Wittgenstein's threefold view on proofs

In his remarks on the philosophy of mathematics, Wittgenstein emphasizes three aspects of proofs: (1) that proofs contribute to the meaning of the concepts involved in theorems, (2) that there is a fundamental difference between proofs and experiments, and (3) that proofs must be surveyable. He sees these aspects as inseparable from each other and as features of the grammar of proofs. This paper illuminates Wittgenstein’s view on mathematical proofs by discussing these three aspects of proofs and by considering how a specific proof – of the Bolzano Weierstrass theorem – exhibits them.