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Tarski’s one and only concept of truth

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Abstract

In a recent article, David (Tarski’s convention T and the concept of truth, pp. 133–156, 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’ (CTF), 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 Sect. 4 of ‘CTF’ and his claims in the Postscript, the alternative view is more likely than the standard one.

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Notes

  1. Better: according to the standard interpretation Tarski provides the method to define \(a\) truth concept for a specified language, since \(L\) is not a variable, but a name for a language.

  2. One should keep in mind that the difference between the standard and the alternative interpretation does not depend on whether Tarski held truth to be domain-relative. After giving his definition of ‘true sentence’ for the calculus of classes (CTF, p. 195), Tarski gives three definitions for truth relative to a domain [viz. ‘true sentence for an individual domain a’, ‘true sentence for an individual domain with k elements’, and ‘true sentence for every individual domain’ (CTF, pp. 200–201)]. So, Tarski did provide domain-relative truth definitions, but these are different from his definition of ‘true sentence’. The dichotomy between the alternative and the standard interpretation concerns solely the question whether the latter definition is language relative or not.

  3. Thanks to an anonymous referee for drawing my attention to the following three examples of adherents of the standard interpretation.

  4. Another possible example is Quine who writes: “Attribution of truth in particular to ‘Snow is white’, for example, is every bit as clear to us as attribution of whiteness to snow. In Tarski’s technical construction, moreover, we have an explicit general routine for defining truth-in-\(L\) for individual languages L which conform to a certain standard pattern and are well specified in point of vocabulary. We have indeed no similar definition of ‘true-in-L’ for variable ‘L’; but what we do have suffices to endow ‘true-in-L’, even for variable ‘L’, with a high enough degree of intelligibility so that we are not likely to be averse to using the idiom.” (Quine 1953, p. 138) However, one could also hold that since Quine claims that there is a “general routine” that he might hold that Tarski had one concept of truth in mind which needs to be defined for a particular language (i.e. that Quine is an adherent of the alternative interpretation).

  5. If, however, Künne is of the opinion that the different predicates all express a single concept of truth, he should be seen as an adherent of the alternative interpretation.

  6. Another example: “[T]arski expressedly aimed to define truth (or, rather, “true-in-\(L\)”) without assuming any semantic notions.” (Raatikainen 2008, 112)

  7. Better: according to the standard interpretation Tarski provides the method to define \(a\) truth concept for a specified language, since \(L\) is not a variable, but a name for a language.

  8. Other possible adherents of the alternative interpretation are Feferman (2008, pp .83–84) and Simons (2009), who both hold that Tarski holds that truth is an absolute notion. But it should be noted—as a referee pointed out to me—that Feferman and Simons do not seem to address the dichotomy between the standard and the alternative interpretation, but rather a dichotomy between on the one hand the alternative interpretation—in which ‘true sentence’ expresses one absolute concept and a third interpretation, on the other hand, according to which ‘true sentence’ is one relative concept. We will not take this third interpretation into account, although the arguments in this paper could possibly also be put forward against it.

  9. Although there is some such evidence: Jan Wolenski has reported that Jan Tarski, Alfred’s son, told him that “his father considered the absoluteness of truth as truth’s important feature.” (Murawski and Wolenski 2008, 33 note 21) Furthermore, Carnap writes in his intellectual autobiography: “When Tarski told me for the first time he had constructed a definition of truth, I assumed that he had in mind a syntactical definition of logical truth or provability. I was surprised when he said that he meant truth in the customary sense, including contingent factual truth.’ (Carnap 1963, p. 60) Together with the assumption that ‘truth in the customary sense’ is absolute, this latter quote suggests that Tarski was, at least himself, of the opinion that there was only one concept of truth.

  10. As long as there are no context-sensitive expressions in the language, otherwise EP would of course fail in those cases.

  11. To repeat, ’\(L\)’ is a name or description of a language, such that (according to the standard interpretation) there is a concept ’true sentence-in-calculus-of-classes’ and a—different!—concept ’true sentence-in-topology’, and so one for various languages.

  12. More precisely: languages of the third kind first have to use the method of unification to ‘lower it down’ (so to speak) to a language of the second kind, then both the method of unification and the method of many-rowed sequences can be applied again. (CTF, pp. 231–235)

Abbreviations

CTF:

On the concept of truth in formalized languages

EP:

Extension Principle

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Acknowledgments

Many thanks to Arianna Betti, Iris Loeb, and three anonymous reviewers for commenting on previous versions of this paper. Thanks also to Jonathan Sozek for proofreading my manuscript. Whatever mistakes remain are entirely my own.

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Correspondence to Jeroen Smid.

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Smid, J. Tarski’s one and only concept of truth. Synthese 191, 3393–3406 (2014). https://doi.org/10.1007/s11229-014-0450-1

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