Set theory as a foundation

Penelope Maddy

pp. 85-96

in: Giovanni Sommaruga (ed), Foundational theories of classical and constructive mathematics, Berlin, Springer, 2011

Abstract

The view of set theory as a foundation for mathematics emerged early in the thinking of the originators of the theory and is now a pillar of contemporary orthodoxy. As such, it is enshrined in the opening pages of most recent textbooks; to take a few illustrative examples: All branches of mathematics are developed, consciously or unconsciously, in set theory. (Levy, 1979, p. 3) Set theory is the foundation of mathematics. All mathematical concepts are defined in terms of the primitive notions of set and membership … From [the] axioms, all known mathematics may be derived. (Kunen, 1980, p. xi).