Diversity Reading List

In Remarks on the Foundations of Mathematics, and elsewhere, Wittgenstein made some general statements about mathematical proof which can only be described as paradoxical. What he says is directed to proofs for which there is no general method of solution such as there is for statements of the form a x b = c where a simple calculation is sufficient. His concern is with propositions for which one cannot in advance of proof describe any procedure which will demonstrate them... In an earlier study,' 'Proof and the Theorem Proved', I singled out a group of propositions for which his account of proof seemed correct, and not paradoxical.... But I did not succeed in making his account of deductions of connections between established concepts paradox-free. I should like to return to his account as applied to such demonstrations, with the aim of explaining what justification there is for it, and what his account comes to.