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Wittgenstein on Colours and Logical Multiplicities, 1930–1932

Published online by Cambridge University Press:  27 April 2009

Andreas Blank
The Cohn Institute, Tel Aviv University


This article explores Wittgenstein's little known remarks on colour from his notebooks of the early 1930s. It emphasizes the importance of the notion of logical multiplicity contained in these remarks. The notion of logical multiplicity indicates that Wittgenstein, as in the years of the Tractatus, is committed to a theory of logical space in which every colour is embedded. However, logical multiplicities in his remarks of the early 1930s do not depend on an apparatus of simple objects, states of affairs, and elementary propositions. I suggest that, in this period, the logical multiplicity of colour space is a matter of how we see colours.

Copyright © Canadian Philosophical Association 2008

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1 Abbreviations: Wittgenstein, Ludwig, Tractatus Logico-Philosophicus [1922], translated by Pears, D. F. and McGuinness, B. F. (London: Routledge and Kegan Paul, 1974)Google Scholar [= TLP]; Wittgenstein, Ludwig, “Some Remarks on Logical Form,” in Ludwig Wittgenstein: Philosophical Occasions, 1912–1951 [1929], edited by Nordmann, A. and Klagge, L. (Indianapolis: Hackett, 1999)Google Scholar [= SRLF]; Wittgenstein, Ludwig, Philosophical Remarks, translated by Hargreaves, R. and White, R. (Oxford: Blackwell, 1975)Google Scholar [= PR]; Wittgenstein, Ludwig, Wiener Ausgabe, edited by Nedo, M. (Vienna: Springer, 1993–)Google Scholar [= WA]; Wittgenstein, Ludwig, The Big Typescript (2000)Google Scholar, in WA, vol. 11 [= BT]; McGuinness, B. F., ed., Wittgenstein and the Vienna Circle, shorthand notes recorded by Waismann, F. (Oxford: Blackwell, 1979)Google Scholar [= WVC]; Wittgenstein, Ludwig, Vorlesungen 1930–1935 (Frankfurt: Suhrkamp, 1984)Google Scholar [= VL 1930–35]; Wittgenstein, Ludwig, Philosophical Grammar, translated by Kenny, A. (Berkeley, CA: University of California Press, 1979)Google Scholar [= PG]; Wittgenstein, Ludwig, Zettel, translated by Anscombe, G. E. M. (Oxford: Blackwell, 1987)Google Scholar [= Z]; Wittgenstein, Ludwig, Philosophical Investigations [1953], translated by Anscombe, G. E. M. (Oxford: Blackwell, 1976)Google Scholar [= PI]. References to PR and BT are to section numbers, references to PG to section numbers in part I. References to WA are to volume, page, and remark number. Translations from WA are my own. All emphases are those of the original texts. Following the text of WA, I use a different font (Arial) for words underlined by Wittgenstein with a wavy line. In order to produce a more legible text, I relegate variants to the footnotes, even if, as more often than not, Wittgenstein did not decide between different variants.

2 Kienzler, Wolfgang, Wittgensteins Wende zu seiner Spätphilosophie 1930–1932: Eine historische und systematische Darstellung (Frankfurt: Suhrkamp, 1997)Google Scholar, chap. 3. See also PR 1; WA 2.102.5; WA 2.118.6–119.1; WA 5.176.2; BT 94. On the role of the problem of colour incompatibility in Wittgenstein's dismissal of the plan of a phenomenological language, see Austin, James, “Wittgenstein's Solutions to the Colour Exclusion Problem” (Philosophy and Phenomenological Research, 41 [19801981]: 142–49)CrossRefGoogle Scholar; and Hacker, P. M. S., Insight and Illusion (Oxford: Oxford University Press, 1972), pp. 8694.Google Scholar

3 Mulligan, Kevin, “Colours, Corners and Complexity: Meinong and Wittgenstein on Some Internal Relations,” in Existence and Explanation: Essays in Honor of Karel Lambert, edited by Spohn, W., Skyrms, B., and van Fraassen, B. (Dordrecht: Kluwer, 1991), pp. 77101; at p. 80.CrossRefGoogle Scholar

4 Noë, Robert Alva, “Wittgenstein, Phenomenology and What It Makes Sense to Say” (Philosophy and Phenomenological Research, 54 [1994]: 142), p. 19.CrossRefGoogle Scholar Indeed, the plan for a phenomenological language in “Some Remarks on Logical Form” (1929)Google Scholar involves such an isomorphic representation: “we can substitute a clear symbolism for the imprecise one by inspecting the phenomena which we want to describe, thus trying to understand their logical multiplicity” (SRLF 32).

5 In “Some Remarks on Logical Form,” Wittgenstein still holds that internal relations between qualities, which admit of degrees (such as colours), are expressed by means of internal relations between elementary propositions. For an interpretation of this view, see Jacquette, Dale, Wittgenstein's Thought in Transition (West Lafayette, IN: Purdue University Press, 1998), pp. 171–74.Google Scholar

6 It should be noted, however, that his official position vis-à-vis the Vienna Circle was more cautious. In the next day's session of January 2, 1930, he distinguishes between what is tenable in the theory of elementary propositions and what is not tenable. He claims that the theory of logical independence of elementary propositions is not tenable, while the theory of concatenations of simple signs is tenable (see WVC 73–74).

7 von Helmholtz, Hermann, “On the Origin and Significance of the Axioms of Geometry,”Google Scholar in von Helmholtz, Hermann, Epistemological Writings: The Paul Hertz/Moritz Schlick Centenary Edition of 1921Google Scholar, with notes and commentary by the editors, translated by Lowe, Malcolm F., edited by Robert S. Cohen and Yehuda Elkana (Dordrecht: Reidel, 1977), pp. 126, esp. p. 12.Google Scholar On Helmholtz's theory of multiplicities and its influence on Wittgenstein's early philosophy, see Hyder, David, The Mechanics of Meaning: Propositional Content and the Logical Space of the Tractatus (Berlin: De Gruyter, 2002)CrossRefGoogle Scholar, esp. chaps. 2 and 6. Hyder also notes that Helmholtz's characterization of a space of possibilities as a “degree of freedom” (Freiheitsgrad)Google Scholar reoccurs in Wittgenstein's discussion in the early 1930s of how a colour octahedron is part of grammar. As Wittgenstein puts it, grammar (e.g., the colour octahedron) determines the “degree of freedom” of language (e.g., of descriptions of colour (WA 2.193.2; see Hyder, , The Mechanics of Meaning, pp. 202203).Google Scholar

8 Helmholtz, , “On the Origin and Significance of the Axioms of Geometry,” p. 13.Google Scholar

9 Ibid., p. 12.

10 Mulligan has pointed out that a possible fourth dimension envisaged by Wittgenstein might be the perception of depth of a colour (“Colours, Corners and Complexity,” p. 93Google Scholar; see also PR 208).

11 See Jackson, Frank, “Epiphenomenal Qualia,” Philosophical Quarterly, 32 (1982): 127–36.CrossRefGoogle Scholar

12 I owe this way of putting the problem to Ohad Nachtomy.

13 Moreover, in the Philosophical Remarks (1930)Google Scholar, Wittgenstein writes, “one can now recognize colours immediately as mixtures of red, green, blue, yellow, black and white” (PR, p. 273).Google Scholar For a discussion of this passage, see Schulte, Joachim, “Mischfarben: Betrachtungen zu einer These Brentanos und einem Gedanken Wittgensteins,” in Schulte, Joachim, Chor und Gesetz: Wittgenstein im Kontext (Frankfurt: Suhrkamp, 1990), pp. 89103, esp. pp. 8990, n.5.Google Scholar

14 Wittgenstein inserted the words “the relation.”

15 The first variant of “with respect to the words” is “in the grammar of the words.”

16 The first variant of “buildings” is “mechanisms.”

17 The first variant of “must show” is “will reveal.”

18 The word “also” was inserted by Wittgenstein.

19 See Blank, Andreas, “Wittgenstein on Expectation, Action, and Internal Relations,” Inquiry, 50 (2007): 270–87.CrossRefGoogle Scholar

20 This paper owes a lot to two people: comments from Stephanie Härtel contributed greatly to getting some clarity into an early version, and the final version took shape in the course of long and very helpful discussions with Ohad Nachtomy.

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