Wittgenstein's Philosophical Development

Phenomenology, Grammar, Method, and the Anthropological View

M. Engelmann

• Publisher: Palgrave Macmillan
• Year: 2013
• ISBN:
  9781137316592
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

The book explains why and how Wittgenstein adapted the Tractatus in phenomenological and grammatical terms to meet challenges of his 'middle period.' It also shows why and how he invents a new method and develops an anthropological perspective, which gradually frame his philosophy and give birth to the Philosophical Investigations.

1

Phenomenology, ‘Grammar,’ and the ‘Limits of Sense’

1.1 Elementary propositions and the nature of necessity

Wittgenstein’s re-evaluation of the philosophy of the T is clearly connected to criticisms made by Ramsey. He recognizes his debt to Ramsey in the preface of the PI:

... since I began to occupy myself with philosophy again, sixteen years ago, I could not but recognize grave mistakes in what I set out in that first book [the T]. I was helped to realize these mistakes – to a degree which I myself am hardly able to estimate – by the criticism which my ideas encountered from Frank Ramsey, with whom I discussed them in innumerable conversations during the last two years of his life. (PI, preface)

Even though Wittgenstein mentions only the last two years of Ramsey’s life (he died in January 1930), he first met Ramsey in 1923.¹ According to Ramsey’s correspondence, he studied the T with Wittgenstein when he visited him in Austria in 1923.² In November 1923 Ramsey asked Wittgenstein if he wanted a copy of the Critical Notice, his review of the T: “Has Ogden sent you my review of Tractatus in Mind? If not, and you would like it I will send it to you, but it is not at all good and you must remember I wrote it before coming to see you” (CL, 192). Even though Ramsey himself says that his Critical Notice wasn’t good, some of his critiques, as we will see, point to the “grave mistakes” of the T and Wittgenstein’s efforts to fix them in 1929.

It is not clear whether Wittgenstein actually read the review, but there is no doubt that he was well aware of its contents.³ Apart from Wittgenstein’s recognition in the preface of the PI of the “grave mistakes” of the T due to discussions with Ramsey, some of his major concerns in 1929 are directly related to Ramsey’s review – Wittgenstein, in fact, wrote extensively on themes presented there.⁴

At the center of Wittgenstein’s worries in 1929 is the problem of the analysis of propositions that attribute degrees of a property to objects (for instance, attributions of colors, heights, weights, etc). Wittgenstein calls those propositions “statements of degree” (SRLF, 167). Ramsey’s criticism in his Critical Notice relates statements of degree (in particular those related to color and space) to one of Wittgenstein’s more important insights in the T, namely, his understanding of the nature of inference and logical necessity:

It is a principle of Mr. Wittgenstein’s ... that every genuine proposition asserts something possible, but not necessary. This follows from his account of a proposition as the expression of agreement and disagreement with truth possibilities of independent elementary propositions, so that the only necessity is that of tautology, the only impossibility that of contradiction. (Ramsey, 473)

Ramsey then introduces the problem that needs to be solved if this view should hold:

There is a great difficulty in holding this; for Mr. Wittgenstein admits that a point in the visual field cannot be red and blue; and, indeed, otherwise, since he thinks induction has no logical basis, we should have no reason for thinking that we may not come upon a visual point which is both red and blue. Hence he says that ‘This is both red and blue’ is a contradiction. This implies that the apparently simple concepts red, blue (supposing us to mean by those words absolutely specific shades) are really complex and formally incompatible. (Ramsey 1923, 473)

Ramsey’s critique showed that central insights of the T were at risk (that all necessity is logical necessity and that propositions of logic are tautologies), for they were grounded on the truth-functional explanation of logical necessity. Ramsey’s specific target is the following remark of the T about color exclusion:

For two colors, e.g. to be at one place in the visual field, is impossible, logically impossible, for it is excluded by the logical structure of color.

Let us consider how this contradiction presents itself in physics. Somewhat as follows: That a particle cannot at the same time have two velocities, i.e. that at the same time it cannot be in two places, i.e. that particles in different places at the same time cannot be identical.

(It is clear that the logical product of two elementary propositions can neither be a tautology nor a contradiction. The assertion that a point in the visual field has two different colors at the same time is a contradiction.) (T 6.3751)

Wittgenstein clearly says that it is “logically impossible” for two colors to be in the same place in the visual field. He also states that in physics the incompatibility is expressed as a contradiction. This means that an appeal to physics would not be appropriate. What physics supposedly shows, then, is that the incompatibility is logical, and not physical. Therefore, contrary to what Ramsey suggests, Wittgenstein does not intend to ground in physics his explanation of the contradiction. Here is Ramsey’s argument:

He [Wittgenstein] tries to show how this may be by analyzing them in terms of vibrations. But even supposing that the physicist thus provides an analysis of what we mean by ‘red’ Mr. Wittgenstein is only reducing the difficulty to that of the necessary properties of space, time, and matter, or the ether. He explicitly makes it depend on the impossibility of a particle being in two places at the same time.

Ramsey is wrong in assuming that the incompatibility, for Wittgenstein, is physical, as seen above. Perhaps, this is the reason he called his review “not good at all” after discussing the T with Wittgenstein. However, he is right in saying that in the T a color statement and a statement using the relation ‘between’ were not reduced to a formal tautology, i.e., to a truth-functional tautology. He continues the passage above:

These necessary properties of space are hardly capable of further reduction of this kind. For example, considering between in point of time as regards my experiences; if B is between A and D and C between B and D, then C must be between A and D; but it is hard to see how this can be a formal tautology. (Ramsey 1923, 473).

The relevant issues in Ramsey’s paper are thus the “structure of color” and the “necessary properties of space.” Perhaps, Wittgenstein could deal with axioms of geometry inside the framework of the T. Axioms of geometry, Wittgenstein argues, can be treated as arithmetical equations, i.e., as rules for inferences among ordinary propositions:

Because of this [the role of equations in inferences] the /apparent/ propositions of geometry cannot really be propositions, but [are] indicated transitions (Uebergaenge) from one proposition about spatial objects to another proposition about spatial objects. Thus, I can pass (uebergehen) directly from the proposition “A and B are between C and D” to “A is either between B and C or between B and D.” The axiom that seems to allow me this transition is a tautology; or there is something different determining about its form, something that can just make it [the axiom] a criterion for both propositions that it connects (MS 105, 51; from the beginning of 1929).

Rules concerning ‘between,’ which supposedly work like tautologies, belong to “mathematical geometry.” They could be taken, prima facie, as a method of logic, i.e., as principles of substitutional transitions between propositions, as the equations of arithmetic (see T 6.234, 6.24). One should have in mind here geometrical equations (MS 105, 17). In this case, the transition from “A and B are between C and D” to “A is either between B and C or between B and D,” would be similar to the transition from “2+2” to “4.” One could then say that the “geometry of a specific space” (the visual space) would behave in relation to “mathematical geometry” like “the sentence two and two plums are four plums and the sentence 2+2=4” (MS 105, 51). However, it is not clear how “mathematical geometry” relates to “geometry as the theory of one [particular] space” (MS 105, 51), i.e., to the geometry of the visual space (the space of the visual field). In the visual field we find “something different”: mathematical space is not colored, but visual space is. It is in the visual space that the structure of color and the structure of space are interconnected or, as Wittgenstein says, “color and space fill (saettigen) each other” (MS 105, 53). In the visual space, “there is no middle link” between color and space (MS 105, 53). That is, we cannot talk of an object – say, a patch of color – having the properties of “being here” and “having a color,” as in the physical space, for the patch is identical with color and position. Thus, it is the visual space that needs investigation if one is concerned with Ramsey’s criticism. This is precisely what Wittgenstein immediately does after his return to Cambridge (see MS 105, 1–11).⁵

Wittgenstein does not specify in the T what “the logical structure of color” is; he does not show how the “concepts red, blue [ ... ] are really complex and formally incompatible,” as Ramsey correctly points out (Ramsey 1923, 473). If “A is red & A is blue” is a contradiction, a logical impossibility, then the conjuncts cannot be elementary propositions (since elementary propositions are logically independent, according to the T). How to carry out the analysis was not an important task in the T. This is because, in the T, discovering which propositions are elementary is not the subject of logic, but of its application (T 5.557).⁶ Such an analysis must be possible and its results cannot collide with what we can know a priori concerning the possible results of such an analysis (4.211 and 5.134). We can know a priori, according to the T, that there must be logically independent elementary propositions, but we cannot tell a priori which propositions these are (5.557). Wittgenstein’s supposition is that the analysis, therefore, must be possible, while Ramsey’s objection could be paraphrased as “If it must be possible, it must be shown how it goes.” Ramsey is thus asking Wittgenstein to introduce a method to determine the elementary propositions that express the incompatibilities.⁷

Wittgenstein tries to meet Ramsey’s challenge with the elucidation of the supposedly intrinsic, implicit, properties of the visual field, for there “the forms color and visual space penetrate (durchdringen) each other” (MS 105, 41). The symbolism of the T might seem, at first, a promising tool for the task of explaining color incompatibilities:

Do not color and visual space relate to each other as argument and function? The forms of argument and function must also penetrate each other. (MS 105, 41).

However, it is immediately clear to Wittgenstein that the forms of argument and function have no intrinsic similarities with the special forms of space and color. Considering what Wittgenstein says in the MSS from the first half of 1929 (especially in MS 105, 01–100; MS 106, 49–101) and in SRLF, we can see what kind of analysis based solely on the forms function and argument he had in mind at the beginning of 1929, and maybe at the time of the T, for color statements.⁸ The intended analysis will indicate why the particular forms of objects (color and space, but also time) need to be taken into account, why they need to be introduced in the conceptual notation. That is, the logical forms, the logical symbols, of function and argument will not be enough for the analysis.

Wittgenstein first thought that statements of degree could be analyzed as the logical product of “simple propositions of quantity” and an extra supplementary clause – “and nothing more” (SRLF, 168). Such analysis should give, then, for instance, the “logical structure of color” (T 6.3751) and show how colors could be truth-functionally analyzed. This analysis, however, doesn’t work. Even if one could assume that the correct analysis of “A is blue” showed that “A is not red” is implicitly given in it and, therefore, that the conjunction of “A is red and A is blue” was a contradiction, the very analysis of “A is blue” is problematic. Suppose, for instance, that E is an entity E and b is its brightness b.⁹ If E has two degrees of brightness, we represent it as E(2b). In this case, however, E(2b) must be analyzed as Eb & Eb, which is obviously absurd since Eb and (Eb & Eb) have the same truth conditions. It is also not possible to distinguish the units of brightness in the conjunction (say E(b’) & E(b’’)), argues Wittgenstein, for then, in the case that we expressed one degree of brightness with Eb, we would have to ask whether b=b’ or b=b’’ (SRLF, 168).¹⁰ Another problem with this kind of analysis concerns color mixture. If one says, “A is reddish-blue,” one cannot analyze it as “A is blue and A is red.” Even though reddish-blue is a mixture of blue and red, reddish-blue excludes red and excludes blue (MS 106, 99). What follows from “A is reddish-blue” is not that “A is blue,” but “the opposite,” as Wittgenstein says, i.e. that it is not blue (see MS 106, 101). If there is a hidden product in color statements, then it follows that the product is not merely a conjunction of units. Since from “A is reddish-blue” it follows that A is not blue, one should expect that the quantity of blue in reddish-blue is 0. Another problem with the idea of truth-functional analysis is the mixing incompatibility between complementary or opposite colors (for instance red and green) (MS 106, 71). There is no such thing as reddish-green, i.e. a logical product of red and green cannot exist. However, one should expect it to be possible if mixed colors are taken merely as conjunctions of colors. This means that Wittgenstein’s truth-functional notation would, again, not express the real multiplicity of color mixture and exclusion. So Wittgenstein ended up assuming that statements of degree cannot be further analyzed by his old logic and are, therefore, elementary.¹¹ Thus, Wittgenstein concluded, there are elementary propositions that are not logically independent.¹²

Note that this conclusion allows, now, the introduction of numbers at the elementary level. This was forbidden in the logical notation of the T, for it entails pre...

Table of contents

• Cover
• Title
• Introduction
• 1   Phenomenology, ‘Grammar,’ and the ‘Limits of Sense’
• 2   Russell’s Causal Theory of Meaning, Rule-Following, the Calculus Conception, and the Invention of the Genetic Method
• 3   The Big Typescript, the Tractatus, Sraffa, and the Anthropological View
• 4   The Road to the Philosophical Investigations (Blue Book, Brown Book, German Brown Book, and MS 142)
• 5   The Philosophical Investigations
• Notes
• Bibliography
• Index