Perennial Intuitionism

Abstract

The basic tenets of intuitionism are the rejection of the law of excluded middle and the view that a judgement is correct if it is knowable, indicating a reversal in priority between the objective and the subjective. Intuitionism revived the age-old problem of universals, and the controversy between nominalism, conceptualism, and realism, now represented by formalism (nominalism), intuitionism (conceptualism), and set-theoretical Platonism (realism). In the old controversy, moderate realism, i.e., the Aristotelic-Thomistic school, came out on top, with its simultaneous rejection of conceptualism and exaggerated realism, on the grounds that the former leads to subjectivism, and the latter is epistemologically untenable. This paper takes a similar stance in the modern foundational debate: set-theoretical Platonism, is rejected on epistemological grounds, and pure conceptualism is rejected on the grounds that if fails to account for the objective nature of mathematics.