Wittgenstein And G(?)del's Theorem

Remarks on the Foundation of Mathematics was published in 1956. Compared with Wittgenstein's major work Philosophical Investigation, this book got a very different reputation. In a long time, Wittgenstein's philosophy of mathematics have been considered to be of very little value, or unintelligible. Even sympathizing scholars often feel it is difficult to defend.There are two subjects which have reseived especially severe criticism. One of them is Wittgenstein's remarks about contradiction; another is his remarks about G(o|¨)del's theorem. Many famous scholars thought Wittgenstein was making random remarks while he didn't understand G(o|¨)del's theorem. G(o|¨)del himself, after reading some of those remarks, said 'it seems nonsense to me'. Such critisizm deepen people's impression: the whole philosophy of mathematics by Wittgenstein is distrustful.Since 1988, 'Wittgenstein on G(o|¨)del' seems to have become a hot subject. Some scholars have been trying to defend for Wittgenstein. The initial motive of this paper is also this.At first, this paper gives an introduction of G(o|¨)del's theorem and its background. At the same time, it describes the change from ancient mathematics to modern mathematics through a study of calculous. After that, it tries to 'introduce' philosophy of mathematics of latter Wittgenstein: not only to bring forward major points of Wittgenstein, but also to understand them. Particularly it gives a justification for Wittgenstein's remarks about contradiction. Finally, this paper summarizes recent papers concerning the theme 'Wittgenstein on G(o|¨)del', and proposes another approach to defend for Wittgenstein.The conclusion of this paper is: Wittgenstein's remarks about G(o|¨)del's theorem are justifiable-even if it is done through a different way from what the critics suppose it should be. And clarifying this theme would be helpful for us to pay more attention to or to admit the value of Wittgenstein's philosophy of mathematics, and in doing this, would provide a radical critisizm at the heart of comtemporary analytic philosophy, supposedly.