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

Mark van Atten
2018 Indagationes mathematicae  
Forthcoming in Indagationes Mathematicae. Abstract 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
more » ... ive, 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.
doi:10.1016/j.indag.2018.06.005 fatcat:4qgl4bi5trd6leisflx5hoyy4q