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

TL;DR

This paper analyzes the Brouwer-Kripke Schema and the Kreisel-Troelstra Theory of the Creating Subject, exploring their origins, applications, and philosophical justification within Brouwer's intuitionism, including defenses against common objections.

Contribution

It provides a detailed examination of the Brouwer-Kripke Schema and the Kreisel-Troelstra Theory, highlighting their historical development, philosophical basis, and presence in Brouwer's writings.

Findings

The Schema and Theory are closely linked to Brouwer's arguments.

Instances of the Schema are identifiable in Brouwer's own texts.

The paper defends the Schema and Theory against several objections.

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 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.