Intuitionism As Generalization

Intuitionism As Generalization (1990)

by Fred Richman

Venue:	Philosophia Math
Citations:	7 - 1 self

Datum	Value	Source
TITLE	INTUITIONISM AS GENERALIZATION	SVM HeaderParse 0.1
AUTHOR NAME	Fred Richman	SVM HeaderParse 0.1
AUTHOR ADDR	Philosophia Mathematica, 5(1990), 124--128	SVM HeaderParse 0.1
ABSTRACT	I was inspired, not to say provoked, to write this note by Michel J. Blais's article A pragmatic analysis of mathematical realism and intuitionism [2]. Having spent the greater part of my career doing intuitionistic mathematics, while continuing to do classical mathematics, I have come to feel that most comparisons of these two approaches to mathematics miss the essential point: intuitionism, in its simplest form, is a generalization of classical mathematics that accomodates both classical and computational models. By intuitionism I mean the approach to mathematics based on intuitionistic logic, a well-defined body of axioms and rules of inference [6] [3]. So, for example, my idea of intuitionism does not include the notion of a choice sequence [8], or the various continuity principles associated with intuitionism [9], and it does not refer to the more bizarre consequences that have been drawn from Brouwer's idea of a creating subject [3]. This lean version of intuitionistic mathematics is usually called constructive mathematics. Blais directs his comments in [2] at constructive mathematics rather than at the more esoteric varieties of intuitionistic mathematics.	SVM HeaderParse 0.1
CITATIONS	8 found	ParsCit 1.0