Identity, Variables, and Impredicative Definitions in The Journal of Symbolic Logic, Vol. 21, No. 3, Sept. 1956, pp. 225-245 AND Vicious Circle Principle and the Paradoxes in The Journal of Symbolic Logic, Vol. 22, No. 3, Sept. 1957, pp. 245-249

The Association of Symbolic Logic. 1st Edition. FIRST EDITION IN ORIGINAL WRAPS, two papers (in two separate issues), of Jaako Hintikka's systematic investigation of Wittgensteinian predicate logic (W-logic), the first ever performed.

Jaakko Hintikka (1929-2015) was a Finnish philosopher known for his work in logic and epistemology. He was awarded the Rolf Schook Prize in Logic & Philosophy in 2005, "widely viewed as the Nobel of its field. He is also one of only four philosophers this century to be the subject of a volume of the Library of Living Philosophers" (The Philosophers' Magazine 40, 2008, 44).

"Hintikka's development of systems of modal logic, the logic of knowledge, and game-theoretic semantics was inspired in part by the Tractatus, and in part by Wittgenstein's notion of a language game" (Shapiro, Oxford Handbook, 114). In the Tractatus, Wittgenstein wrote: ‘Identity of the object I express by identity of the sign and not by means of a sign of identity. Difference of the objects by difference of the signs.' Wittgenstein, however, only proposed the problem; he did not posit the answer.

The two Hintikka papers offered here amplify Wittgenstein's elimination of identity (as enunciated in the Tractatus) by constructing a logic without identity. "Hintikka distinguishes the usual ‘inclusive' reading of the variables (i.e. we are allowed to assign the same object to distinct variables) from the ‘exclusive' reading, and then proves [his] key theorem: "[E]verything expressible in terms of the inclusive quantifiers and identity may also be expressed by means of the weakly exclusive quantifiers without using a special symbol for identity" (Logic Matters Portal; Hintikka 1956). CONDITION & DETAILS: Two issues in original paper wraps. [No place]: The Association for Symbolic Logic. Quarto. (10 x 7 inches; 250 x 175mm). Volume 21, Number 3, September 1956: Slight creasing (see photo). Bright and clean inside and out. Very good condition. Volume 21, Number 3, September 1957: Near fine condition. Bright and clean inside and out.