C for Constructivism

C for Constructivism According to constructivism, all mathematical entities and truths about them should be the result of a construction. At present this view of the nature of mathematics is essentially ignored by the vast majority of mathematicians. This is perhaps due to historical reasons and is accompanied by deep-rooted dogmas, misunderstandings, misinformation, prejudices, etc. We briefly analyse them and recall some information which could be useful to go beyond them and reach a more balanced view on constructivism. In particular, we suggest that the present accepted attitude of mathematicians is the result of a denial of the problem of foundations of mathematics and of the impact of Gödel’s incompleteness theorems. We claim that a constructive view is fully compatible with an evolutionary view of mathematics, which would bring it closer to all other natural sciences and enliven it. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Lettera Matematica Springer Journals

C for Constructivism

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Publisher
Springer Milan
Copyright
Copyright © 2017 by Centro P.RI.ST.EM, Università Commerciale Luigi Bocconi
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Applications of Mathematics; History of Mathematical Sciences; History of Science
ISSN
2281-6917
eISSN
2281-5937
D.O.I.
10.1007/s40329-017-0169-1
Publisher site
See Article on Publisher Site

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