The Mechanism of Meaning-Generation in Wittgenstein's Tractatus Logico-Philosophicus

Version of May 19, 2023

This English version is a machine translation of the Japanese original, made with Claude (Anthropic). Quotations other than those from the Tractatus (which follow C. K. Ogden’s 1922 translation) were translated from the Japanese editions cited, so they are translations of translations and do not match the original texts or their published English translations.

In the Tractatus Logico-Philosophicus the picture theory forms the core of the theory of meaning, but at first sight the picture theory seems to express a simple view of language. That is, language copies the facts that exist on the side of the world as propositions, and to each constituent of a fact there corresponds a constituent of the proposition. Moreover, this correspondence seems to be posited in advance, with no explanation whatsoever of how it becomes possible. Furthermore, recalling the descriptions in later works such as the Blue Book, one may be tempted to read the proposition as a mysterious entity existing in a private medium (the mind), which is what makes such a representing relation possible. In this essay I attempt a critique of such readings. The Tractatus contains a careful argument about the conditions that make picturing possible. The various claims of the Tractatus (the distinction between what can be said and what can be shown, the various claims about logical form, and so on) are asserted on the basis of these conditions of the possibility of meaning-generation. In light of these conditions of the possibility of meaning-generation, it becomes clear that the picture theory by no means presupposes a simple correspondence between the world and language. Rather, it rests on there being a subject that generates meaning, and on that subject’s constructing pictures of the world under a certain aspect. The Tractatus, however, does not necessarily say explicitly who this subject is. This seems to be the reason why the Tractatus has traditionally been read as if the form of representation were posited in advance. But the subject is presumably not spoken of explicitly because, since the Tractatus tries to speak of logical form, the most general form, it would have been undesirable to thematize any particular subject. And the subject that generates meaning, and the site where it does so, seem to be taken up as a problem in the later philosophy. In this essay I start from the concepts of “form, formal series, internal relation, and physiognomy” and attempt to ground the metaphysics and the picture theory of the Tractatus. For, as 2.17 says, picturing is possible because reality and the picture share a “form of representation.” The form of representation is not simply a copy of a form that is in the world. Rather, it is through the subject of meaning reading a pattern into the world that the form of the world, the form of its picture (the proposition), and the representing relation that holds between them are given at the same time.

How to Read the Tractatus

How the Tractatus should be read is, needless to say, not a simple question. I do not have the ability to discuss this question in detail, but let me briefly state the position of this essay. First, this essay aims at reading the book Tractatus itself. Accordingly, even what Wittgenstein himself said is, as a rule, not used as a clue for reading the Tractatus if it lies outside the text of the Tractatus. For example, the drafts of the Tractatus, private letters, and even the preface are as a rule excluded from consideration. These represent the process by which Wittgenstein groped toward the thought that bore fruit as the Tractatus, and I do not think they are necessarily useful for understanding the Tractatus in its final form. However, since I discuss its relation to Wittgenstein’s later philosophy, I do refer to the Philosophical Investigations. I also touch very briefly, as a supplement, on what appears in biographical accounts to be the intellectual background of Wittgenstein’s thought. This is because the reading of the logical parts of the Tractatus and the intellectual tendencies of Wittgenstein that can be read from biographical accounts do not seem to me to have always been well connected so far. I can hardly discuss the many secondary sources here. This is due to the limits of my ability, but it is also because in this essay I want first of all to concentrate on reading the Tractatus itself. For the Japanese translations of the Tractatus Logico-Philosophicus and the Philosophical Investigations I used those by Shizuya Okazawa [1,2], and consulted as needed the original text, the facing-page English translation by Ramsey and Ogden [3], and the English translation by Pears and McGuinness [4]. That said, I need to touch on the “resolute reading” of Cora Diamond and others [5]. Usually, the utterances in the Tractatus are thought to be classified into nonsense such as “oink oink oink,” propositions that speak about what can be said, such as scientific propositions, and “sayings” that try to “show” something that cannot be said. The resolute reading, however, draws no distinction between plainly nonsensical talk such as “oink oink oink” and talk that tries to show something. Consequently, since the Tractatus as a whole tries to show something about what cannot be said, it is regarded as the same as the nonsensical utterance “oink oink oink.” Cora Diamond therefore does not interpret the Tractatus as a text; instead she tries to “imagine” Wittgenstein, the human being who finds himself trying to make such nonsensical utterances (such as “oink oink oink”). The validity of the resolute reading is an intricate matter, and examining it exhaustively here is again beyond my ability. Still, the following problems with the resolute reading can be pointed out. Tractatus 4.1212 says, “What can be shown cannot be said.” It feels natural to read this proposition as presupposing that there is something that “can be shown.” For example, on reading passages such as

4.1211 Thus a proposition “fa” shows that in its sense the object a occurs, two propositions “fa” and “ga” that they are both about the same object. If two propositions contradict one another, this is shown by their structure; similarly if one follows from another, etc.

it seems that “the object a occurs in the proposition ‘fa’” is presented not as nonsensical talk such as “oink oink oink” but as conveying some positive content. Moreover, “the object a occurs in the proposition ‘fa’” is too technical; it seems hard to regard it as something that, though nonsensical, says something about the person Wittgenstein who tries to say it. Also, the resolute reading starts its argument from the wording of 6.54, “dass sie der, welcher mich versteht,” that is, if he understands me (and not, for example, “my sentences,” as in Okazawa’s translation); but staking the whole interpretation on one particular sentence seems to me to go too far. Rather, it seems to me that a work should be interpreted by “surveying” it as a whole. Now, one motivation of the resolute reading is presumably to resolve the contradiction that the Tractatus speaks volubly about what the Tractatus itself says should be discarded as “what cannot be said.” In this essay I respond to this problem by holding that the Tractatus is trying to present a certain aspect under which the world is seen. Exactly the same figure (the world) gives an entirely different “look” through a change of aspect, yet this change of aspect cannot be replaced by presenting any fact about the figure (by saying), for example, that this line is connected to that line. But one can give, in language, a prompt that brings about a change of aspect, for example, “Look here, don’t you see an ear?” What the Tractatus aims at is such a change of aspect, and the Tractatus seems to me to claim that, after one has experienced such a change of aspect, one can understand the nonsensicality of metaphysical talk by having it pointed out that such talk contains nonsense. In this essay I take the position that what is “shown” in the Tractatus (what cannot be said) is an aspect of the world. Further, I suggest that this “aspect” is precisely what the Tractatus calls “form.” I want to examine whether this position makes a coherent reading of the Tractatus possible.

Form, Formal Series, Internal Relation, Physiognomy

A clue for thinking about what “form” is for Wittgenstein is the “formal series.”

4.1252 Series which are ordered by internal relations I call formal series. The series of numbers is ordered not by an external, but by an internal relation. Similarly the series of propositions “aRb”, “(∃x) : aRx . xRb”, “(∃x,y) : aRx . aRy . yRb”, etc. (If b stands in one of these relations to a, I call b a successor of a.) Here, as an example of a formal series, Wittgenstein considers an infinite series of propositions that defines the successor relation. Now, defining the successor relation in this way is not what is usually done. Russell and Whitehead, for example, defined the successor relation R* of a relation R as follows.

The successor relation aR*b is the smallest relation satisfying the following:

The advantage of such a definition is that, as long as the language of set theory is assumed, the successor relation can be defined with finitely many propositions. Wittgenstein, however, rejects such a definition. In the language of the Tractatus one cannot state properties of properties, such as being the smallest relation. This is because the Tractatus sharply distinguishes things from relations, and that in turn is because it distinguishes relations that hold between things (“external” (extern) relations) from relations that hold between atomic facts (“internal” (intern) relations). Relations that hold between relations are also internal relations, not external ones. For an external relation is a function that combines with things to make up atomic facts. Instead, Wittgenstein defines the successor relation by a “series” (formenreihen) of propositions “ordered by internal relations” (4.1252). Wittgenstein’s method, however, requires infinitely many propositions, and at first sight the successor relation becomes impossible to grasp. But according to Wittgenstein these propositions can be grasped by seeing their internal relations, or the physiognomy of facts, “a feature of this fact” (4.1221). Put differently, the infinite series is grasped through the subject of meaning grasping a pattern (physiognomy) that holds among the elements of the infinite series. That is, form is something that comes about when the subject of meaning sees among facts a certain kind of pattern recognition (which cannot itself be put into words). Let me add that one can also see here the germ of the later philosophy’s concern with aspects. The concept of aspect is generally thought to be specific to Wittgenstein’s later philosophy. I want to point out, however, that a concept similar to that of aspect appears in the Tractatus in the form of “feature” (Zug, 4.126) and “physiognomy” (Gesichtszüge, 4.1221). In 4.126 “an internal property of a fact,” and in 4.1221 “the expression of a formal property,” “the sign that signifies the characteristics of a formal concept,” and the “characteristic feature” of a propositional variable, are called physiognomies (the relations among internal property, formal property, the sign that signifies the characteristics of a formal concept, the characteristic feature of a propositional variable, and so on). That is, “internal properties” and “formal concepts” come about through the subject of meaning reading a certain “feature” or “physiognomy” from facts and expressions.

The Picture Theory: Picture, Logical Picture, Logical Form

Before turning to the picture theory, I want to set out the metaphysics of the Tractatus. First, the Tractatus says that the world is the totality of facts (1). A fact is an atomic fact that obtains (2). An atomic fact is a combination of entities and things (2.01). As explained throughout 2.01, a thing is destined in advance to occur in atomic facts in certain ways. 2.01231 calls this the “internal qualities” of the object. And 2.0141 also calls it “the form of the object.” This metaphysics of the Tractatus is given without any particular justification and seems to be a dogmatic claim. But what if we take the “internal qualities” of 2.01231 and the “form” of 2.0141 to be the “internal relations” and “form” discussed in Section 2? Then the form of an object can be thought of not as something given in the world in advance, but as something that the subject of meaning sees as a “physiognomy” of the world. Now I want to turn to the picture theory. 2.13 says, “To the objects correspond in the picture the elements of the picture.” Reading this alone, it may look as though the relation between objects and the elements of the picture is posited in advance. But that is not so. 2.17 says the following.

2.17 What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation.

That is, a picture becomes a picture by sharing the form of representation with reality. In particular, the most general form, the form that every picture describing the world has in common, is logical form, and it is by sharing logical form with reality that a picture can represent the world. Now, could we not take the form in “form of representation” to be the form we saw in Section 2? Consider, for example, the problem of expressions discussed from 3.31 onward. According to 3.311, an expression is defined as the class of all propositions that contain it, as the characteristic mark that characterizes that class. Further, according to 3.312, it is also represented as the form of the propositions that represent that class. In that form the expression is fixed (a constant) and everything else is a variable. In particular, when every expression is a variable, the form is called logical form. Conversely, according to 3.317, the form obtained by fixing a variable of logical form to a certain expression, that is, the form that characterizes that expression, is obtained by enumerating the propositions in which that variable is fixed. Characterizing a form by this enumeration can be regarded as the formal series discussed in Section 2. That is, the form that gives an expression is given by a formal series, or in other words, by internal relations. It follows that understanding an expression consists in the subject of meaning seeing the feature common to the propositions in which that expression occurs. Accordingly, the form of a proposition in which every expression has become a variable, that is, logical form, would likewise be obtained by grasping the feature that those propositions have in common. And as evidence of this, in proposition 4, which discusses language, it is said that

4.014 The gramophone record, the musical thought, the score, the waves of sound, all stand to one another in that pictorial internal relation, which holds between language and the world.

and so we see that the form of representation is a pictorial internal relation, an internal relation. A picture becomes a picture of the world because the subject of meaning sees a feature common to both.

What Is Said and What Is Shown Now, Wittgenstein repeatedly draws the distinction that external relations are what is said, whereas internal relations cannot be said but are shown. From the discussion in Section 3 above, logical form and the representing relation are also internal relations, and so they cannot be said but are shown. Let us consider why internal relations cannot be said but are shown, drawing on the distinction between “declarative knowledge” and “procedural knowledge.” In epistemology this distinction is said to correspond, for example, to knowing what'' andknowing how’’ introduced by Ryle [6], but here I want to rely on the general understanding in cognitive psychology and related fields [7]. There are various controversies over whether a distinction between “knowing what” and “knowing how” exists [8]. Examining these controversies is also beyond my ability. Yet, as appears plainly in, for example, section 78 of the Philosophical Investigations,

Compare “knowing” and “saying” about the following: how many meters high Mont Blanc is – how the word “game” is used – what a clarinet sounds like.

Wittgenstein seems to me to have the anti-intellectualist tendency spoken of in the literature cited above. (Let me add that, owing to his romantic tendency, Wittgenstein seems to have found a special significance in music [8]. Wittgenstein may have thought that not understanding music, and the tendency to overlook the knowledge that makes music possible, was not merely an intellectual error but revealed a baseness of spirit.) Still, what Wittgenstein is concerned with is the difference between “knowing” and “saying,” not the distinction between “declarative knowledge” and “procedural knowledge” itself. Rather, my position is that Wittgenstein claims that “saying something meaningfully” requires procedural knowledge, and that in this sense declarative knowledge is part of procedural knowledge. Now, declarative knowledge is knowledge that can be expressed in words, for example the knowledge that “the Tractatus Logico-Philosophicus was written by Wittgenstein.” Procedural knowledge, on the other hand, is, for example, how to ride a bicycle or how to play music, and cannot be expressed in words. Pattern recognition, an important cognitive function, can also be called procedural knowledge. Procedural knowledge has the following characteristics.

If grasping internal relations, or in other words grasping features, is the recognition of patterns, as I said in the previous section, then it seems natural to think that it is procedural knowledge. Hence, might not the distinction between “what can be said / what is shown” correspond to the distinction between declarative and procedural knowledge? Seen this way, Wittgenstein’s statement that “What can be shown cannot be said” becomes intelligible. If, as in the usual explanation, one says that “the form of representation cannot be said because it is not an event in the world,” then it becomes unclear why one can positively claim that it “can be shown.” Moreover, since it is said that the picture is also a fact (2.141) and that the representing relation also belongs to the picture (2.1513), one cannot in the first place say that the form of representation is not an event in the world. If the form of representation is a pattern (feature) of the way the world is, then recognizing it relies on procedural knowledge that cannot be described in language. That the world appears with a certain pattern is taught as procedural knowledge, through oneself and others grasping the world meaningfully.

What the Tractatus Logico-Philosophicus Aims At Now, although the Tractatus Logico-Philosophicus states at its conclusion, “Whereof one cannot speak, thereof one must be silent,” it has been criticized ever since its publication for the apparent contradiction of speaking of “whereof one cannot speak.” Resolving this problem is also one motivation of Cora Diamond’s resolute reading mentioned above. I want to think about this problem as follows. What Wittgenstein tries to present is one way of grasping the world (an aspect, a feature). And the ability to see the world under a certain aspect is not knowing some proposition (statement). Rather, it is a cognitive ability or stance of seeing a certain pattern in the world; it is procedural knowledge. Procedural knowledge cannot be “said.” Trying to “say” it can even hinder its performance. Still, it is not that procedural knowledge cannot be taught. One way is to actually show how it is done. Verbal instruction is also effective to some extent. For example, to see the “rabbit—duck” figure as a rabbit, it may be effective to give the verbal instruction “Think of this part as the ears.” This instruction does not necessarily make one immediately able to see the “rabbit—duck” figure as a rabbit, but these words may bring about a change of aspect, so that one becomes able to see the “rabbit—duck” figure as a rabbit. And once one has experienced such a change of aspect, one becomes able to describe the “rabbit—duck” figure as a rabbit. Likewise, might not the Tractatus aim to bring about a certain change of aspect in its reader? Reading the Tractatus does not necessarily bring about a change of aspect. This is because the aspect of the world that the Tractatus tries to show, being an aspect, is not knowledge that can be stated. Even so, among those who “understand me” there may be some who experience a certain change of aspect and see the way the world is that the Tractatus tries to show. And under this aspect “there is then no question left.” And the reader throws away the ladder that is the Tractatus.

Acknowledgments This research started from joint research with Saori Makino and owes much to her. I would like to thank her here. The considerations in this research are inseparably bound up with Ms. Makino’s, and my views cannot be clearly separated from hers. However, the understanding of the grasp of aspects as procedural knowledge is my own view. The writing of the paper was done by me alone. I therefore bear full responsibility for any problems in this paper.

References

  1. Ludwig Wittgenstein, Shizuya Okazawa (trans.). Tractatus Logico-Philosophicus (Japanese translation, 論理哲学論考). Kobunsha, 2014.

  2. Ludwig Wittgenstein, Shizuya Okazawa (trans.). Philosophical Investigations (Japanese translation, 哲学探究). Iwanami Shoten, 2013.

  3. Ludwig Wittgenstein. Tractatus Logico-Philosophicus: German and English Edition (Trans. C.K. Ogden). Routledge, 1981.

  4. Ludwig Wittgenstein. Tractatus Logico-Philosophicus (Trans. Pears and Mcguinness). Routledge, 1961.

  5. Cora Diamond. Ethics, imagination and the method of Wittgenstein’s Tractatus. The New Wittgenstein, pp. 159–183. Routledge, 2002.

  6. Gilbert Ryle. The concept of mind. Routledge, 2009.

  7. Timon Ten Berge and Rene van Hezewijk. Procedural and declarative knowledge. Theory & Psychology, Vol.~9, No.~5, pp. 605–624, 1999.

  8. Carlotta Pavese. Knowledge How. In Edward~N. Zalta and Uri Nodelman, editors, The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University, Fall 2022 edition, 2022.

  9. Ray Monk. Ludwig Wittgenstein: The Duty of Genius. New York, NY, USA: Penguin Books, 1990.