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The creating subject, the Brouwer-Kripke schema, and infinite proofs. (English) Zbl 1437.03173
Summary: Kripke’s Schema (better the Brouwer-Kripke Schema) and the Kreisel-Troelstra Theory of the Creating Subject were introduced around the same time for the same purpose, that of analysing Brouwer’s ‘Creating Subject arguments’; other applications have been found since. I first look in detail at a representative choice of Brouwer’s arguments. Then I discuss the original use of the Schema and the Theory, their justification from a Brouwerian perspective, and instances of the Schema that can in fact be found in Brouwer’s own writings. Finally, I defend the Schema and the Theory against a number of objections that have been made.

MSC:
03F55 Intuitionistic mathematics
03F60 Constructive and recursive analysis
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