Wittgenstein on the Arbitrariness of Grammar


What is the nature of a conceptual scheme? Are there alternative conceptual schemes? If so, are some more justifiable or correct than others? The later Wittgenstein already addresses these fundamental philosophical questions under the general rubric of "grammar" and the question of its "arbitrariness"--and does so with great subtlety. This book explores Wittgenstein's views on these questions.

Part I interprets his conception of grammar as a generalized (and otherwise modified) ...

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What is the nature of a conceptual scheme? Are there alternative conceptual schemes? If so, are some more justifiable or correct than others? The later Wittgenstein already addresses these fundamental philosophical questions under the general rubric of "grammar" and the question of its "arbitrariness"--and does so with great subtlety. This book explores Wittgenstein's views on these questions.

Part I interprets his conception of grammar as a generalized (and otherwise modified) version of Kant's transcendental idealist solution to a puzzle about necessity. It also seeks to reconcile Wittgenstein's seemingly inconsistent answers to the question of whether or not grammar is arbitrary by showing that he believed grammar to be arbitrary in one sense and non-arbitrary in another.

Part II focuses on an especially central and contested feature of Wittgenstein's account: a thesis of the diversity of grammars. The author discusses this thesis in connection with the nature of formal logic, the limits of language, and the conditions of semantic understanding or access.

Strongly argued and cleary written, this book will appeal not only to philosophers but also to students of the human sciences, for whom Wittgenstein's work holds great relevance.

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What People Are Saying

Paul Horwich
Nuanced and convincingly supported, Forster's work reaches conclusions of great intrinsic interest.
Paul Horwich, University College, London and City University of New York
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Product Details

  • ISBN-13: 9780691123912
  • Publisher: Princeton University Press
  • Publication date: 10/17/2005
  • Pages: 264
  • Product dimensions: 6.06 (w) x 8.44 (h) x 0.51 (d)

Meet the Author

Michael N. Forster is Professor of Philosophy and Chairman of the Philosophy Department at the University of Chicago.

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Wittgenstein on the Arbitrariness of Grammar

By Michael N. Forster

Princeton University Press

Michael N. Forster
All right reserved.

ISBN: 0691113661

Chapter One


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).


Excerpted from Wittgenstein on the Arbitrariness of Grammar by Michael N. Forster Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Table of Contents

Acknowledgments ix
Abbreviations xi
Introduction 1
1. Wittgenstein's Conception of Grammar 7
2. The Sense in Which Grammar Is Arbitrary 21
3. The Sense in Which Grammar Is Non-Arbitrary 66
4. Some Modest Criticisms 82
5. Alternative Grammars? The Case of Formal Logic 107
6. Alternative Grammars? The Limits of Language 129
7. Alternative Grammars? The Problem of Access 153
Appendix. The Philosophical Investigations 189
Notes 193
Index 241

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