Jan Wolenski

University of Cracow

Poland

"The Undefinability of Truth in Frege, Moore,Goedel and Tarski"

Abstract:

Philosophers always focused on the concept of truth and usually considered it as a logical notion. Although most of them offered definitions of truth, some considered truth as undefinable (or 'ineffable'). For Frege logic was the science of truth. He considered the meaning of 'true' as clear and, therefore, maintained that we do not need to define the concept of truth. Frege's skepticism toward truth-definitions was strengthened by various difficulties of the correspondence theory (regressum ad infinitum, the obscure character of the idea of an agreement with reality, etc.). Moore in his early views was thinking about 'true' as expressing a primitive property, which is not analyzable. Clearly, he was guided by his metaethical views. Although truth is not analyzable and non-definable, similar to goodness, we recognize it without special difficulties. It is interesting to note that Moore kept his views about the primitivity of 'good', but abandoned his early views concerning 'true' and accepted a kind of correspondence theory. Goedel and Tarski are usually considered together. The metamathematical theorem stating that the set of true sentences of arithmetic is not arithmetically definable, is normally attributed to Tarski. However, according to most historians of logic, Goedel had this theorem before Tarski (see Goedel's letter to Zermelo from 1931). However, this view is problematic. Guided by the Kantian idea of truth as a regulative idea, Goedel seems to regard this concept as exceeding any mathematical treatment. Tarski, on the other hand, defined truth generally, but proved that it is undefinable in special circumstances. Both logicians considered truth as exceeding provability, but they differed in their diagnoses of why that is so.

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