Two Constructivist Aspects of Category Theory

Colin McLarty
2006 Philosophia Scientiæ  
Category theory has two unexpected links to constructivism: First, why is topos logic so close to intuitionistic logic? The paper argues that in part the resemblance is superficial, in part it is due to selective attention, and in part topos theory is objectively tied to the motives for later intuitionistic logic little related to Brouwer's own stated motives. Second, why is so much of general category theory somehow constructive? The paper aims to synthesize three hypotheses on why it would be
more » ... on why it would be so, with three that suggest it is not. Philosophia Scientiae, Cahier spécial 6, 2006, 95-114. Category theory conceals non-constructivity in its basic terms. 3. Category theory is too young yet to need nonconstructive proofs. 4. Category theory looks constructive because so much of it has been created for computer science. 5. Category theory gives such direct access to structure that it naturally finds explicit solutions to its problems. 6. The category axioms have such a weak logical form that there is little occasion for non-constructive methods.
doi:10.4000/philosophiascientiae.413 fatcat:jqeovpr3sjddvg6r4iaebr2crq