Alfred Tarski

Semantic Conception of Truth. What It Is and What It Is Not

by Ladislav Koren

This is a slightly corrected and revised version of the thesis for PhD degree: "Truth and Meaning: the Dialectics of Theory and Practice".

Alfred Tarski’s semantic conception of truth is arguably the most influential – certainly, most discussed - modern... more Alfred Tarski’s semantic conception of truth is arguably the most influential – certainly, most discussed - modern conception of truth. It has provoked many different interpretations and reactions, some thinkers celebrating it for successfully explicating the notion of truth, whereas others have argued that it is no good as a philosophical account of truth. The aim of this work is to offer a systematic and critical investigation of its nature and significance, based on the thorough explanation of its conceptual, technical as well as historical underpinnings.

The methodological strategy adopted in the thesis reflects the author’s belief that in order to evaluate the import of Tarski’s conception we need to understand what logical, mathematical and philosophical aspects it has, what role they play in his project of theoretical semantics, which of them hang in together, and which should be kept separate. Chapter 2 therefore starts with a detailed exposition of the conceptual and historical background of Tarski’s semantic conception of truth and his method of truth definition for formalized languages, situating it within his project of theoretical semantics, and Chapter 3 explains the formal machinery of Tarski’s truth definitions for increasingly more complex languages. Chapters 4 - 7 form the core of the thesis, all being concerned with the problem of significance of Tarski’s conception. Chapter 4 explains its logico-mathematical import, connecting it to the related works of Gödel and Carnap. Having explained the seminal ideas of the model-theoretic approach to semantics, Chapter 5 tackles the question to what extent Tarski’s ‘The Concept of Truth in Formalized Languages’ (and related articles from the 1930s) anticipates this approach, and what elements might be missing from it. Chapter 6 then deals with the vexed question of its philosophical import and value as a theory of truth, reviewing a number of objections and arguments that purport to show that the method fails as an explanation (explication) of the ordinary notion of truth, and, in particular, that it is a confusion to think that Tarski’s truth definitions have semantic import. Finally, Chapter 7 is devoted to the question whether Tarski’s theory of truth is a robust or rather a deflationary theory of truth.

On the basis of a careful analysis, the thesis aims to substantiate the following view. [A] Tarski’s theory with its associated method of truth definition was primarily designed to serve logico-mathematical purposes. [B] It can be regarded a deflationary theory of a sort, since it completely abstracts from meta- semantical issues concerning the metaphysical or epistemological basis or status of semantic properties. Indeed, [C] this can be interpreted as its laudable feature, since by separating formal (or logico-mathematical) from meta-semantical (or foundational) aspects it usefully divides the theoretical labour to be done in the area of meaning and semantic properties in general. [D] In spite of the fact that Tarski’s conception of truth has this deflationary flavour, the formal structure of its method of truth-definition is quite neutral in that it can be interpreted and employed in several different ways, some of them deflationary, others more robust.

Jump Liars and Jourdain's Card via the Relativized T-scheme

by Ming Xiong

Studia Logica, Vol. 91 (2), pp. 239-271, December 2009.

A relativized version of Tarski’s T-scheme is introduced as a new principle of the truth predicate. Under the... more A relativized version of Tarski’s T-scheme is introduced as a new principle of the truth predicate. Under the relativized T-scheme, the paradoxical objects, such as the Liar sentence and Jourdain’s card sequence, are found to have certain relative contradictoriness. That is, they are contradictory only in some frames in the sense that any valuation admissible for them in these frames will lead to a contradiction. It is proved that for any positive integer n, the n-jump liar sentence is contradictory in and only in those frames containing at least an n-jump odd cycle. In particular, the Liar sentence is contradictory in and only in those frames containing at least an odd cycle. The Liar sentence is also proved to be less contradictory than Jourdain’s card sequence: the latter must be contradictory in those frames where the former is so, but not vice versa. Generally, the relative contradictoriness is the common characteristic of the paradoxical objects, but different paradoxical objects may have different relative contradictoriness.

Mechanical theorem proving in Tarski's geometry

by Julien Narboux

Tarski’s undefinability theorem. Very short introduction. Version 1.2

by Bartosz Janik

draft

Logica. Da zero a Gödel

by Francesco Berto

PhD Dissertation:The Many Versions of the Logical Consequence

by Matteo Bianchetti

The aim of my dissertation is to show how and why the concept of logical consequence is manifold. I divided the... more The aim of my dissertation is to show how and why the concept of logical consequence is manifold. I divided the dissertation into two parts:
1) theoretical investigations of historical examples (Aristotle, Descartes, Kant, Bolzano, Frege, the algebraist tradition of logic, the axiomatic investigation of mathematics, Brouwer, Gentzen, Tarski, Prawitz, Etchemendy)
2) theoretical investigations of formal results from the field of the algebraic logic and universal logic (closure relation, structurality, matrix semantics, matrix congruences, Lindenbaum bundle).

DISSERTATION SUMMARY

by Matteo Bianchetti

Tarski on the Necessity Reading of Convention T

by Douglas Patterson

Tarski's Claim Thirty Years Later

by Adrian Rezus

(Unpublished draft: September 29, 2010)

Tarski’s Claim (TC = Theorem 8 in [13]) follows from simple considerations in (type-free) lambda-calculus. The present... more Tarski’s Claim (TC = Theorem 8 in [13]) follows from simple considerations in (type-free) lambda-calculus. The present note records essentially a proof of Lemma 1.1 in [16], i.e. TCL = the type-free lambdacalculus variant of TC, as well as a few historical comments appearing there. Additional remarks are meant to insure the fact that TCL can be transferred verbatim to typed lambda-calculus [TCLT]. (TCLT is just a notational variant of the derivation of TC in ordinary  Lukasiewicz / traditional style.) The Addendum contains a transcription, in type-free lambda-calculus terms, of a  Lukasiewicz / traditional style derivation of TC (notationally equivalent to TCLT), due to John Halleck [6] (September, 2010).

[6] John Halleck [2010] e-mail to Adrian Rezus et al., September 23, 2010.

[13] Jan  Lukasiewicz, and Alfred Tarski [1930] Untersuchungen ¨uber den Aussagenkalk¨ul, Comptes Rendus des S´eances de la Soci´et´e des Sciences et des Lettres de Varsovie (Classe III-`eme), 1930, pp. 39–50.

[16] Adrian Rezus [1980] Singleton Bases for Subsets of Lambda_0^K and a Result of Alfred Tarski, Preprint 150, April 1980, Department of Mathematics, University of Utrecht, 43 pp. (Dated: January 1980; most of it written actually in Geneva, 1979.)

Errata [20101001] for: Tarski's Claim Thirty Years Later [September 29, 2010]

by Adrian Rezus

Errata (October 1, 2010) for:
Adrian Rezus, Tarski’s Claim Thirty Years Later
(September 29, 2010) more Errata (October 1, 2010) for:
Adrian Rezus, Tarski’s Claim Thirty Years Later
(September 29, 2010)

Page 6, the last lines in the proof should read:

|- FK...K = <X1, ... , Xn]K...K = <X1, ... , Xk]
(n-k times K postponed, k in {1, ... ,n-1}, so, in particular,
|- FK = <X1, ... , Xn]K = X1 (for k = n-1, i.e., n-k=1), and
|- Fk(KK)K = <X1, ... ,Xk](KK)K = Xk, for all k in {2,. . . ,n}. QED.

instead of

|- FK...K = <X1, ... , Xn]K...K = <X1, ... , Xk]
(n-k times K postponed, k in {1,... ,n-1},
|- F(KK)K = <X1, ... , Xk](KK)K, for all k in {1,... ,n}. QED.

Page 10 (sub References): read
[3] Alonzo Church [1932] for [3] Alonzo Church 1932
[4] Alonzo Church [1933] for [4] Alonzo Church 1933

September 30, 2010

[Two more corrections from John Halleck: e-mail,  Thu, Sep 30, 2010 at 10:00 PM]

Page 8 (Addendum)
"counting form 0" should be "counting from 0"
"a construction due to" should be "an approach due to"

October 1, 2010

On a Theorem of Tarski

by Adrian Rezus