[QUINE:] Completeness of the Propositional Calculus (+) On the Theory of Types (+) [KLEENE:] On Notation for Ordinal Numbers.

(Wisconsin), The Association for Symbolic Logic, 1937. Lex8vo. Original printed wrappers, no backstrip. In "The Journal of Symbolic Logic, Volume 3, 1938." Entire issue offered. Internally very fine and clean. [Quine:] Pp. 37-40" Pp. 125-39. [Entire issue: IV, 212 pp.]. First printing of these papers which include Kleene's milestone paper in which Kleene's O (Ordial numbers), a recursive function, is introduced. In set theory and computability theory, Kleene's is a canonical subset of the natural numbers when regarded as ordinal notations."In the seventeenth century, Leibniz envisaged a universal language that would allow one to reduce mathematical proofs to simple computations. Then, during the nineteenth century, llgicians such as Charles Babbage, Boole, Frege and Peano tried to formalize mathematical reasoning by an "algebraization" of logic. Finally, [.] Gödel, Church and Stephen Kleene introduced the notion of recursive functions. (The Princeston Companion to Mathematics. P. 111).