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C for Constructivism

Beyond clichés

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Lettera Matematica

Abstract

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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121, Padova, Italy

    Giovanni Sambin

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  1. Giovanni Sambin
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Correspondence to Giovanni Sambin.

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Sambin, G. C for Constructivism. Lett Mat Int 5, 87–91 (2017). https://doi.org/10.1007/s40329-017-0169-1

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  • DOI: https://doi.org/10.1007/s40329-017-0169-1

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