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Proofs, Reasoning and the Metamorphosis of Logic

  • Jean-Baptiste JoinetEmail author
Chapter
Part of the Trends in Logic book series (TREN, volume 39)

Abstract

With the “mathematical watershed”, Logic had been transformed into a foundational theory for mathematics, a theory of truth and proofs—far away from its philosophical status of theory of the intellectual process of reasoning. With the recent substitution of the traditional proofs-as-discourses paradigm by the proofs-as-programs one, Logic is now becomming a foundational theory for computing. One could interpret this new watershed as being “yet another technological drift”, bringing Logic always closer to practical ingeneering, always further from the human intellectual process of reasoning. This article promotes the dual point of view: enlightened by the contemporary analysis of the dynamic of proofs, which bring us to a new understanding of the semantic counterpart of processes operationality (including the links between semantic dereliction due to inconsistency and computational exuberance), Logic has never appeared so close to being, finally, the theory of reasoning.

Keywords

Proof Computation Reasoning Philosophy of logic 

Notes

Acknowledgments

I would like to thank Gilles Dowek (french National Institute for Research in Computer Science and Automatics, I.N.R.I.A.) for the friendly and serious moments we spent, walking and talking in the tropical garden of the PUC university campus in Rio, John Tain for his help concerning English and François Rivenc for his remarks and advice about an earlier version of this article. My participation to the conference Natural Deduction, Rio 2002 was supported by the French National Center for Scientific Research (Proofs-Programs-Systems team) and the Brazilian Ministry for Research.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Faculté de philosophieUniversité Jean Moulin - Lyon 3LyonFrance

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