WITTGENSTEIN’S PHILOSOPHY OF MATHEMATICS
For reading a book, Please sign in to your account.
loginThis book is intended to be an exposition, as unbiased as possible, of theconceptions on mathematics which were progressively elaborated byWittgenstein during the entire course of his reflections on the subject (fromthe Tractatus up to 1944). The fact that I have based my work exclusivelyon already published material (including notes on lectures and onconversations) does not mean that I believe a philologically crediblereconstruction of the evolution of Wittgenstein’s thought – obtained byaccurately analysing the manuscripts and typescripts he left – to be of littleimportance. Rather, I have set myself to do something which could contributeto a critical reading of the texts which have not yet been published: that is, toadvance general interpretative conjectures, which may later find furtherconfirmation in those texts (in addition to that furnished, in my opinion, bythe published writings), or else refutation. Although this strategy properlyapplies to the writings after 1929 and not to the Tractatus, a systematicexposition of Wittgenstein’s view of mathematics has appeared to meindispensable also in relation to his first work. The results that I have reachedon this subject are reported in Chapter 1. As far as the writings of his so-called intermediate phase (1929–33) are concerned, and those of the decade1934–44, I have tried to extract the general lines of Wittgenstein’s approachto mathematics in these two periods. I have singled out the watershed betweenthem to be the radical development of his considerations on rule-followingand his consequent abandoning of a certain strong version of verificationism,which he endorsed in the intermediate phase. Even here there is a justificationfor the direction my work has taken: in my opinion, in spite of how heconceived, in those years, his own philosophical work, and hence of theform that his reflections assumed, Wittgenstein developed – with increasingcoherence – an overall conception of mathematics, which I have called “quasi-formalism” (a conception – to some extent – already present in the Tractatus,and whose mature core is a full-blooded nominalistic view of necessity).Certainly, this is not a novelty at all. But I believe that even today it is usefulto seek to give a less rhapsodic and more systematic formulation ofWittgenstein’s views on mathematics. Indeed, often those who are not struckby the fascination of his writings “throw the baby away with the bath water
