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Published online by Cambridge University Press: 25 February 2009
Some readers, even though well versed in philosophy, may be bewildered by Wittgenstein's posthumous book on the philosophy of mathematics and unable to find a dominant theme running through even a part of it; to list the main contents–headings would make them none the wiser. Although two main themes may in the end be discerned in it, they do not pervade the book after the usual manner of themes; one has rather the sense of wandering about the corridors of a maze; and, to add to the reader's perplexity, the maze has no definite centre. This mode of presentation, leading one through a maze, whose “centre” is the discovery that there is no centre, in itself conveys some philosophical message. Can we possibly say what Wittgenstein was trying to do? To answer this, seeing that this work is largely in line with the rest of his philosophizing, I propose to bid the present book a long farewell, to take an excursion into the field of Wittgensteinian and related philosophy, and against this background to try to give some picture and assessment of the contents of the work.
page 338 note 1 Wittgenstein, Ludwig, verso Bemerkungen über die Grundlagen de Mathematik, recto Remarks on the Foundations of Mathematics, Basil Blackwell, Oxford, 1956, pp. xix + 204, 37s. 6d.Google Scholar
page 340 note 1 To regard the essence of philosophy as consisting of a language game, however, is not to commit the essentialist fallacy, but to make a theory, for a (natural) language does not have flexible boundaries in the way philosophy has.
page 341 note 1 First cousin to behaviourism is epiphenomenalism which is incompatible with phenomenalism—a point that seems to have escaped notice.
page 342 note 1 Popper, K. R., The Open Society and Its Enemies, London, 1957, Vol. II, pp. 296–7.Google Scholar
page 344 note 1 In a somewhat different form Bertrand Russell made the same point some while ago, when he argued that use was influenced not only by context but by ideas (“The Cult of ‘Common Usage’ “, Brit. J. for Phil. of Sc., 1953, 8, 304). (He no more explained his illustration than he would in the last century have translated a Latin quotation; but one wonders if Latin quotations were so widely understood.)
page 344 note 2 In the Newtonian theory of gravitation the deductions about planetary motion are relatively short.
page 345 note 1 Von Mises brought this out (Mises, R. von, Probability, Statistics, and Truth,.London, 1939, Ch. I. esp. pp. 4–5), where he discusses the scientific and the ordinary use of “probability” and “force”. Mises’ comments fell on ears that were deaf to scientific contexts.Google Scholar
page 345 note 2 Popper, K. R., The Logic of Scientific Discovery, London, 1959, pp. 68–70, 121, esp.193;Google ScholarWatkins, J. W. N., “Between Analytic and Empirical”, Philosophy, 1957, 32, 112–31;CrossRefGoogle Scholar“Confirmable and Influential Metaphysics”, Mind, 1958, 67, 344–65.Google Scholar
page 346 note 1 See Smart, J. J. C., “A Note on Categories”, Brit. J. for Philos.of Sc, 1953, 4, 227–8.CrossRefGoogle Scholar
page 347 note 1 My colleague Dr. Agassi adds the point that, in discussing category–mistakes, the intention is to find out linguistic errors, e.g. the misuse of the word “mind”, but we find in addition ontological errors, like the supposedly faulty idea that minds exist—thus the category–argument involves a “higher–order” category–mistake. I am indebted to Dr. Agassi for a number of valuable comments.
page 347 note 2 A new attitude may be embryonic: there are a few who recognize contributions by Wittgenstein even if they do not rate these at all highly, and there are a few who regard his work with great respect without agreeing with it.
page 349 note 1 I draw attention to this sentence in case it should seem that I regard the modesty as bogus. Some of it was surely genuine. The juxtaposition of modesty and vanity is of course an interesting phenomenon.
page 352 note 1 Tarski, A., “On the Concept of Logical Consequence”, Logic, Semantics, Meta–mathematics, Oxford, 1956, pp. 415 ff.Google Scholar