Abstract

The primary purpose of this book is to probe the "deep common sources" of Wittgenstein’s Investigations and Remarks on the Foundation of Mathematics in his later philosophy of language. The question is whether Wittgenstein’s thought about mathematics can be presented sympathetically, and so defended from charges of superficiality or eccentricity which have often been levelled against it. There are other strands in this complex, simultaneously gripping and maddening work, including confrontations of varying extent with relevant doctrines of Dummett, Davidson, and Quine, to cite the main cases. The character of Wittgenstein’s own thought was far from systematic, yet this does not seem to justify the virtual lack of systematic presentation of his defense by Wright. We can, nevertheless, pick out the main thrust of Wright’s case. The author takes his bearings by the quarrel within twentieth century philosophy of mathematics between platonism and intuitionism. Platonism may be briefly described as the view that, if p is a mathematical proposition, we know what would be the case if p were true, even if we can't show that p is true. For intuitionism, on the other hand, to know what would be the case if p were true, is impossible unless we can show that p is indeed true.