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Proof-Theoretic Semantics and Feasibility

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

Abstract

It is well known that classical mathematics have been widely criticised by the proponents of constructive mathematics on the ground that the former rests on a realist conception of the realm of mathematical objects. It must be recalled that the latter is not completely immune to such a reproach inasmuch as some vestige of realism is still present in its foundations (1). This realism takes the form of two different idealisations of human abilities: the creative ones and the mechanical ones (1.1). It can be argued that the first idealisation is avoided by the proof theoretic-semantics of constructive mathematics but not the second one (1.2). Different definitions of feasible functions and systems of feasible mathematics have been proposed that makes possible to avoid the second idealisation too (2). It is of special interest to see if they allow, at least partially, some proof-theoretical semantics (2.2).

Keywords

Reduction Rule Elimination Rule Introduction Rule Constructive Mathematic Expansion Rule 
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.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Université Paris 1 Panthéon-Sorbonne – IHPSTParisFrance

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