Arianna Betti,
Lesniewski's Early Solution to the Liar, and Tarski

Abstract:

Stanislaw Lesniewski's influence upon his sole doctoral student Alfred Tarski is generally speaking recognised. On the opening pages of his famous 1933 monograph on the concept of truth, Tarski himself credits his master with almost everything he says about "expressions in inverted commas and semantical antinomies", acknowledging his debt also later (1944). However, the conceptual relationships between them have not yet been thoroughly investigated. My aim will be here to show that who takes on such an investigation must take into account not only the Lesniewski of the logical systems, but also the Lesniewski of the so-called 'prelogistic phase' (1911-13). Tarski's words have been quoted several times accompanied with the disconsolate remark that we find no treatment of semantical paradoxes in Lesniewski's writings. But an early piece, which he later rejected, "A Critique of the Logical Principle of the Excluded Middle" (1913), in fact contains an interesting solution to Epimenides' Paradox. The latter is not very similar to Tarski's, as it is contextual, makes use of a ban on self-reference and is based on tokens. Yet in this almost unknown Lesniewskian attempt we can recognise many elements of Tarski's classical background, and, most of all, we find a clear statement regarding the impossibility of giving a satisfactory theory of denotation and truth for ordinary language. We have here in print evidence of the idea that it is necessary to sanitize ordinary language for scientific purposes, an idea which Lesniewski introduced - with a splendid metaphor (the "Porohy on the Dniepr") - twenty years before Tarski.

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