Peano, logicism, and formalism

Michael Segre

pp. 133-142

in: I. C. Jarvie, Nathaniel Laor (eds), Critical rationalism, metaphysics and science, Berlin, Springer, 1995

Abstract

Giuseppe Peano (1858–1932), the great mathematician and linguist, is famous, above all, for the five axioms in arithmetic that bear his name despite his no less important, and often impressive, contributions to other branches of mathematics.¹ Moreover, Peano is usually mentioned in works concerning the foundations of mathematics, and his work has been presented — incorrectly — as part and parcel of the Logicist tradition, fostered by Bertrand Russell and Alfred North Whitehead, claiming that mathematics is a branch of logic.² Peano no doubt influenced Russell, but, despite their mutual esteem, the two mathematicians criticized each other and grasped mathematics differently. Above all, whereas Russell thought that all mathematical terms could be expressed in logical terms, Peano believed that some mathematical terms cannot be defined at all.

Cited authors

Russell Bertrand

Whitehead Alfred North

Peano Giuseppe