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How Tarski Defined the Undefinable

Published online by Cambridge University Press:  29 January 2015

Cezary Cieśliński
Cezary Cieśliński*
Affiliation:
Logic Department of the Institute of Philosophy, University of Warsaw, Poland. E-mail: [email protected]
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Abstract

This paper describes Tarski’s project of rehabilitating the notion of truth, previously considered dubious by many philosophers. The project was realized by providing a formal truth definition, which does not employ any problematic concept.

Type
Focus: Logic and Philosophy in Poland
Information
European Review , Volume 23 , Issue 1 , February 2015 , pp. 139 - 149
Copyright
© Academia Europaea 2015 

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References

References and Notes

1.For a comprehensive history of the Lvov-Warsaw school, see Woleński, J. (1989) Logic and Philosophy in the Lvov-Warsaw School (Dordrecht: Kluwer Academic).Google Scholar
2.Tarski, A. (1923) O wyrazie pierwotnym logistyki. Doctoral dissertation, published in Przegląd Filozoficzny, 26, pp. 68–89. An English translation appears in A. Tarski (1983) Logic, Semantics, Metamathematics. Papers from 1923 to 1938 (translations by J. H. Woodger) (Indianapolis, Indiana: Hackett Publishing), pp. 1–23, under the title ‘On the primitive term of logistic’.Google Scholar
3.Tarski’s biography by A. Feferman and S. Feferman (2004) Alfred Tarski. Life and Logic (Cambridge: Cambridge University Press) contains a lot of information about Tarski and his milieu, both in Poland and in the US.Google Scholar
4.Banach, S. and Tarski, A. (1924) Sur la décomposition des ensembles de points en parties respectivement congruentes. Fundamenta Mathematicae, 6, pp. 244–277. Here is a popular jocular version of the paradox: a pea can be decomposed into finitely many pieces; then these pieces can be rearranged forming a ball the size of the sun. A word of caution, however: the theorem does not translate in such a way into physical reality!Google Scholar
5.The primary source is A. Tarski (1933) Pojęcie prawdy w językach nauk dedukcyjnych. Towarzystwo Naukowe Warszawskie. Translated by J.H. Woodger as The concept of truth in formalized languages, in A. Tarski (1983) Logic, Semantics, Metamathematics. Papers from 1923 to 1938 (translations by J. H. Woodger) (Indianapolis, Indiana: Hackett Publishing), pp. 152–278; see also Tarski, A. (1944) The semantic conception of truth and the foundations of semantics. Philosophy and Phenomenological Research, 4, pp. 341–376.Google Scholar
6.Aristotle, Metaphysics, Γ, 7, 27.Google Scholar
7.Thomas Aquinas, Summa Theologica I, Q 16.Google Scholar
8.I. Kant, Critique of Pure Reason, A 57-8/B 82.Google Scholar
9.Alternatively, imagine a book where the first sentence on page 1 reads: ‘The first sentence on page 1 in this book is false’. Since it is in fact the first sentence on page 1 (we can check it empirically), it states in effect its own falsity. The formulation provided above does not require such an empirical checking.Google Scholar
10.A fragment of a letter to Yossef Balas; see Gödel, K. (2003) Collected Works, vol. IV (Oxford: Oxford University Press), p. 10.Google Scholar
11.Carnap, R. (1948) Introduction to Semantics (Cambridge, MA, Harvard University Press), pp. vii–viii.Google Scholar
12.If the examples seem trivial or non-informative, just keep in mind our assumption that the object language is contained in the metalanguage. For comparison consider the T-biconditional: ‘Es regnet heute’ is true if and only if it is raining today,which could be in fact quite informative for someone who does not speak German.Google Scholar