Notes by RBJ on

Platonism, Constructivism, and
Computer Proof vs. Proofs by Hand

by Yuri Gurevich

This article, rendered as a dialogue between "Quisani" and the author, is presented in the following sections:

(untitled introduction) Quisani enquires about the relevance of constructivism to computer sceince.
1Paradoxes and the Related Foundational Crisis Platonism is introduced and blamed for the antinomies in informal set theory. The significance of these matters for the foundations of mathematics is discussed.
2Constructivism Constructivism is introduced, its (lack of) impact touched upon.
3Good Things About Constructivism Five benign effects are attributed to constructivism, falling short of the truth of any part of its critique of classical mathematics.
4Computer Proofs vs. Proofs by Hand Mainly about proofs of programs arising from constructive existence proofs. Touching upon the "four colour problem" kind of computer proof.
5Critique of Constructivism Constructivism is criticised, first because of the value of the non-constructive methods which it abjures, and secondly because the concern for effectiveness did not embrace the study of feasibility.

UP HOME © RBJ created 96/1/15 modified 97/2/3