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THE IRREDUCIBILITY OF THE NUMBER CONCEPT

THE IRREDUCIBILITY OF THE NUMBER CONCEPT THE IRREDUCIBILITY OF THE NUMBER CONCEPT BY McGill University, Montreal 1. Introduction The question wherther it is possible to malm some kind of OIlItology the basis of modem mathematics is left open by most people p1"esently working in the mathematical fields. Fearing to introduce into mathematics arguments of a metaphysical nature, the philosophically minded mathematician will avoid as much as possible reference to mathematical existence independent of human thought. The intuitionistic attitude, for example, with respect to mathematical existence is weil known. Furthermore, among those mathematicians who want to consider set theory or logic as the basis or origin of all of mathematics, the problem whether some kind of "Platonism" can be avoided of whether the greater part of mathematics is a "fa~on de parler", is still in discussion. In general it can be said that under the impact of the pragmatisrt attitude, for philosophers of mathematics the workability of mathematical systems rather than rtheir interprertability has become a central point of view. Reflections of an epistemological nature as well as reflections regarding for example mathematical truth are not readily und ertaken by mathematicians of the pragmatistic type 1. In this paper 2 we inrvestigate the nature and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Philosophia Reformata Brill

THE IRREDUCIBILITY OF THE NUMBER CONCEPT

KUYK, WILLEM
Philosophia Reformata , Volume 31 (1-2): 37 – Feb 20, 1966
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Publisher
Brill
Copyright
© Copyright 1966 by Koninklijke Brill NV, Leiden, The Netherlands
ISSN
0031-8035
eISSN
2352-8230
DOI
10.1163/22116117-90001116
Publisher site
See Article on Publisher Site

Abstract

THE IRREDUCIBILITY OF THE NUMBER CONCEPT BY McGill University, Montreal 1. Introduction The question wherther it is possible to malm some kind of OIlItology the basis of modem mathematics is left open by most people p1"esently working in the mathematical fields. Fearing to introduce into mathematics arguments of a metaphysical nature, the philosophically minded mathematician will avoid as much as possible reference to mathematical existence independent of human thought. The intuitionistic attitude, for example, with respect to mathematical existence is weil known. Furthermore, among those mathematicians who want to consider set theory or logic as the basis or origin of all of mathematics, the problem whether some kind of "Platonism" can be avoided of whether the greater part of mathematics is a "fa~on de parler", is still in discussion. In general it can be said that under the impact of the pragmatisrt attitude, for philosophers of mathematics the workability of mathematical systems rather than rtheir interprertability has become a central point of view. Reflections of an epistemological nature as well as reflections regarding for example mathematical truth are not readily und ertaken by mathematicians of the pragmatistic type 1. In this paper 2 we inrvestigate the nature and

Journal

Philosophia Reformata – Brill

Published: Feb 20, 1966

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