Abstract
Alfred Tarski (1944) wrote that “the condition of the ‘essential richness’ of the metalanguage proves to be, not only necessary, but also sufficient for the construction of a satisfactory definition of truth.” But it has remained unclear what Tarski meant by an ‘essentially richer’ metalanguage. Moreover, DeVidi and Solomon (1999) have argued in this Journal that there is nothing that Tarski could have meant by that phrase which would make his pronouncement true.
We develop an answer to the historical question of what Tarski meant by ‘essentially richer’ and pinpoint the general result that stands behind his essential richness claim. In defense of Tarski, we then show that each of the several arguments of DeVidi and Solomon are either moot or mistaken.
One of the fruits of our investigation is the reclamation of what Tarski took to be his central result on truth. This is a reclamation since: (i) if one does not understand ‘essential richness’, one does not know what that result is, and (ii) we must unearth a heretofore unrecognized change that occurs in Tarski's view – an alteration of his main thesis in light of a failing he discovered in it.
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References
DeVidi, D. and Solomon, G. (1999) Tarski on ‘essentially richer’ metalanguages, J. Philos. Logic 28, 1–28.
Mostowski, A. (1950) Some impredicative definitions in the axiomatic set theory, Fund. Math. 37, 111–124. Reprinted in 1979, Foundational Studies: Selected Works [of Andrej Mostowski] 1, Ed. Kuratowski, Kazimierz, et al., Amsterdam, North-Holland, pp. 479–492.
Tarski, A. (1935) Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica 1, 261–405. Translated as “On the concept of truth in formalized languages” in 1983, Logic, Semantics, Metamathematics, 2nd edn, Trans. Woodger, J. H., Indianapolis, Hackett Publishing, pp. 152–278.
Tarski, A. (1939) On undecidable statements in enlarged systems of logic and the concept of truth, J. Symbolic Logic 4, 105–112.
Tarski, A. (1944) The semantic conception of truth and the foundations of semantics, Philosophy and Phenomenological Research 4, 341–375.
Tarski, A. (1956) Logic, Semantics, Metamathematics, 1st edn, Hackett Publishing, Indianapolis.
Tarski, A. (1969) Truth and proof, Scientific American 220(6), 63–77.
Tarski, A. (1983) Logic, Semantics, Metamathematics, 2nd edn, Hackett Publishing, Indianapolis.
Wang, H. (1951) Arithmetic translations of axiom systems, Trans. Amer. Math. Soc. 71, 283–293.
Wang, H. (1952) Truth definitions and consistency proofs, Trans. Amer. Math. Soc. 73, 243–275. Reprinted in 1970, Logic, Computers, and Sets, New York, Chelsea Publishing, pp. 443–477.
Wang, H. (1970) Logic, Computers, and Sets, Chelsea Publishing, New York.
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Ray, G. On the Matter of Essential Richness. J Philos Logic 34, 433–457 (2005). https://doi.org/10.1007/s10992-004-7801-1
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DOI: https://doi.org/10.1007/s10992-004-7801-1