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By Jacques Dubucs, Michel Bourdeau

Preface; Jacques Dubucs and Michel Bourdeau.- bankruptcy 1. optimistic Recursive capabilities, Church's Thesis, and Brouwer's thought of the growing topic: Afterthoughts on a Parisian Joint consultation; Goran Sundholm.- bankruptcy 2. The advancements of the concept that of computer computability from 1936 to the Sixties; Jean Mosconi.- bankruptcy three. Kolmogorov Complexity in point of view, half I: details conception and Randomness; Marie Ferbus-Zanda and Serge Grigorieff.- bankruptcy four. Kolmogorov Complexity in standpoint, half II: category, details Processing and Duality; Marie Ferbus-Zanda.- bankruptcy five. Proof-theoretic semantics and feasibility; Jean Fichot.- bankruptcy 6. Recursive capabilities and confident arithmetic; Thierry Coquand.- bankruptcy 7. Godel and intuitionism; Mark van Atten.

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Extra info for Constructivity and Computability in Historical and Philosophical Perspective

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Accordingly, in these Afterthoughts I return to some of the things I said in my Paris talk in 2006, as well as present later reflections, caused by rethinking some of the issues and rereading many of the original sources. The material on Brouwer’s Creating Subject that is presented here was not part of my Paris lecture. It stems from research carried out during a Visiting Professorship at Lille, February to April 2012, and I am grateful to my host Shahid Rahman and his students for being such a keen audience.

At this point the reformulation of KS into BKP proves helpful. The assumption of a closed verification-object c for BKP allows us to obtain the required Kripke functions uniformly and contentfully. Let A be a proposition. 9’ 2 N ! A// W N ! cA ; x/ ¤Bool f/: These witnessing Kripke functions cA are obtained uniformly in the verificationobject c of BKP and the chosen proposition A and make it possible to define the Kreisel-Myhill connective explicitly as a proposition in Martin-Löf’s CTT. It must be stressed, though, that the meaningfulness is a relative one: given a verificationobject for Kripke’s Schema it is possible to define the connective.

Pdf. Sundholm, G. (2013). Demonstrations versus proofs, being an afterword to constructions, proofs, and the meaning of the logical constants. In M. S. ), Judgement and the epistemic foundation of logic (pp. 15–22). Dordrecht: Springer. , & van Atten, M. (2008). The proper explanation of intuitionistic logic: On Brouwer’s proof of the Bar theorem. In M. van Atten, P. Boldini, M. Bourdeau, & G. ), One hundred years of intuitionism (1907–2007). The Cerisy conference. Basel: Birkhäuser. Tait, W. (2006).

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