The Creating Subject, the Brouwer–Kripke Schema, and infinite proofs

• Published in: Indagationes mathematicae Vol. 29; no. 6; pp. 1565 - 1636
• Main Author: van Atten, Mark
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2018; Elsevier Science Ltd
• Subjects: Brouwer, L. E. J., Brouwer–Kripke schema; Creating subject; Infinite proofs; Intuitionistic logic; Intuitionistic mathematics; Kreisel, G., Kripke, S., Myhill, J., Troelstra, A.S., Theory of the creating subject; Logic; Numerical analysis; Proof theory; Theoretical mathematics; Kreisel, G., Kripke, S., Myhill, J., Troelstra, A.S., Theory of the creating subject; Brouwer, L. E. J., Brouwer–Kripke schema; Intuitionistic logic; Infinite proofs; Creating subject; Intuitionistic mathematics
• ISSN: 0019-3577; 1872-6100
• DOI: 10.1016/j.indag.2018.06.005

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.