Internal Logic. A Radically Constructive Logic for Mathematics and Physics

Abstract

By the terms ‘internal logic’ I mean what Hilbert, Weyl and Brouwer have all called, although from different points of view, inhaltliche Logik to contrast it with formal logic. It has been sometimes rendered in English by ‘contentual’; it could also be considered as an equivalent to the ‘intrinsic’ logic H. Weyl has defined in (Weyl, 1968. p. 705) Each field of knowledge, when it crystallizes into a formal theory, seems to carry with it its intrinsic logic which is part of the formalized symbolic system and this logic will, generally speaking, differ in different fields.