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(2014) Constructivity and computability in historical and philosophical perspective, Dordrecht, Springer.
Constructive recursive functions, Church's thesis, and Brouwer's theory of the creating subject
afterthoughts on a Parisian joint session
Göran Sundholm
pp. 1-35
The first half of the paper discusses recursive versus constructive functions and, following Heyting, stresses that from a constructive point the former cannot replace the latter. The second half of the paper treats of the Kreisel-Myhill theory CS for Brouwer's Creating Subject, and its relation to BHK meaning-explanations and Kripke's Schema. Kripke's Schema is reformulated as a principle and shown to be classically valid. Assuming existence of a verification-object for this principle, a modification of a proof of conservativeness of Van Dalen's, is shown to give a relative BHK meaning explanation for the Kreisel-Myhill connective. The result offers an explanation of why Kripke's Schema can be used as a replacement of the Theory of Creating Subject when formulating Brouwerian counter-examples. It also shows that the Theory of Creating Subject is classically valid.
Publication details
DOI: 10.1007/978-94-017-9217-2_1
Full citation:
Sundholm, G. (2014)., Constructive recursive functions, Church's thesis, and Brouwer's theory of the creating subject: afterthoughts on a Parisian joint session, in J. Dubucs & M. Bourdeau (eds.), Constructivity and computability in historical and philosophical perspective, Dordrecht, Springer, pp. 1-35.
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