formalism; 1.1.3 Formalism; 1.2 Le Ìsniewski; 1.2.1 Le Ìsniewski's early work; 1.2.2 Le Ìsniewski's later work; 1.3 Kotarbi Ì nski; 1.4 Tarski in context; 1.4.1 The axiomatic method; 1.4.2 Monism vs tolerance; 1.4.3 Five doctrines; 1.4.4 Tarski's project
2 Tarski as Intuitionistic Formalist2.1 The early metamathematical works; 2.1.1 Axiomatizing consequence; 2.1.2 Relativization to a deductive science; 2.2 Explicit definition; 2.2.1 Defining definition; 2.2.2 Two conceptions of definition; 2.2.3 Padoa's method; 2.3 Categoricity and completeness of terms; 2.3.1 Provable monotransformability; 2.3.2 Absolute monotransformability; 2.4 Theory and concept; 3 Semantics; 3.1 Philosophical resistance; 3.1.1 The quantifier; 3.1.2 Paradox; 3.2 Mathematical acceptance; 3.3 Intuitionistic Formalism in "On Definable Sets"
3.3.1 The intuitive notion of definability3.3.2 Defining definable sets vs defining "Defines"; 4 Truth; 4.1 Convention T; 4.1.1 Terminological notes; 4.1.2 Truth in the Lvov-Warsaw school; 4.1.3 Semantic concepts in a mathematical theory; 4.1.4 T-sentences; 4.2 Tarski's definitions; 4.2.1 Truth for the language of the calculus of classes; 4.2.2 Higher order and polyadicity; 4.2.3 Domain relativization and consequence; 4.3 Evaluating Tarski's account; 4.3.1 Familiar questions; 4.3.2 Tarskian definitions and Tarski's "theory"; 4.3.3 Reduction and physicalism
4.3.4 Correspondence and deflationism5 Indefinability and Inconsistency; 5.1 Indefinability; 5.1.1 Indefinability before 1931; 5.1.2 Theorem I: textual issues; 5.1.3 Theorem I and Intuitionistic Formalism; 5.1.4 Axiomatic semantics; 5.2 Inconsistency in everyday language; 5.2.1 Inconsistent Kotarbi Ì nskian conventions; 5.2.2 Tarski after Kotarbi Ì nski; 6 Transitions: 1933-1935; 6.1 The 1935 postscript; 6.2 Carnap on analyticity and truth; 6.3 The establishment of scientific semantics; 7 Logical Consequence; 7.1 Tarski's definition; 7.1.1 Synopsis; 7.1.2 Objections to Tarski's account
7.2 Consequence in Logical Syntax7.2.1 L-consequence and condition F; 7.2.2 Tractarianism in the Vienna circle; 7.3 The overgeneration problem and domain variation; 7.3.1 Domain variation; 7.3.2 Consequence in GoÌdel's completeness theorem; 7.3.3 Tarski's fixed domain; 7.4 The modality problem and "Tarski's Fallacy"; 7.4.1 Modalities; 7.4.2 Consequence and truth; 7.4.3 Tarski's "must"; 7.5 The formality problem and the logical constants; 7.5.1 Constant and consequence; 7.5.2 Anachronistic readings; 7.5.3 Carnap on formality; 7.5.4 The ?-rule and GoÌdel sentences
7.5.5 Antitractarianism and the nature of logic
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.
2 Tarski as Intuitionistic Formalist2.1 The early metamathematical works; 2.1.1 Axiomatizing consequence; 2.1.2 Relativization to a deductive science; 2.2 Explicit definition; 2.2.1 Defining definition; 2.2.2 Two conceptions of definition; 2.2.3 Padoa's method; 2.3 Categoricity and completeness of terms; 2.3.1 Provable monotransformability; 2.3.2 Absolute monotransformability; 2.4 Theory and concept; 3 Semantics; 3.1 Philosophical resistance; 3.1.1 The quantifier; 3.1.2 Paradox; 3.2 Mathematical acceptance; 3.3 Intuitionistic Formalism in "On Definable Sets"
3.3.1 The intuitive notion of definability3.3.2 Defining definable sets vs defining "Defines"; 4 Truth; 4.1 Convention T; 4.1.1 Terminological notes; 4.1.2 Truth in the Lvov-Warsaw school; 4.1.3 Semantic concepts in a mathematical theory; 4.1.4 T-sentences; 4.2 Tarski's definitions; 4.2.1 Truth for the language of the calculus of classes; 4.2.2 Higher order and polyadicity; 4.2.3 Domain relativization and consequence; 4.3 Evaluating Tarski's account; 4.3.1 Familiar questions; 4.3.2 Tarskian definitions and Tarski's "theory"; 4.3.3 Reduction and physicalism
4.3.4 Correspondence and deflationism5 Indefinability and Inconsistency; 5.1 Indefinability; 5.1.1 Indefinability before 1931; 5.1.2 Theorem I: textual issues; 5.1.3 Theorem I and Intuitionistic Formalism; 5.1.4 Axiomatic semantics; 5.2 Inconsistency in everyday language; 5.2.1 Inconsistent Kotarbi Ì nskian conventions; 5.2.2 Tarski after Kotarbi Ì nski; 6 Transitions: 1933-1935; 6.1 The 1935 postscript; 6.2 Carnap on analyticity and truth; 6.3 The establishment of scientific semantics; 7 Logical Consequence; 7.1 Tarski's definition; 7.1.1 Synopsis; 7.1.2 Objections to Tarski's account
7.2 Consequence in Logical Syntax7.2.1 L-consequence and condition F; 7.2.2 Tractarianism in the Vienna circle; 7.3 The overgeneration problem and domain variation; 7.3.1 Domain variation; 7.3.2 Consequence in GoÌdel's completeness theorem; 7.3.3 Tarski's fixed domain; 7.4 The modality problem and "Tarski's Fallacy"; 7.4.1 Modalities; 7.4.2 Consequence and truth; 7.4.3 Tarski's "must"; 7.5 The formality problem and the logical constants; 7.5.1 Constant and consequence; 7.5.2 Anachronistic readings; 7.5.3 Carnap on formality; 7.5.4 The ?-rule and GoÌdel sentences
7.5.5 Antitractarianism and the nature of logic
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.
