Wittgensteinian linguistics 9783111323213, 9783110981049

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APPROACHES TO SEMIOTICS P A P E R B A C K SERIES

edited by

THOMAS A. SEBEOK Research Center for the language Sciences Indiana University

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WITTGENSTEINIAN LINGUISTICS by

CECIL H. B R O W N Department of Anthropology Northern Illinois University

1974

MOUTON THE HAGUE · PARIS

© Copyright 1974 in The Netherlands. Mouton & Co. Ν.V., Publishers, The Hague. No part of this book may be translated or reproduced in any form by print, photoprint, microfilm, or any other means, without written permission from the publishers.

LIBRARY OF CONGRESS CATALOG CARD NUMBER: 74-78289

Printed in The Netherlands, by Mouton, The Hague

TABLE OF CONTENTS

Foreword by F. P. Dinneen, S. J

7

Preface

11

Introduction

13

I. Wittgenstein and Ordinary Usage

20

1. Ordinary Usage and Misusage

20

2. Wittgenstein's Rejection of Artificial Language . . . .

22

3. Rules-of-Usage

24

4. Acquisition of Linguistic Competence

27

II. Formulation of Rules-of-Usage

30

1. A Rule Formulation

30

2. Rules Which Codify Usage

31

3. A Formulation of Competence: The 'Language-Game' Assertion

33

4. Application of Rules

37

5. Choosing Rules and Choosing Symbols

42

III. Distinction Between Formulations

45

6

CONTENTS

1. Transformational'Deep Structure': An Ideal Language

45

2. Theories of Category

47

3. Transformational Rules

49

4. Elliptical Sentences and Deletion

51

5. The Language-Game'Interrogation'

53

IV. Aspects of the Formulation

56

1. Usage Circumscription

56

2. Linguistic Orderliness

58

3. Dimensions of Usage

59

4. Concept Recoding

62

V. Language Acquisition and the Innate Order

72

1. Transformationalist's View

72

2. Wittgenstein's View

76

VI. Rules and Symbols

83

1. Wittgenstein's Theory of Language

83

2. Decline of Theories of Category

85

3. Going Beyond the Given: Transformational Grammar .

88

VII. Wittgenstein's Definition of Meaning as Use 1. Wittgenstein's Rejection of Unitary Meaning

93 94

2. Private and Public Meaning

110

3. Summary and Conclusion

120

Bibliography

122

Index

125

FOREWORD TO BROWN'S WITTGENSTEINIAN LINGUISTICS

In the field of linguistics there is considerable diversity in the definition of the proper object of study, 'language'. Factors that are certainly 'linguistic' from some point of view are deliberately omitted from consideration in one approach or another. In this outline of a Wittgensteinian linguistics, Professor Brown returns to a concept of language that is remarkably like the views expounded in the works of B. Malinowski (1923, 1935) and J. R. Firth (1957). Malinowski considered language as a form of behavior in society which should be examined in terms of its societal functions and effects. In his view, the meaning of an utterance was to be explained in terms of what it does in some definable context of situation. There is striking parallelism between Brown's rejection of Chomsky's concept of competence, based on a predominantly cognitive analysis, and Malinowski's insistence that language is "a mode of action, rather than a counter-sign of thought" (1923: 287 ff.). For Malinowski, the most obvious functions of language were to preserve a favorable environment or to change an unfavorable one. For both Malinowski and Wittgenstein, meaning is clearly equated with use. J. R. Firth adopted Malinowski's approach to the study of meaning, since, in equating meaning with use, he could sidestep the problems involved in the concept of mind, and also avoid the entanglements of referential meaning (1957:2 if.). Since contexts of situation cannot be exhaustively listed, Firth also saw clearly that in this approach, it would be unrealistic to expect a systematic account of a language as a whole (1957: 30). Instead, he recom-

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FOREWORD

mended the study of 'restricted' languages, such as greetings, or the formulae of drilling, giving orders, etc. An example of such a study is found in Terence Mitchell's "The Language of Buying and Selling in Cyrenaica" (Hespéris, xliv [1957], 31-71). Scholars differ in their definitions of, and approach to, language, principally because of their belief that a given point of view is more 'realistic' than rival positions. Wittgenstein's later work was produced under the conviction that the only reality to which we should devote our attention was the reality available to us in the day to day use of language, not some ideal abstracted from it (1953: 54e). Brown notes in passing that the establishment of classifications and definitions results from a choice to follow a certain rule. Surely Wittgenstein was aware that he himself was playing but one of many possible language games. Viewing these approaches to language as games by no means detracts from their seriousness, nor from the possibility of providing convincing reasons for preferring one to another. One's position on the 'reality' of the object of study will inevitably reflect the perduring controversies about the nature of the real in our culture. It is still disputed whether we can meaningfully affirm (or deny) the reality of the fixed and ideal (e.g. competence, la langue), or of the flux of empirical observation (e.g. performance, la parole), or both. Professor Brown prefers Wittgenstein's approach over Chomsky's on the basis of a particular understanding of linguistic reality. In his view, Chomsky's deep structure categories are to be rejected as gratuitous, since they are invented, not merely observed. Chomsky, from this point of view, is mistakenly doing pure semiotics, while Wittgenstein's approach involves us only in descriptive semiotics, which Brown considers, "...need not entail more than observation and description". Firth would undoubtedly have rejected this claim, with one of his favorite quotations from Goethe, "Das höchste wäre zu begreifen das alles Faktische schon Theorie ist": all 'facts' are only facts in the light of some theory (1957: 1). There are profound epistemological and psychological reasons for Wittgenstein's abandonment of pure semiotics in the Tractatus

FOREWORD

9

Logico-Philosophicus (1922) for his later descriptive semiotics. Part of the epistemological problem involved his inability to establish empirical definitions for important expressions. Part of the psychological problem involved the level of awareness involved in people's ordinary use of language. Most, if not all of us, rarely employ expressions with fixed definitions in mind, and Wittgenstein accounts for this neatly with his distinction of activities which are according to a rule as opposed to those involving a rule. Brown quotes one of Wittgenstein's examples to illustrate some of these problems : a man asks a friend to teach a child a game. The friend then instructs the toddler in how to shoot craps. When the objection is raised that this was not the kind of game that was 'intended', Wittgenstein queries whether, as a matter of fact, there was a conscious exclusion involved in the original instructions. Clearly, such a meaning did not 'exist' in the speaker's concomitant awareness, at the time he made the request. On the other hand, responsible people are held accountable for what they say, for the 'meanings', intelligibility, and implications involved. These implications may only be potential, or 'recoverable' in some concept of competence. In Sapir's words, "from the point of view of language, thought may be defined as the highest latent potential content of speech" (1921:14-15). One does not have to agree with the epistemological and psychological assumptions of Professor Brown's work to be excited and stimulated by it. He has provided a challenging account of how a situational approach, suggested but little developed by Malinowski and Firth, can be fleshed out. New insights into the way language is actually used abound in this work. Francis P. Dinneen, S. J. School of Languages and Linguistics Georgetown University Washington, D.C.

PREFACE

Since the completion of this manuscript, several important contributions to theoretical linguistics have been published that in one way or another bear upon ideas treated here. In part these developments converge upon my own view. The Wittgensteinian interpretation of meaning and linguistic use, for example, is not too distantly removed from recent notions of the non-Chomskian generativists Charles J. Fillmore (1968) and James D. McCawley (1968) that semantics and syntax are to be at least partially explained in terms of one another. Marshall Durbin's (1973) attempt to integrate Fillmore's 'case grammar' and a functional approach also takes current linguistic theorizing another step toward the Wittgensteinian conception of language and its uses. On the other hand, it is clear that these developments have not discarded transformational 'deep structure', nor have they even replaced it with a less objectionable construct. Arguments against deep structure presented in this work apply with equal force against any theory that proposes something hidden behind our ordinary use of language, and in this respect should be regarded as equally forcible against that notion in recent developments in transformationalgenerative theory. C. H. B.

INTRODUCTION

This work grows out of my interest in recent - and to a considerable extent fashionable - developments in two coordinate branches of semiotics, linguistics and the philosophy of language. These developments are respectively transformational grammar as specifically described by Noam Chomsky, and the ordinary language philosophy of Ludwig Wittgenstein. Readers who have encountered the works of both Chomsky and Wittgenstein are no doubt aware of the pronounced difference in the manner in which each explains the essential nature of patterned communication in the modality of natural language. This difference emerges at the most general levels of analysis. Chomsky is concerned with pure semiotics, the development of a language to talk about signs. Wittgenstein emphasizes descriptive semiotics, the study of actual sign use. In 1957 Chomsky published Syntactic Structures in which the initial formulation of transformational grammar is presented. In later discussions - especially in Aspects of the Theory of Syntax (1965) - he alters a number of his original notions, but nevertheless retains the core formulation of the earlier work. In general, transformational grammar attempts to describe explicitly the rules to which a speaker of a language attends in order to use signs grammatically and meaningfully. These rules are described as existing in the speaker's head as knowledge of the language he speaks, and are said to represent the speaker's linguistic 'competence'. The so-called 'base rules' of transformational grammar constitute a kind of language which can be used to explicate the use of signs

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INTRODUCTION

in any natural language. For this reason transformational grammar should be described as a branch of pure semiotics. Syntactic Structures represents an effort to set forth the explicit structure of rules, knowledge of which permits an individual to use signs grammatically, but not necessarily meaningfully. In this respect Syntactic Structures is in line with traditional descriptive linguistics, which has, as Greenberg puts it (1968: 55), "for the most part left to the logicians" questions concerning meaning. In later works, particularly in Aspects, Chomsky incorporates devices into rules which could account for meaningful as well as grammatical use of signs. The most extensive efforts aimed at including a semantic component in transformational grammar have been made by Jerrold J. Katz and Jerry A. Fodor (1964) and by Uriel Weinreich (1966). While numerous problems concerning meaning raised by these scholars have yet to be resolved, it now appears that meaning in transformational theory resides in the 'deep structure' of language. Deep structure, generated by the base rules of a grammar (Chomsky 1965: 136), is a fundamental abstract language which underlies natural languages. It is a language with which actual sentences of any natural language - the 'surface structure' of language - can be compared and consequently understood. So defined, Chomsky (1965: 136) suggests that transformational deep structure is a concept which is identical to the concept of 'artificial language' in logical positivism. The emphasis of the logical positivists, like that of Chomsky, is upon pure semiotics. Their artificial or symbolic languages, like base rules and deep structure of transformational grammar, are explicitly constructed as devices for talking about and understanding signs and their use in natural languages. An artificial language for the logicians is a mechanism for clearing up errors born in the grammars of natural languages which could lead to philosophical confusion. Ludwig Wittgenstein, perhaps more than any other single individual, is responsible for the introduction of the idea of artificial language into twentieth century philosophy. In Wittgenstein's first work, Tractatus Logico-Philosophicus

INTRODUCTION

15

(1922), he describes past philosophy as full of confusion, such errors as there were deriving from the medium in which philosophical problems and solutions were presented, i.e. natural language. Wittgenstein writes in the Tractatus : Language disguises thought. So much so, that from outward form of the clothing it is impossible to infer the form of the thought beneath it, because the outward form of the clothing is not designed to reveal the form of the body, but for entirely different purposes (4.002).

The fundamental confusions of past philosophy were produced in philosophers by grammar. Wittgenstein in the Tractatus suggests a remedy: the construction of a sign-language that excludes errors inherent in the grammars of languages. In such a language propositions are set perfectly clear, "...in suitable notation we can in fact recognize the formal properties of propositions by mere inspection of the propositions themselves" (1922: 6.122). The logical positivists owe much to the Tractatus. Most of their fundamental tenets were initially worked out in Wittgenstein's work. The Tractatus develops the idea that there is some kind of relationship between empirical objects and the signs for them, and that this relationship in some way bears upon how the meaning of signs is realized. The Tractatus is not so concerned with the meaning of individual signs per se, but rather with how relationships are stated to hold between objects in the empirical world through use of signs. To the logicians, it is the propositional relationship holding between named things that is significant. The meaning of signs is generally thought by them to reside in propositions expressed in an artificial language - which reflect the actual sense of assertions only vaguely expressed in natural languages (Wittgenstein 1922: 3.314). For numerous reasons Wittgenstein came to reject the comments he made in his widely accepted first work. The change in Wittgenstein's thinking had occurred, or was beginning to occur, when, after having ignored the philosophy of language for some time, he took it up again in 1929 (Wittgenstein 1953: xe). Wittgenstein's 1930-33 Cambridge lecture series - as described by G. E. Moore in

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INTRODUCTION

his Philosophical Papers (1959) - are evidence that a full alteration in Wittgenstein's views had by then taken place. Wittgenstein explains his change of thought in the preface of Philosophical Investigations (1953) : For since beginning to occupy myself with philosophy again, sixteen years ago [this passage was written January 1945], I have been forced to recognize grave mistakes in what I wrote in that first book. I was helped to realize these mistakes - to a degree which I myself am hardly able to estimate - by the criticism which my ideas encountered from Frank Ramsey with whom I discussed them in numerable conversations during the last two years of his life. Even more than to this - always certain and forcible - criticism I am indebted to that which a teacher of this university, Mr. P. Sraffa, for many years unceasingly practiced on my thought. I am indebted to this for the most consequential ideas of this book (xc). Wittgenstein's later thoughts begin to appear in Philosophische Bemerkungen (1964), the volume written next after the Tractatus. Philosophische Bemerkungen, which has yet to be translated into English from German, represents a transitional stage in Wittgenstein's thinking from the Tractatus to The Blue and Brown Books (1958) in which Wittgenstein's new ideas are totally in evidence. Written next after the latter work is Remarks on the Foundations of Mathematics (1956) in which he applies his new concepts to the special language of mathematics. Wittgenstein's last major work is Philosophical Investigations published in 1953, two years after his death. The latter work and Zettel (1967), a collection of fragments left in a file box found after his death, are clearly extensions of thoughts first expressed in The Blue and Brown Books. The change in Wittgenstein's thoughts can be described, at the most general level, as a transfer of emphasis from pure to descriptive semiotics. Wittgenstein, in his later works, denies the utility of constructing artificial languages to talk about signs, and concentrates upon description of the ordinary use of signs in natural language. It is important to note that his ultimate objective, the avoidance of philosophical confusion, had not changed. What had altered was his methods of avoiding confusion, and of clearing up philosophical problems. His rejection of his earlier view and his

INTRODUCTION

17

later understanding emerge in the following quotation from Philosophical Investigations: It is clear that every sentence in our language "is in order as it is". That is to say, we are not striving after an ideal, as if our ordinary vague sentences had not yet got a quite unexceptionable sense, and a perfect language awaited construction by us. - On the other hand it seems clear that where there is sense there must be perfect order. - So there must be perfect order even in the vaguest sentence (54e). Where Wittgenstein alludes to "perfect language" to be "constructed by us", he has in mind the artificial languages of logical positivists (including the author of the Tractatus). In his later view, he sees the construction of an artificial language as unwarranted. His understanding is clear: any language, be it artificial or natural, is understood not in terms of some other language, but in terms of itself, in the manner in which its signs are ordinarily used. Some ideas relating to very general questions run parallel in the works of Chomsky and the later Wittgenstein. Chief among these is the notion that at least some part of the knowledge necessary for using language is innately given. Chomsky and Wittgenstein differ, however, on what they consider the constituents of this knowledge to be. Chomsky believes the symbols and instructions which make up base rules to be innate. In this respect, he claims that the same deep structure, generated by base rules, underlies the surface structures of all natural languages. Wittgenstein, in contrast, believes that the capacity to follow linguistic rules, rather than rules themselves, constitutes innate knowledge of language. While this distinction may seem slight, it is, nevertheless, a significant one. The problem relating to the distinction concerns a very basic confusion which is attributable to transformational grammar and logical positivism alike. This is a confusion of levels of analysis, of pure and descriptive semiotics. Before turning to the specific problem, a few general comments are necessary. Descriptive semiotics - the study of actual signs, their conformation and use - need not entail more than observation and description. Pure semiotics involves a dimension in addition to observation and description, i.e. invention - invention of a language to talk about signs. Con-

18

INTRODUCTION

fusion arises when the invention aspect of pure semiotics is forgotten, when the elaborated language is confused with the language it is constructed to talk about. Transformationalists have lost sight of the fact that base rules and the deep structure generated by them are first and above all invented for the purpose of explicating use of signs in natural languages. As consequence of this, base rules and deep structure have been taken as being objects of description on a level with the primary object of description, i.e. natural language, rather than as being what they first of all are, i.e. mechanisms for description. The postulation of the innateness and universality of base rules and deep structure by Chomsky is, in my view, gratuitous, because the real explanation of their being lies in the simple and obvious fact that they are invented. Wittgenstein in his later works clearly avoids a similar confusion which he attributes to logical positivism. He objects to the idea that an artificial language can be derived which represents an abstract condition underlying every natural language. To accept such an idea is again to confuse a language invented to talk about natural language with natural language. This is one reason why Wittgenstein avoids assigning innate status to linguistic rules. The language that one could invent for describing the way in which signs behave in natural languages would be just that, invented, and consequently could not be part of natural language as an innate condition or otherwise. Wittgenstein does not deny the existence of linguistic rules - he calls them "rules-of-usage" - he denies the possibility of ever isolating and describing them. He consequently assigns innateness only to the capacity for following them. Wittgenstein rejects the possibility of describing a rule-of-usage because the rule described would be the wrong kind of rule, or, what I call a prepositional rule-of-usage. Such a rule instructs the propositional conditions under which a sign is to be used; for example, the sign (sentence) "Is it raining?" is used under the propositional conditions that one does not know it is raining and wants to find out. Wittgenstein no more thinks that propositional conditions underlie our use of language than he believes that some

INTRODUCTION

19

abstract conditon represented by an artificial language underlies it. Wittgenstein's rules-of-usage tend to emerge in undefined but nevertheless apparent forms in his numerous descriptions of incidents of ordinary use of language. I disagree with Wittgenstein in that I believe the right sort of rule-of-usage can be explicitly formulated and I do so in this work (my formulation is offered as an alternative to transformational grammar). My disagreement with Wittgenstein is not, however, of any consequence. A rule-ofusage can be explicitly defined if Wittgenstein's many warnings are heeded. Chief among these is avoidance of the confusion mentioned above, of taking the language of description for the language described, of confusing pure and descriptive semiotics.

I WITTGENSTEIN AND ORDINARY USAGE

1. ORDINARY USAGE AND MISUSAGE

In the Tractatus Wittgenstein describes language as depicting the logical structure of facts. Every fact is conceived as having only one logical form correctly depicted by one proposition. Behind all natural languages there is only one logical language, consisting of a number of basic propositions. It is this propositional system Wittgenstein's artificial language - that interests him in his early investigations. Later his interest shifts radically. He comes to see language as expressing more than actual facts, and finds its everyday application more philosophically relevant than artificial systems. In his later works, Wittgenstein investigates only ordinary language and its uses. The later Wittgenstein is not so interested in all possible ways in which signs could be used, as he is in the way they are normally used. To make ordinary usage clear, he often points out instances of uncommon usage : We use the phrase "two books have the same colour" but we could perfectly well say: "they can't have the same colour, because, after all, this book has its own colour, and the other book has its own colour too". This also would be stating a grammatical rule - a rule, incidentally, not in accordance with our ordinary usage (1958:55). The statement of such a rule induces us to believe that there is some kind of physical impossibility connected with the utterance "two books have the same colour". Wittgenstein suggests that when faced

WITTGENSTEIN AND ORDINARY USAGE

21

with such cases, the thing to do "is always to look how words in question are actually used in our language" (1958: 56). Wittgenstein views the misuse of language as being the source of physical speculation in philosophy. He claims, for example, that the doctrine of 'solipsism' - the doctrine that one can be certain only of his own existence and must be in doubt concerning the existence of other people - arises from misuse of language. Solipsism arises from utterances such as "I can't feel your pain." Based on this statement alone, one could presume that the ability to feel the sensations of others is a physical impossibility. How can one ever be sure that others have sensations, that others exist? Are there other minds? Wittgenstein does not attempt a solution of solipsism, he simply points to its origin in the misuse of statements containing words such as "pain". To understand the cases in which such an expression is misused, we must be aware of the contexts in which the ordinary use of "pain" is embedded. The use of "pain" commonly occurs in the context of what Wittgenstein calls pain-behavior. Pain-behavior is the primitive natural expression of the sensations involved in having pains, for example, crying or groaning (1953: 89e). Utterances such as "I have pain" are not to be thought of as naming a sensation but rather as used as an expression of one's reaction to a painful sensation. As painbehavior such statements derive not from experience, but from within, like a cry or a groan. Misled by surface grammar one might imagine the statement "I can't feel your pain" is the same sort of statement as, for example, "I can't put your shoes on" (Peursen 1969: 87). The former statement is not to be compared with physical statements or empirical propositions whose validity is testable against facts of experience; rather it is equivalent to a priori propositions such as "You won't get two yards out of fifty inches", or "I can't play patience with you" (Peursen 1969:88). Such statements do not refer to physical impossibilities, but rather to logical impossibilities. They do not, consequently, imply a solipsistic philosophy. When interpreted otherwise, they are misused.

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WITTGENSTEIN AND ORDINARY USAGE

2. WITTGENSTEIN'S REJECTION OF ARTIFICIAL LANGUAGE

There are countless different kinds of use to which sentences of natural language may be put. Wittgenstein mentions that sentences can be used to ask questions, to give commands, to describe the appearance of an object, to report an event, to speculate about an event, to make a joke, to ¡form hypotheses, to test hypotheses, etc. Herein lies the reason for Wittgenstein's later denial of the utility of artificial languages in philosophical investigation. His view is that the assertion or proposition which is the fundamental element of artificial languages is only one among many different kinds of sentences. With this in mind he writes, - It is interesting to compare the multiplicity of the tools in language and the ways they are used, the multiplicity of kinds of word and sentence, with what logicians have said about the structure of language (Including the author of the Tractatus Logico-Philosophicus) (1953:12e).

His reference here is to the logicians' and his own earlier notion that language describes the logical structure of facts, and hence is reducible to a number of propositions expressed in an artificial language which truthfully or falsely report them. Wittgenstein holds in Philosophical Investigations that the ordinary use of language is a way of behaving, that the various uses of language represent different kinds of behavior of which assertion is but one. Interrogation, for example, is a kind of behavior whose linguistic expression is the question. Any question may be conceived as containing a proposition or assertion (1953: 12e). The question "Is it raining?" may, for instance, entail the assertion, "I do not know that it is raining", or "I wish someone would tell me". Knowledge of this, as Wittgenstein points out, does not bring the two different forms of behavior (interrogation and assertion) any closer together. The interrogative and assertive uses of language cannot be conceptually compromised (1953: 12e). Wittgenstein's observation of this fact is the basis upon which he rejects the proposition as an analytic device. The transformation of questions into propositions simply obscures the fact of their autonomous uses.

WITTGENSTEIN AND ORDINARY USAGE

23

In the Tractatus Wittgenstein describes each sentence of a language as having a correct logical form depicted by only one proposition. Such propositions are moreover concealed by surface grammar, by the grammatical conformation of the sentence itself (Hartnack 1965: 37). It is, furthermore, the philosopher's task to set clear these propositions. By so doing he rids language of vagaries which could lead to metaphysical speculation and false philosophical problems. The early Wittgenstein and the logical positivists share this belief, and thus proceed in their investigations along similar paths. Russell, for example, transforms the statement (1) "The golden mountain does not exist" into what he considers its logical depiction, (2) "It is false that there is an entity c such that the propositional function 'X is a moutain and of gold' is true if χ is c and otherwise false" (Hartnack 1965: 76). Now according to the Wittgenstein of Philosophical Investigations such a transformation is simply unnecessary. In Wittgenstein's terms, both statements (1) and (2) are "in perfect order". The fact that (1) can be transformed into (2) is not significant. The fact that under certain conditions (1) and (2) are used alike is. The occurrence of (2) throws light upon the ordinary use of (1), and hence upon the function it has, the purpose it serves. The occurrence of (1) similarly illuminates (2). It is, moreover, knowledge of the use of (1) and (2) which is philosophically important. If we know the ordinary applications of sentences, we know the instances in which they are misapplied, we know the origin of metaphysical problems. Accordingly, a propositional transformation of any statement is only important in that it aids in the better understanding of the use of that statement (Hartnack 1965:77). The Tractatus regards Russell's translation (2) as a correction of (1). Since only assertion (2) reports the logical form of reality, therefore only this statement is correct. Russell himself does not believe that (2) is the most accurate transformation of (1). In Russell's opinion a correct translation can only be rendered in the symbolic language of Principia Mathematica (Hartnack 1965: 77).

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WITTGENSTEIN AND ORDINARY USAGE

The general view of the logical positivists is that the only escape from the vagaries inherent in the grammar of natural languages is in the construction of a symbolic language in which all propositional relationships are set perfectly clear. Accordingly, given such statements as " I a m ill", Ich bin krank, or Je suis malade, there can

be found a proposition ρ of the symbolic language with which all are absolutely synonymous. As Quine critically points out (1960: 200), given such a notion, one can well go on to assert that some proposition ρ is the meaning of every one of these statements - that underlying any sentence of a natural language is a proposition which is its meaning. This is not, however, Wittgenstein's concept of meaning.

3. RULES-OF-USAGE

Wittgenstein very early in his major work, Investigations, gives his definition of meaning, "...the word 'meaning' ...can be defined thus: the meaning of a word is its use in the language" (1953: 20e). Later, in the same work he discusses the relationship between meaning and rules for a sign's use - which he calls "rules-of-usage" : "For without these rules the word has as yet no meaning; and if we change the rules, it now has another meaning (or none), and in that case we may just as well change the word too" (1953:147e). Wittgenstein does not describe rules-of-usage. What is significant to him is the way in which rules "do something". He is interested in describing the consequence of following a ride, not in defining the explicit structure of rules-of-usage. That a rule-of-usage sets forth the conditions under which a word may be used in a certain way is an hypothesis which is not attributable to Wittgenstein. It is, nevertheless, an intriguing one, and worth considering in light of what Wittgenstein does have to say about rules-of-usage and language use in general. Consider again the question "Is it raining?". While this sentence may be taken to mean either (1) "I do not know that it is raining", or (2) "I wish someone would tell me", (1) and (2) can also be

WITTGENSTEIN AND ORDINARY USAGE

Ï5

thought of as two possible conditions under which the question is asked. Put in a general way, any sentence may be used interrogatively when one of two assertions may be made: (a) that someone is in a state of doubt about something, or (b) that someone wants an answer. Following William P. Alston's (1964) suggestion, this relationship can be notationally realized.1 Given two sentences si and s2, we can write "si—s2/a, b", where — stands for equivalence of use, a for the assertion (a), and b for the assertion (b). SI and s2 are here stated used alike (interrogatively) when either a or b is the case. This expression could be interpreted as a rule which lies behind interrogative behavior, a rule which governs our interrogative use of sentences. I shall refer to such formulations as prepositional rules-of-usage. A propositional rule-of-usage can be found for every instance of ordinary application of signs. Intuitively one might suppose that a propositional rule-of-usage represents the explicit structure of Wittgenstein's rule-of-usage. As mentioned in section 2, Wittgenstein rejects the idea that underlying any sentence is a proposition which is its meaning. He also objects to the similar notion that ordinary usage is determined (in every instance) by propositional rules. His understanding is clear; we use language without having particular or fixed propositions or definitions in mind. In defense of this position, he points out the unlikelihood that, when using language, we circumscribe the propositional or definitional condition or conditions which presumably lie behind our usage : When I say "N is dead", then something like the following may hold for the meaning of the name "Ν" : I believe that a human being has lived, whom I (1) have seen in such-and-such places, who (2) looked like this (pictures), (3) has done such-and-such things, and (4) bore the name "Ν", I should ennumerate all or some of these points, and different ones on different occasions. So my definition of "N" would perhaps be "the man of whom all this is true". - But if some point now proves false?Shall I be prepared to declare the proposition "N is dead" false - even if it is only something which strikes me as incidental that has turned out false? But where are the bounds of the incidental? (1953: 37e). 1

The formulation presented here, while similar to Alston's is not identical to it. The idea that equivalence of use can be notationally realized is the debt I owe Alston.

26

WITTGENSTEIN AND ORDINARY USAGE

Wittgenstein finds it inconceivable that, when using language, we ordinarily attend to all probable definitional conditions which could be isolated. It is equally unlikely that we are constantly making choices among the many alternative definitions available when we speak. It is only when we begin to scrutinize closely our utterances, that we come to realize that we have no fixed meaning in mind at all. This becomes clearer when we take a closer look at what Wittgenstein means by a rule. He writes. "The word 'agreement' and the word 'rule' are related to one another, they are cousins" (1953: 86e). A rule is something which is agreed upon, shared, part of the public domain. Suppose, suggests Wittgenstein (1953: 100e), that a number of people have boxes with a beetle inside, and that they have decided each is to describe his own beetle. No one is to look inside another's box, and everyone knows what a beetle is by looking at his own. They proceed by telling each other what their beetles look like, what color they are, and so on. Now what would happen if the contained beetles suddenly disappear? Couldn't people go on describing beetles regardless? The process continues to run smoothly because actual beetles play no role in it. The thing in the box which must not be public is not essential. On the other hand, the rules by which the group proceeds in their actions are. They are conventional (Peursen 1969:91). A definition or proposition is like a beetle in one of Wittgenstein's boxes : it is nonessential to the actual use of language. The rules behind ordinary usage are public, and moreover unrelated to definitional or propositional conditions. How many propositional conditions can be found which prescribe the synonymous use of two or more signs? The number of propositional conditions under which any two words could be used alike is contingent upon the number of ways in which the things they name could be similarly classified. As Ayer (1946: 91) points out, when one classifies something, he is not merely attending to its perceptual properties; rather he is going beyond what is immediately given in sense-content. An act of classification is a logical act, an act of hypothesization. It is therefore conceivable that the number of ways in which a thing

WITTGENSTEIN AND ORDINARY USAGE

27

could be classified and defined approaches infinity, that we could go on forever isolating definitional or propositional conditions under which two or more words which name such things could be used alike. Given this, could a propositional rule-of-usage ever be public? Could it be the common denominator of language use? In Wittgenstein's view, propositional conditions are not given with rules-of-usage, for they cannot be shared - they cannot be conventional. The rules behind ordinary usage are public, and, therefore, unrelated to proposition or definition. If asked to give the definition of a rule behind our usage, we are unable to do so, "not because we don't know their real definition, but because there is no real 'definition' to them" (Wittgenstein 1958: 25).

4. ACQUISITION OF LINGUISTIC COMPETENCE

In Wittgenstein's view, the manner in which we learn to use language - the way in which we become linguistically competent - is no different from the way we learn to make mathematical calculations. In learning to square numbers, for example, we may first be given examples, for instance, 1 x 1 = 1, 2 χ 2=4, etc. Through practice and attention to examples we become competent in making this calculation. We come to act as if we are following the rule yxy=y2. Wittgenstein distinguishes between "a process being in accordance with a rule" and "a process involving a rule" (1958: 13). Our behavior in squaring accords with the rule y x y = y 2 ; it is not necessarily involved with it. We cannot say that one who has learned to calculate squares in his head actually refers to this rule on every occasion of that behavior. We may say rather that the rule represents an aspect of his mathematical competence. Similarly, through example and practice (1953: 83e) a child becomes linguistically competent. He learns to use language in an ordinary way. His usage appears to accord with some rules, but, as in the case of squaring, we cannot be certain that his behavior is involved with them.

28

WITTGENSTEIN AND ORDINARY USAGE

According to Wittgenstein, explicit definitions are involved in the process of language acquisition. Again a mathematical parallel can be found. Suppose in learning to square numbers we are given explicit rules to follow rather than examples. On one occasion we may be y told, "follow this rule,y x y = y 2 , and on another, this one, ) yi—y2, i=l which instructs that the square of a number is equal to that number added to itself as many times as that number indicates. By following one rule at one time, and the other at another, we eventually become competent in squaring - we no longer have to look at either rule to perform the calculation. We can further say that this competence may be represented by either rule, but that it is, in fact, neither. In a similar manner, in learning language we may attend to explicit rules which instruct the conditions under which a sign is to be used in a certain way. We may be told, for example, or we may discover for ourselves that sentences are used interrogatively when (a) someone is in a state of doubt about something, and/or (b) someone wants an answer. We may base our initial use of interrogative sentences - our language practice - on either one or both of these definitions. As our linguistic competence emerges, we no longer think about what we intend by questions, we simply ask them, i.e. we behave interrogatively. Noam Chomsky, in Aspects of the Theory of Syntax, accredits Wittgenstein with conceiving of language as an "adventitious construct" taught by "drill and explicit explanation" (1965: 51). Chomsky's own view is essentially rationalistic: the form of language, the schema for its grammar must already be present in the mind before learning begins. Chomsky assumes that learning a language consists in the drawing out of what is innate in the mind. This stand is to be contrasted with the empiricist point of view: that language is totally acquired through experience, that the innate properties of the mind involved are solely constituted by procedures and mechanisms which permit language acquisition. Wittgenstein totally rejects the empiricist hypothesis. He emphasizes linguistic training for the sole purpose of setting clear the relation-

WITTGENSTEIN AND ORDINARY USAGE

29

ship holding between the procedures through which we become competent in using language, and the innate order which presupposes the linguistic phenomena encountered in the normal course of exposure to language. This is an important aspect of his investigation, and will be considered in detail in Chapter V.

II FORMULATION OF RULES-OF-USAGE

1. A RULE FORMULATION

The innate and learned aspects of linguistic competence are described by both Chomsky and Wittgenstein as contingent upon rules. Wittgenstein is not interested in representing the form or structure of rules. He uses the concept rule-of-usage to explain how language is, and consequently how language relates to philosophical investigation. Chomsky, on the other hand, addresses himself to a number of specific linguistic phenomena. In one instance, for example, he seeks to explain how rules can generate an indefinitely large number of linguistic structures, all of which retain the characteristic of being grammatical and understandable. For this he theorizes the explicit conformation of rules and the precise nature of the system to which they belong. His theory of generative or transformational grammar on the whole accounts for the facts he seeks to explain. Wittgenstein, nevertheless, limits the range of models which could possibly represent a rule-of-usage. A rule-of-usage is public. Propositions and definitions are private. If a rule-of-usage instructs the conditions under which two or more signs are used alike, such conditions cannot be propositional or definitional. Denied explicit definition or proposition as a condition, the only resource - apart from non-verbal contexts - which is available as a condition is usage itself : one usage standing as a condition under which another may or may not occur. Given this interpretation, a rule-of-usage can take the following form: a = b / c = d , which reads "signs a and

FORMULATION OF RULES-OF-USAGE

31

b may be used alike in the context of use of sign c like sign d or vice versa". Rules-of-usage may also specify the conditions under which a usage may not occur: thus a ^ b / c = d , which reads, "a and b may not be used alike in the context of usage c = d " . Consider the following example. "Brother" and "sister" are interchangeable - used alike - in these occurrences: "big brother", "bigsister"; "older brother", "older sister". This fact is expressed x = y where χ is "brother" and y is "sister". " M a n " and "woman" are used alike in these phrases : "big man", "big woman" ; "large man", "large woman". This usage is expressed w = z where "man" is w and "woman" is z. Note that "big" and "older" are interchangeable in the context of x—y, but are not ordinarily used alike in the context of w—z. Two rules-of-usage may be written which express this fact: u = v / x = y and u ^ v / w = z , where u is "big" and ν is "older". Reciprocity is a characteristic of such rules. The converse of the former rule, for instance, is equally applicable: x = y / u = v , which reads, " 'brother' is used like 'sister' in the context of 'big' used like 'older'". Similarly, each one of the following representations expresses an alternative way in which the rule u φ ν/ w = z might be realized : w = z / u Φ ν, u = v / w Φ ζ, or w φ z / u = v .

2. RULES WHICH CODIFY USAGE

In Wittgenstein's view, the semantic and grammatic aspects of rulesof-usage cannot be disassociated : 2 What does it mean to say that "is" in "The rose is red" has a different meaning from the "is" in "twice two is four"? If it is answered that it means that different rules are valid for these two words, we can say that we have only one word here. - And if all I am attending to is grammatical rules, these do allow the use of the word "is" in both connexions. - But the rule which shows that the word "is" has different meanings in these 2

Wittgenstein's understanding of the interrelation of grammar and meaning is the converse of the more recent notion of Fodor and Katz, who structure their "Semantic Theory" around the formula "LINGUISTIC DESCRIPTION MINUS GRAMMAR EQUALS SEMANTICS" (1964: 483).

32

FORMULATION OF RULES-OF-USAGE

sentences is the one allowing us to replace the word "is" in the second sentence by the sign of equality, and forbidding this substitution in the first sentence (1953:149e). The rule-of-usage to which Wittgenstein refers not only serves a semantic function, but by allowing "is" to be used in both connections may also be construed as serving a grammatic one. In Wittgenstein's view the grammatic and semantic aspects of language use are not autonomous, and should not be theoretically distinguished. The same rules function to determine both. Sentences such as "twice two is red" or "the rose is four" are not to be characterized as either unsemantic or, conceivably, grammatically ill-formed, but simply described as examples of uncommon usage behind which may lie rules that are not ordinarily employed in English. The same may be said for sentences such as "the rose red is" or "twice two four is". A rule-of-usage can be found which instructs that the word "is", or signs similarly used - such as "equals" or "possesses the color" - are to be ordinarily used in a central position in English sentences which are themselves used for a specific purpose - in our sample case for making assertions. In language the various uses of sentences are often codified. We may assume, for example, that one can distinguish an English sentence used to ask a question from one which asserts a fact, on the basis of the peculiar manner in which each is codified. The internal structure, the positioning of lexemic units, of each could be the distinguishing factor. Rules-of-usage may not only govern the way in which signs substitute for one another, they may also determine how such units are used in the total context of a sentence, the positions in which they are used, and hence the manner in which their uses are codified. A rule-of-usage which serves to codify, while essentially no different from the rule formulated in section 1, must be notationally represented in a slightly different manner. For descriptive purposes, signs which are used alike under certain conditions are considered all members of a set U, which I shall call a usage set. Now suppose we have two usage sets Ua and Ub. We may assume, as an example, that all members of Ua belong to this set by reason of their equi-

FORMULATION OF RULES-OF-USAGE

33

valent use as noun phrases. Likewise, all members of Ub may be thought of as commonly used as verb phrases. Now suppose that any member χ of Ub (x e Ub) precedes any member y of Ua (y e Ua) whenever the sentence in which they are found is used interrogatively. We may assume that such a sentence belongs to a usage set Uc which consists of all sentences used alike - in this case, interrogatively. Therefore, any sentence ζ of Uc (z e Uc) is used like any other sentence of that set. The rule which determines how χ and y are used in such a sentence - how they are positioned relative to one another - and how the use of the sentence (s) itself is codified may be expressed as follows: (x, y) Es ->x-y/s=z. This rule reads, "the unordered pair, χ and y, (indicated: (x, y)), which are the lexemic constituents (indicated: E) of the sentence s, are to be used (indicated: ->) in the positions χ precedes y and y follows χ (indicated: x-y), when s is used like any member ζ of the usage set Uc (indicated : /s=z).

3. A FORMULATION OF COMPETENCE: THE «LANGUAGE-GAME' ASSERTION

Having described what may be the explicit structure of rules-ofusage, we are now in a position to consider questions whose mechanical solutions held no great interest for Wittgenstein, but which have received considerable attention from Chomsky and other transformationalists: What is the nature of linguistic competence? How does one get from competence to performance, the actual ixse of language? Assume Wittgenstein's examples, "the rose is red" and "twice two is four", represent ordinary uses of words and sentences regularly encountered in the English language. Both sentences are used assertively. Similar assertions may be isolated: "twice two is the square root of sixteen", "the flower is scarlet", "the rose possesses the color red", "four is the same as the square root of sixteen", "four equals twice two" etc. Anyone who encounters the above sentences may recognize the

34

FORMULATION OF RULES-OF-USAGE

fact that some of these expressions may substitute for others, and that some words embedded in them may be interchanged for other words of other sentences without effecting a drastic change of meaning or sense. That we make such substitutions in our ordinary use of language is an incontestable fact. Harris' "discourse analysis" (1964), for instance, shows not only that we make such substitutions, but that we make them in a highly consistent manner. His findings suggest that the way we use words, phrases, and sentences on any particular occasion, the substitutions to which we attend when writing or speaking, depend upon our immediate orientation towards subject matter, literary style, etc. (1964: 356). We might therefore assume that interchangeable signs are not only isolable through discourse analysis, but that we isolate them in some sense whenever we use ordinary language. We must have the capacity to orient ourselves to what is being said, or to what we ourselves are saying ; we must be able to discriminate among the ordinary uses which we encounter. One of the innate linguistic mechanisms which permits speech and understanding must consist in the ability to circumscribe at a given instance ordinary usage. (The mechanics of usage circumscription are discussed in Chapter IV.) Wittgenstein (1958 ; 1953 : passim) gives us a clue to the nature of this mechanism. He compares an instance of language use to the playing of a game. When playing a game, we attend to its rules. There are any number of different games which may be played. Some have fixed, set rules which are unalterable. When playing other games, we choose rules as we go along, or, to borrow Wittgenstein's expression, we "draw boundaries", we establish the limits to what can and cannot be done. Similarly, when using language, we are continuously drawing boundaries, choosing rules which are appropriate to the kind of "language-game" - another of Wittgenstein's expressions - which we may wish to play. We choose among rules-of-usage which pertain to various language-games, such as "asking a question", "making a joke", "making an hypothesis", "making riddles", "making an assertion", "giving commands", "reporting an event", "guessing riddles",

FORMULATION OF RULES-OF-USAGE

35

"instructing", etc. Through choosing rules, we establish the boundaries of our linguistic behavior, and, consequently, circumscribe the ordinary use of signs which pertains to that behavior. Rules-of-usage are conventional or public like our linguistic behavior, or like the language-games in which we commonly participate. To know the language-game which is being played, to know the topic of conversation, the purpose of a communication, its function, is equivalent to knowledge of the rules-of-usage behind it, and also to knowledge of the ordinary use of signs which pertains to that language-game. Taking the sample sentences as a segment of linguistic behavior which is bounded by rules-of-usage, we may assume that their use entails circumscription of a number of common usages. Such usages may be conveniently represented by means of the usage set. By attending to these expressions in much the same way as when performing discourse analysis, the following usage sets can be isolated: U1 : U2: U3 : U4: US : U6: U7: U8: U9:

the rose, the flower twice two, four, the square root of sixteen is, equals, is the same as is, possesses the color red, scarlet SI, S2, S3, etc. U1+U2 U3+U4 U2+U5

Members of any one of the sets U l , U2, U3, U4, and U5 may substitute for one another in any one of the expressions in which they occur without effecting a change in what may be the expression's intended sense. "U7: U 1 + U 2 " expresses the fact that all members of usage sets Ul and U2 are also members of usage set TJ7. All members of U7 are used in the initial position of a sentence. Members of U8 are used in the central position, and members of U9 in the terminal position. Members of U6 are sentences which, in this case, are all used alike in the sense that their ordinary use entails assertion. In Wittgenstein's view, assertion is simply one of many language-

36

FORMULATION OF RULES-OF-USAGE

games which can be played. Like all language-games, assertion is bounded by rules-of-usage. The usage defined above is in some manner governed by rules-of-usage that pertain to the languagegame assertion. The rules which bound this game - that may represent the linguistic competence underlying the ordinary usage we are considering - can be expressed as follows : (i) (g, h, i) E s

g-h-i/s=f

(ii)

/

fg^a g=b

h^c Me i=b

Lower case letters stand for any χ which is included (e) in some usage set. Each covers as follows : f-xeU6 g-xeU7 h-xeU8 i-xeU9

a-xeUl b-xeU2 c-xeU3 d-xeU4 e-xeU5

Rule i serves to codify the usage of any sentence s which is used like any sentence f which is a member of usage set U6, i.e. any sentence that is used assertively. This rule reads like the rule-ofusage formulated in section 2. The braces of rule ii are used to abbreviate the listing of conditions under which g=i. g is used like i under any one of the six conditions listed. The reciprocals of rule ii are also applicable. Rule ii may be taken to represent the following relationships in addition :

/

h=c i=b

/

/

g=b

/

/

/

/ g=i

g^i

/

/

/

g=a h=d h^c i=e

g=a g*b h=d h/c i=e

FORMULATION OF RULES-OF-USAGE

37

4. APPLICATION OF RULES

Rules i and ii generate sentences which are ordinarily used in the language-game 'assertion'. Sentences which could be characterized as being grammatically ill-formed are not commonly a part of this language-game. Rules i and ii, consequently, like the rules of transformational grammar, generate only well-formed sentences. The nature of these rules with respect to their application becomes apparent when compared with the functionally equivalent rules of transformational grammar. A transformational or generative grammar consists of two types of rules, 'base' rules and 'transformational' rules. (The discussion which immediately follows is devoted entirely to base rules. Transformational rules are considered in following chapters.) These rules operate upon 'class' and 'terminal' symbols (Koutsoudas 1966: 6). Class symbols stand for the higher order constituents of a sentence, for example, NP (noun phrase) and VP (verb phrase). Terminal symbols are the lower order constituents, and may be thought of as being actual lexemic or morphemic units, for example, "boy" and "see". Base rules instruct that symbols be rewritten - indicated by an arrow - in a certain manner. The rule "S-»NP+VP", for example, instructs that S is to be rewritten as or expanded into its constituents NP and VP. This rule, in addition, specifies that NP and VP are to be ordered in a sentence in a specific manner: in this case NP is to occur before VP. Base rules are partially ordered in their application: some rules are necessarily applied before others. The above rule, for instance, must be applied before "VP->V+NP", where V is a class symbol representing verb. The symbol VP logically cannot be expanded before some rule specifies that it is a constituent of some sentence S. The following series of partially ordered base rules represents a grammar fragment that is capable of generating grammatical or well-formed English sentences: 1. 2. 3. 4.

S-> NP+VP+Adv VP-> V + N P NP-> D e t + N Det-> the, a

38

FORMULATION OF RULES-OF-USAGE 5. N - > girl, flower

6. V-s-cut 7. Adv-* yesterday

Rules 4-7 expand class symbols into terminal symbols. By first applying rule 1, followed by application of 2 and 3, and finally 4-7, the sentence "a girl cut the flower yesterday" may be generated. Each sentence generated by a transformational grammar has a 'derivational history' (Koutsoudas 1966: 15). The application of each rule represents a chapter in the derivational history of our sample sentence: NP+VP+Adv NP+V+NP+Adv Det+N+V+Det+N+Adv a+girl + cut + the+flower+yesterday

(by (by (by (by

application application application application

of of of of

1) 2) 3) 4-7)

A unit such as "NP+VP-f Adv" is called a 'non-terminal string'. Non-terminal strings consist of at least one class symbol which has not been expanded. The final string given above is a 'terminal' string and may not be expanded further. Any string may be understood as representing the constituent structure of some sentence. With respect to this structure, any string may be considered in order as it is whether it is terminal or non-terminal. The symbols upon which rules-of-usage (given in section 3) operate are in no way equivalent to the class symbols of transformational grammar. Rather, in every instance of their occurrence they should be regarded as cover symbols which represent actual lexemic units or terminal symbols. By definition any lower case letter included in either rule i or ii is any lexemic unit which is a member of some usage set. Rules-of-usage, therefore, operate solely upon terminal symbols. There is then no necessity for including expansion or rewrite rules among rules, and, consequently, there is no reason why they should be considered ordered in application. Rule i serves the function of a base rule: it generates strings of ordered symbols. Rule i is only one of the rules behind the language-game 'assertion'. Taken in isolation, it cannot, unlike a base rule, generate a string which represents the constituent structure of a sentence pertaining to the latter game. For example, the symbols

FORMULATION OF RULES-OF-USAGE

39

g, h, and i of rule i may be taken respectively as covers for the signs "the rose", "equals", "red". Rule i orders these signs in the following manner: "the rose"-"equals"-"red". The latter string is obviously not in order in terms of what is normally considered an ordinary usage which pertains to the language-game 'assertion', nor can it be said to represent the constituent structure of an assertive sentence. There are, conceivably, language-games which include such a usage - perhaps it belongs to games in which jokes are told, or in which instructions are given for playing some children's game - 'assertion', however, is not one of them. In isolation rule i can also generate the string "the rose"-"is"-"red". We cannot, nevertheless, be assured that even this string is in order with respect to the game being played. "Is", for example, might be drawn from a usage set which includes "equals" but not "possesses the color". In such a case, the string would not pertain to the language-game 'assertion', and it would not represent the constituent structure of an assertive sentence. Either rule i or rule ii on its own is capable of generating a number of symbols which might be construed as actual language. Consider rule ii alone. Suppose one symbol b is the sign "twice two". "Twice two" by definition has several uses. It is, for example, used like some member of the usage set U7, thus, "twice two"=g. Since "twice two" and b are the same entities, then b = g . By rule ii when g = b , then g=i. Again, by a reciprocal of rule ii, when g = i , then h = c and i—b. Suppose c is "equals" or, in other words, h="equals", and another symbol b is "four", or i="four". Thus by rule ii "twice two", "equals", and "four" may occur together when each is used in a certain manner, that is when "twice two"=g, "equals"=h, and "four"—i. In language, when lexemic units occur together, they are constituents of utterances. It is important to understand, nevertheless, that no probable or possible ordering of the above generated constituents can be postulated, with any degree of certainty, as being the constituent structure of a sentence which pertains to the language-game 'assertion'. Rules i and ii may be chosen for the purpose of playing a specific language-game. If any other rules are selected, or if only one of

40

FORMULATION OF RULES-OF-USAGE

these two is chosen, the language-game would not be the same, and, consequently, we could expect a linguistic performance unrelated to assertion. When rules are chosen, we behave as if we were following them simultaneously. Individual rules, when singularly applied, generate terminal strings which, in every instance, may be understood as being actual sentences. The sequential application of rules i and ii would be equivalent to playing first one kind of language-game and then playing another. In order to play only the game 'assertion', we must assume for the moment that rules i and ii are actually simultaneously followed. This notion, however, will be subject to revision in Chapter IV. When our behavior is actually involved with rules - again, using Wittgenstein's distinction - when we consciously or conscientiously follow their instructions, we are logically coerced to take them one at a time, to bring our attention first to one rule and then to another. The procedure of explaining how rules account for ordinary usage is equivalent to involvement with those rules, and, consequently, it is difficult, if not impossible, to demonstrate graphically how rules are followed simultaneously. That we can and do follow many different kinds of rules at once is obvious. For example, when a ball is hit in a baseball game, a player knows to run, and, moreover, to run in a particular direction, i.e. towards home plate via a specific route. His behavior is consonant with two rules of the game: (1) run when a ball is hit, and (2) on any occasion of running - such as when a ball is hit, or when one steals a base - to run in a certain direction. In this case we cannot say that the player is actually applying or following two rules at once, we say that he is behaving in a way that accords with simultaneous attention to rules (1) and (2). Similarly, when one plays the language-game 'assertion', his behavior, the way he uses signs, is in accordance with simultaneous attention to rules i and ii. The innate mechanism which permits us to behave in accordance with rules without actually attending to them is the same device which allows us to participate effectively in language-games which are bounded by more than one rule-of-usage. (This is taken up again in Chapter IV.)

FORMULATION OF RULES-OF-USAGE

41

For explicative purposes, rules i and ii are here followed sequentially. They may be followed in any sequence, for, as mentioned earlier, there is no reason to assume them ordered. Rule i, for example, may generate the string "the rose"-"equals"-"red". By applying rule ii to the same symbols, it is discovered that there are no conditions under which these three signs are constituents of a sentence which pertains to 'assertion'. Accordingly, the string is rejected and not used. Similarly, rule i may generate other strings whose symbols are proven by rule ii to be constituents of an assertive sentence, and hence such strings are retained and used in the language-game. On the other hand, by first attending to rule ii we find that "twice two", "equals", and "four" may be constituents of an assertive sentence. These signs occur together only under the conditions that "twice two"=g, "equals"=h, and "four"—i. By rule i "twice two" is used like g, "equals" like h, and "four" like i, when they occur in the positions "twice two""equals"-"four". The sentence "twice two equals four" is consequently a constituent of the language-game 'assertion'. Any sentence described as ordinary may also be characterized as grammatical or well-formed. All sentences generated by rules i and ii are grammatical. The following expressions are not generated: (1) the rose red is twice two the square root of sixteen is the same as possesses the color the rose red We may assume that there are no rules of ordinary usage in English which account for the deviations included in 1. Rules i and ii do not generate all possible grammatical combinations of the terminal symbols upon which they operate. The following do not occur: (2) is the rose red is twice two four The well-formed strings of (2) are interrogatives, and consequently

42

FORMULATION OF RULES-OF-USAGE

belong to a language-game other than 'assertion'. Rules i and ii do not pertain to such usage. Other sentences, which may conceivably be construed as grammatical, are not generated: (3) the rose equals red twice two is red

Such sentences also are not constituents of the language-game 'assertion'. We may, however, entertain the possibility that there are some rules of ordinary usage in English with which they accord.

5. CHOOSING RULES AND CHOOSING SYMBOLS

The formulated rules, like the rules of transformational grammar, are capable of generating an indefinitely large number of novel strings of symbols all of which are grammatical. In both formulations, this capacity is accountable to two kinds of options associated with rules: the option of choosing the rules themselves, and the option of choosing symbols upon which rules operate. Consider the rules of transformational grammar. Rule 1 of the grammar fragment presented in section 4 might have been correctly written "S->NP+VP+(Adv)". The symbol Adv is parenthesized indicating that it may or may not occur as a constituent of some sentence S. This option is reflected in the terminal string where the sign "yesterday" may or may not occur. Rule 5 presents another kind of option. It instructs that the class symbol Ν (noun) be rewritten as either "girl" or "flower". By augmenting the number of optional symbols in the base rules of a grammar, the number of different strings which can be generated becomes indefinitely large. Base rules are not optional. Each appropriate base rule of a grammar must be applied until all class symbols have been expanded into terminal symbols. As originally formulated by Chomsky in Syntactic Structures, transformational rules - which operate upon

FORMULATION OF RULES-OF-USAGE

43

terminal and non-terminal strings generated by base rules of the 'base component' of the grammar - may be either obligatory or optional. Certain types of optional transformational rules constitute the 'recursive power' of a grammar (Koutsoudas 1966: 232). The recursive power of a grammar accounts for the fact that a speaker can make a sentence as long as he wishes. For example, an indefinite number of sentences may be embedded into a single sentence by use of an optional double-based transformational rule. Suppose the base component of a grammar generates two strings: (a) "the flower is red" and (b) "the flower was picked yesterday". An optional double-base transformational rule - so called because it operates upon two strings generated by the base can be applied which embeds (b) in (a). The resulting string might read, (c) "the flower which was picked yesterday is red". By applying such a rule over and over a sentence may be made indefinitely long. In Aspects of the Theory of Syntax Chomsky revises his notion regarding the status of transformational rules. He makes all transformations obligatory and relegates the recursive power of a grammar to the base component. In the revised version of his formulation, a rule such as "NP->(Det) Ν (S')" may be written (1965: 100). Essentially this rule instructs that some sentence S' may or may not (option indicated by parentheses) be embedded in some other sentence S of which NP is a constituent. Assume that S is (a) above, that S' is (b), and that Ν is "flower" of (a). When S' is chosen, an obligatory transformational rule must be applied which modifies S' so that it can stand as a subordinate clause which modifies "flower". The resulting string might read as (c) above. In Aspects a grammar's capacity for generating an indefinitely large number of strings owes solely to the fact that some symbols upon which rules operate are optional. A grammar consequently does not have optional rules. In the case of the formulation presented here, all symbols as well as all rules are optional. There is, moreover, only one constraint upon the selection of a symbol. A rule instructs that a symbol be drawn from a specific usage set. Theoretically, the number of symbols

44

FORMULATION OF RULES-OF-USAGE

included within any usage set is indefinitely large. In addition, sentences, phrases, and clauses, as well as single words may constitute the membership of usage sets. Recursiveness in the formulation is attributable to the fact that the symbols of rules are optional, and that usage sets may consist of phrases and clauses which can be of any length. For example with reference to usage sets of our original language-game - we may postulate that "the flower which was picked yesterday" is at some times defined as a member of Ul. Operating upon this symbol, rules i and ii may generate a string such as "the flower which was picked yesterday is red". In terms of the theory we are considering, it makes little sense to describe the latter string as possessing an embedded element. The sentence "the flower was picked yesterday" relates solely to the language-game of which it is a part. It very likely bears no relationship in this use to the sentence "the flower is red". The latter sentence is very likely a constituent of a different language-game. The notion of embedding implies that language-games can be combined in some way, that we can play more than one game at once. With respect to embedding, Chomsky's revision in Aspects represents a move toward the kind of idea I am presenting. His proposal accords with the notion that entities such as subordinate clauses are primarily constituents of sentences that relate - if at all - only incidentally to the actual sentences they resemble.

III DISTINCTION BETWEEN FORMULATIONS

1. TRANSFORMATIONAL 'DEEP STRUCTURE': AN IDEAL LANGUAGE

A fundamental distinction between my formulation and transformational grammar pertains to the manner in which each accounts for relationships holding among words, phrases, and sentences. Of utmost significance in the former account is the assumption that no relationships whatsoever hold among sentences which have dissimilar uses; the only sentences which are in some way related are those belonging to the same language-game. Transformational grammar, on the other hand, fails to distinguish among the multitude of functions which sentences serve. It takes language as a coherent structure and describes it in terms of a set of systematically interrelated rules. Consider the manner in which transformational grammar might account for the following two strings: (1) "twice two is four", and (2) "is twice two four". The assumption is made that these expressions are fundamentally equivalent. This equivalence is owed to the understanding that both are derivations from or transformations of a single underlying 'preterminal string' (Chomsky 1965: 84), which is generated by the base component of a grammar. A preterminal string contains two kinds of symbols, "grammatical formatives" and "complex symbols". Grammatical formatives are all those signs of a language that serve strict syntactic functions, for example, "of", "that", "which", and conceivably "the" (Chomsky 1965: 65). A complex symbol is a set of specific "syntactic

46

DISTINCTION BETWEEN FORMULATIONS

features". These are elements which could serve to define a word, for example, "animate", "inanimate", "human", "count", etc. A complex symbol or set of syntactic features is generated by 'subcategorization' rules. These rules always operate upon class or category symbols, for example, "N->CS/X", where CS stands for a specific complex symbol, and /X for some condition (usually the occurrence in the same string of other syntactic features) under which Ν (noun) may be thusly expanded. Since class symbols are ordered by base rules before the application of subcategorization rules, generated complex symbols are necessarily ordered in strings. The following preterminal string might underlie strings 1 and 2 : " A + B + C " (where A, B, and C stand for complex symbols). To get from a preterminal string to a terminal string which represents actual linguistic performance, a number of transformations must be made. One type of transformational rule effectuates the substitution of actual signs for complex symbols. For example, if a lexeme meets the definitional qualifications of a set of syntactic features represented by a complex symbol, it may then substitute for the symbol. Assume that C is the complex symbol (+inanimate, +number) - plus signs indicate that the features are present. Accordingly, "four", conceivably defined by such units, may substitute for C. Assume in addition that "is" substitutes for B, and "twice two" for A. A preterminal string may also contain a 'dummy element' (Chomsky 1965: 103), which is optionally generated as its constituent. Its occurrence in a string indicates that another type of transformation must be undertaken. Assume for instance that a dummy element X appears in the above string, and that its presence obligates the application of a permutation transformation. A rule may transform this string as follows: " X + A + B + C - > B + A + C " . The preterminal string that underlies both strings 1 and 2 may be represented as follows: "(X) A + B + C " , where dummy element X is indicated as optional. When all appropriate transformations are made, then either terminal string 1 or 2 is generated by the base. The revisions of Aspects represent readjustments in the base component of a grammar so that it can stand as that part of com-

DISTINCTION BETWEEN FORMULATIONS

47

petence which is innate and universal (1965: 117). Accordingly, the base component or 'deep structure' of language is no longer viewed by Chomsky as capable of generating terminal strings the 'surface structure' of language. Deep structure consists of preterminal strings which can underlie terminal strings of any language. On the other hand, the transformation component of a grammar is that part of competence learned through exposure to "primary linguistic data". Transformations serve to map the unique phonological and grammatical features of a natural language onto an innate and universal underlying language. As so conceived, as Chomsky himself suggests (1965: 136), the deep structure of language is comparable to the logical systems or artificial languages of logical positivism. The deep structure is a kind of ideal language with which sentences of natural languages can be compared and consequently understood. Wittgenstein would reject the deep structure of transformational theory for the same reasons he dismisses the 'ideal' artificial languages of logical positivism. Ideal languages give no clue to the nature of the actual use or function of sentences, and therefore only reflect incidentally the surface structure of language. "Every sentence in our language 'is in order as it is'." If we wish to understand what the order of any sentence may be, we look to ordinary language to discover the function it has, or the purpose it serves there (1953: 109e). The deep structure of language as described in Aspects accounts neither for the multitude of applications that sentences have, nor - as 1 hope to show later - for the ordinary uses of constituents of sentences.

2. THEORIES OF CATEGORY

In Aspects Chomsky describes two kinds of linguistic universals which pertain to the base component. These are formal and substantive universals. A formal universal is a certain abstract condition which is a general property of all natural languages (1965: 27-28). Base rules, for example, are formal universals. A

48

DISTINCTION BETWEEN FORMULATIONS

substantive universal is a category or class common to all languages. A theory of substantive universale proposes that the items of any any specific language must be drawn from a fixed class of items common to all languages. While Chomsky is not prepared to say once and forever what the substantive universale of the base may be, he tentatively proposes that NP (noun phrase), VP (verb phrase), and conceivably V (verb) and Ν (noun) belong to this category (1965: 117-118). If universal, all rules, base and transformational alike, operate in every instance upon these symbols or upon constituents of these symbols. This is to say that the categories or classes pertaining to rules of transformational grammar are forever given, that the lexemic constituents of every sentence which can be uttered are members of universal and fixed classes. Such a notion is consonant with the general overall concept of language of transformationalists : that it is a coherent, well-integrated structure, serving a single function, communication. An implicit assumption of transformational grammar is that universal categories in every instance pertain to the act of constructing sentences, to the way in which we use language. A distinction must be drawn between that which can be attributed to language, and that which actually pertains to its use. Consider this analogy. The formula y X y—y2 may be attributed to pure mathematics. As mentioned earlier, the actual act of squaring numbers may not, in many instances, be involved with this formula. In all cases, however, the calculation of squaring accords with it. The formula is best described as being a meta-representation of the calculation, or rather, of the act of calculating (cf. Bateson 1958: 293). The universal categories which transformationalists isolate may be no more than meta-representations or mere artifacts of the act of using language - artifacts attributable to language without really being involved with its use. I return to this point in ChapterVI. The categories or classes which pertain to rules of transformational grammar are forever given. On the other hand, cover symbols of rules formulated here are given only when selection of rules is made. By choosing rules i and ii, for example, we circum-

DISTINCTION BETWEEN FORMULATIONS

49

scribe some usages which pertain only to the rules selected, and hence only to the language-game 'assertion'. For example, the usage "is"='"equals" can be shown to pertain only to these rules. "Is" and "equals" are used alike in the following expressions: (1) "twice two equals four" and (2) "twice two is four". Suppose we have chosen another set of rules for the purpose of playing another language-game, this time 'interrogation'. Following our selected rules we might say, "is twice two four", but under ordinary circumstance we would never say "equals twice two four". We would not use "is" and "equals" in the same way when behaving interrogatively. By choosing other rules, we circumscribe another use of "is". "Is" belongs to another category of usage of which "equals" is not a member.

3. TRANSFORMATIONAL RULES

A grammatical transformation - such as the permutation transformation considered in section 1 - "typically applies to a string with a particular

structural

description"

(Chomsky

1965: 89).

Consider the string to which the permutation transformation was applied, " X + A + B + C " . A class symbol dominates each complex symbol of this string. The particular "structural description" of this string is " X + N + V + N " . To accord with Chomsky's understanding, we must assume that the specific rule which effectuates the permutation applies only to a string possessing the latter structural description. Essentially a permutation rule transforms one structural description into another. The specific rule to which we are attending is correctly represented as follows: " X + N + V + N - > Y + N + N " . Assume this rule serves to transform assertion into interrogation. It accomplishes this by operating upon the class symbols or categories which represent the higher order constituents of any assertion. The assumption implicit in such an operation is that the class or category symbols pertaining to both assertion and interrogation are identical. Assertions and interrogations are then only dis-

50

DISTINCTION BETWEEN FORMULATIONS

tinguishable with respect to how their identical higher order constituents are positioned. Accordingly, a single transformation is postulated which accounts for the structural difference between these two types of sentence. If the categories or classes associated with particular kinds of sentence pertain only to those sentences - as assumed here - the concept of transformation becomes unworkable. Assume, for example, that rule i and ii generate the assertions "twice two is four" and "twice two equals four". Both sentences may be represented by g-h-i. We may also assume that there is a single rule which transforms the former expression into the interrogation "is twice two four?" This rule must also be able to account for all well-formed interrogations which might be made in English, of which "does twice two equal four" is one. By operating upon the cover symbols in the string g-h-i, the rule is incapable of generating the latter interrogation. The failure of the transformation is understandable when one takes note of the different kinds of usage involved. "Is" in the assertion "twice two is four" has two uses: (1) it is used like members of usage set U3 which includes "equals", and (2) it is used like members of usage set U8, all of which are used in the central position of assertions. Consider how "is" is used in the question "is twice two four". To do this, we must ask ourselves what signs may substitute for "is" without changing the sense of the expression, or effecting a structural change in any other part of the sentence. We are then looking for some lexical unit other than "is" which can substitute for X in the string "X twice two four", and which meets the stated conditions. There is, of course, no such unit. The use of "is" here becomes clear when compared with the interrogative "does twice two equal four?" "Is" serves the same function as "does", codifying the use of sentences which belong to the language-game 'interrogation' by occurring in the initial position of such sentences. It is used like a number of other words, in addition to "does", which serve the identical function - for example, "what", "how", "when", etc. - all of which commonly introduce interrogations and consequently codify them. Such words belong to a usage

DISTINCTION BETWEEN FORMULATIONS

51

set which pertains only to the rules of usage governing the languagegame 'interrogation'. The transformation that we are considering does not work because the usages pertaining to assertion and interrogation are unique to each.

4. ELLIPTICAL SENTENCES AND DELETION

It is clear that "is" in the expression "is twice two four" does not function as a verb, or at least is not used like other words we are accustomed to take for verbs. We may describe the latter interrogation as being a verbless sentence. Verbless sentences are a common feature of ordinary language. Our normal use of language entails a number of sentences which are not only verbless, but in many cases nounless. Just think of "What?", "How?", "How come?", "Come here!", "Again!", "Quickly!", etc. Such expressions are called 'elliptical' sentences. Elliptical sentences may be interpreted as shortened forms of other sentences. "What?", for example, might be understood as an abbreviated version of the sentence "What did you say?". With this understanding one might go on to say "What?" is not really a verbless sentence because "did you say" is attached to it in thought. The manner in which transformational grammar accounts for such expressions is consonant with the notion that elliptical sentences leave out something that is thought when uttered. For example, the base component of a grammar generates the string or structural description of the string "what did you say". A transformational rule may be applied which deletes from the string "did you say" or its higher order constituents and generates the single expression "what". In Wittgenstein's terms the relationship holding between "What?" and "What did you say?" is of a functional rather than structural order. "What?" and "What did you say?" are used alike; they are member sentences of the same language-game. These interrogatives could have been the focus of the following passage from Philosophical Investigations:

52

DISTINCTION BETWEEN FORMULATIONS

"You grant that the shortened and the unshortened sentences have the same sense?" - But doesn't the fact that sentences have the same sense consist in their having the same use - (In Russian one says "stone red" instead of "the stone is red" ; do they feel the copula to be missing in the sense, or attach it in thought?) (1953:10e) In Wittgenstein's view Russians do neither, they simply use the sentence "stone red" in the same way they would use any other sentence belonging to the language-game of which it is a part. It is no more queer to discover verbless sentences in English than it is in Russian. What might appear unusual to the casual observer of language is that "is twice two four" contains a word traditionally thought of as a verb in the given context, yet which serves a function entirely unrelated to its use as the sign of equivalence. Accepting this, one might still suppose that a verb is attached to this query in thought. Perhaps what we mean when we say "Is twice two four?" is "Is it that twice two is four?" (In the latter question the first "is" is used like the "is" in the former, and the second "is" is the sign of equivalence.) We could consequently assume that some deletion transformation applied to the latter expression accounts for the former. But is the latter really the sense of the former? We may say that it is if both expressions are ordinarily used alike, if both belong to the same language-game. Consider the circumstances under which we would ordinarily use "Is it that twice two is four?" Suppose someone tells us a strange tale whose conclusion is unpredictable in terms of the contents of the story. When he finishes his narration, he might say, "Now how do you suppose that came about?" Ordinarily we might answer by beginning a sentence with "Is it that..." and then stating our explanation. Sentences beginning with "is it that" are not commonly part of the language-game 'interrogation' ; rather, they belong to the language-game 'guessing'. On such a basis we must distinguish between the senses of "Is twice two four?" and "Is it that twice two is four?"

DISTINCTION BETWEEN FORMULATIONS

53

5. THE LANGUAGE-GAME 'INTERROGATION' Consider the manner in which the formulated rules could account for the sentence "is twice two four". The following rules are chosen for playing the language-game 'interrogation' : (iii) (y, ζ) E s -*· y-z/s=p (iv) z=x

Each lower case letter is some member χ of some circumscribed usage set: p-xeuio q-xeUll r -xeU12 s -xeU13 t -xeU14 u-xeU15 v-xeU16 W-X6U17 x-xeU18 y -xeU19 ζ -xeU20 The lexemic constituents of each set are : U10: Uli: U12: U13 : U14 : U15 : U16: U17: U18 : U19: U20:

SI,S2,S3...etc. "is the rose", "is the flower", "is twice two", "is four" "does the rose", "does the flower", "does twice two", "does four" "red", "scarlet", "twice two", "four" "possess the color red", "possess the color scarlet", "equal twice two", "equal four" "is the flower", "is the rose", "does the flower", "does the rose" "is twice two", "is four", "does twice two", "does four" "red", "scarlet", "possess the color red", "possess the color scarlet" "twice two", "four", "equal twice two", "equal four" U l i andU12and/or U15andU16 U13 and U14 and/or U17 and U18

Rules iv and ν may be understood in one instance as enumerating a

54

DISTINCTION BETWEEN FORMULATIONS

number of conditions under which "is twice two" and "four" are used together as constituents of an interrogation. For the moment assume that y is "is twice two" and that ζ is "four". When y is used like ν (y=v), then ζ must be used like χ (z=x), by rule v. Accordingly, when both conditions y = v and y = q hold - and they do when "is twice two" is chosen - then both usages, z = x and z = s , must occur. Suppose we have not already selected z. Again, y is "twice two". Under the stated conditions we must select some ζ that is ordinarily used in interrogative sentences like both χ and s. There are only two lexemes that meet this description. Only "twice two" and "four" are members of both usage sets from which χ and s are drawn. Therefore, when y is "is twice two", ζ must be either one or the other of these signs. The generation of the sentence "is twice two four", consequently, is achieved by following rules without attributing a hidden or left-out verbal sense to it. Rules iii-v account for a number of well-formed interrogative strings in addition to "is twice two four". A sample list follows : (4) is the rose red is the flower red does the rose possess the color red does twice two equal four As the membership of each set alters, the number of sentences accountable to these rules becomes indefinitely large. The following and similar constructions do not ordinarily belong to the languagegame 'interrogation', and consequently are not generated : (5) is red the rose does the rose scarlet possess the color (6) is the rose twice two does twice two possess the color red (7) is twice two equal four does twice two four

DISTINCTION BETWEEN FORMULATIONS

55

is the rose possess the color red does the rose red (8) the rose is red the rose possesses the color red twice two is four twice two equals four The lexemic constituents of sentences of 5 are not drawn from usage sets which pertain to rules iii-v. For example, the unit "is red" is found in no set. We may assume, moreover, that such a unit is not commonly a member of any usage set which pertains to the language-game 'interrogation'. Expressions of 6 are in one sense equivalent to those listed under 3 in section 4 of Chapter II. While they do not belong to the particular language-game to which we are attending, there are circumstances under which their occurrence would not be considered extraordinary. Sentences of 7 are simply described as uncommon English usage. Sentences of 8, of course, belong to another language-game. We do not change language-games by transforming the sentences of one into the sentences of another, or by generating sentences of both games from a common underlying structure. To play different language-games we simply choose different rules, and, consequently, circumscribe different usages.

IV ASPECTS OF THE FORMULATION

1. USAGE CIRCUMSCRIPTION

Rules-of-usage, as formulated here, presuppose the existence of usage sets which pertain to them by instructing relationships which hold among members of different sets. Rule-of-usage do not, however, presuppose the actual lexemic constituency of sets. Set membership must be assumed established over a period of time, built up or even reconstructed on every occasion of application of a particular rule or set of rules. Consider, for example, the sequential application of rule ii. On each occasion of its application it specifies the conditions under which specific terminal symbols may or may not be used in a particular way. Suppose that on one occasion it instructs how el (which is any specific e) and bl (which is any specific b) are to be used. Under the condition g Φ\, el is used like i (el = i ) and bl must not be used like i (bl ^i). On another occasion the rule operates upon e2 and b2. Under the same condition, g ^ i , then e2=i and b 2 ^ i . Reciprocally, when g=i, then e ^ i , e2#i, and b2=i. We have in fact isolated two corollaries of rule ii : (A) e l = e 2 / g * i (B) b l = b 2 / g = i Assume that el is "red", e2 is "scarlet", bl is "four", and b2 is "twice two". Corollary A, for instance, instructs that when "red" is a terminal symbol upon which rule ii operates, it must be used like "scarlet". This is tantamount to saying that "red" must be

ASPECTS OF THE FORMULATION

57

drawn from a usage set of which "scarlet" is also a member. Similarly Β instructs that "four" be drawn from a usage set of which "twice two" is a member. Note that the epistemological status of the corollaries of rule ii is contingent upon its sequential application. Consequently, the actual membership of usage sets - in this case U2 and U5 - depends upon the terminal symbols to which the rule has been applied on a number of different occasions. By actually following rules - by actually participating in a language-game we may come to circumscribe the usage which pertains to them. This is, to a degree, circular. It is assumed, for instance, that the symbols upon which rule ii operates - on two separate occasions were already members of some specific usage sets. The corollaries which are isolated simply reflect this assumption. This is not to deny the functional status of such corollaries. A rule-of-usage and its corollaries may be compared with a cybernetic circuit. Cybernetics stems from the concept of feedback. Feedback is the basis of automatic control devices. For example, when a rocket is launched, it is given a set of instructions which says, "Do X until Y happens and then do Z." If the rocket swerves from its course by doing X + 1 instead of X, this deviation is automatically fed back into the circuit to change the original instructions such that Ζ becomes Z-l, and the rocket is put back on its original course (cf. Smith 1966: 2). Thus a cybernetic circuit will always seek equilibrium or steady state. The sequential application of a rule, or the actual use of language, determines the instructions which a corollary of such a rule represents. The corollary instructs the usage of specific lexical items which pertain to that rule, and serves as a feedback mechanism. As a consequence, linguistic behavior tends to seek a kind of equilibrium which consists in the ordinary usage we circumscribe. To say that we circumscribe usage of signs by actually using them implies that we have a priori knowledge of that usage.This is not exactly the case. We have knowledge of and access to the ordinary use of our language, because it is public, there on the surface, available for all to experiment with.3 3

We can observe, for example - assuming ignorance of the fact - that "red"

58

ASPECTS OF THE FORMULATION 2. LINGUISTIC ORDERLINESS

Our capacity for drawing boundaries, for attending to specific rules when playing particular language-games, must in part be attributed to the intrinsic orderliness of the game itself, and in part to our innate ability to recognize it. Orderliness is not, however, attributable to language as a whole. Language is not a Gestalt in which each sign is perceived against a background of every word, phrase, and sentence with which it may or may not interchange. Orderliness is localized in language. It pertains only to specific language-games and the rules that govern them. Consider again the language-game 'interrogation'. Rules i ν and ν specify the lexemic constituency of an interrogative sentence. Sequential application of these two rules also serves to establish the lexemic membership of usage sets (all sets with the exception of U10). Notice in section 5 of Chapter III that each item listed in one set is repeated in two others. This redundance of course reflects the fact that any specific item has more than one ordinary use which pertains to this language-game. Accordingly, three corollaries of rule iv and ν instruct that a specific item belongs simultaneously to three separate sets. Figure 1 represents a revision Figure I.

Paradigmatic presentation of usage sets U11-U20 (A) Uli

U16

is twice two is four

U12 does twice two does four U19

U15

is the rose is the flower

does the rose does the flower

is sometimes used like "scarlet" and vice versa by others. Mental retention of this observation establishes the basis for our own experimentation with using the signs "red" and "scarlet".

ASPECTS OF THE FORMULATION

59

(B) U13

U18

twice two four

U14 equal twice two equal four U20

U17

red scarlet

possess the color red possess the color scarlet

of presentation of usage sets U11-U20 (derived through corollaries of rules iv and v), which accommodates the fact of simultaneous set membership. The rules-of-usage to which we attend when playing specific language-games permit us to class and segregate words and phrases on the basis of their use in a particular game and only in that game. As a consequence of using the kinds of rules we do, we necessarily impose order upon the vocabulary to which we attend on any occasion of using language in a particular way. Expressed differently, order is necessarily imposed upon us - another aspect of linguistic cybernetics. If we assume that the rules we follow when speaking are in some sense internalized, we must assume that the order intrinsically bound to them is also internalized. There is no question of recognizing the way in which words and phrases are classed and segregated by use. If we use language in an ordinary way, we simply cannot prevent ourselves from attending to it. We are, in a way, coerced by the rules we follow to circumscribe usage.

3. DIMENSIONS OF USAGE

The paradigmatic order of Figure 1 represents a highly efficient and economical way of cataloguing signs with respect to their use. The rules we follow must be geared to reduce redundance to a minimum and hence serve to diminish the conceptual load involved in usage circumscription. As so ordered, the usage to which we attend is

60

ASPECTS OF THE FORMULATION

easily recovered or reproduced on any occasion of replaying a particular language-game. When choosing rules, we automatically address ourselves to a limited number of dimensions of usage which may serve and may have previously served to class and segregate, in the most economical way possible, a set of signs. A major aspect of drawing boundaries - of choosing rules - must be the selection of a limited number of dimensions upon which primary linguistic data can be organized. The manner in which we order linguistic data is contingent upon the nature of the rules to which we attend when using language. Here, there is no objection to the converse but asymmetrical argument that we draw boundaries because our innate capacity for synthesizing linguistic information is limited. George Miller (1967) calls attention to an impressive corpus of data that suggests this capacity to be severely restricted. He points to a number of independently performed perception tests which indicate that the number seven (plus or minus two) is the limit on the span of absolute judgment or immediate memory. Given this, we should suspect that the number of different dimensions of usage to which one could attend simultaneously would rarely exceed the number seven (plus or minus two). I view this limitation as a decisive factor in the process of language use. On the one hand, it can be taken as an explanation of why we must draw boundaries, or restrict ourselves to a small number of dimensions of usage. On the other hand, the limitation itself can be explained as a consequence of the structure of the mechanism which permits us to behave linguistically in the way we do, i.e., the rule-of-usage. (This, too, is another aspect of linguistic cybernetics.) In all, ten dimensions of usage (described as U11-U20) pertain to rules iv and v. For strictly analytical reasons, these dimensions are divided into two sub-sets that relate to two separate lexical domains (see Figure 1). Paradigms A and Β are best described as the meta-representation of the simultaneous application of all corollaries of rules iv and v. This meta-representation is subject to revision. It graphically misrepresents the event it presumably reports. If all corollaries are assumed applied simultaneously,

61

ASPECTS OF THE FORMULATION

then the meta-representation must consist in one paradigm. The following are selected sub-sets of corollaries of rules iv and v: (a) (b)

/\ί:ή /{a}

»-*

··-»

/|κ)

/{;::•

Consider first sub-set a. The conditions under which ql is drawn from a usage set of which q2 is also a member are identical to the conditions under which si is drawn from a set of which s2 is a member. Similarly, sub-set b illustrates that the dimensions of usage which rl = r 2 and tl = t 2 represent are likewise conditionally related. The following dimensions of mage are involved here: ql=q2: Uli s l = s 2 : U13

r l = r 2 : U12 t l = t 2 : U14

The two dimenions U l i and U13, as well as U12 and U14, are eternally related in the language-game 'interrogation'. Attention to one presupposes attention to the other. Such dimensions while conceivably conceptually redundant - are here taken as variables of single meta-dimensions. Meta-dimensions reflect the use of signs as co-occurring constituents of sentences. The metarepresentation of the event we are considering is one paradigm (see Figure 2). Figure 2. Meta-representation

of simultaneous application of corollaries of rules iv and f

uv Uli

UW U13

' four twice two

UY

is twice two is four

ux

is the rose red is the flower ' scarlet UZ

U12

U14

does twice two does four

" equal four equal twice two

does the rose does the flower

* possess the color red ' possess the color . scarlet UZ

62

ASPECTS OF THE FORMULATION

The meta-dimensions of Figure 2 and their respective variables are : UV: U l i , U13 UW: U12, U14 UX: U15, U17

UY: U16, U18 UZ: U19, U20

The isolation of meta-dimensions reduces the total number of dimensions pertaining to rules iv and ν to five. In Figure 2 complete partitioning of the lexical domain is achieved without attending to the variables of meta-dimensions UY, UX, and UZ. As it is, the domain is classed and segregated by four variables (of metadimensions UV and UW) and three meta-dimensions, making a total of seven significant distinctions. Assuming that UV and UW are also significant, the number is nine. The meta-representation may also be presented as shown in Figure 3. Regardless of the dimensional affiliation of operative variables, the number of pertinent discriminating judgments necessary for complete partitioning can be taken as somewhere in the vicinity of seven. This accords with Miller's observation that the number of different dimensions to which one could attend simultaneously fluctuates around the number seven, by plus or minus two. At the level of meta-dimension, usage circumscription pertaining to rules iv and ν consists in the classification and segregation of signs with respect to what items may or may not occur together as lexemic consituents of an interrogative sentence. This is suggested in Figures 2 and 3 by allowing unbroken lines to encompass items which are comparable with respect to any three metadimensions. Usage circumscription always entails presupposition of all the relationships which rules themselves instruct. It is consequently impossible to distinguish between sequential application of rules and usage circumscription. They may be understood as bearing a cybernetic relationship, or simply taken as one and the same event.

4. CONCEPT RECODING

Our ability to behave as if we were following two or more rules

ASPECTS OF THE FORMULATION

63

Figure 3. Alternative meta-representation UY U16

·

UX U18

' four 1 twice two

U15

·

is the rose is the flower

' °

U17

uv

is twice two is four

red scarlet

uw

does twice two ' equal four does four j equal . twice two

does the rose ' possess the color red does the flower j possess the color . scarlet

UZ

UZ

simultaneously was explained earlier as owing to an innate mechanism that permits us to behave in accordance with rules without actually involving ourselves with them. A paradigmatic model such as that presented in Figure 3 - presumably accounts for simultaneous following of rules, and hence conceivably reflects a structural aspect of the mechanism that allows accordance behavior. As Miller observes, there may be a strict limitation upon the number of discriminating decisions which can be made simultaneously. We should not therefore presume that the mechanism that accounts for such complex behavior as grammatical and meaningful speech relates solely to a paradigmatic order. On the other hand, it is difficult to conceptualize how sequential following of a number of rules could produce a behavior so spontaneous as actual language use. Faced with parallel considerations Miller intuitively isolates a psychological phenomenon that could account for accordance behavior. Miller calls this phenomenon "recoding" (1967). Miller characterizes data organized by a restricted number of immediate or simultaneous judgments as being a "chunk". The amount of information which each chunk contains is described in the jargon of communication theory - as a number of bits of information. The number of bits which pertains to a single chunk is a function of the number of alternatives involved in making discriminating judgments. For example, if we are to decide if a

64

ASPECTS OF THE FORMULATION

man is either less or more than six feet tall, and if we know our chances in guessing correctly are 50-50, then we need only one bit of information upon which to base an accurate judgment. With two bits of information we can discriminate among four equally probable alternatives, with three bits among eight, with four bits among sixteen, etc. (1967). Recoding, as described by Miller, essentially consists in taking a great number of chunks, each of which contain but a few bits, and reorganizing them into fewer chunks with more bits per chunk. Miller gives the following example : A man just beginning to learn radio-telegraph code hears each dit and dah as a separate chunk. Soon he is able to organize these sounds into letters and then he can deal with the letters as chunks. Then the letters organize themselves as words, which are still larger chunks, and he begins to hear whole phrases... I am simply pointing to the obvious fact that the dits and dahs are organized by learning into patterns and that as these larger chunks emerge the amount of message that the operator can remember increases correspondingly. In the terms I am proposing to use, the operator learns to increase the bits per chunk (1967:24). Recoding is a way of organizing and reorganizing data so that it can be easily recalled. By augmenting the number of bits per chunk while at the same time diminishing the number of chunks to be recalled on any occasion, recoding serves to increase the span of

immediate memory. An expanded memory has an obvious place in the explanation of accordance behavior. Rather than actually involving ourselves with specific rules on every occasion of behaving in a certain way, an expanded memory would permit us to recall past behavior determined by those rules which could be used as a model upon which our immediate behavior is based. As Wittgenstein points out, it is frequently impossible to distinguish a memory event from an event involved with rules. To illustrate this he asks us to try the following experiment: "say the numbers 1 to 12. Now look at the dial of your watch and read them" (1953: 65e). Next he asks us to consider what we call the 'reading' in the latter case. Were we actually following some rules which translate the symbols on the dial into actual sounds? Or

ASPECTS OF THE FORMULATION

65

were we simply saying numbers off by heart as we did in the former case? In Wittgenstein's view what we commonly refer to as 'reading' is a compromise between calling something off by heart and actually following rules. He writes, And remember too that there is a continuous series of transitional cases between that in which a person repeats from memory what he is supposed to be reading, and that in which he spells out every word without being helped at all by guessing from the context or knowing by heart (1953: 64e). One of the simplest ways of recoding, according to Miller, is to group a number of chunks into one chunk and give the synthesized chunk a new name. Rather than remember the individual names of the input chunks, one need only recall the new name (1967: 25). This is probably a customary kind of recoding. Consider Miller's example: When we witness some event we want to remember, we make a verbal description of the event and then remember our verbalization. Upon recall we recreate by secondary elaboration the details that seem consistent with the particular verbal recoding we happen to have made (1967: 27). There is a related but distinct type of recoding which Miller does not explain. For example, when learning a radio-telegraphic code, an operator does not give new names to the different stages of organization that emerge. Rather each new stage is differentiated from those below it on the basis of the kinds of rules which uniquely pertain to it. For instance, the rules that determine the way dits and dahs are sequentially organized, are different from the rules that govern the way in which letters distribute themselves to form words. Similarly, the rules that pertain to words are different from those associated with phrases and so on. To facilitate his recall mechanism, an operator need not name each new stage of organization, he need only attend to the rules defining such levels. There is another aspect of this type of recoding. The different orders of data which arise in learning a telegraphic code, or in learning to read, or in learning any kind of language, are not attributed by a novice to the data. There is something about the data

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themselves which allows them to be organized in a certain way. The rules that serve to distinguish each level of organization also serve to recode one order of events into another. For example, letters are organized into words by the same rules that differentiate letters from the dits and dahs of a code. On the one hand, an operator recognizes different orders of organization through attention to the rules pertaining to each. On the other, rules themselves constitute a device that permits the operator to recode what he observes. The rules to which I refer are of course rules-of-usage. As formulated here, a rule-of-usage functions as a recoding mechanism. As such, it functions to increase the span of immediate memory that is obviously involved in language use. Again, for examples I turn to rules iii-v. Borrowing terminology from communication theory, the use of items circumscribed through application of these rules over a number of occasions - i.e. by corollaries - is here characterized as a number of chunks each of which consists of a number of bits of information. Taking the paradigm of Figure 3, for example, as a meta-representation of application of corollaries of iv and v, eight chunks of data are represented: eight is the total number of spaces defined by intersection of all variables and metadimensions. Accordingly, the number of bits of information per chunk is the same as the number of uses which distinguish any one is twice two for instance contains is four three bits of information. These bits are expressed as UV, UY, and U16. There are then three bits per chunk. Corollaries of rules iv and ν also function to recode these eight chunks into four larger ones. The larger chunks are the four spaces defined solely by the intersection of meta-dimensions (i.e. items encompassed by unbroken lines). The information content of each larger chunk is the aggregation of the number of bits of the smaller chunks of which it is composed, plus the number of bits representing the uses that distinguish a larger chunk from all other larger chunk from all the rest. Chunk

is twice two : four for instance consists of is four : twice two eight bits : the sum of the number of bits of the chunks of which chunks. Chunk

ASPECTS OF THE FORMULATION

67

it is composed (six), plus two others expressed by UY and UV. There are then eight bits per each larger chunk. Larger chunks represent the related but unordered constituents of interrogative sentences. Smaller chunks, on the other hand, are constituents taken in isolation. They are not to be thought of as verbalized units; rather they possess the status of the meta-representations from which they are derived : here each chunk represents the knowledge of use of signs necessary for using them in interrogative sentences. If, following Wittgenstein (1953: 144e), knowledge of the use of a sign is taken as the concept which stands behind it, then chunks are concepts. Accordingly, the amount of conceptual knowledge which is any chunk is precisely the number of bits which pertain to it. Corollaries of rule iii instruct that specific sentences belong to usage set U10 and no other set. With respect to whole interrogative sentences there is therefore only one dimension of usage that is discriminatingly significant. The meta-representation of the instructions of corollaries is: U10

si 52 53 etc.

This meta-representation is one chunk of data, or one concept of usage. Essentially rule iii codifies the usage of an interrogative sentence by ordering the unordered constituents related through instructions of rules iv and v. I see this as being of a conceptual rather than verbal order. Implicit here is the assumption that rule iii operates upon concepts. In the terms we are now using, rule iii recodes the four larger chunks mentioned above into a single chunk which is the meta-representation of the instructions of corollaries of rule iii. The information value of the single chunk is thirty-three bits: that is the sum of the number of bits of all the chunks of which it is composed (4 times 8), plus one bit represented by U10.

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ASPECTS OF THE FORMULATION

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