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Published online by Cambridge University Press: 01 January 2020
What is the source of the hardness of the logical must? What does the necessity of mathematical and logical inference consist in? If I am plotting the curve y = x2 and assume that x = 2 I must conclude that y = 4; no other consequence can be drawn. What is the nature of this ‘must'?
Understanding Wittgenstein's answer to this question is essential to understanding his later philosophy. The question of the nature of logical or mathematical necessity is as fundamental for the Investigations as it obviously was for the Tractatus. Barry Stroud's article “Wittgenstein and Logical Necessity” certainly is still one of the most illuminating and important of the papers dealing with this question.
1 I am indebted to Professors R. B. deSousa, Hans Herzberger and john Hunter for helpful comments on an earlier draft of this paper.
2 The Philosophical Review, LXXIV (1965), 504-518; reprinted in Pitcher, G. (ed.), Wittgenstein, The Philosophical Investigations (New York, 1966), pp. 477–496Google Scholar. Page references are to this reprint.
3 Trans. G. E. M. Anscombe (Oxford, 1963).
4 Remarks on the Foundations of Mathematics, trans. Anscombe, G. E. M. (Oxford, 1964), Part I, §§ 148, 149.Google Scholar
5 The size paradigm cloud always hovers in the centre of their sky; a striking meteorological phenomenon.
6 The idea that the people are blind to a contradiction inherent in their language rests on a mistaken view of language. Language and custom are inseparably related. In inventing language games we are sketching social practices. These sketches can be developed and filled in in any number of ways. It isn't a question of the sketch's implications being drawn out so that a contradiction emerges. In particular we can imagine that it is the people's practice to not make the kinds of interconnections between practices that, as we would say, lead to a contradiction. It should also be noted that if Wittgenstein's view of language is adopted, the idea of a contradiction itself changes, and with it the importance of a contradiction. When language is thought of as an homogeneous field, a contradiction in language is viewed as reaching throughout that field, and in some sense as destroying it. But when language is viewed as an anthropological phenomenon, a heterogeneous collection of language games, the meaning and import of a contradiction is itself dependent on social practices for producing, discerning and dealing with it. And these are various.
7 Brown Book, Part II, § 5.
8 Philosophical Investigations, § 186.
9 Part II,§ 5.
10 Remarks on the Foundations of Mathematics, Part I,§ 5.
11 Ibid.
12 Ibid., § 4.
