CORCORAN-PARK ON QUINE’S PEANO

CORCORAN-PARK ON QUINE’S PEANOA review of Quine’s “Peano as logician”. Hist. Philos. Logic 8 (1987), no. 1, 15–24.Giuseppe Peano (1858–1932) is remembered mainly for having axiomatized number theory. It is only somewhat less widely known that Peano conjectured and proved that his axiom set is independent in the sense that no one of the axioms is implied by the others. Beyond these two achievements, which alone are sufficient to ensure him a permanent place in history, Peano’s work in logic is not well known. Indeed, the construction of nonstandard models for axiom sets, which is a central feature of Peano’s independence proof, and which was far from being original with Peano, is occasionally attributed to even later logicians such as Hilbert or even Löwenheim. The author, well known to philosophers and mathematicians for his own contributions to logic, does not limit himself merely to identifying Peano’s innovations and tracing their development within the vast corpus of Peano’s logical writings. He also submits Peano’s work to critical appraisal in the light of modern logic and he traces the trajectories of Peano’s influence on subsequent developments. This rich article manifests on every page not only the importance ofPeano’s analysis of mathematical language but also the author’s mastery both of the Peano corpus and of the intricacies of modern logic. It is a rare event when a modern master undertakes an appraisal of a historic master. This article will be of interest not only to historians of logic but also to logicians who seek some understanding of their debt to the past.