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Modality and the Tractatus*

  • Nicholas Griffin (a1)

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It would be hard to deny that there is some modal doctrine in Wittgenstein's Tractatus, for the Tractatus contains the standard semantics for the classical propositional calculus and the standard semantics is modal. Moreover, the work makes serious use of modal concepts, especially that of a possible state of affairs (möglich Sachverhalt). Given the centrality of this notion, it is curious that commentators have so readily ignored the modal aspects of the Tractatus Raymond Bradley's excellent, full-blown study of Wittgenstein's early modalism is, therefore, all the more welcome as a corrective.

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1 It is astonishing, for example, that the only reference to modality in Carruthers's, PeterTractarian Semantics (Oxford: Blackwell, 1989) occurs in a brief discussion of the distinction between transparent and opaque contexts for names (pp. 141–42). There are, however, honourable exceptions to this neglect, most notably Stenius, Eric, Wittgenstein's Tractatus: A Critical Exposition of the Main Lines of Thought (Oxford: Basil Blackwell, 1960), and Stegmiiller, Wolfgang, “Eine modeltheoretische Präzisierung der wittgensteinschen Bildtheorie,” Notre Dame Journal of Formal Logic, 7, 2 (1966): 181–95; and, more recently, Wright's, G. H. von “Modal Logic in the Tractatus” in his Wittgenstein (Minneapolis: University of Minnesota Press, 1982), pp. 185200.

2 Wittgenstein, Ludwig, Tractatus Logico-Philosophicus, translated by Pears, D. F. and McGuiness, B. F. (London: Routledge and Kegan Paul, 1961), 2.0222.023. Henceforth cited as TLP. All quotations are from this translation, unless otherwise noted.

3 A parallel passage is to be found in the 1913 manuscript “Notes on Logic” in Wittgenstein, Ludwig, Notebooks, 1914–1916, edited by Wright, G. H. von and Anscombe, G. E. M., translated by Anscombe, G. E. M., 2nd ed. (Chicago: University of Chicago Press, 1979), p. 104(2). Henceforth cited as NB.

4 Strictly, Bradley argues that it is an extension of S5, Crossley and Humberstone's system S5A, obtained by adding to S5 a modal operator ‘A’ (read: ‘Actually’), such that ‘Ap’ is true iff ‘p’ is true in the actual world. See Crossley, J. N. and Humberstone, I. L., “The Logic of ‘Actuality’,”Reports on Mathematical Logic, 8 (1977): 1129. Wright, G. H. von, Wittgenstein (Minneapolis: University of Minnesota Press, 1982), also asserts that S5 was Wittgenstein's logic for modal propositions.

5 On the other hand, identity is not so easily added to the Tractatus system. Suppose that ‘ø(a)’ is putatively an elementary proposition, in which ‘a’ is putatively a name. Then, whether ‘ø(a)’ has sense depends upon whether ‘a’ has a bearer. In a system with identity, this condition can be expressed by the proposition ‘(∃x)(x = a)’, upon the truth of which the sense of ‘φ(a)’ will thus depend—thereby violating Wittgenstein's important requirement that whether one proposition has sense cannot depend upon whether another proposition is true TLP, 2.0211).

6 Russell, Bertrand, “The Philosophy of Logical Atomism”, in The Collected Papers of Bertrand Russell, Vol. 8, The Philosophy of Logical Atomism and Other Essays: 1914–19, edited by Slater, John (London: Allen and Unwin, 1986), p. 186.

7 Rescher, Nicholas, “Russell and Modal Logic,” in Bertrand Russell Memorial Volume, edited by Robert, G. W. (London: George Allen and Unwin, 1979).

8 Wright, G. H. von, Wittgenstein, p. 192, takes the same view.

9 Hintikka, M. B. and Hintikka, J., Investigating Wittgenstein (Oxford: Basil Blackwell, 1987).

10 Ibid., p. 65.

11 This, of course, exactly repeats Wittgenstein's most powerful criticism of Russell's theory of types, namely, that any attempt to state the theory generally will violate the significance constraints imposed by the theory itself.

12 In addition, Wittgenstein sometimes uses ‘proposition’ to refer only to contingent propositions, and sometimes more broadly to include the “pseudopropositions” which are strictly unsayable.

13 I am grateful to Anthony Jenkins for several recent discussions on the Tractatus. My research was supported by the Social Sciences and Humanities Research Council of Canada.

* Raymond Bradley, The Nature of All Being (Oxford and New York: Oxford University Press, 1992), xxi + 244 pp., $55.95. Page references are to this work.

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Modality and the Tractatus*

  • Nicholas Griffin (a1)

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