The philosophy of strict finitism

Theoria 2 (2):575-582 (1987)
Abstract
The philosolphy of strict finitism is a research programme containing developmental theory and mathematics as its main branches. The first branch is concerned with the ontogenetic and historicaldevelopment of various concepts of infinity. The frame work is Jean Piaget’s genetic epistemology. Based upon these develop mental studies, the mathematical branch introduces a new concept of infinity into mathematics. Cantor propagated the actual infinite, Brouwer and the constructivists the potential infinite. Still more radical is strict finitism, favoring the natural infinite, i.e. the phenomena of the unsurveyable, unfeasible, unreachable. There exist by this time strict finitistic reconstructions for arithmetic, geometry, calculus, and even for infinitistic set theory
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