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Published online by Cambridge University Press: 13 April 2010
That Wittgenstein in the Tractatus likens logic to geometry has been noticed; however, the extent and force of the analogy he develops between logical form and a broadly Kantian account of geometry has not been sufficiently appreciated. In this paper, I trace Wittgenstein's analogy in detail by looking closely at the relevant texts. I then suggest that we regard the fact that Wittgenstein develops his account of logical form by analogy with a Kantian account of geometry as evidence for the bold thesis that Wittgenstein belongs within a Kantian epistemological tradition. Finally, I supply two small pieces of the interpretive puzzle needed to support the larger thesis: first, evidence that Wittgenstein's concern with logical form involves a crucial epistemological component; second, a sketch of how Wittgenstein's account of logical and mathematical knowledge can be viewed as continuing a Kantian tradition.
1 A shortened version of this section of the paper is to appear as “Logical Form and Kan-tian Geometry: Wittgenstein's Analogy,” in Wittgenstein: Towards a Re-Proceedings of the Fourteenth International Wittgenstein Symposium, edited by Haller, R. and Brandl, J. (Vienna: Höder-Pichler-Tempsky, 1990)CrossRefGoogle Scholar.
2 Unless otherwise noted, all references are to Wittgenstein, Ludwig, Tractatus Logico-Philosophicus, translated by Pears, D. F. and McGuinness, B. F., with an Introduction by Russell, Bertrand (London: Routledge and Kegan Paul, 1961).Google ScholarReferences to the Notebooks 1914–1916, edited by Wright, G. H. von and Anscombe, G. E. M., translated by Anscombe, G. E. M. (New York: Harper & Row, 1961)Google Scholar are cited as NB. References o t the Prototractatus: An Early Version of Tractatus Logico-Philosophicus, edited by McGuinness, B. F., Nyberg, T. and Wright, G. H. von, translated by Pears, D. F. and McGuinness, B. F., with an historical introduction by Wright, G. H. von (Ithaca: Cornell University Press, 1971), are cited as PTGoogle Scholar.
3 I do not claim that Wittgenstein was influenced directly by Kant; it may well be that Wittgenstein is more directly indebted for his Kantianism to Hertz, Schopenhaur and Frege than he is to Kant himself. However, it is now known that Wittgenstein did read and discuss Kant with Ludwig Hänsel during the time he was a prisoner in Monte Casino. See McGuinness, Brian, Wittgenstein: A Life: Young Ludwig 1889–1921 (London: Duckworth, 1988), p. 270Google Scholar.
4 Some will object (as did a referee for this journal) that there is a point of disanalogy that overrides any points of analogy: according to the Tractatus, the world possesses logical form whether or not we construct representations of it; representation is possible because the elements of representation and the elements of reality share a common set of logical possibilities of combination, not because we impose form onto an otherwise formless reality. This “representational realism,” so the objection goes, contrasts with Kant's “transcendental idealism” in a way that rules out the claim that Wittgenstein continues a broadly Kantian tradition. In response to this objection, notice first that the claim that Wittgenstein espouses “representational realism” in the Tractatus is itself controversial; it has been contested by serious scholars such as Newton Garver, Hide Ishiguro and Brian McGuinness, among others. For example, Garver believes that Wittgenstein in the Tractatus adopts a metaphysical dualism that combines empirical realism with transcendental idealism: the world consists of facts, not objects, whereas the substance of the world consists of objects, not facts; the substance of the world determines the possibilities; possibilities are entirely different from facts; whereas the latter are empirical, the former are transcendental. See Garver, Newton, “Wittgenstein and the Critical Tradition,” History of Philosophy Quarterly, 7, 2 (03 1990): p. 227–239,Google Scholar and his “The Metaphysics of the Tractatus,” in Wittgenstein: Towards a Re-Evaluation: Proceedings of the Fourteenth International Wittgenstein Symposium (Vienna: Holder-Pichler-Tempsky, 1990): 84–94.Google Scholar See also Ishiguro, Hide, “Use and Reference of Names,” in Studies in the Philosophy of Wittgenstein, edited by Winch, Peter (London, 1969), p. 20–50Google Scholar and McGuinness, Brian, “The So-called Realism of Wittgenstein's Tractatus,” in Perspectives on the Philosophy of Wittgenstein, edited by Block, Irving (Cambridge, MA: MIT Press, 1981), p. 60–73.Google Scholar Notice second that metaphysical claims about what constitutes or determines logical or geometrical form are not equivalent to epistemological claims about the ways in which we come to know or to grasp such form. Thus, even if it were true that Wittgenstein and Kant differ in their metaphysical accounts of form, it would not follow that they differ in their epistemological accounts of the way in which we grasp form. Finally, the five points of analogy outlined in this paper are themselves important whether or not there is an important disanalogy between Wittgenstein and Kant.
5 Wittgenstein, , Tractatus Logico-Philosophicus translated by Ogden, C. K., with an introduction by Russell, Bertrand (London: Routledge and Kegan Paul, 1922)Google Scholar.
6 The Tractarian passages cited concerning construction apparently refute David Pears's recent remark that the Tractatus (to use Schopenhauer's terminology) presents only the “world as idea” and contains nothing of the “world as will.” See Pears, David, The False Prison: A Study of the Development of Wittgenstein's Philosophy (Oxford: Clarendon Press, 1987), Vol. 1, p. 6CrossRefGoogle Scholar and 177. Newton Garver drew my attention to this consequence of the passages cited.
7 Of course Wittgenstein does not accept Kant's views unmodified, and much more needs to be said about the specific respects in which the Tractatus is epistemological. For one thing, neither Wittgenstein nor Kant is interested in refuting scepticism, as many epistemologists in the history of Western philosophy have been (see footnote 11 below); for another, Wittgenstein changes Kant's question about the possibility of synthetic a priori knowledge to a question about the possibility of representation. Still, I believe, Wittgenstein answers his question by insisting that representation is possible only if we have some non-trivial a priori knowledge and his account of that knowledge is Kantian in outline. See sections 2 and 3 of this article.
8 Some who attribute epistemology to the Tractatus would deny that it is Kantian. For example, the logical positivists thought that the Tractatus espouses an empiricist epistemology, and the Hintikkas have recently revived this interpretation by arguing that the simple objects of the Tractatus are Russellian objects of acquaintance. See Hintikka, Merrill B. and Hintikka, Jaakko, Investigating Wittgenstein (Oxford: Basil Blackwell, 1986).Google Scholar Some who attribute Kantianism to the Tractatus would deny that it is epistemo-logical. For example, Henry Finch urges that, once historians of philosophy have finished their work, “Wittgenstein will be seen to have as much claim to be a true descendant of Kant as any of the rest of Kant's vast philosophical progeny,” but he also thinks that Wittgenstein displaces epistemological concerns from the centre of philosophy in favour of concerns about language. See Finch, Henry, Wittgenstein: The Early Philosophy (Atlantic Highlands, NJ: Humanities Press, 1971), p. 267Google Scholar and 252. Finally, some would deny that the Tractatus is either Kantian or epistemological. See, e.g., Dummett, Michael, Frege: Philosophy of Language (London: Harper & Row, 1973), p. 679Google Scholar; Dummett, , “Frege and Kant on Geometry,” Inquiry, 25 (06 1982): 233–254;CrossRefGoogle Scholar and Dummett, , “Wittgenstein's Philosophy of Mathematics,” in Wittgenstein: The Philosophical Investigations, edited by Pitcher, George (Notre Dame: University of Notre Dame Press, 1968), p. 446Google Scholar.
9 Some of those who emphasize parallels with Kant have recently become more sympathetic to the idea that there may be epistemology in the Tractatus. For example, in 1969 David Pears claimed that “the aloofness” of Wittgenstein's “theory of meaning and its detachment from any particular theory of knowledge are conspicuous.” See Pears, Ludwig Wittgenstein (New York: Viking Press, 1969), p. 70.Google Scholar More recently, however, he has acknowledged that arguments against reading Russellian empiricism into the Tractatus leave open the possibility that Wittgenstein was concerned with the foundations of empirical knowledge: “True, his approach would be entirely different from Russell's: it would be an a priori deduction of the essential structure of empirical knowledge, in the style of Kant. Nevertheless, the Tractatus would still be about empirical knowledge and its main thesis would be that objects belong to the world as we find it.” See Pears, The False Prison, p. 91. Still, he ultimately rejects this thesis, on the arguably irrelevant ground that there is a “basic realism” in the Tractatus. See Kannisto, Heikki, “Thoughts and Their Subject: A Study of Wittgenstein's Tractatus,” Acta Philosophica Fennica, 40 (Helsinki, Finland, 1986),Google Scholar for an example of a philosopher who finds both Kantianism and epistemology in the Tractatus.
10 Recently a number of philosophers have urged that we should read Gottlob Frege's work as continuing the tradition of Kantian epistemology: Currie, Gregory, “Frege on Thoughts,” Mind, 89 (1980): 234–248CrossRefGoogle Scholar and Frege: An Introduction to His Philosophy (Totowa, NJ: Barnes and Noble, 1982)Google Scholar; Kitcher, Philip, “Frege's Epistemology,” The Philosophical Review, 88 (03 1979): 235–262;CrossRefGoogle ScholarSluga, Hans, Gottlob Frege, The Arguments of the Philosophers (London: Routledge and Kegan Paul, 1980)Google Scholar; Weiner, Joan, “Putting Frege in Perspective,” in Frege Synthesized, edited by Haaparanta, Leila and Hintikka, Jaakko (Dordrecht, Holland: D. Reidel, 1986), p. 9–27CrossRefGoogle Scholar.
11 Scholars have noticed important parallels between Wittgenstein's central question (How is representation possible?) and Kant's (How is synthetic a priori knowledge possible?). The questions asked presuppos e that representation and synthetic a priori knowledge, respectively, are possible. Accordingly, neither Wittgenstein nor Kant is concerned to answer the sceptic by showin g that representation or knowledge are in fact possible. Eric Stenius was perhaps the first to emphasize the important parallel between the questions Wittgenstein and Kant ask. See his Wittgenstein's Tractatus: A Critical Exposition of Its Main Lines of Thought (London: Basil Blackwell, 1960).Google Scholar See also Garver, “Wittgenstein and the Critical Tradition,” for an extremely rich and suggestive discussion of a number of parallels between Wittgenstein and Kant. Garver, however, resists the attribution of Kantian epistemology to the Tractatus.
12 He cannot say the latter, since, according to him, “all the propositions of logic are of equal status: it is not the case that some of them are essentially primitive propositions and others essentially derived propositions” (6.127).
13 Philip Kitcher emphasizes this point in “Frege's Epistemology,” p. 250.
14 Baker, G. P. and Hacker, P. M. S., Wittgenstein: Understanding and Meaning (Chicago: University of Chicago Press, 1980), Vol. 1, p. 527–528Google Scholar.
15 In addition, uncritical comparisons of Wittgenstein's notion of analyticity with Kant's notion may be misleading, since Kant's multiple senses of 'analytic' come apart after Frege introduces his new logic. For example, Jaakko Hintikka has argued that Kant's analytic/synthetic distinction is drawn within what we now call quantification theory. See Hintikka, Jaako, Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic (Oxford: Clarendon Press, 1973), p. 174–198.Google Scholar For another example, Michael Friedman has suggested that, if logic is syllogistic or monadic, as Kant thought, then Euclidean constructive proofs do require an “extra-logical element,” though if logic is polyadic, they do not. See Friedman, Michael, “Kant's Theory of Geometry,” The Philosophical Review, 44, 4 (10 1985): 455–506CrossRefGoogle Scholar.
16 “Light on Kant's question 'How is pure mathematics possible?' through the theory of tautologies” (NB 19.10.14, p. 15).
17 Casimir Lewy is reported (by a referee for this journal) to have said that once when Wittgenstein was asked if he thought mathematics was part of logic, he replied by denying it, offering as proof that whereas logic consists of tautologies, mathematics consists of equations.
18 Compare 6.126–6.127 with 6.23–6.241.
19 H. O. Mounce suggests that it is significant that Wittgenstein offers his account of number (6.02f.) just after he has given the general form of the proposition (6). In fact, Mounce argues, according to Wittgenstein in the Tractatus there is “an internal connection between the notion of number and that of the operation by which one proposition is generated from another.” See Mounce, H. O., Wittgenstein's Tractatus Introduction (Chicago: University of Chicago Press, 1988), p. 60.Google Scholar According to Mounce, Wittgen-stein does not think, as Russell and Frege did, that the propositions of mathematics can be derived from some particular set of logical propositions. But mathematics “is an aspect of the fundamental logical operation by which any proposition is derived from another” (ibid., p. 64).
20 This is as true of geometry as of arithmetic (6.35). Constructing geometrical figures reveals the structure of space (though geometrical figures say nothing about the “actual form and position” of objects). Since space is at the same time logical “space,” and logical propositions reveal the structure of logical “space,” geometrical constructions are a “logical method” in Wittgenstein's broad sense of logical. Of course, logical “space” is a metaphor, but actual space is really at the same time logical “space,” in the sense that spatial representations are “propositions” with logical features and they share those features with the situations they represent.
21 Insofar as we have a priori insights about the forms in which propositions about the world can be cast, Wittgenstein would deny that they are scientific laws; insofar as something is a genuine scientific law, Wittgenstein would deny that it is a priori. See, for example 6.32 (“The law of causality is not a law but the form of a law”) and 6.3431 (“The laws of physics, with all their logical apparatus, still speak, however indirectly, about the objects of the world”).
22 I am indebted to Karl Ameriks, Pieranna Garovaso, Newton Garver, Penelope Maddy, Pat Manfredi, Mark Risjord and referees for this journal for helpful comments on earlier versions of this work, and to helpful audiences at the Fourteenth Annual Wittgen-stein Symposium, Kirchberg, Austria, August 1989 and at the Central Division Meeting of the American Philosophical Association, New Orleans, April 1990.
