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Wittgenstein on the Arbitrariness of Grammar
Michael N. Forster

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Chapter 1


We should begin by considering what Wittgenstein means by "grammar." For, although, as we shall see later, he himself sometimes in fact implies otherwise, he at least seems to employ this word as a term of art with a meaning which bears only a rather remote resemblance to that which it has in everyday usage.

Wittgenstein's most basic conception of grammar is that it consists in rules which govern the use of words and which thereby constitute meanings or concepts.1 Thus, he identifies grammar in general with the "rules for use of a word" (PG, I, #133; cf. BT, p. 136); or to cite a more specific example, he says of mathematics, which he understands to be an important part of grammar, that "in mathematics we are convinced of grammatical propositions; so the expression, the result, of our being convinced is that we accept a rule" (RFM, III, #26). And since, famously, he believes that a word's use may (generally) be equated with its meaning, he holds that the rules for use of words which make up grammar "determine meaning (constitute it)" (PG, I, #133), that "the meaning of a sign lies . . . in the rules in accordance with which it is used/in the rules which prescribe its use" (BT, p. 84); or to cite a more specific example, the mathematical part of grammar again, he says that "mathematics forms concepts" (RFM, VII, #67).2

Wittgenstein maintains, in an important and persistent analogy, that "grammar . . . has somewhat the same relation to the language as . . . the rules of a game have to the game" (PG, I, #23; cf. WWK, pp. 103-5; LC, pp. 48 ff.; BT, pp. 138-39, 168; WLC, pp. 3-4; OC, #95). Hence in his notorious characterization of linguistic practices as "language-games," grammar plays the role of the rules which govern these "games" in contrast to the moves that are made within them.3 To pursue some of the more central implications of this analogy:

(1) Just as the rules of a game constitute the game and first make possible the moves which occur within it, likewise grammar constitutes an area of language and first makes possible the linguistic moves which occur within it.4

(2) More specifically, just as in a game such as chess the rules prescribe or permit certain moves and proscribe others for the pieces (for example, the bishop may move diagonally but not orthogonally), and thereby also constitute the identity of the pieces required for making particular moves within the game (for example, the bishop in essential part simply is the piece subject to the rule just mentioned), likewise grammar prescribes or permits certain linguistic moves and proscribes others (for example, it prescribes or permits that in a context where one has counted 2 items and another 2 items one judge there to be a total of 4 items, and it proscribes that one judge there to be a total of 5 items), and thereby also constitutes the identity of the concepts required for making particular linguistic moves (for example, the concept "2" in essential part simply is the concept subject to the mathematical rule just mentioned).5

(3) Just as the rules of games not only govern and essentially constitute the particular moves made within games but also provide a standard for adjudicating these moves' success or failure, so the rules of grammar in addition to governing and essentially constituting particular linguistic moves also provide a standard for adjudicating their success or failure.6

(4) Just as the rules of a game are not assertions but instead more like commands or imperatives, similarly grammatical rules are not assertions but more like commands, commandments, or categorical imperatives (RFM, V, #13, #17; VI, #30; VII, #72).

(5) Like the rules of games, grammatical rules are in some sense conventions: "Grammar consists of conventions" (PG, I, #138; cf. BT, p. 167; PI, #354-55).7

(6) Just as the rules of games may be either explicitly formulated in language (as in most commercial board games, for example) or else implicit (as in some young children's games, for instance), and in the latter case they may subsequently achieve explicit formulation (see PI, #54), likewise the rules of grammar may either be explicitly formulated in language (as they are in the case of the principles of mathematics, for example) or else implicit, and if they are implicit they may subsequently achieve explicit formulation.8

(7) Again, just as the rules of games may in some cases be definite but in others vague or fluctuating, so the rules of grammar may in some cases be definite but in others vague or fluctuating (PI, #79-83; Z, #438-41).


The above gives what one might perhaps call Wittgenstein's generic conception of "grammar." However, he usually employs this term in more specific applications, and it is especially important to focus on one of these in particular. Not every actual or conceivable "language-game" need include propositions, candidates for truth and falsehood. For example, the primitive language-game played by the builder and his assistant which Wittgenstein describes near the start of the Philosophical Investigations does not (PI, 32; cf. WLC, pp. 11-12). However, many of our language-games do, of course, include them, and Wittgenstein's interest in grammar is above all an interest in the grammar which constitutes such "true-false games" (PG, I, #68).9

The role of the grammar of "true-false games" is a special case of the role of the grammar of a language-game in general, as this was described above. Here the main linguistic moves which are regulated by the grammar and made possible by its constitution of their concepts, and whose success or failure is adjudicated by means of a standard set by the grammar, are what Wittgenstein describes as "empirical" or "factual" assertions. Their success is truth and their failure falsehood.

Wittgenstein's basic two-component model of "true-false games"--one component consisting of empirical or factual claims which are true or false, the other of the grammatical rules which regulate them, constitute their concepts, and set a standard for adjudicating their truth or falsehood--is reflected not only in his metaphor of "move within a game" and "rule of a game" but also in various other metaphors which he uses. For example, he writes that "the limit of the empirical--is concept-formation" (RFM, IV, #29; emphasis added), where "concept-formation" is identical with grammar (cf. PI, p. 230). Or again, he likens empirical propositions to the waters of a river and grammar to the channel or bed of the river (OC, #96-99).

Wittgenstein is happy to allow that the line between empirical or factual propositions, on the one hand, and grammatical rules, on the other, is not a sharp one, and also that it may shift with time so that principles on one side of the line cross over to the other; but he nonetheless insists that there is such a line to be drawn (OC, #96-97; cf. RC, I, #32; WLC, pp. 90-91).

What sorts of principles does Wittgenstein recognize as rules of grammar governing our "true-false games"? He believes, first and foremost, that all principles which have the character of necessity--or, more precisely, of a necessity that is more than mere causal necessity (more than "the causal must" [RFM, I, #121])--are grammatical rules. Thus the Philosophical Grammar and the Philosophical Investigations both suggest the following slogan in the context of discussing grammatical rules: "The only correlate in language to an intrinsic necessity is an arbitrary rule" (PG, I, #133; PI, #372; cf. PI, #371; RFM, I, #73-74, #128; LC, p. 55; WLC, pp. 16, 18; BT, pp. 24, 166). One striking feature of Wittgenstein's later philosophy is indeed his practice of using the presence of (non-causal) necessity as a sort of heuristic litmus test for detecting the grammatical status of a principle ("This must shows . . ." [RFM, VI, #8]).

Accordingly, all principles of formal logic and pure mathematics belong to grammar (hence, for example, the remark quoted earlier that "in mathematics we are convinced of grammatical propositions" [RFM, III, #26]). Likewise, necessities which have traditionally been classified as analytic, such as "Every rod has a length" (PI, #251). Likewise, various other necessities which the philosophical tradition has been reluctant to classify as analytic, such as "There must be a cause" (WLC, p. 16), "Green and blue cannot be in the same place simultaneously" (BB, p. 65; cf. LC, p. 94), and "There is no such thing as a reddish green" (Z, #346).

The grammar governing our "true-false games" also for Wittgenstein includes certain sorts of principles which we do not usually think of as exhibiting necessity--though I think that Wittgenstein would say that on closer inspection they really do; in other words, I think that for him (non-causal) necessity is not only a sufficient condition of grammaticality, as explicit remarks such as the ones recently quoted imply, but also in some sense a necessary condition of grammaticality.10 Thus ostensive definitions such as "This color is called 'red'" or "This color is red" also belong to grammar for Wittgenstein: "The interpretation of written and spoken signs by ostensive definitions is not an application of language, but part of the grammar" (PG, I, #45; cf. #46). So too do criteria, such as the behavioral criteria which warrant ascribing mental states to another person: "To explain my criterion for another person's having toothache is to give a grammatical explanation about the word 'toothache' and, in this sense, an explanation concerning the meaning of the word 'toothache'" (BB, p. 24). And, especially according to Wittgenstein's last work, On Certainty, so too do a variety of fundamental propositions which appear to be empirical in character, such as those which G. E. Moore claimed to know--for example, "Here is a hand" and "There are physical objects" (OC, #51-53, #57). For, Wittgenstein argues in On Certainty, "not everything which has the form of an empirical proposition is one" (OC, #308), and "propositions of the form of empirical propositions, and not only propositions of logic [i.e., formal logic],11 form the foundation of all operating with thoughts (with language)" (OC, #401).12

On closer scrutiny, it is easy enough to see that these further parts of grammar can plausibly be considered to possess (non-causal) necessity along with the more paradigmatic cases: If "This color is red" really serves as an ostensive definition, then what it expresses is in a certain sense necessary rather than contingent; if the criteria of a psychological state are realized (at least in an appropriate context), then this in a sense necessitates the presence of the state in question (or at least the appropriateness of a judgment that it is present);13 and Wittgenstein clearly thinks that the apparently-empirical propositions of grammar in a sense cannot but hold.


The connection which I have just stressed between Wittgenstein's conception of the grammar of "true-false" language-games and necessity is crucially important. For it reveals one of the fundamental motives behind his--prima facie, rather surprising--conception that the sorts of principles which have just been listed are all grammatical in the sense of being not assertions of facts but something more like commands or imperatives with which we regulate our factual assertions, channeling them in certain directions and away from others.

Essentially, Wittgenstein is here adopting, but radically extending, and otherwise modifying, a position of Kant's.14 Kant had believed that there were several quite sharply different types of necessity: logical necessity; analytic necessity, which in Kant's view was either reducible to logical necessity (Kant usually says more specifically: to that of the law of contradiction) or a matter of truth-in-virtue-of-meaning (Kant says more specifically, but too restrictively: the containment of a predicate-concept in a subject-concept); and the necessity of synthetic a priori propositions (which for Kant saliently include, for example, the proposition that every event has a cause, and the propositions of pure mathematics). Kant's position on the nature of necessity rested on an important (and usually overlooked) assumption which he took over from earlier tradition: namely that modal facts (i.e., facts involving necessity or possibility) cannot simply be primitive but must instead in some way or other be constituted by and explicable in terms of non-modal ones, in terms of actualities.15 He was not puzzled by the necessity of logical or analytic principles, because he thought that in these cases it was easy enough to identify the non-modal facts, the actualities, which constituted the necessity in question: the necessity of logic consisted in the fact that logic was constitutive of the very nature of thought,16 and the necessity of analytic propositions consisted either in such logical necessity once again or in truth-in-virtue-of-meaning (the containment of a predicate-concept in a subject-concept). However, he was deeply puzzled about the necessity of synthetic a priori propositions. For in this case (and this much follows simply from the definition of "synthetic" as "non-analytic") the necessity resisted the foregoing, seemingly easy, explanations. Consequently, he found himself driven to offer an alternative, and very surprising, explanation for this case: the non-modal fact, the actuality, which constituted synthetic a priori necessity was that our (human) minds impose the principles in question, constituting and structuring all of our experience and its objects in accordance with them, and that our (human) minds are somehow constrained to do so by their very (noumenal) nature. In other words, his explanation was a "transcendental idealist" one.17

Wittgenstein is essentially offering the same sort of solution to the same sort of puzzle. However, he is also generalizing both to cover not only what Kant would have classified as synthetic a priori necessities but also what Kant would have classified as logical and analytic necessities (as well as making some further modifications). This generalization is due to the fact that Wittgenstein does not believe that logical and so-called analytic necessities are susceptible to the sorts of easy alternative explanations that Kant thought he had for them. Roughly, he believes that Kant's explanation of logical necessities as consisting in logic's constitutiveness of the very nature of thought is at best inadequate, and that truth-in-virtue-of-meaning is a philosophical illusion (we will see why he believes these things in chapters 2 and 5). Consequently, for Wittgenstein these necessities are no less puzzling than the so-called synthetic a priori ones. And he therefore extends Kant's solution for the latter to cover the former as well.18

In the process, Wittgenstein also makes several further significant modifications, including the following (most of which will be discussed in more detail later in this essay). First, and perhaps obviously, unlike Kant, who was still wedded to a common Enlightenment assumption--which was already beginning to be challenged in his day by philosophers such as Herder--that thought and conceptualization are in principle autonomous of language, Wittgenstein accords language a fundamental role in his account.19 Second, Wittgenstein's notion that grammatical principles not only channel empirical ones but also constitute concepts is foreign to Kant's way of understanding the role of synthetic a priori principles. Kant, lacking the conception, which is (at least relatively) new with Wittgenstein, of a type of principle that is internal to concepts not in the sense of being derivable from them by analysis but in the sense of constituting them,20 would have tended to see any such notion as making the principles in question analytic, and hence susceptible to an entirely different sort of explanation. Third, Wittgenstein accommodates a plurality of alternative principles in each area of grammar, in a way that is quite alien to Kant's conception of synthetic a priori principles or necessary principles in general (see chapter 2). Fourth, Wittgenstein modifies the second limb of Kant's explanation of synthetic a priori necessities--Kant's claim that our human minds are somehow constrained by their noumenal nature to impose the principles in question--in a more naturalistic and complex direction: He argues that we are indeed in a way constrained towards imposing the necessary principles that we do by our nature, but by our empirical (not noumenal) nature; and he argues that we are also constrained in imposing them by our social practices and traditions, and by the principles' usefulness and empirical applicability. (These are the several aspects of grammar's non-arbitrariness which will be explored in chapter 3.)21 Fifth, because of the preceding modifications, Wittgenstein's full account of the nature of necessity is in certain ways both different and richer than Kant's explanation of the nature of synthetic a priori necessity: Whereas Kant makes no essential reference to language, Wittgenstein does. Whereas Kant appeals only to the human mind's imposition of certain principles in making empirical judgments and to human nature's constraint of the human mind to this imposition, Wittgenstein in addition appeals to the internality of the principles in question to the concepts which they involve (i.e., to the impossibility of rejecting the principles without thereby changing the concepts).22 Whereas Kant appeals simply to the human mind's imposition of certain principles, Wittgenstein appeals to diverse human minds imposing diverse principles. Whereas Kant appeals to noumenal human nature constraining the human mind to this, Wittgenstein appeals to empirical human nature as one of the things that does so. Whereas Kant only appeals to human nature as such a constraint, Wittgenstein also appeals to social practices and traditions, as well as the usefulness and empirical applicability of the principles in question.


Does this make Wittgenstein's position, like Kant's, a form of idealism, then? The answer, I think, is that it does.23 This is so for two reasons.

First, like Kant's position, Wittgenstein's entails that many fundamental, necessary features of our experience which we are prephilosophically inclined to ascribe to a world independent of our minds--namely, grammatical features, such as the impossibility of two colors being in the same place simultaneously, or the "fact" that 2 + 2 = 4--turn out instead to have their source in our minds. Hence, for example, Wittgenstein writes in Zettel, "Do the [color/number] systems reside in our nature or in the nature of things? How are we to put it? Not in the nature of things" (Z, #357).

Second, it seems that, again like Kant's position, Wittgenstein's also entails that all other features of our experience, because they essentially depend on grammar for their essential form--specifically, in the sense that grammar both constitutes all of the concepts which articulate our factual judgments and regulates which (combinations of ) factual judgments it is appropriate for us to make and which not--in essential part have their source in our minds as well. Hence he suggests that (mathematical) grammar "create[s] the form of what we call facts" (RFM, VII, #18).24

Wittgenstein's Lectures on Philosophical Psychology 1946-47 contains an (admittedly, not fully dependable or easily interpretable) passage which is intriguing in this connection, both for an apparent implication of the two types of idealism just mentioned and for a nod towards Kant in connection with them. In the course of discussing the grammatical principle of an asymmetry in the use of psychological terms in the first and third persons, Wittgenstein says: "Objection: This is not characteristic of psychological concepts but of psychological phenomena. Answer: . . . When we try to describe phenomena which we think are mirrored in our concepts, we go wrong over and over again; therefore we describe concepts . . . Remember Kant. (1) shows us how we look at the phenomena and (2)--someone might say--shows us what phenomena are like" (WLPP, p. 154). The last part of this seems to be an allusion to Kant's famous slogan that "the a priori conditions of a possible experience in general are at the same time conditions of the possibility of objects of experience" (Critique of Pure Reason, AIII).

Attributing the former of these two types of idealism to Wittgenstein is less controversial than attributing the latter. For example, Anscombe and Bloor have both argued for his commitment to an idealism of the former type (albeit without noticing its Kantian background), but not for his commitment to an idealism of the latter type.25

Wittgenstein certainly himself seems much more confidently committed to the former than to the latter. But, besides the sort of textual evidence for his commitment to the latter that has just been cited, there is also a deep reason of principle why he cannot easily avoid it. Philosophers who stress the human mind's activity in constituting concepts and who then go on to infer that reality itself is (in essential part) mind-dependent sometimes encounter a protest that this inference is a non sequitur, that one can quite well affirm the mind's activity in constituting concepts without incurring any such counterintuitive idealist consequence: we may indeed create the concepts, but the reality which we cognitively grasp with them is nonetheless independent of our minds. Such a protest is often reasonable, but not against the particular form of such an account that Wittgenstein has developed. For his account says not only that it is our imposition of grammatical principles that constitutes the concepts in terms of which we articulate any factual judgments, but also that this imposition of grammatical principles regulates which (combinations of) factual judgments it is appropriate for us to make and which not. And indeed, it is essential to his account's fundamental goal of explaining necessity that it include this feature.

In sum, it seems to me that, for the two reasons mentioned, Wittgenstein's position can quite properly be described as idealist, in a sense closely analogous to that in which Kant's was.26


Finally, two further aspects of Wittgenstein's conception of grammar should be discussed briefly. First, as I hinted earlier, Wittgenstein sometimes implies, contrary to a strong initial impression which one receives from his treatment of the subject, that he is not using the word "grammar" as a term of art with an unusual sense but in the same sense that it usually bears (and that only the examples on which he focuses, the nature of the problems to which they give rise, and his purposes in focusing on them differ from those involved in standard grammar).27

It is somewhat tempting to dismiss this as merely a case (among several others which we shall encounter) of Wittgenstein's dubious conceptual quietist, or "ordinary language is all right as it is," side getting the better of him. Further encouraging such a diagnosis, there are in fact other passages in which he seems more inclined to concede that his "grammar" is importantly different in nature from ordinary grammar.28

However, it is, I think, possible to make better sense of his tendency to say that he is using the word in its usual meaning, namely by focusing on what I above called his generic conception of grammar, defined by the idea of rules for the use of words which constitute meaning, and by the analogy with the rules of games. For if one goes through the several components of that generic conception, a claim that it defines not only Wittgensteinian grammar but also the usual concept of grammar looks at least somewhat plausible.

This suggestion helps, not only because it leaves many of Wittgenstein's most distinctive views about grammar, such as his whole quasi-Kantian account of the grammar of "true-false games" described above, out of the very concept and so prevents these from constituting a semantic difference between his term "grammar" and the ordinary one, but also because, conversely, it in a plausible way leaves many of traditional grammar's more distinctive features out of the very concept, such as an emphasis on morphology as a principle of classification (in contrast to Wittgenstein's own emphasis on use in context regardless of morphology), and so prevents these from constituting a semantic difference as well.29

The second aspect of Wittgenstein's conception of grammar which calls for some explanation is the following. Wittgenstein sometimes seems to use the term "grammar," not in the primary sense that has been explained above, but in a secondary sense in which it refers to the description of grammar in the primary sense, or the discipline which describes it. For example, he writes that grammar "describes . . . the use of signs" (PI, #496), and he characterizes it as "the account books of language" which "must show the actual transactions of language" (PG, I, #44; cf. WLC, p. 31; BT, pp. 50, 351).30 Such a secondary sense also seems natural given Wittgenstein's just discussed assimilation of his grammar to ordinary grammar (since in ordinary usage the word "grammar" can similarly refer either to aspects of languages or to the description thereof, or the discipline which describes them). Not surprisingly, therefore, much of the secondary literature explicitly distinguishes such a secondary sense from the primary sense in Wittgenstein.31

However, Wittgenstein was himself at least not clear that there was such a distinction between two different senses of the word. This can be seen from the following passage, for example: "Grammar describes the use of words in the language. So it has somewhat the same relation to the language as the description of a game, the rules of a game, have to the game" (PG, I, #23, emphasis added; cf. BT, pp. 171-72; also Moore's report at WL, p. 62 that Wittgenstein himself failed to draw any such distinction). And I would suggest that this apparent conflation is in fact quite deliberate on Wittgenstein's part. Thus at one point in the Lectures on the Foundations of Mathematics, Cambridge 1939 he explicitly rejects the idea that whereas the rules of chess are arbitrary, there are by contrast descriptions of those rules which are true, and that an analogous distinction holds for mathematics (LFM, pp. 142-43).

Why does Wittgenstein thus deliberately conflate what look like two quite different senses? The explanation is, I think, twofold. First, this conflation has a strong attraction for him because it appeals to his theoretical quietist side, the side of him that wants to deny that in doing philosophy he is in any sense developing a theory, a set of novel claims (PI, #128: "If one tried to advance theses in philosophy, it would never be possible to debate them, because everyone would agree to them"; LFM, p. 95: "Turing: I see your point. Wittgenstein: I have no point"; WLC, p. 97: "On all questions we discuss I have no opinion . . . I cannot teach you any new truths"). Thus he says at one point, in this spirit: "When we discover rules for the use of a known term we do not thereby complete our knowledge of its use, and we do not tell people how to use the term. Logical analysis is an antidote. Its importance is to stop the muddle someone makes on reflecting on words" (WLC, p. 21; cf. WWK, pp. 183-86).

Second, the conflation also has a justification of sorts, albeit one which ultimately does not really work. This justification lies in a thesis of Wittgenstein's (which we shall consider in more detail later) to the effect that in order to understand a grammatical principle, one must be committed to it as a regulating imperative, in particular to the exclusion of alternative grammatical principles which would regulate in incompatible ways (see, for example, WL, p. 52; LC, pp. 36-37). For such a thesis entails that in order really to describe a piece of grammar, one must simultaneously have this sort of commitment to it (given that really describing it presumably requires understanding it). This seems to be part of the force of the following remark, for example: "You cannot describe a calculus without using it, you cannot describe language without giving its meaning" (LC, p. 61).32

However, this justification does not really warrant effacing the distinction, as Wittgenstein supposes it to. For one thing, even if one concedes the thesis in question, all that it shows is that "grammar" qua the description of "grammar" qua the commitment to imperatives must itself include the latter, not that it must be exhausted thereby or identical therewith. For another thing, as we shall see later (chapter 7), there are compelling reasons why Wittgenstein ought to abandon the thesis in question anyway. It therefore remains appropriate and important to distinguish between the two different senses of "grammar," despite Wittgenstein's own contrary inclination.

In what follows, this essay will be concerned mainly with "grammar" in its primary sense, and insofar as it governs our "true-false games."

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