1994: Logical Truth: Comments on Etchemendy's Critique of Tarski Author (original) (raw)
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1999: Tarski and Carnap on Logical Truth - or: what is Genuine Logic
1998
In (1936), Tarski presented for the first time, in Gemnan, his new semantic definition of logical consequence and logical truth. He starts to motivate his definition by cdtizicing traditional syntactic definitions. He gives two reasons why syntactic definitions are not satisfactory. First, the traditional calculus-based syntactic definitions (defined by a set of axioms and rules, and a recursive notion of proof) are too weak to capture the ordinary notion of logical consequence. Tat'ski gives the example of w-incomplete themies of Pea no arithmetics. Here it may be the case that P(n) is derivable (within the theory) for every natural number n, without having thatl.lxP(x) be dedvable, although the latter sentence intuitively follow (Tarski 1936, p. 41Of). Tarski continues that this is just one aspect of the incompleteness of first order arithmetics, which shows that calculus-based recursive definitions are 77 J. Wale,1ski and E. Kohler (eds.), Alfred Tarski and the Vienna Cire/e. 77~94.
Tarski's One and Only Concept of Truth
Synthese, 2014
In a recent article, Marian David (2008) distinguishes between two interpretations of Tarski's work on truth. The standard interpretation has it that Tarski gave us a definition of truth in-L within the meta-language; the non-standard interpretation, that Tarski did not give us a definition of true sentence in L, but rather a definition of truth, and Tarski does so for L within the meta-language. The difference is crucial: for on the standard view, there are different concepts of truth, while in the alternative interpretation there is just one concept. In this paper we will have a brief look at the distinction between these two interpretations and at the arguments David gives for each view. We will evaluate one of David's arguments for the alternative view by looking at Tarski's 'On the Concept of Truth in Formalized Languages', and his use of the term 'extension' therein, which, we shall find, yields no conclusive evidence for either position. Then we will look at how Tarski treats 'satisfaction', an essential concept for his definition of 'true sentence'. It will be argued that, in light of how Tarski talks about 'satisfaction' in §4 of 'On the Concept of Truth in Formalized Languages' and his claims in the Postscript, the alternative view is more likely than the standard one.
Tarski's Convention T and the Concept of Truth
New Essays on Tarski and Philosophy, 2008
In this paper, I want to discuss in some detail the original version of Tarski's condition of adequacy for a definition of truth, his Convention T. I will suggest that Tarski designed Convention T to serve two functions at once. I will then distinguish two possible interpretations of Tarski's work on truth: a standard interpretation and a non-standard, alternative interpretation. On the former, but not on the latter, the very title of Tarski's famous article about the concept of truth harbors a lie. Using the symbol 'Tr' to denote the class of all true sentences, the above postulate can be expressed in the following convention: CONVENTION T. A formally correct definition of the symbol 'Tr', formulated in the metalanguage, will be called an adequate definition of truth if it has the following consequences: (α) all sentences which are obtained from the expression 'x Tr if and only if p' by substituting for the symbol 'x' a structural-descriptive name of any sentence of the language in question and for the symbol 'p' the expression which forms the translation of this sentence into the metalanguage;
Dedicated to Professor Roberto Torretti, philosopher of science, historian of mathematics, teacher, friend, and collaborator—on his eightieth birthday. This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework—like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as ‘the class of all individuals’. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework—like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple universes of discourse serving as different ranges of the individual variables in different interpretations—as in post-WWII model theory. In the early 1960s, many logicians—mistakenly, as we show—held the ‘contrary alternative’ that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege–Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski’s philosophy underwent many other radical changes.