Tarski On Logical Notions

We try to explain Tarski’s conception of logical notions, as it emerges from a lecture of his, delivered in 1966 and published posthumously in 1986 (History and Philosophy of Logic, 7, pp. 143-154), a conception based on the idea of invariance. The evaluation of Tarski’s proposal leads us to consider an interesting (and neglected) reply to Skolem in which Tarski hints at his own point of view on the foundations of set theory. Then, comparing the lecture of 1966 with Tarski’s last work and with an earlier paper written with Lindenbaum, it is shown that Tarski’s conception of logical notions, with its essentially type-theoretic character, did not undergo any significant modifications throughout his life. A remark on Tarski’s prudential attitude on the topic in the famous paper on the concept of logical consequence (and elsewhere) concludes our paper. 1. What are logical notions? In his lecture “What are Logical Notions?”, delivered in London in 1966, repeated in Buffalo in 1973, and published posthumously in 1986 by John Corcoran in History and Philosophy of Logic (Vol. 7, pp. 143-154), Alfred Tarski proposed calling a notion logical if and only if “it is invariant under all possible one-one transformations of the world onto itself” (Tarski 1986, p. 149).