Intuitionism as generalization (1990) [4 citations — 0 self]
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.
Citations
| 33 | Varieties of Constructive Mathematics – Bridges, Richman - 1987 |
| 8 | Choice sequences, a chapter of intuitionistic mathematics – Troelstra - 1977 |
| 4 | Choice implies excluded middle – Goodman, Myhill - 1978 |
| 1 | A pragmatic analysis of mathematical realism and intuitionism – Blais |
| 1 | Cambridge lectures on intuitionism, edited by D – Brouwer - 1981 |
| 1 | A course in constructive algebra, Springer-Verlag – Mines, Richman, et al. - 1988 |
| 1 | of constructive mathematics, Mathematical logic, edited by Jon Barwise, North-Holland – Aspects - 1977 |
| 1 | Cambridge lectures on intuitionism, edited by D.van Dalen – Brouwer - 1981 |
