Meaning and Signs

Version of July 5, 2023

This English version is a machine translation of the Japanese original, made with Claude (Anthropic). Quotations 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 this essay I argue that language is not a system of signs. To this end, I present an argument that reconstructs the “remarks” in the opening part of Wittgenstein’s Philosophical Investigations, and I criticize semiotics, in particular Umberto Eco’s theory of signs.

The argument consists of the following four parts.

The intuitive argument: appealing to commonsense intuitions, I argue that the working of language is not mere sign-function.
The genealogical argument: going back to the origin of the idea that language is a system of signs, I show that this idea has no ground.
The argument from ostensive definition: applying to sign-functions Wittgenstein’s argument that ostensive definition cannot fix meaning, I argue that sign-functions cannot determine meaning unless an understanding of the language as a whole is already given.
The argument from the rule-following paradox: applying the rule-following paradox, I argue that sign-functions cannot determine language use at all unless there is a grasp of language that is not based on sign-functions.

In addition, I briefly examine the question of whether Wittgenstein claimed that a theory of meaning is impossible.

Introduction

The claim of this essay is that language is not a system of signs. Here, by “language” I mean anything that has meaning (Japanese, English, Chinese, sign languages, programming languages, road signs, chess pieces, and so on), and by “sign” I mean anything that stands for something (icons in GUI programs, symbols in religion and elsewhere, phonetic symbols, and so on). More precisely, I claim the following three things.

The meaning-function of language (its working of meaning) is not a sign-function (the working of standing for something).
It is true that some linguistic elements (this is what I call the constituents of language that are usually called linguistic signs; I also call them words) can be regarded as signs, but many linguistic elements are not signs.
Even for those linguistic elements that can be regarded as signs, their meaning-function is not explained by their sign-function alone.

To avoid misunderstanding, let me add that what I take issue with is the very idea that “the meaning-function is the sign-function”. I am neither trying to answer the question “what is meaning?” (this question presupposes the idea that language is a sign of “meaning”), nor trying to discuss some ontological status of “meaning”. For example, Umberto Eco argues in his book A Theory of Semiotics that the meaning of a sign is not the object it points to but a “cultural unit” [1]; but whether it is an object or a cultural unit, I criticize such views insofar as they assume that language “signifies” something. The very concept of the meaning of a sign is confused to begin with.

Wittgenstein’s Philosophical Investigations

To establish the claim of this essay, I mainly follow the argument presented in Wittgenstein’s Philosophical Investigations. This reflects the following view of mine. Wittgenstein’s Philosophical Investigations is not a loose collection of aphorisms; it develops a coherent argument. It is true that Wittgenstein himself writes in the preface that the book is no more than a sketch, but this only means that Wittgenstein was unable to work out an argument as complete as he aimed for, not that there is no argument. At least from the standpoint of the relation between language and signs, Wittgenstein’s argument is extremely clear. I take the Investigations to contain the following argument.

The intuitive argument — taking as material cries such as “Water!” and “Oh!” [2], the language-game with the building stones [3], and so on, it examines, on the basis of intuition, the meaning of linguistic elements that at first sight seem to be nothing but signs of something. The “genealogical” argument — repeatedly pointing out where the idea that “linguistic elements are signs” comes from, that is, its origin (its genealogy), it shows that these origins provide no ground
The argument from ostensive definition — what Wittgenstein argues directly is that ostensive definition is insufficient to determine meaning; by applying this line of argument to sign-functions instead of ostensive definition, it shows that sign-functions are insufficient to determine meaning.
The argument from the rule-following paradox — taking the argument from ostensive definition one step further, it shows by means of the rule-following paradox that sign-functions cannot determine “the use of words”.

Two further points should be made. The first is that my interpretation does not take what Wittgenstein wrote literally, as it stands, but adapts the argument I take to be there to my own problem. Wittgenstein probably did not read Saussure, and probably had no contact with him. Accordingly, Wittgenstein did not draw much of a distinction between the idea of construing meaning in terms of signs and the idea that meaning points to some object. Accordingly, many of Wittgenstein’s arguments are written as criticisms of the “object theory of meaning” or the “mental-image theory of meaning”, and they do not directly appear to be applicable to the proposition “the meaning-function is the sign-function” in general. So one could say that what I am doing is a philosophical reconstruction. My concern is not the question (supposing such a question makes sense) of “what Wittgenstein was thinking in his head”, but how what Wittgenstein wrote bears on my problem. The other point is that Wittgenstein is often taken to have denied the possibility of constructing a general theory of meaning. This probably comes mainly from Wittgenstein’s emphasis on the family resemblance of language and his holding that language has no general essence. It is true that Wittgenstein seems not to have thought that a theory of language could be built a priori, starting from principles, in the way that Saussure, for example, conceived of a semiology that would encompass linguistics on the basis of the proposition “language is a system of signs”. My position, however, is that he did not deny the possibility of constructing, a posteriori, a general theory of the languages that human beings can use. I will return to this point later.

The Intuitive Argument

“When we give things names, we can talk about them. We can also refer to them.” — As if the act of giving a name already settled what we are to do with it afterwards. As if there were only one thing possible, namely “talking about things”. But in fact we do a great variety of things with sentences. Take calls alone: they have a great variety of functions. Water!

Get lost!

Oh!

Help!

Good!

Wrong!

Looking at these examples, do you still want to call these words “names given to things (objects)”?

[4] This passage of the Investigations is usually taken as a criticism of the “object theory of meaning”, that is, the theory that the meaning of a word is the object it names. But what Wittgenstein is discussing here is clearly the diversity of what “we do by means of names” (the function), not the diversity of the ontological status, so to speak, of what the function is directed at (the meaning). The question is not whether the meaning of a word is an object, or a “cultural unit” as Eco says, or something called by words given novel meanings, such as signifié or noesis.

The opening part of the Investigations (up to about §27) thus repeatedly criticizes the idea that words are things that stand for something. Giving various “language-games” as examples, Wittgenstein shows that this idea is an overly simplified view of language, one whose correctness can be felt intuitively in only a few cases. But one might object as follows. The call “Water!” does, after all, denote the cultural unit “water”, and this is construed as the command “Bring water!”, or expresses fear during a flood. Where this is culturally coded, it is a connotation [5]; where it is not, it is not a question of meaning.

Of course, since the argument here is merely intuitive, a full rebuttal has to wait until later. But what is a “cultural unit” that could be the meaning of language? Eco says: “A cultural unit makes itself stand out against the background of a society’s capacity to connect these signs to one another in relations of equivalence.” [6]. To put it in a word, a “cultural unit” could be defined as an equivalence class of a series of synonymous interpretants. That is, for a word to point to a certain cultural unit would be for that word to belong to a certain equivalence class.

Setting aside for the moment the problems contained in the “synonymy relation”, it is certainly possible in this way to construct a “denotational” semantics each time a synonymy relation is given. This is exactly how the completeness theorem of logic is proved. But how useful is such a concept of “denotation”? Such a “denotational” semantics can be constructed from any semantics (that gives synonymy), but does this not rather mean that such a “denotational semantics” gives no insight at all?

Of course, Eco takes the analysis further and proposes a “revised model” of meaning [7]. In the revised model, the presence or absence of semantic markers makes it possible to express not only synonymy relations but also relations of opposition between meanings. But just as in the case of synonymy alone, even if relations of opposition can be expressed, it cannot be said that “meaning” has been expressed. Even if we found out that the ancient Japanese regarded “blue” and “green” as synonymous, that alone would not enable us to use color words as the ancient Japanese did. And the situation does not improve even if we find out that these were recognized as different from “vermilion”. For even if they had mistaken “vermilion” for “blue = green” and “blue = green” for “vermilion”, the same system of identities and oppositions would still be obtained. To explain the ability to “use” “words”, merely giving relations of identity and opposition is not enough.

One might object, however, that the goal of a theory of meaning is not to explain the use of words (that is the subject of a theory of sign production), but to construct a theory of the codes that make such use possible. But this way of setting the problem is already based on the presupposition that meaning is a sign-function. The “genealogical” argument, which we look at in the next section, shows that this presupposition has no ground.

The Genealogical Argument

In the latter half of the previous section, we looked at Eco’s argument that meaning is a “cultural unit”. There Eco claimed that meaning is an equivalence class formed by interpretants, not a referent. In this section I show that if the concept of “reference” is banished from meaning, the very motivation for thinking that “the meaning-function is the sign-function” is lost as well. Wittgenstein’s argument for this is the “genealogical argument”. “Genealogy” is, of course, Nietzsche’s term. Wittgenstein seems to have read Nietzsche [8], but I do not want to claim that there was a direct influence. It is just that Wittgenstein and Nietzsche have a method in common: freeing those held captive by a philosophical claim by asking about the origin (motive) of that claim. Nietzsche tries, for example, to reveal the “slavish” origin of something like “the virtue of humility” by tracing through history the motives by which it was formed. Wittgenstein, on the other hand, is more cautious than Nietzsche. Nietzsche seems to think that the “genealogy” produced by his analysis is actual history, or at least a sketch of it, but Wittgenstein’s “genealogy” is not actual history. Rather, it consists of concrete examples that bring to light the motives from which the prejudices of those who do philosophy derive. If we trace the origin of the idea that “the meaning-function is the sign-function”, it is clear that we arrive at an example like the following.

Let us imagine a language of the kind Augustine described. It is a language that serves for communication between a master builder A and an apprentice B. The master builder puts up a building out of building stones. The stones are blocks, pillars, plates, and beams. B is to hand the stones over. Moreover, he must hand them over in the order in which A needs them. For this purpose the two of them use a language made up of the words “block”, “pillar”, “plate”, and “beam”. When A calls out one of the words — B, hearing it, has learned to bring the stone that corresponds to that word. — I would like you to think of this as a complete primitive language.

[9] It is possible to call a system of communication like this a language. Let us call this kind of account of the meaning of language “the model of reference”. Then, for a language in which the model of reference holds, it is certainly fair to say that “the meaning-function is the sign-function”. But the model of reference is something that can be said “only within a very narrowly limited domain” [10].

Now let us consider the following way of using language. I am going to have someone go shopping for me. I hand over a note on which “five red apples” is written. When the person I asked hands the note to the shopkeeper, the shopkeeper opens a case labeled “apples”. Then he looks up the word “red” in a chart, finds the color sample that goes with it, counts 1, 2, 3 … up to five — here I am assuming that the shopkeeper knows the cardinal numbers — and each time he counts one, he takes out of the case one apple of the sample’s color. — Well, it is in a way similar to this that we handle words [11]

We can see that each of the words “red”, “apples”, and “five” contained in “five red apples” is doing a completely different job. It is from trying to fit this into the model of reference that the concepts of an abstract “meaning” or “content”, distinct from the bearer of the name, begin. Because one tries to explain what is a characteristic of the working of the meaning-function as a property of the object of the sign-function, one cannot take the object of the sign-function to be the referent of the sign itself. In Plato, that is, at the very beginning of Western philosophy, the Ideas were introduced precisely as such things. And Western philosophy was thereafter to be plagued by “chimera hunts” [12] over universals, particulars, mathematical objects, and the like. If, however, instead of applying the model of reference to every word, we acknowledge that the category of meaning-function differs for each category of word, there will be no need to introduce an abstract “meaning” or “content”, and the introduction of ideal entities will also become unnecessary. Furthermore, there will no longer be any need to introduce strange objects, such as “mind” or “culture”, that breathe meaning into signs. Western philosophy quietly comes to rest [13].

The Argument from Ostensive Definition

The intuitive argument and the genealogical argument suggest that the claim “language is a system of signs” is too general and does not reflect what language actually is. But they cannot be said to be a direct refutation of the claim “language is a system of signs”. In this section, I first replace Wittgenstein’s argument about ostensive definition with an argument about sign-functions, and show that sign-functions are insufficient to fix the meaning-function.

Now, one can define the name of a person, the names of colors, the names of materials, the names of numbers, the names of directions, and so on, by pointing. “This is ‘2’” — saying this while pointing at two nuts — to define the number 2 in this way is a perfectly exact method. — But how is “2” defined in that way? After all, the person who is taught the definition does not know, in that case, what it is that is meant to be called “2”. The person who is taught the definition will think that this group of nuts is what is called “2”! … (omitted) … That is, a definition by pointing can, in every case, be interpreted this way or that way. [14]

Here, ostensive definition can be replaced by the sign-function. The meaning of “2”, on this view, is represented by what it denotes, say, two nuts. Of course, as Wittgenstein points out, this idea does not work. For if meaning is defined in this way, there is a danger that the meaning of “2” will be misunderstood as “two nuts”. Can we, then, exclude the possibility of such misunderstanding and fix meaning by means of the sign-function? One idea is that what “2” denotes is not two actually existing things (which are always exposed to misunderstanding) but the mathematical object “2”. But even if that were so, it is hard to believe that the room for misunderstanding would disappear. For it is possible to misunderstand “2” as referring to “two ideal objects” and as not applicable to actual “nuts”. More generally, Wittgenstein’s argument here can be read as a criticism of the claim that the meaning of language is its referent. What, then, if the meaning of language is not its referent but, as Eco says, its “content”? In the revised semantic model [15], content (if we ignore selection by context) consists of a collection of semantic markers that represent a position within the system of meanings. It is not all that obvious how the number “2” should be represented in this model, but let us suppose, for example, that “2” has the semantic marker “number”. Then the claim that the object of the sign-function of “2” is a meaning that has the semantic marker “number” becomes the following, when we once again replace the sign-function with the argument about ostensive definition.

It may be said that 2 can be defined only when one points while saying something like “This number is 2”. For in that case it is clear in which place in language, that is, in grammar, the word “number” is put. But this means that an explanation of the word “number” is needed before the definition by pointing is understood. … (omitted) … But can the words “color” and “length” be understood only in that way? — Then that needs to be properly explained. — That is, it has to be explained by means of other words! Then what is the last explanation in such a chain of explanations like? [16]

For the meaning of “2” to be fixed by the sign-function, the meaning of the semantic marker it denotes must be known in advance. Of course, on Eco’s position, a semantic marker such as “number” is itself a sign and becomes the object of further analysis. That is, unlimited semiosis [17] arises; but in that case, unless such a chain of semiosis (Model Q) is understood, the meaning of the sign will not be fixed either. To borrow Wittgenstein’s words, it would go like this.

Now, could we not say the following? Augustine describes human beings’ learning of language as if it were a situation in which a child comes to a foreign land and does not understand the language of that land. That is, as if it were a situation in which the child already understands one language and merely does not understand the language of that land. Or as if it were a situation in which the child can already think, and merely cannot speak. [18]

The Argument from the Rule-Following Paradox

Then, if a “chain of semiosis” such as Model Q is given, can we regard it as the meaning of words? The criticism of this idea is the rule-following paradox.

Our paradox was this: “A rule cannot determine a way of acting, because any way of acting can be made to accord with the rule.” The answer to it was this: “If any way of acting can be made to accord with the rule, it can also be made to contradict the rule. So here there is neither accord nor contradiction.” [19] A sign-function is something like the table described in §86 of the Investigations.

Let us play a language-game like (2) using a table. The signals that A gives to B are now written characters. B has a table; in its first column are written the characters used in the game, and in its second column are pictures of the shapes of the building stones. When A shows B a character, B looks for it in the table and attends to the picture paired with it. … (omitted) … Now suppose that various ways of reading the table were introduced. … (omitted) … Could we not think of yet another rule in order to explain this rule? [20]

Given a sign-function, it is possible to introduce a further rule for interpreting it. And another rule for interpreting that rule can also be introduced. As the first paragraph of §201 of the Investigations says, any language use whatever can be made to accord with a given sign-relation if the rules of interpretation are suitably chosen. Hence sign-functions cannot determine language use. I am not claiming here anything like “language is a text open to interpretation”. Of course, there is indeterminacy in the interpretation of language, and what is indeterminate may itself be indeterminate.

In tennis there is no rule about how high or how hard you may hit the ball, but tennis is a proper game, and it has rules. [21]

But the paradox here shows that use cannot be determined at all by sign-functions; in other words, that any use can be said to follow the sign-function and can equally be said not to follow it; and hence that sign-functions play no role whatever in language use. Now, of course, as Wittgenstein points out in the second paragraph of §201 of the Investigations, this paradox (that is, that language use cannot be determined at all by sign-functions) rests on a misunderstanding. That there is a misunderstanding here is clear also from the fact that, while we are thinking in this way, we pile interpretation upon interpretation. It is as if every interpretation reassures us, at least for a moment, but we immediately go on to think of the interpretation behind that interpretation. That is, what this shows is that there is a grasp of a rule that is not an interpretation of the rule [22] So sign-functions (if there is such a thing as a sign-function) do, after all, play a certain role in language use. Still, as for what that misunderstanding is: it is the idea that whenever we use language, we are always performing some interpretation (a replacement of signs by meanings). On that view, when we use language we replace signs by meanings, but how to follow the meaning thus substituted also requires a further replacement by meanings. Moreover, how the replacement by meanings should be carried out cannot be determined unless an interpretation is given for it. But to follow this interpretation, too, an interpretation is likewise needed. And so on: we fall into an infinite regress. To cut off this infinite regress, a grasp of language that is not a grasp of it as sign-function is required. The idea that language has meaning by way of sign-functions can be compared to the idea that following a rule requires an “inner voice”: as if, when we use words, we were guided by the (semantic) content that is the object of their sign-function.

If intuition is an inner voice — how do I know how I ought to follow that voice? How do I know that intuition is not misleading me? For if intuition can lead me rightly, it can also mislead me. [23]

But if (semantic) content can guide us rightly, then it is also possible that words themselves guide us rightly. If so, we ought to apply Ockham’s razor here. That is, we ought to hold that there is such a thing as language use not mediated by sign-functions.

The Meaning of Signs

“By connecting the rod and the lever, I fix the brake” — provided, of course, that the other mechanisms are in order [24]

The rod and the lever can be thought of as a sign and the object of its sign-function. It is true that certain words are signs. For example, the word “dog” may stand for a particular dog, or for the set of dogs, or for an image of a dog. Exactly what it is a sign of needs separate discussion, but it is presumably a fact that it is often used as a sign of something. But, as I pointed out in the previous section, for a sign to have meaning, “other mechanisms” besides the sign-function are needed, that is, language use not mediated by sign-functions. Now, I have stressed the existence of language use not mediated by sign-functions, but that does not mean that I want to claim the existence of something like an ideal language that requires no interpretation at all and is grasped directly. What actually happens is probably something like this: a given word is, in some cases, used without the mediation of a sign-function, and in other cases used as a sign, as a proxy for some other (semantic) content. Furthermore, when it is used as a sign, how “deep” an interpretation it is subjected to (that is, how many layers of interpretation are carried out before the word is used, with the content the word stands for becoming in turn an object of interpretation, and so on), and also what the “standing for” in “the word stands for something” means in the first place (what a sign-function is to begin with), surely depend on the situation. Even so, this does not mean that language is something like Model Q, which exhaustively covers all the interpretations, differing from situation to situation, that are carried out one after another. To borrow Wittgenstein’s words,

Please don’t say “There is no ‘last’ explanation.” That would be just like trying to say, “There is no last house on this street. You can always build one more.” [25]

When we use language, it is necessary at some point to break off interpretation and “act without grounds” [26]. “Unlimited semiosis” functions only when it is supported by “acting without interpretation”.

The Possibility of a Theory of Meaning

With the preceding sections, arguments have been given for all the claims listed in the introduction. Those claims, however, did not positively reveal anything about language. This is only to be expected.

But instead of pointing out “something” common to everything that is called language, I want to say this. There is nothing at all that these phenomena have in common. There is no common element that would allow us to use the same word for all of them. [27]

There is no principle, no a priori essence of language, from which the various properties of languages could be derived. The general linguistics that Saussure conceived of does not exist. It seems, however, that Wittgenstein’s claim is generally taken to be a stronger one, denying the existence of any theory of the meaning of language whatsoever. For example, on Eco’s interpretation, Wittgenstein’s Philosophical Investigations “represents the most rigorous (and most suggestive) attempt to render a formal treatment of meaning impossible.” [28] Now, as an interpretation of Wittgenstein, Eco’s understanding does not seem to me to be correct. It is true that Wittgenstein emphasizes the family resemblance of the concept “language”. But what follows from this is the impossibility of starting from what holds generally in language and developing linguistics a priori, as Saussure tried to do. What is at issue here is “language”, not meaning, and not “formal treatment” either. Or perhaps what Eco has in mind is the part that describes the diversity of meaning-functions, as discussed in the passage quoted at the beginning. But, as is clear on reading it, Wittgenstein’s point is not the impossibility of a theory of meaning but the diversity of meaning-functions. I think that Wittgenstein did not deny the possibility of an a posteriori theory of meaning that holds only for the languages human beings use. At least, the existence of such a theory does not conflict with Wittgenstein’s argument. For example, is not Montague semantics, to a considerable extent, an empirical theory of meaning for a certain subsystem of English (albeit only for the limited language-game of assigning truth values)? Wittgenstein, though, would probably not think that constructing such a theory is the task of philosophy.

Conclusion

In this essay I have argued, following Wittgenstein’s Philosophical Investigations, that “to mean” is not “to signify”. The theory of signs I have taken as the target of my criticism is mainly Eco’s, but my criticism is not directed at any particular theory of signs. It is directed at their basic presupposition, and it is a criticism of every attempt to build a theory of meaning on an a priori theory of signs. What, then, is to be done from here? First, as I pointed out in the previous section, Wittgenstein’s criticism does not go so far as to deny the construction of an a posteriori theory of meaning. And I think it quite possible that the concept of a sign will occupy a certain place within an a posteriori theory of meaning. Indeed, even the referential theory and the mental-image theory of meaning may come to be taken up positively. As long as it is not claimed to be correct a priori, a theory of signs, too, will make a positive contribution to the construction of a future theory of meaning. That said, this is no longer the domain of philosophy but of linguistics, and not something philosophy ought to do. As for the interpretation of Wittgenstein, what I have used for the argument of this essay is the opening part of the Investigations, up to §201 at most. The rest of the Investigations seems to pursue an intricate discussion centered on the idea that meaning is something that appears in consciousness. If so, its relation to phenomenology ought to be considered. But that calls for a separate essay.

Sources

For Wittgenstein’s Philosophical Investigations (Philosophische Untersuchungen), I consulted the Japanese translation 『哲学探究』 by Shizuya Okazawa (Iwanami Shoten, edition of August 29, 2013). Page numbers are also those of this edition. I also consulted the German original in places, using the German–English parallel-text edition published by Blackwell Publishing in 2009. For Umberto Eco’s A Theory of Semiotics, I consulted the Japanese translation 『記号論 I・II』 in the Dōjidai Library series (Iwanami Shoten, 1996). Page numbers are those of this Japanese edition. I also consulted the English original, the 1976 edition published by Indiana University Press. Bibliographic information for the other references is included in the notes to the text.

A Theory of Semiotics I, p. 106
Philosophical Investigations, §27, p. 27
Philosophical Investigations, §2, p. 9
Philosophical Investigations, §27, p. 27
A Theory of Semiotics I, p. 149
A Theory of Semiotics I, p. 124
A Theory of Semiotics I, p. 184
Ray Monk, Ludwig Wittgenstein: The Duty of Genius; Japanese translation 『ウィトゲンシュタイン』, Misuzu Shobō, 1994
Philosophical Investigations, §2, p. 9
Philosophical Investigations, §3, p. 9
Philosophical Investigations, §1, p. 8
Philosophical Investigations, §94, p. 85
Philosophical Investigations, §133, p. 99
Philosophical Investigations, §28, p. 28
A Theory of Semiotics I, p. 184
Philosophical Investigations, §29, p. 29
A Theory of Semiotics I, p. 122
Philosophical Investigations, §32, p. 32
Philosophical Investigations, §201, p. 155
Philosophical Investigations, §86, p. 76
Philosophical Investigations, §68, p. 64
Philosophical Investigations, §201, p. 155
Philosophical Investigations, §213, p. 161
Philosophical Investigations, §6, p. 11
Philosophical Investigations, §29, p. 30
Philosophical Investigations, §211, p. 160
Philosophical Investigations, §65, p. 61
A Theory of Semiotics I, p. 130