Extensionalism without Logicism: Ambrose and Extensional Logic

Abstract

Drawing primarily on her early work (1931-1934), I argue that Alice Ambrose develops a philosophical project centered on preserving the rigor of extensional logic while rejecting the metaphysical and epistemological endorsements of logicism because of its commitment to the notion of material infinity. Positioning Ambrose as a transitional figure between formalism (Russell) and the constructivist turn represented by intuitionism (Brouwer), I demonstrate how Ambrose offers a practice oriented statement of finitist extensionalism. Employing only extensional methods (considering classes, relations, and propositions by reference to their members and truth values instead of mental processes), Ambrose reformulates an existential claim about pi as an explicit infinite disjunction of concrete instances insisting, against intensional projects, that such claims gain meaning only through a finite stopping rule that produces a witness.