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Recursive Functions and Constructive Mathematics

  • Thierry CoquandEmail author
Chapter
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 34)

Abstract

The goal of this paper is to discuss the following question: is the theory of recursive functions needed for a rigorous development of constructive mathematics? I will try to present the point of view of constructive mathematics on this question. The plan is the following: I first explain the gradual loss of appreciation of constructivity after 1936, clearly observed by Heyting and Skolem, in connection with the development of recursivity. There is an important change in 1967, publication of Bishop’s book, and the (re)discovery that the theory of recursive functions is actually not needed for a rigorous development of constructive mathematics. I then end with a presentation of the current view of constructive mathematics: mathematics done using intuitionistic logic, view which, surprisingly, does not rely on any explicit notion of algorithm.

Keywords

Constructive Mathematics Recursive Function Heyting Skolem Rigorous Development 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I would like to thank Göran Sundholm for interesting discussions on the topic of this paper and for sending me the references (Heyting 1957).

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Chalmers Tekniska Högskola ochGöteborgs UniversitetGöteborgSuède

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