1 Abbreviations: Wittgenstein Ludwig, Tractatus Logico-Philosophicus , translated by Pears D. F. and McGuinness B. F. (London: Routledge and Kegan Paul, 1974) [= TLP]; Wittgenstein Ludwig, “Some Remarks on Logical Form,” in Ludwig Wittgenstein: Philosophical Occasions, 1912–1951 , edited by Nordmann A. and Klagge L. (Indianapolis: Hackett, 1999) [= SRLF]; Wittgenstein Ludwig, Philosophical Remarks, translated by Hargreaves R. and White R. (Oxford: Blackwell, 1975) [= PR]; Wittgenstein Ludwig, Wiener Ausgabe, edited by Nedo M. (Vienna: Springer, 1993–) [= WA]; Wittgenstein Ludwig, The Big Typescript (2000), in WA, vol. 11 [= BT]; McGuinness B. F., ed., Wittgenstein and the Vienna Circle, shorthand notes recorded by Waismann F. (Oxford: Blackwell, 1979) [= WVC]; Wittgenstein Ludwig, Vorlesungen 1930–1935 (Frankfurt: Suhrkamp, 1984) [= VL 1930–35]; Wittgenstein Ludwig, Philosophical Grammar, translated by Kenny A. (Berkeley, CA: University of California Press, 1979) [= PG]; Wittgenstein Ludwig, Zettel, translated by Anscombe G. E. M. (Oxford: Blackwell, 1987) [= Z]; Wittgenstein Ludwig, Philosophical Investigations , translated by Anscombe G. E. M. (Oxford: Blackwell, 1976) [= 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), 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 [1980–1981]: 142–49); and Hacker P. M. S., Insight and Illusion (Oxford: Oxford University Press, 1972), pp. 86–94.
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. 77–101; at p. 80.
4 Noë Robert Alva, “Wittgenstein, Phenomenology and What It Makes Sense to Say” (Philosophy and Phenomenological Research, 54 : 1–42), p. 19. Indeed, the plan for a phenomenological language in “Some Remarks on Logical Form” (1929) 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.
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,” in von Helmholtz Hermann, Epistemological Writings: The Paul Hertz/Moritz Schlick Centenary Edition of 1921, with notes and commentary by the editors, translated by Lowe Malcolm F., edited by Robert S. Cohen and Yehuda Elkana (Dordrecht: Reidel, 1977), pp. 1–26, esp. p. 12. 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), esp. chaps. 2 and 6. Hyder also notes that Helmholtz's characterization of a space of possibilities as a “degree of freedom” (Freiheitsgrad) 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. 202–203).
8 Helmholtz , “On the Origin and Significance of the Axioms of Geometry,” p. 13.
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. 93; see also PR 208).
11 See Jackson Frank, “Epiphenomenal Qualia,” Philosophical Quarterly, 32 (1982): 127–36.
12 I owe this way of putting the problem to Ohad Nachtomy.
13 Moreover, in the Philosophical Remarks (1930), Wittgenstein writes, “one can now recognize colours immediately as mixtures of red, green, blue, yellow, black and white” (PR, p. 273). 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. 89–103, esp. pp. 89–90, n.5.
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.
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.