Logic and philosophy for linguists: A book of readings 9783111546216, 9783111177588

Citation preview

Logic and Philosophy for Linguists: A Book of Readings

Logic and Philosophy for Linguists: A Book of Readings Edited by

J. M. E. MORAVCSIK Stanford University

m MOUTON PUBLISHERS THE HAGUE - PARIS

& HUMANITIES PRESS ATLANTIC HIGHLANDS N. J.

© Copyright 1974 Mouton & Co. B.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

American edition published by Humanities Press Inc. - Atlantic Highlands, N. J. Library of Congress Cataloging in Publication Data Main entry under title: Logic and philosophy for linguists. Bibliography: p. 1. Languages - Philosophy - Addresses, essays, lectures. 2. Logic - Addresses, essays, lectures. 3. Semantics (Philosophy) - Addresses, essays, lectures. 4. Linguistics Methodology - Addresses, essays, lectures. I. Moravcsik, J. M. E. P39.L59 1975 401 75-23015 ISBN 0 391 00399 2

Printed in The Netherlands by Mouton & Co., The Hague

Contents

Introduction PART i : MEANING AND FORMAL SEMANTICS

7 13

G. Frege On Sense and Reference R. Carnap Meaning and Synonymy in Natural Languages R. Rogers A Survey of Formal Semantics W. V. O. Quine "Truth", in: Philosophy of Logic chpt. 3 R. Montague English as a Formal Language H. Reichenbach "Analysis of Conversational Language", in: Elements of Symbolic Logic # 5 1 J. Hintikka Semantics for Propositional Attitudes J. Hintikka Knowledge, Belief, and Logical Consequence D. M. Gabbay Tense Logics and the Tenses of English

177

PART II: ALTERNATIVE APPROACHES TO MEANING

187

J. L. Austin The Meaning of a Word

187

13 33 48 83 94 122 142 165

6

Contents

M. Dummett, Truth J. O. Urmson Criteria of Intentionality

203 226

PART H i : PHILOSOPHERS ON GRAMMAR

238

P. T. Geach A Program for Syntax W. V. 0. Quine Methodological Reflections on Current Linguistic Theory . . P. F. Strawson Grammar and Philosophy PART IV: THE THEORY OF KNOWLEDGE AND LINGUISTIC THEORY

G. Frege The Thought: A Logical Inquiry J. M. E. Moravcsik Competence, Creativity, and Innateness T. Nagel Linguistics and Epistemology R. Schwartz Linguistics as Psychology Selected Bibliography (by parts)

.

.

238 251 263 279

279 299 327 336 344

Introduction

WHY SHOULD LINGUISTS STUDY LOGIC AND PHILOSOPHY?

HOW TO USE THIS BOOK

The study of language — like language itself — is a many-splendored thing. Being an all-pervasive phenomenon, language became the object of study for several disciplines. Anthropology, linguistics, philosophy, psychology, and certain parts of physics and medicine are all concerned with some aspect of language. In this respect, the study of language parallels the study of material bodies. There is no single science dealing with material bodies. Geometry, chemistry, physics, and other sciences deal with a variety of aspects of material things. To study a certain set of phenomena rigorously means to concentrate on certain aspects of those phenomena. Thus science involves abstraction in two ways; on the one hand we abstract when we decide which aspects of a set of phenomena we will study, and on the other hand in the study of such aspects we will posit theoretical constructs — entities that are not observable, but the existence of which seems required in order to explain the observable. These general observations apply to the study of language in the same way in which they apply to the study of anything else. It follows from this that linguists will study only certain aspects of the use of language. To make this anthology relevant to the concerns of linguists, it will be shown, briefly, why the study of what logicians and philosophers said about language helps the linguist in pursuing the work that serves his interest. Logic deals with the rules of justified inference. Deductive logic deals with those inferences that exhibit the task of drawing out of a set

8

Introduction

of premisses sentences whose meaning, in a sense, is already contained in the premisses. In this way, the study of the rules of deductive logic, as they apply to natural languages, is tied in with questions of meaning, and since legitimate inferences depend on the structural composition of sentences, also with questions of grammar. This in itself is a non-trivial claim. It is interesting to speculate on what it would be like to have a system of communication in which questions of sentence-formation and meaning would be totally distinct from and unrelated to the application of the rules of deductive inference. On the assumption, then, that rules of reasoning are intimately tied to rules of meaning and syntax, there is strong motivation for linguists to become familiar with some of the results of logic, and some of the technical devices that have proved themselves to be so useful in the study of deductive inferences. The preoccupation of philosophers with language goes back at least to Socrates. To sum up the situation briefly, one of the strong recurrent themes in the history of Western philosophy has been the claim that a careful study of the general features of human languages will help to comprehend the nature of human understanding. Thus philosophers have made repeated attempts to answer such questions as: what is meaning? what is truth? what are the essential features of human languages? Needless to say, answers to these questions are of great interest to linguists who — like other scientists — have some concern with the theoretical foundations of their discipline. The branch of logic that is strongly represented in this volume is often called FORMAL SEMANTICS. This discipline takes as its data some of the purely cognitive aspects of language use, i.e. the facts that we use language to refer to things, to describe them, to assert truths and falsehoods, and to reason about things. Formal semantics attempts to present a rigorous theory which represents these aspects of linguistic competence. The work on formal semantics that is represented in this book can be described on three levels. First, there are papers introducing the reader to theories of reference, satisfaction, and truth, applicable to simple indicative sentences without modals, complements, and names for properties of properties, such as 'colour', or 'excellence'. These papers also help to explain how we can determine the descriptive and inferential content of complex sentences by starting with the analysis of their simple constituents. On the second level, there are papers that extend formal semantics to cover the analysis of sentences involving modals such as 'necessarily, or 'possibly', and sentences with complements such as 'John believes that ...' or 'Mary hopes that ...'. Thirdly, there are papers that extend the analysis to cover sentences containing reference to tenses as well as to places that are specified relative to the speaker and intended audience.

Introduction

9

In emphasizing the central role of the notions of reference, predication, and truth, formal semantics represents meaning, and semantic rules, as involving essentially relations between language and reality. It is admitted that there are other aspects of meaning as well. There is the issue of MOOD, a variety of communicative aspects of language use (such as the facts that we use language to perform certain acts, e.g. of promising, warning, etc.), and there is the aspect of meaning best described as association; but it is assumed that the analysis of these presupposes the analysis performed by formal semantics while the dependency does not hold in the opposite direction. This is a controversial assumption, and the section on alternative conceptions of meaning includes some writings that deny this thesis. When one compares the conception of semantics embodied in these papers on formal semantics with the conceptions familiar from the recent linguistic literature (componential analysis, semantic markers as in the system of Fodor and Katz, etc.) the crucial difference lies in the emphasis of the former on the relation between language and reality and the preoccupation of the latter with rules relating parts of language to other parts of language. Thus linguists concern themselves with questions of synonymy, paraphrase, and disambiguation. The position taken by most people working in formal semantics is that the adequate solution of such issues presupposes a theory of reference, satisfaction, and truth. To borrow a felicitous phrase from D. F. Pears — who employed it in a different context — we can put semantics on a firm footing only when we find and explicate the "way out of the maze of words", i.e. the points at which language is related by the competent speaker-hearer to reality. Formal semantics attempts to present a theory about these points, and linguists should be at least familiar with such theories before deciding on the extent of their relevance and utility for their own research. What are presented as alternative conceptions of meaning either attempt a different representation of cognitive content, or else suggest that the priority of such content may not be a useful assumption in an adequate analysis of all of the uses of human languages. The structure that determines the inference-potential and conditions of truth for sentences has been called at times THE LOGICAL FORM of a sentence. There are serious disagreements on the question of whether sentences of natural languages have one unique logical form, or whether to posit a logical form for a sentence is like formulating an empirical hypothesis — in the sense that the latter activity goes naturally with the assumption that a variety of hypotheses may explain the same set of phenomena equally well. Thus one of the questions that philosophers ask is whether a sentence must have just one logical form. Another is the question of the extent to which syntactic rules in natural languages admit

10

Introduction

of semantic justification. That is to say, we must examine the logical form, or logical forms, of a sentence, and see what the relation of that structure is to what is syntactically the fundamental structure of a sentence. The issue of the relation between logical form and syntactic deep structure is one of the most important questions facing linguists today. The first section of this book helps to understand what logical form really is, and the third section contains some philosophical considerations on why the two structures should or should not be independent. Both of these questions are discussed in the papers contained in the third part of this book. A related question emerging from the papers in this section is: to what extent, if any, can one assume that the rules, and the primitive entities in terms of which the rules are specified, have psychological reality? Finally, it is useful for linguists to become aware of the debates that have taken place in recent philosophy concerning the desirable methodology for the science of linguistics. Some of the crucial issues that come up in this connection are: what is the proper range of phenomena that should be regarded as evidence for or against hypotheses in linguistics? What is the proper explanatory power of linguistic hypotheses? What are useful theoretical constructs to be employed within linguistics? In connection with the last question perhaps the most important controversies take place with regard to some of the new technical terms introduced by Chomsky, such as innate knowledge, internalization of rules, tacit knowledge of rules, creativity, etc. Several of these terms have a long history in philosophy; others are new in every way. The proper context for these discussions is the comparison of linguistics to other sciences. E.g. is the notion of competence in linguistics analogous to the notion of idealization in the other sciences? Are the theoretical constructs proposed by recent linguists such as Chomsky related to empirical evidence analogously to the indirect relations between theoretical entities and empirical evidence that one finds in the modern natural sciences? Finally, a question that underlies much of the discussion in parts II, III, and IV, is: what are the limitations of the range of phenomena that linguistics should be concerned with? As was pointed out in the beginning of this brief introduction, every science has to limit itself to studying certain aspects of a set of events. How are we to delimit the relevant aspect for linguistics? A careful perusal of the several papers contained in this volume will give — indirectly — a variety of different answers to this question. Needless to say, this issue is currently a much debated topic among linguists. Thus in this context too, an issue within a specific discipline, i.e. linguistics, can benefit from the kind of conceptual analysis that is one of the main tasks of philosophy. As this brief introduction shows, the sections are arranged in natural

Introduction

11

order. One cannot discuss relations between syntax and semantics, syntactic deep structure and logical form before one has a thorough grasp of what rigorous semantics is really like, and what specific proposals have been made concerning logical form. It is advisable to read the papers in the first section in the order in which they are presented. Frege's classic paper lays out the main issues of semantics, and the main subjects of analysis: singular term, general term, sentence. The subsequent papers deal with the development of formal semantics at various stages. Montague's paper shows how formal semantics can be applied to a fragment of English, and Reichenbach's selection shows the problems we face when trying to account for tenses and adverbial constructions. The last two papers lead us to some of the pioneerwork done today on formal semantics. This section should be studied either by those who already had some introduction to symbolic logic (such as selections from the introductory books by Mates, Quine, or Suppes — see bibliography), and some elementary familiarity with modal logic (such as can be acquired from some of the early chapters of Hughes and Cresswell — see bibliography), or by those without any background in logic, for whom selections from the textbooks mentioned are assigned as the instructor sees fit, in conjunction with the assignments from this anthology. The alternative approaches outlined in part II all assume general familiarity with the main outlines of formal semantics. For those wishing to look at alternatives in greater depths, it is advisable to look in detail at Wittgenstein's Philosophical Investigations, and J. L. Austin's How To Do Things With Words. The most profitable way of reading parts III and IV is that of keeping the main outlines of transformational grammar and Chomsky's comments on methodology in one's mind. For that is the kind of linguistic theory that the authors of these sections are concerned with; both with regard to its methodology, and with regards to its relationship to semantical considerations. Presumably a general introductory course to transformational grammar would be a sufficient background for these sections, provided that such a course paid attention to some of the recent methodological reflexions of linguists as well. In the past seven years philosophers have turned in increasing numbers to the careful study of recent developments in linguistics. Recently, this attention has been reciprocated by linguists. Such cooperation and mutual interest is obviously desirable, if the claims made in the beginning of this introduction are correct. But it is very important that in the attempt to master a related field, the practitioner should get a thorough grounding in the fundamentals, including those basic techniques and formal devices the understanding of which is absolutely essential for a deep grasp of the

12

Introduction

significance of the field and specific results within it. It is hoped that this volume will make a modest contribution toward enabling students of linguistics to achieve proper understanding of formal semantics and the related work in the philosophy of language. Stanford, 1972

J. M. E. Moravcsik

Parti MEANING AND FORMAL SEMANTICS

G. Frege

ON SENSE AND REFERENCE

[25] Equality1 gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A relation between objects, or between names or signs of objects? In my Begrijfsschrift21 assumed the latter. The reasons which seem to favour this are the following: a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labelled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a [26] matter of course. Now if we were to regard equality as a relation between that which the names V and designate, it would seem that a = b could not differ from a — a (i.e. provided a — b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. What is intended to be said by a — b seems to be that the signs or names 'a' and designate the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only in so far Reprinted from: G. Frege, Philosophical Writings ed. and transl. by P. Geach and M. Black (New York, Philosophical Library, 1952), 56-78. First published in Zeitschriftfur Philosophic undphilosophische Krilik 100 (1892), 25-50. 1 I use this word strictly and understand 'a = b' to have the sense of 'a is the same as b' or 'a and b coincide'. * [The reference is to Frege's Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (Halle, 1879). Ed.]

14

G. Frege

as they named or designated something. It would be mediated by the connexion of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a—b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means. But in many cases this is just what we want to do. If the sign 'a' is distinguished from the sign only as object (here, by means of its shape), not as sign (i.e. not by the manner in which it designates something), the cognitive value of a = a becomes essentially equal to that of a = b, provided a = b is true. A difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated. Let a, b, c be the lines connecting the vertices of a triangle with the midpoints of the opposite sides. The point of intersection of a and b is then the same as the point of intersection of b and c. So we have different designations for the same point, and these names ('point of intersection of a and b\ 'point of intersection of b and c') likewise indicate the mode of presentation; and hence the statement contains actual knowledge. It is natural, now, to think of there being connected with a sign (name, combination of words, letter), besides that to which the sign refers, which may be called the reference of the sign, also what I should like to call the SENSE of the sign, wherein the mode of presentation is contained. In our example, accordingly, the [27] reference of the expressions 'the point of intersection of a and b' and 'the point of intersection of b and c' would be the same, but not their senses. The reference of 'evening star' would be the same as that of 'morning star', but not the sense. It is clear from the context that by 'sign' and 'name' I have here understood any designation representing a proper name, which thus has as its reference a definite object (this word taken in the widest range), but not a concept or a relation, which shall be discussed further in another article.3 The designation of a single object can also consist of several words or other signs. For brevity, let every such designation be called a proper name. The sense of a proper name is grasped by everybody who is sufficiently familiar with the language or totality of designations to which it belongs;4 ' [See his "Ober Begriff und Gegenstand", Vierteljahrsschrift fur wissenschaftliche Philosophie XVI (1892), 192-205. Ed.] * In the case of an actual proper name such as 'Aristotle' opinions as to the sense may differ. It might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the Great. Anybody who does this will attach another sense to the sentence 'Aristotle was born in Stagira' than will a man who takes as the sense of the name: the teacher of Alexander the Great who was born in Stagira. So long as the

On Sense and Reference

15

but this serves to illuminate only a single aspect of the reference, supposing it to have one. Comprehensive knowledge of the reference would require us to be able to say immediately whether any given sense belongs to it. To such knowledge we never attain. The regular connexion between a sign, its sense, and its reference is of such a kind that to the sign there corresponds a definite sense and to that in turn a definite reference, while to a given reference (an object) there does not belong only a single sign. The same sense has different expressions in different languages or even in the same language. To be sure, exceptions to this regular behaviour occur. To every expression belonging to a complete totality of signs, there should certainly correspond [28] a definite sense; but natural languages often do not satisfy this condition, and one must be content if the same word has the same sense in the same context. It may perhaps be granted that every grammatically well-formed expression representing a proper name always has a sense. But this is not to say that to the sense there also corresponds a reference. The words 'the celestial body most distant from the Earth' have a sense, but it is very doubtful if they also have a reference. The expression 'the least rapidly convergent series' has a sense; but it is known to have no reference, since for every given convergent series, another convergent, but less rapidly convergent, series can be found. In grasping a sense, one is not certainly assured of a reference. If words are used in the ordinary way, what one intends to speak of is their reference. It can also happen, however, that one wishes to talk about the words themselves or their sense. This happens, for instance, when the words of another are quoted. One's own words then first designate words of the other speaker, and only the latter have their usual reference. We then have signs of signs. In writing, the words are in this case enclosed in quotation marks. Accordingly, a word standing between quotation marks must not be taken as having its ordinary reference. In order to speak of the sense of an expression 'A' one may simply use the phrase 'the sense of the expression "A"'. In reported speech one talks about the sense, e.g., of another person's remarks. It is quite clear that in this way of speaking words do not have their customary reference but designate what is usually their sense. In order to have a short expression, we will say: In reported speech, words are used INDIRECTLY or have their INDIRECT reference. We distinguish accordingly the CUSTOMARY from the INDIRECT reference of word; and its CUSTOMARY sense from its INDIRECT sense. The indirect reference of a word is acreference remains the same, such variations of sense may be tolerated, although they are to be avoided in the theoretical structure of a demonstrative science and ought not to occur in a perfect language.

16

G. Frege

cordingly its customary sense. Such exceptions must always be borne in mind if the mode of connexion between sign, sense, and reference in particular cases is to be correctly understood. [29] The reference and sense of a sign are to be distinguished from the associated idea. If the reference of a sign is an object perceivable by the senses, my idea of it is an internal image,® arising from memories of sense impressions which I have had and acts, both internal and external, which I have performed. Such an idea is often saturated with feeling; the clarity of its separate parts varies and oscillates. The same sense is not always connected, even in the same man, with the same idea. The idea is subjective : one man's idea is not that of another. There result, as a matter of course, a variety of differences in the ideas associated with the same sense. A painter, a horseman, and a zoologist will probably connect different ideas with the name 'Bucephalus'. This constitutes an essential distinction between the idea and the sign's sense, which may be the common property of many and therefore is not a part of a mode of the individual mind. For one can hardly deny that mankind has a common store of thoughts which is transmitted from one generation to another. 4 In the light of this, one need have no scruples in speaking simply of THE sense, whereas in the case of an idea one must, strictly speaking, add to whom it belongs and at what time. It might perhaps be said: Just as one man connects this idea, and another that idea, with the same word, so also one man can associate this sense and another that sense. But there still remains a difference in the mode of connexion. They are not prevented from grasping the same sense; but they cannot have the same [30] idea. Si duo idem faciunt, non est idem. If two persons picture the same thing, each still has his own idea. It is indeed sometimes possible to establish differences in the ideas, or even in the sensations, of different men; but an exact comparison is not possible, because we cannot have both ideas together in the same consciousness. The reference of a proper name is the object itself which we designate by its means; the idea, which we have in that case, is wholly subjective; in between lies the sense, which is indeed no longer subjective like the idea, but is yet not the object itself. The following analogy will perhaps clarify these relationships. Somebody observes the Moon through a telescope. I compare the Moon itself to the reference; it is the object of the observation, mediated by the real image projected by the object ' We can include with ideas the direct experiences in which sense-impressions and acts themselves take the place of the traces which they have left in the mind. The distinction is unimportant for our purpose, especially since memories of sense-impressions and acts always help to complete the perceptual image. One can also understand direct experience as including any object, in so far as it is sensibly perceptible or spatial. * Hence it is inadvisable to use the word 'idea' to designate something so basically different.

On Sense and Reference

17

glass in the interior of the telescope, and by the retinal image of the observer. The former I compare to the sense, the latter is like the idea or experience. The optical image in the telescope is indeed one-sided and dependent upon the standpoint of observation; but it is still objective, inasmuch as it can be used by several observers. At any rate it could be arranged for several to use it simultaneously. But each one would have his own retinal image. On account of the diverse shapes of the observers' eyes, even a geometrical congruence could hardly be achieved, and an actual coincidence would be out of the question. This analogy might be developed still further, by assuming A's retinal image made visible to B; or A might also see his own retinal image in a mirror. In this way we might perhaps show how an idea can itself be taken as an object, but as such is not for the observer what it directly is for the person having the idea. But to pursue this would take us too far afield. We can now recognize three levels of difference between words, expressions, or whole sentences. The difference may concern at most the ideas, or the sense but not the reference, or, finally, the reference as well. With respect to the first level, it is to be [31] noted that, on account of the uncertain connexion of ideas with words, a difference may hold for one person, which another does not find. The difference between a translation and the original text should properly not overstep the first level. To the possible differences here belong also the colouring and shading which poetic eloquence seeks to give to the sense. Such colouring and shading are not objective, and must be evoked by each hearer or reader according to the hints of the poet or the speaker. Without some affinity in human ideas art would certainly be impossible; but it can never be exactly determined how far the intentions of the poet are realized. In what follows there will be no further discussion of ideas and experiences; they have been mentioned here only to ensure that the idea aroused in the hearer by a word shall not be confused with its sense or its reference. To make short and exact expressions possible, let the following phraseology be established: A proper name (word, sign, sign combination, expression) EXPRESSES its sense, STANDS FOR or DESIGNATES its reference. By means of a sign we express its sense and designate its reference. Idealists or sceptics will perhaps long since have objected: 'You talk, without further ado, of the Moon as an object; but how do you know that the name 'the Moon' has any reference? How do you know that anything whatsoever has a reference?' I reply that when we say 'the Moon', we do not intend to speak of our idea of the Moon, nor are we satisfied with the sense alone, but we presuppose a reference. To assume that in the sentence 'The Moon is smaller than the Earth' the idea of the

18

G. Frege

Moon is in question, would be flatly to misunderstand the sense. If this is what the speaker wanted, he would use the phrase 'my idea of the Moon'. N o w we can of course be mistaken in the presupposition, and such mistakes have indeed occurred. But the question whether the presupposition is perhaps always mistaken [32] need not be answered here; in order to justify mention of the reference of a sign it is enough, at first, to point out our intention in speaking or thinking. (We must then add the reservation: provided such reference exists.) So far we have considered the sense and reference only of such expressions, words, or signs as we have called proper names. W e now inquire concerning the sense and reference for an entire declarative sentence. Such a sentence contains a thought.7 Is this thought, now, to be regarded as its sense or its reference? Let us assume for the time being that the sentence has reference. If we now replace one word of the sentence by another having the same reference, but a different sense, this can have no bearing upon the reference of the sentence. Yet we can see that in such a case the thought changes; since, e.g. the thought in the sentence 'The morning star is a body illuminated by the Sun' differs from that in the sentence 'The evening star is a body illuminated by the Sun'. Anybody who did not know that the evening star is the morning star might hold the one thought to be true, the other false. The thought, accordingly, cannot be the reference of the sentence, but must rather be considered as the sense. What is the position now with regard to the reference? Have we a right even to inquire about it? Is it possible that a sentence as a whole has only a sense, but no reference? At any rate, one might expect that such sentences occur, just as there are parts of sentences having sense but no reference. And sentences which contain proper names without reference will be of this kind. The sentence 'Odysseus was set ashore at Ithaca while sound asleep' obviously has a sense. But since it is doubtful whether the name 'Odysseus', occurring therein, has reference, it is also doubtful whether the whole sentence has one. Yet it is certain, nevertheless, that anyone who seriously took the sentence to be true or false would ascribe to the name 'Odysseus' a reference, not merely [33] a sense; for it is of the reference of the name that the predicate is affirmed or denied. Whoever does not admit the name has reference can neither apply nor withhold the predicate. But in that case it would be superfluous to advance to the reference of the name; one could be satisfied with the sense, if one wanted to go no further than the thought. If it were a question only of the sense of the sentence, the thought, it would be unnecessary to bother with the reference of a part of the sentence; only the sense, not the reference, of the part is relevant to the 7 By a thought I understand not the subjective performance of thinking but its objective content, which is capable of being the common property of several thinkers.

On Sense and Reference

19

sense of the whole sentence. The thought remains the same whether 'Odysseus' has reference or not. The fact that we concern ourselves at all about the reference of a part of the sentence indicates that we generally recognize and expect a reference for the sentence itself. The thought loses value for us as soon as we recognize that the reference of one of its parts is missing. We are therefore justified in not being satisfied with the sense of a sentence, and in inquiring also as to its reference. But now why do we want every proper name to have not only a sense, but also a reference? Why is the thought not enough for us? Because, and to the extent that, we are concerned with its truth value. This is not always the case. In hearing an epic poem, for instance, apart from the euphony of the language we are interested only in the sense of the sentences and the images and feelings thereby aroused. The question of truth would cause us to abandon aesthetic delight for an attitude of scientific investigation. Hence it is a matter of no concern to us whether the name 'Odysseus', for instance, has reference, so long as we accept the poem as a work of art. 8 It is the striving for truth that drives us always to advance from the sense to the reference. We have seen that the reference of a sentence may always be sought, whenever the reference of its components is involved; and that this is the case when and only when we are inquiring after the truth value. [34] We are therefore driven into accepting the TRUTH VALUE of a sentence as constituting its reference. By the truth value of a sentence I understand the circumstance that it is true or false. There are no further truth values. For brevity I call the one the True, the other the False. Every declarative sentence concerned with the reference of its words is therefore to be regarded as a proper name, and its reference, if it has one, is either the True or the False. These two objects are recognized, if only implicitly, by everybody who judges something to be true — and so even by a sceptic. The designation of the truth values as objects may appear to be an arbitrary fancy or perhaps a mere play upon words, from which no profound consequences could be drawn. What I mean by an object can be more exactly discussed only in connexion with concept and relation. I will reserve this for another article.9 But so much should already be clear, that in every judgment, 10 no matter how trivial, the step from the level of thoughts to the level of reference (the objective) has already been taken. 8

It would be desirable to have a special term for signs having only sense. If we name them, say, representations, the words of the actors on the stage would be representations; indeed the actor himself would be a representation. * [See his "Über Begriff und Gegenstand", Vierteljahrsschrift für wissenschaftliche Philosophie XVI (1892), 192-205. Ed.] 10 A judgment, for me is not the mere comprehension of a thought, but the admission of its truth.

20

G. Frege

One might be tempted to regard the relation of the thought to the True not as that of sense to reference, but rather as that of subject to predicate. One can, indeed, say: 'The thought, that 5 is a prime number, is true.' But closer examination shows that nothing more has been said than in the simple sentence '5 is a prime number'. The truth claim arises in each case from the form of the declarative sentence, and when the latter lacks its usual force, e.g. in the mouth of an actor upon the stage, even the sentence 'The thought that 5 is a prime number is true' contains only a thought, and indeed the same thought as the simple '5 is a prime number'. It follows that the relation of the thought to the True may not be compared with that of subject to predicate. [35] Subject and predicate (understood in the logical sense) are indeed elements of thought; they stand on the same level for knowledge. By combining subject and predicate, one reaches only a thought, never passes from sense to reference, never from a thought to its truth value. One moves at the same level but never advances from one level to the next. A truth value cannot be a part of a thought, any more than, say, the Sun can, for it is not a sense but an object. If our supposition that the reference of a sentence is its truth value is correct, the latter must remain unchanged when a part of the sentence is replaced by an expression having the same reference. And this is in fact the case. Leibniz gives the definition: Eadem sunt, quae sibi mutuo substituí possunt, salva veritate. What else but the truth value could be found, that belongs quite generally to every sentence if the reference of its components is relevant, and remains unchanged by substitutions of the kind in question? If now the truth value of a sentence is its reference, then on the one hand all true sentences have the same reference and so, on the other hand, do all false sentences. From this we see that in the reference of the sentence all that is specific is obliterated. We can never be concerned only with the reference of a sentence; but again the mere thought alone yields no knowledge, but only the thought together with its reference, i.e. its truth value. Judgments can be regarded as advances from a thought to a truth value. Naturally this cannot be a definition. Judgment is something quite peculiar and incomparable. One might also say that judgments are distinctions of parts within truth values. Such distinction occurs by a return to the thought. To every sense belonging to a truth value there would correspond its own manner of analysis. However, I have here used the word 'part' in a special sense. I have in fact transferred the relation between the parts and the whole of the sentence to its reference, by calling the reference of a word part of the reference of the sentence, if the [36] word itself is a part of the sentence. This way of speaking can certainly be attacked, because the whole reference and one part of it do

On Sense and Reference

21

not suffice to determine the remainder, and because the word 'part' is already used in another sense of bodies. A special term would need to be invented. The supposition that the truth value of a sentence is its reference shall now be put to further test. We have found that the truth value of a sentence remains unchanged when an expression is replaced by another having the same reference: but we have not yet considered the case in which the expression to be replaced is itself a sentence. Now if our view is correct, the truth value of a sentence containing another as part must remain unchanged when the part is replaced by another sentence having the same truth value. Exceptions are to be expected when the whole sentence or its part is direct or indirect quotation; for in such cases, as we have seen, the words do not have their customary reference. In direct quotation, a sentence designates another sentence, and in indirect quotation a thought. We are thus led to consider subordinate sentences or clauses. These occur as parts of a sentence complex, which is, from the logical standpoint, likewise a sentence — a main sentence. But here we meet the question whether it is also true of the subordinate sentence that its reference is a truth value. Of indirect quotation we already know the opposite. Grammarians view subordinate clauses as representatives of parts of sentences and divide them accordingly into noun clauses, adjective clauses, adverbial clauses. This might generate the supposition that the reference of a subordinate clause was not a truth value but rather of the same kind as the reference of a noun or adjective or adverb — in short, of a part of a sentence, whose sense was not a thought but only a part of a thought. Only a more thorough investigation can clarify the issue. In so doing, we shall not follow the grammatical categories strictly, but rather group together what is logically of the same kind. Let us first search for cases in which the sense of the subordinate clause, as we have just supposed, is not an independent thought. [37] The case of an abstract11 noun clause, introduced by 'that', includes the case of indirect quotation, in which we have seen the words to have their indirect reference coinciding with what is customarily their sense. In this case, then, the subordinate clause has for its reference a thought, not a truth value; as sense not a thought, but the sense of the words 'the thought, that ...', which is only a part of the thought in the entire complex sentence. This happens after 'say', 'hear', 'be of the opinion', 'be convinced', 'conclude', and similar words.12 There is a 11

[A literal translation of Frege's 'abstracten Nennsatzen' whose meaning eludes me. Ed.] la In 'A lied in saying he had seen B', the subordinate clause designates a thought which is said (1) to have been asserted by A (2) while A was convinced of its falsity.

22

G. Frege

different, and indeed somewhat complicated, situation after words like 'perceive', 'know', 'fancy', which are to be considered later. That in the cases of the first kind the reference of the subordinate clause is in fact the thought can also be recognized by seeing that it is indifferent to the truth of the whole whether the subordinate clause is true or false. Let us compare, for instance, the two sentences 'Copernicus believed that the planetary orbits are circles' and 'Copernicus believed that the apparent motion of the sun is produced by the real motion of the Earth'. One subordinate clause can be substituted for the other without harm to the truth. The main clause and the subordinate clause together have as their sense only a single thought, and the truth of the whole includes neither the truth nor the untruth of the subordinate clause. In such cases it is not permissible to replace one expression in the subordinate clause by another having the same customary reference, but only by one having the same indirect reference, i.e. the same customary sense. If somebody were to conclude: The reference of a sentence is not its truth value, for in that case it could always be replaced by another sentence of the same truth value; he would prove too much; one might just as well claim that the reference of 'morning star' is not Venus, since one may not always say 'Venus' in place of 'morning star'. One has the right to conclude only that the reference of a sentence is not ALWAYS its truth value, and that 'morning star' does not always [38] stand for the planet Venus, viz. when the word has its indirect reference. An exception of such a kind occurs in the subordinate clause just considered which has a thought as its reference. If one says 'It seems that ...' one means 'It seems to me that ...' or 'I think that ...' We therefore have the same case again. The situation is similar in the case of expressions such as 'to be pleased', 'to regret', 'to approve', 'to blame', 'to hope', 'to fear'. If, toward the end of the battle of Waterloo, 13 Wellington was glad that the Prussians were coming, the basis for his joy was a conviction. Had he been deceived, he would have been no less pleased so long as his illusion lasted; and before he became so convinced he could not have been pleased that the Prussians were coming — even though in fact they might have been already approaching. Just as a conviction or a belief is the ground of a feeling, it can, as in inference, also be the ground of a conviction. In the sentence: 'Columbus inferred from the roundness of the Earth that he could reach India by travelling towards the west', we have as the reference of the parts two thoughts, that the Earth is round, and that Columbus by travelling to the west could reach India. All that is relevant here is that Columbus was convinced of both, and that the one conviction was a ground for the 13

[Frege uses the Prussian name for the battle — 'Belle Alliance'. Ed.]

On Sense and Reference

23

other. Whether the Earth is really round, and whether Columbus could really reach India by travelling to the west, are immaterial to the truth of our sentence; but it is not immaterial whether we replace 'the Earth' by 'the planet which is accompanied by a moon whose diameter is greater than the fourth part of its own'. Here also we have the indirect reference of the words. Adverbial final clauses beginning 'in order that' also belong here; for obviously the purpose is a thought; therefore: indirect reference for the words, subjunctive mood. A subordinate clause with 'that' after 'command', 'ask', 'forbid', would appear in direct speech as an imperative. Such a clause has no reference but only a sense. A command, a request, are indeed not thoughts, yet they stand on the same level as thoughts. Hence in subordinate clauses depending upon [39] 'command', 'ask', etc., words have their indirect reference. The reference of such a clause is therefore not a truth value but a command, a request, and so forth. The case is similar for the dependent question in phrases such as 'doubt whether', 'not to know what'. It is easy to see that here also the words are to be taken to have their indirect reference. Dependent clauses expressing questions and beginning with 'who', 'what', 'where', 'when', 'how', 'by what means', etc., seem at times to approximate very closely to adverbial clauses in which words have their customary references. These cases are distinguished linguistically [in German] by the mood of the verb. With the subjunctive, we have a dependent question and indirect reference of the words, so that a proper name cannot in general be replaced by another name of the same object. In the cases so far considered the words of the subordinate clause had their indirect reference, and this made it clear that the reference of the subordinate clause itself was indirect, i.e. not a truth value but a thought, a command, a request, a question. The subordinate clause could be regarded as a noun, indeed one could say: as a proper name of that thought, that command, etc., which it represented in the context of the sentence structure. We now come to other subordinate clauses, in which the words do have their customary reference without however a thought occurring as sense and a truth value as reference. How this is possible is best made clear by examples. Whoever discovered the elliptic form of the planetary orbits died in misery. If the sense of the subordinate clause were here a thought, it would have to be possible to express it also in a separate sentence. But this does not work, because the grammatical subject 'whoever' has no independent

24

G. Frege

sense and only mediates the relation with the consequent clause 'died in misery'. For this reason the sense of the subordinate clause is not a complete thought, and its reference is Kepler, not a truth value. One might object that the sense of the whole does contain a thought as part, viz. that there was somebody who first discovered the elliptic form of the planetary orbits; for whoever takes the whole to be true cannot [40] deny this part. This is undoubtedly so; but only because otherwise the dependent clause 'whoever discovered the elliptic form of the planetary orbits' would have no reference. If anything is asserted there is always an obvious presupposition that the simple or compound proper names used have reference. If one therefore asserts 'Kepler died in misery', there is a presupposition that the name 'Kepler' designates something; but it does not follow that the sense of the sentence 'Kepler died in misery' contains the thought that the name 'Kepler' designates something. If this were the case the negation would have to run not Kepler did not die in misery but Kepler did not die in misery, or the name 'Kepler' has no reference. That the name 'Kepler' designates something is just as much a presupposition for the assertion Kepler died in misery as for the contrary assertion. Now languages have the fault of containing expressions which fail to designate an object (although their grammatical form seems to qualify them for the purpose) because the truth of some sentences is a prerequisite. Thus it depends on the truth of the sentence: There was someone who discovered the elliptic form of the planetary orbits whether the subordinate clause Whoever discovered the elliptic form of the planetary orbits really designates an object or only seems to do so while having in fact no reference. And thus it may appear as if our subordinate clause contained as a part of its sense the thought that there was somebody who discovered the elliptic form of the planetary orbits. If this were right the negation would run: Either whoever discovered the elliptic form of the planetary orbits did not die in misery or there was nobody who discovered the elliptic form of the planetary orbits.

On Sense and Reference

25

[41] This arises from an imperfection of language, from which even the symbolic language of mathematical analysis is not altogether free; even there combinations of symbols can occur that seem to stand for something but have (at least so far) no reference, e.g. divergent infinite series. This can be avoided, e.g., by means of the special stipulation that divergent infinite series shall stand for the number 0. A logically perfect language {Begriffsschrift) should satisfy the conditions, that every expression grammatically well constructed as a proper name out of signs already introduced shall in fact designate an object, and that no new sign shall be introduced as a proper name without being secured a reference. The logic books contain warnings against logical mistakes arising from the ambiguity of expressions. I regard as no less pertinent a warning against apparent proper names having no reference. The history of mathematics supplies errors which have arisen in this way. This lends itself to demagogic abuse as easily as ambiguity — perhaps more easily. 'The will of the people' can serve as an example; for it is easy to establish that there is at any rate no generally accepted reference for this expression. It is therefore by no means unimportant to eliminate the source of these mistakes, at least in science, once and for all. Then such objections as the one discussed above would become impossible, because it could never depend upon the truth of a thought whether a proper name had a reference. With the consideration of these noun clauses may be coupled that of types of adjective and adverbial clauses which are logically in close relation to them. Adjective clauses also serve to construct compound proper names, though, unlike noun clauses, they are not sufficient by themselves for this purpose. These adjective clauses are to be regarded as equivalent to adjectives. Instead of 'the square root of 4 which is smaller than 0', one can also say 'the negative square root of 4'. We have here the case of a compound proper name constructed from the expression for a concept with the help of the singular definite article. This is at any rate permissible if the [42] concept applies to one and only one single object.14 Expressions for concepts can be so constructed that marks of a concept are given by adjective clauses as, in our example, by the clause 'which is smaller than 0'. It is evident that such an adjective clause cannot have a thought as sense or a truth value as reference, any more than the noun clause could. Its sense, which can also be expressed in many cases by a single adjective, is only a part of a thought. Here, as in the case of the 14 In accordance with what was said above, an expression of the kind in question must actually always be assured of reference, by means of a special stipulation, e.g. by the convention that 0 shall count as its reference, when the concept applies to no object or to more than one.

26

G. Frege

noun clause, there is no independent subject and therefore no possibility of reproducing the sense of the subordinate clause in an independent sentence. Places, instants, stretches of time, are, logically considered, objects; hence the linguistic designation of a definite place, a definite instant, or a stretch of time is to be regarded as a proper name. Now adverbial clauses of place and time can be used for the construction of such a proper name in a manner similar to that which we have seen in the case of noun and adjective clauses. In the same way, expressions for concepts bringing in places, etc., can be constructed. It is to be noted here also that the sense of these subordinate clauses cannot be reproduced in an independent sentence, since an essential component, viz. the determination of place or time, is missing and is only indicated by a relative pronoun or a conjunction. 15 In conditional clauses, also, there may usually be recognized to [43] occur an indefinite indicator, having a similar correlate in the dependent clause. (We have already seen this occur in noun, adjective, and adverbial clauses.) In so far as each indicator refers to the other, both clauses together form a connected whole, which as a rule expresses only a single thought. In the sentence If a number is less than 1 and greater than 0, its square is less than 1 and greater than 0 the component in question is 'a number' in the conditional clause and 'its' in the dependent clause. It is by means of this very indefiniteness that the sense acquires the generality expected of a law. It is this which is responsible for the fact that the antecedent clause alone has no complete thought as its sense and in combination with the consequent 16

In the case of these sentences, various interpretations are easily possible. The sense of the sentence, 'After Schleswig-Holstein was separated from Denmark, Prussia and Austria quarrelled' can also be rendered in the form 'After the separation of SchleswigHolstein from Denmark, Prussia and Austria quarrelled'. In this version, it is surely sufficiently clear that the sense is not to be taken as having as a part the thought that Schleswig-Holstein was once separated from Denmark, but that this is the necessary presupposition in order for the expression 'after the separation of Schleswig-Holstein from Denmark' to have any reference at all. To be sure, our sentence can also be interpreted as saying that Schleswig-Holstein was once separated from Denmark. We then have a case which is to be considered later. In order to understand the difference more clearly, let us project ourselves into the mind of a Chinese who, having little knowledge of European history, believes it to be false that Schleswig-Holstein was ever separated from Denmark. He will take our sentence, in the first version, to be neither true nor false but will deny it to have any reference, on the ground of absence of reference for its subordinate clause. This clause would only apparently determine a time. If he interpreted our sentence in the second way, however, he would find a thought expressed in it which he would take to be false, beside a part which would be without reference for him.

On Sense and Reference

27

clause expresses one and only one thought, whose parts are no longer thoughts. It is, in general, incorrect to say that in the hypothetical judgment two judgments are put in reciprocal relationship. If this or something similar is said, the word 'judgment' is used in the same sense as I have connected with the word 'thought', so that I would use the formulation: 'A hypothetical thought establishes a reciprocal relationship between two thoughts.' This could be true only if an indefinite indicator is absent,16 but in such a case there would also be no generality. If an instant of time is to be indefinitely indicated in both conditional and dependent clauses, this is often achieved merely by using the present tense of the verb, which in such a case however does not indicate the temporal present. This grammatical form is then the indefinite indicator in the main and [44] subordinate clauses. An example of this is: 'When the Sun is in the tropic of Cancer, the longest day in the northern hemisphere occurs'. Here, also, it is impossible to express the sense of the subordinate clause in a full sentence, because this sense is not a complete thought. If we say: 'The Sun is in the tropic of Cancer', this would refer to our present time and thereby change the sense. Just as little is the sense of the main clause a thought; only the whole, composed of main and subordinate clauses, has such a sense. It may be added that several common components in the antecedent and consequent clauses may be indefinitely indicated. It is clear that noun clauses with 'who' or 'what' and adverbial clauses with 'where', 'when', 'wherever', 'whenever' are often to be interpreted as having the sense of conditional clauses, e.g. 'who touches pitch, defiles himself'. Adjective clauses can also take the place of conditional clauses. Thus the sense of the sentence previously used can be given in the form 'The square of a number which is less than 1 and greater than 0 is less than 1 and greater than 0'. The situation is quite different if the common component of the two clauses is designated by a proper name. In the sentence: Napoleon, who recognized the danger to his right flank, himself led his guards against the enemy position two thoughts are expressed: 1. Napoleon recognized the danger to his right flank. 2. Napoleon himself led his guards against the enemy position. When and where this happened is to be fixed by the context, but is nevertheless to be taken as definitely determined thereby. If the entire 16

At times an explicit linguistic indication is missing and must be read off from the entire context.

28

G. Frege

sentence is uttered as an assertion, we thereby simultaneously assert both component sentences. If one of the parts is false, the whole is false. Here we have the case that the subordinate clause by itself has a complete thought as sense (if we complete it by indication of place and time). The reference of the subordinate clause is accordingly a truth value. We can therefore expect that it may be replaced, without harm to the truth value of the whole, by a sentence having the same truth [45] value. This is indeed the case; but it is to be noticed that for purely grammatical reasons, its subject must be 'Napoleon', for only then can it be brought into the form of an adjective clause belonging to 'Napoleon'. But if the demand that it be expressed in this form be waived, and the connexion be shown by 'and', this restriction disappears. Subsidiary clauses beginning with 'although' also express complete thoughts. This conjunction actually has no sense and does not change the sense of the clause but only illuminates it in a peculiar fashion. 17 We could indeed replace the conditional clause without harm to the truth of the whole by another of the same truth value; but the light in which the clause is placed by the conjunction might then easily appear unsuitable, as if a song with a sad subject were to be sung in a lively fashion. In the last cases the truth of the whole included the truth of the component clauses. The case is different if a conditional clause expresses a complete thought by containing, in place of an indefinite indicator, a proper name or something which is to be regarded as equivalent. In the sentence If the Sun has already risen, the sky is very cloudy the time is the present, that is to say, definite. And the place is also to be thought of as definite. Here it can be said that a relation between the truth values of conditional and dependent clauses has been asserted,viz. such that the case does not occur in which the antecedent stands for the True and the consequent for the False. Accordingly, our sentence is true if the Sun has not yet risen, whether the sky is very cloudy or not, and also if the Sun has risen and the sky is very cloudy. Since only truth values are here in question, each component clause can be replaced by another of the same truth value without changing the truth value of the whole. To be sure, the light in which the subject then appears would usually be unsuitable; the thought [46] might easily seem distorted; but this has nothing to do with its truth value. One must always take care not to clash with the subsidiary thoughts, which are however not explicitly expressed and therefore should not be reckoned in the sense. Hence, also, no account need be taken of their truth values.18 17 18

Similarly in the case of 'but', 'yet'. The thought of our sentence might also be expressed thus: 'Either the Sun has not

On Sense and Reference

29

The simple cases have now been discussed. Let us review what we have learned. The subordinate clause usually has for its sense not a thought, but only a part of one, and consequently no truth value as reference. The reason for this is either that the words in the subordinate clause have indirect reference, so that the reference, not the sense, of the subordinate clause is a thought; or else that, on account of the presence of an indefinite indicator, the subordinate clause is incomplete and expresses a thought only when combined with the main clause. It may happen, however, that the sense of the subsidiary clause is a complete thought, in which case it can be replaced by another of the same truth value without harm to the truth of the whole — provided there are no grammatical obstacles. An examination of all the subordinate clauses which one may encounter will soon provide some which do not fit well into these categories. The reason, so far as I can see, is that these subordinate clauses have no such simple sense. Almost always, it seems, we connect with the main thoughts expressed by us subsidiary thoughts which, although not expressed, are associated with our words, in accordance with psychological laws, by the hearer. And since the subsidiary thought appears to be connected with our words of its own accord, almost like the main thought itself, we want it also to be expressed. The sense of the sentence is thereby enriched, and it may well happen that we have more simple thoughts than clauses. In many cases the sentence must be understood in this way, in others it may be doubtful whether the subsidiary thought belongs to the sense of the sentence or only [47] accompanies it.19 One might perhaps find that the sentence Napoleon, who recognized the danger to his right flank, himself led his guards against the enemy position expresses not only the two thoughts shown above, but also the thought that the knowledge of the danger was the reason why he led the guards against the enemy position. One may in fact doubt whether this thought is merely slightly suggested or really expressed. Let the question be considered whether our sentence be false if Napoleon's decision had already been made before he recognized the danger. If our sentence could be true in spite of this, the subsidiary thought should not be understood as part of the sense. One would probably decide in favour of this. The alternative would make for a quite complicated situation: We would have more simple thoughts than clauses. If the sentence risen yet or the sky is very cloudy' — which shows how this kind of sentence connexion is to be understood. 19 This may be important for the question whether an assertion is a lie, or an oath a perjury.

30

G. Frege Napoleon recognized the danger to his right flank

were now to be replaced by another having the same truth value, e.g. Napoleon was already more than 45 years old not only would our first thought be changed, but also our third one. Hence the truth value of the latter might change — viz. if his age was not the reason for the decision to lead the guards against the enemy. This shows why clauses of equal truth value cannot always be substituted for one another in such cases. The clause expresses more through its connexion with another than it does in isolation. Let us now consider cases where this regularly happens. In the sentence: Bebel mistakenly supposes that the return of Alsace-Lorraine would appease France's desire for revenge two thoughts are expressed, which are not however shown by means of antecedent and consequent clauses, viz.: (1) Bebel believes that the return of Alsace-Lorraine would appease France's desire for revenge [48] (2) the return of Alsace-Lorraine would not appease France's desire for revenge. In the expression of the first thought, the words of the subordinate clause have their indirect reference, while the same words have their customary reference in the expression of the second thought. This shows that the subordinate clause in our original complex sentence is to be taken twice over, with different reference, standing once for a thought, once for a truth value. Since the truth value is not the whole reference of the subordinate clause, we cannot simply replace the latter by another of equal truth value. Similar considerations apply to expressions such as 'know', 'discover', 'it is known that'. By means of a subordinate causal clause and the associated main clause we express several thoughts, which however do not correspond separately to the original clauses. In the sentence: 'Because ice is less dense than water, it floats on water' we have (1) Ice is less dense than water; (2) If anything is less dense than water, it floats on water; (3) Ice floats on water. The third thought, however, need not be explicitly introduced, since it is contained in the remaining two. On the other hand, neither the first and third nor the second and third combined would furnish the sense of our sentence. It can now be seen that our subordinate clause

On Sense and Reference

31

because ice is less dense than water expresses our first thought, as well as a part of our second. This is how it comes to pass that our subsidiary clause cannot be simply replaced by another of equal truth value; for this would alter our second thought and thereby might well alter its truth value. The situation is similar in the sentence If iron were less dense than water, it would float on water. [49] Here we have the two thoughts that iron is not less dense than water, and that something floats on water if it is less dense than water. The subsidiary clause again expresses one thought and a part of the other. If we interpret the sentence already considered After Schleswig-Holstein was separated from Denmark, Prussia and Austria quarrelled in such a way that it expresses the thought that Schleswig-Holstein was once separated from Denmark, we have first this thought, and secondly the thought that at a time, more closely determined by the subordinate clause, Prussia and Austria quarreled. Here also the subordinate clause expresses not only one thought but also a part of another. Therefore it may not in general be replaced by another of the same truth value. It is hard to exhaust all the possibilities given by language; but I hope to have brought to light at least the essential reasons why a subordinate clause may not always be replaced by another of equal truth value without harm to the truth of the whole sentence structure. These reasons arise: (1) when the subordinate clause does not stand for a truth value, inasmuch as it expresses only a part of a thought; (2) when the subordinate clause does stand for a truth value but is not restricted to so doing, inasmuch as its sense includes one thought and part of another. The first case arises: (a) in indirect reference of words (b) if a part of the sentence is only an indefinite indicator instead of a proper name. In the second case, the subsidiary clause may have to be taken twice over, viz. once in its customary reference, and the other time in indirect reference; or the sense of a part of the subordinate clause may likewise be a component of another thought, which, taken together with the thought

32

G. Frege

directly expressed by the subordinate clause, makes up the sense of the whole sentence. It follows with sufficient probability from the foregoing that the cases where a subordinate clause is not replaceable by another of the same value it cannot be brought in disproof of our view [50] that a truth value is the reference of a sentence having a thought as its sense. Let us return to our starting point. When we found 'a = a' and 'a = b' to have different cognitive values, the explanation is that for the purpose of knowledge, the sense of the sentence, viz., the thought expressed by it, is no less relevant than its reference, i.e. its truth value. If now a — b, then indeed the reference of is the same as that of 'a', and hence the truth value of 'a = 6' is the same as that of 'a = a'. In spite of this, the sense of may differ from that of l a\ and thereby the sense expressed in 'a = b' differs from that of 'a = a'. In that case the two sentences do not have the same cognitive value. If we understand by 'judgment' the advance from the thought to its truth value, as in the above paper, we can also say that the judgments are different.

R. Carnap

MEANING AND SYNONYMY IN NATURAL LANGUAGES

1. MEANING ANALYSIS IN PRAGMATICS AND SEMANTICS

The analysis of meanings of expressions occurs in two fundamentally different forms. The first belongs to PRAGMATICS, that is, the empirical investigation of historically given NATURAL LANGUAGES. This kind of analysis has long been carried out by linguists and philosophers, especially analytic philosophers. The second form was developed only recently in the field of symbolic logic; this form belongs to SEMANTICS (here understood in the sense of pure semantics, while descriptive semantics may be regarded as part of pragmatics), that is, the study of constructed LANGUAGE SYSTEMS given by their rules. The theory of the relations between a language — either a natural language or a language system — and what language is about may be divided into two parts which I call the theory of extension and the theory of intension, respectively.1 The first deals with concepts like denoting, naming, extension, truth, and related ones. (For example, the word 'blau' in German, and likewise the predicate 'B' in a symbolic language system if a rule assigns to it the same meaning, denote any object that is blue; its extension is the class of all blue objects; 'der Mond' is a name of the moon; the sentence *der Mond ist blau' is true if and only if the moon is Reprinted from: R. Caraap, Meaning and Necessity (Chicago, Phoenix, 1956), 233-47. 1 This distinction is closely related to that between radical concepts and L-concepts which I made in Introduction to Semantics (Cambridge, Mass., 1942). The contrast between extension and intension is the basis of the semantical method which I developed in Meaning and Necessity. Quine calls the two theories "theory of reference" and "theory of meaning", respectively.

34

R. Carnap

blue.) The theory of intension deals with concepts like intension, synonymy, analyticity, and related ones; for our present discussion let us call them INTENSION CONCEPTS. (I use 'intension' as a technical term for the meaning of an expression or, more specifically, for its designative meaning component; see below. For example, the intension of 'blau' in German is the property of being blue; two predicates are synonymous if and only if they have the same intension; a sentence is analytic if it is true by virtue of the intensions of the expressions occurring in it.) From a systematic point of view, the description of a language may well begin with the theory of intension and then build the theory of extension on its basis. By learning the theory of intension of a language, say German, we learn the intensions of the words and phrases and finally of the sentences. Thus the theory of intension of a given language L enables us to UNDERSTAND the sentences of L. On the other hand, we can apply the concepts of the theory of extension of L only if we have, in addition to the knowledge of the theory of intension of L, also sufficient empirical knowledge of the relevant facts. For example, in order to ascertain whether a German word denotes a given object, one must first understand the word, that is, know what is its intension, in other words, know the general condition which an object must fulfil in order to be denoted by this word; and secondly he must investigate the object in question in order to see whether it fulfils the condition or not. On the other hand, if a linguist makes an empirical investigation of a language not previously described, he finds out first that certain objects are denoted by a given word, and later he determines the intension of the word. Nobody doubts that the pragmatical investigation of natural languages is of greatest importance for an understanding both of the behavior of individuals and of the character and development of whole cultures. On the other hand, I believe with the majority of logicians today that for the special purpose of the development of logic the construction and semantical investigation of language systems is more important. But also for the logician a study of pragmatics may be useful. If he wishes to find out an efficient form for a language system to be used, say, in a branch of empirical science, he might find fruitful suggestions by a study of the natural development of the language of scientists and even of the everyday language. Many of the concepts used today in pure semantics were indeed suggested by corresponding pragmatical concepts which had been used for natural languages by philosophers or linguists, though usually without exact definitions. Those semantical concepts were, in a sense, intended as explicata for the corresponding pragmatical concepts. In the case of the semantical intension concepts there is an additional motivation for studying the corresponding pragmatical concepts. The reason is that some of the objections raised against these semantical con-

Meaning and Synonymy in Natural Languages

35

cepts concern, not so much any particular proposed explication, but the question of the very existence of the alleged explicanda. Especially Quine's criticism does not concern the formal correctness of the definitions in pure semantics; rather, he doubts whether there are any clear and fruitful corresponding pragmatical concepts which could serve as explicanda. That is the reason why he demands that these pragmatical concepts be shown to be scientifically legitimate by stating empirical, behavioristic criteria for them. If I understand him correctly, he believes that, without this pragmatical substructure, the semantical intension concepts, even if formally correct, are arbitrary and without purpose. I do not think that a semantical concept, in order to be fruitful, must necessarily possess a prior pragmatical counterpart. It is theoretically possible to demonstrate its fruitfulness through its application in the further development of language systems. But this is a slow process. If for a given semantical concept there is already a familiar, though somewhat vague, corresponding pragmatical concept and if we are able to clarify the latter by describing an operational procedure for its application, then this may indeed be a simpler way for refuting the objections and furnish a practical justification at once for both concepts. The purpose of this paper is to clarify the nature of the pragmatical concept of intension in natural languages and to outline a behavioristic, operational procedure for it. This will give a practical vindication for the semantical intension concepts; ways for defining them, especially analyticity, I have shown in a previous paper (Carnap, 1952). By way of introduction I shall first (in §2) discuss briefly the pragmatical concepts of denotation and extension; it seems to be generally agreed that they are scientifically legitimate.

2. THE DETERMINATION OF EXTENSIONS

We take as example the German language. We imagine that a linguist who does not know anything about this language sets out to study it by observing the linguistic behavior of German-speaking people. More specifically, he studies the German language as used by a given person Karl at a given time. For simplicity, we restrict the discussion in this paper mainly to predicates applicable to observable things, like 'blau' and 'Hund'. It is generally agreed that, on the basis of spontaneous or elicited utterances of a person, the linguist can ascertain whether or not the person is willing to apply a given predicate to a given thing, in other words, whether the predicate denotes the given thing for the person. By collecting results of this kind, the linguist can determine first, the extension of the predicate 'Hund' within a given region for Karl, that is, the class of the

36

R. Carnap

things to which Karl is willing to apply the predicate, second, the extension of the contradictory, that is, the class of those things for which Karl denies the application of 'Hund', and, third, the intermediate class of those things for which Karl is not willing either to affirm or to deny the predicate. The size of the third class indicates the degree of vagueness of the predicate 'Hund', if we disregard for simplicity the effect of Karl's ignorance about relevant facts. For certain predicates, e.g., 'Mensch', this third class is relatively very small; the degree of their extensional vagueness is low. On the basis of the determination of the three classes for the predicate 'Hund' within the investigated region, the linguist may make a hypothesis concerning the responses of Karl to things outside of that region, and maybe even a hypothesis concerning the total extension in the universe. The latter hypothesis cannot, of course, be completely verified, but every single instance of it can in principle be tested. On the other hand, it is also generally agreed that this determination of extension involves uncertainty and possible error. But since this holds for all concepts of empirical science, nobody regards this fact as a sufficient reason for rejecting the concepts of the theory of extension. The sources of uncertainty are chiefly the following: first, the linguist's acceptance of the result that a given thing is denoted by 'Hund' for Karl may be erroneous, e.g., due to a misunderstanding or a factual error of Karl's; and, second, the generalization to things which he has not tested suffers, of course, from the uncertainty of all inductive inference.

3. THE DETERMINATION OF INTENSIONS

The purpose of this paper is to defend the thesis that the analysis of intension for a natural language is a scientific procedure, methodologically just as sound as the analysis of extension. To many linguists and philosophers this thesis will appear as a truism. However, some contemporary philosophers, especially Quine,2 and White (1950), believe that the pragmatical intension concepts are foggy, mysterious, and not really understandable, and that so far no explications for them have been given. They believe further that, if an explication for one of these concepts is found, it will at best be in the form of a concept of degree. They acknowledge the good scientific status of the pragmatical concepts of the theory of extension. They emphasize that their objection against the intension concepts is based on a point of principle and not on the generally recognized facts of the technical difficulty of linguistic investigations, the inductive uncertainty, and the vagueness of the words of ordinary language. I shall * W. V. Quine (1953); for his criticism of intension concepts see especially Essays II (Quine 1951), III, and VII.

Meaning and Synonymy in Natural Languages

37

therefore leave aside in my discussion these difficulties, especially the two mentioned at the end of the last section. Thus the question is this: GRANTED THAT THE LINGUIST CAN DETERMINE THE EXTENSION OF A GIVEN PREDICATE, HOW CAN HE GO BEYOND THIS AND DETERMINE ALSO ITS INTENSION?

The technical term 'intension', which I use here instead of the ambiguous word 'meaning', is meant to apply only to the cognitive or designative meaning component. I shall not try to define this component. It was mentioned earlier that determination of truth presupposes knowledge of meaning (in addition to knowledge of facts); now, cognitive meaning may be roughly characterized as that meaning component which is relevant for the determination of truth. The non-cognitive meaning components, although irrelevant for questions of truth and logic, may still be very important for the psychological effect of a sentence on a listener, e.g. by emphasis, emotional associations, motivational effects. It must certainly be admitted that the pragmatical determination of intensions involves a new step and therefore a new methodological problem. Let us assume that two linguists, investigating the language of Karl, have reached complete agreement in the determination of the extension of a given predicate in a given region. This means that they agree for every thing in this region, whether or not the predicate in question denotes it for Karl. As long as only these results are given, no matter how large the region is — you may take it, fictitiously, as the whole world, if you like — it is still possible for the linguists to ascribe to the predicate different intensions. For there are more than one and possibly infinitely many properties whose extension within the given region is just the extension determined for the predicate. Here we come to the core of the controversy. It concerns the nature of a linguist's assignment of one of these properties to the predicate as its intension. This assignment may be made explicit by an entry in the German-English dictionary, conjoining the German predicate with an English phrase. The linguist declares hereby the German predicate to be synonymous with the English phrase, THE INTENSIONALIST THESIS in pragmatics, which I am defending, says that the assignment of an intension is an empirical hypothesis which, like any other hypothesis in linguistics, can be tested by observations of language behavior. On the other hand, THE EXTENSIONALIST THESIS asserts that the assignment of an intension, on the basis of the previously determined extension, is not a question of fact but merely a matter of choice. The thesis holds that the linguist is free to choose any of those properties which fit to the given extension; he may be guided in his choice by a consideration of simplicity, but there is no question of right or wrong. Quine seems to maintain this thesis; he says: "The finished lexicon is a case evidently of ex pede

38

R. Carnap

Herculem. But there is a difference. In projecting Hercules from the foot we risk error but we may derive comfort from the fact that there is something to be wrong about. In the case of the lexicon, pending some definition of synonymy, we have no stating of the problem; we have nothing for the lexicographer to be right or wrong about" (1953:63). I shall now plead for the intensionalist thesis. Suppose, for example, that one linguist, after an investigation of Karl's speaking behavior, writes into his dictionary the following: (1)

Pferd, horse,

while another linguist writes: (2)

Pferd, horse or unicorn.

Since there are no unicorns, the two intensions ascribed to the word 'Pferd' by the two linguists, although different, have the same extension. If the extensionalist thesis were right, there would be no way for empirically deciding between (1) and (2). Since the extension is the same, no response by Karl, affirmative or negative, with respect to any actual thing can make a difference between (1) and (2). But what else is there to investigate for the linguist beyond Karl's responses concerning the application of the predicate to all the cases that can be found? The answer is, he must take into account not only the actual cases, but also possible cases.8 The most direct way of doing this would be for the linguist to use, in the German questions directed to Karl, modal expressions 'corresponding to "possible case" or the like. To be sure, these expressions are usually rather ambiguous; but this difficulty can be overcome by giving suitable explanations and examples. I do not think that there is any objection of principle against the use of modal terms. On the other hand, I think that their use is not necessary. The linguist could simply describe for Karl cases, which he knows to be possible, and leave it open whether there is anything satisfying those descriptions or not. He may, for example, describe a unicorn (in German) by something corresponding to the English formulation: "a thing similar to a horse, but having only one horn in the middle of the forehead". Or he may point toward a thing and then describe the intended modification in words, e.g.: "a thing like this one but having one horn in the middle of the forehead". Or, finally, he might just point to a picture representing a unicorn. Then he asks Karl whether he is willing to apply ' Some philosophers have indeed defined the intension of a predicate (or a concept closely related to it) as the class of the possible objects falling under it. For example, C. I. Lewis defines: "The comprehension of a term is the classification of all consistently thinkable things to which the term would correctly apply." I prefer to apply modalities like possibility not to object but only to intensions, especially to propositions or to properties (kinds). (Compare Meaning and Necessity, 66f.) To speak of a possible case means to speak of a kind of objects which is possibly non-empty.

Meaning and Synonymy in Natural Languages

39

the word 'Pferd' to a thing of this kind. An affirmative or a negative answer will constitute a confirming instance for (2) or (1) respectively. This shows that (1) and (2) are different empirical hypotheses. All LOGICALLY POSSIBLE cases come into consideration for the determination of intensions. This includes also those cases that are causally impossible, i.e., excluded by the laws of nature holding in our universe, and certainly those that are excluded by laws which Karl believes to hold. Thus, if Karl believes that all P are Q by a law of nature, the linguist will still induce him to consider things that are P but not Q, and ask him whether or not he would apply to them the predicate under investigation (e.g., 'Pferd'). The inadequacy of the extensionalist thesis is also shown by the following example. Consider, on the one hand, these customary entries in German-English dictionaries: (3)

Einhorn, unicorn. Kobold, goblin,

and, on the other hand, the following unusual entries: (4)

Einhorn, goblin. Kobold, unicorn.

Now the two German words (and likewise the two English words) have the same extension, viz., the null class. Therefore, if the extensionalist thesis were correct, there would be no essential, empirically testable difference between (3) and (4). The extensionalist is compelled to say that the fact that (3) is generally accepted and (4) generally rejected is merely due to a tradition created by the lexicographers, and that there are no facts of German language behavior which could be regarded as evidence in favor of (3) as against (4). I wonder whether any linguist would be willing to accept (4). Or, to avoid the possibly misguiding influence of the lexicographers' tradition, let us put the question this way: would a man on the street, who has learned both languages by practical use without lessons or dictionaries, accept as correct a translation made according to (4)? In general terms, the determination of the intension of a predicate may start from some instances denoted by the predicate. The essential task is then to find out what variations of a given specimen in various respects (e.g. size, shape, color) are admitted within the range of the predicate. The intension of a predicate may be defined as its range, which comprehends those possible kinds of objects for which the predicate holds. In this investigation of intension, the linguist finds a new kind of vagueness, which may be called INTENSIONAL VAGUENESS. A S mentioned above, the extensional vagueness of the word 'Mensch' is very small, at least in the accessible region. First, the intermediate zone among animals now living on earth is practically empty. Second, if the ancestors of man are considered, it is probably found that Karl cannot easily draw a line; thus there is an

40

R. Carnap

intermediate zone, but it is relatively small. However, when the linguist proceeds to the determination of the INTENSION of the word 'Mensch', the situation is quite different. He has to test Karl's responses to descriptions of strange kinds of animals, say intermediate between man and dog, man and lion, man and hawk, etc. It may be that the linguist and Karl know that these kinds of animals have never lived on earth; they do not know whether or not these kinds will ever occur on earth or on any other planet in any galaxy. At any rate, this knowledge or ignorance is irrelevant for the determination of intension. But Karl's ignorance has the psychological effect that he has seldom if ever thought of these kinds (unless he happens to be a student of mythology or a science-fiction fan) and therefore never felt an urge to make up his mind to which of them to apply the predicate 'Mensch'. Consequently, the linguist finds in Karl's responses a large intermediate zone for this predicate, in other words, a high intensional vagueness. The fact that Karl has not made such decisions means that the intension of the word 'Mensch' for him is not quite clear even to himself, that he does not completely understand his own word. This lack of clarity does not bother him much because it holds only for aspects which have very little practical importance for him. The extensionalist will perhaps reject as impracticable the described procedure for determining intensions because, he might say, the man on the street is unwilling to say anything about nonexistent objects. If Karl happens to be over-realistic in this way, the linguist could still resort to a lie, reporting, say, his alleged observations of unicorns. But this is by no means necessary. The tests concerning intensions are independent of questions of existence. The man on the street is very well able to understand and to answer questions about assumed situations, where it is left open whether anything of the kind described will ever actually occur or not, and even about nonexisting situations. This is shown in ordinary conversations about alternative plans of action, about the truth of reports, about dreams, legends, and fairy tales. Although I have given here only a rough indication of the empirical procedure for determining intensions, I believe that it is sufficient to make clear that it would be possible to write along the lines indicated a manual for determining intensions or, more exactly, for testing hypotheses concerning intensions. The kinds of rules in such a manual would not be essentially different from those customarily given for procedures in psychology, linguistics, and anthropology. Therefore the rules could be understood and carried out by any scientist (provided he is not infected by philosophical prejudices).4 * After writing the present paper I have become acquainted with a very interesting new book by Arne Naess (1953). This book describes in detail various procedures for testing hypotheses concerning the synonymity of expressions with the help of ques-

Meaning and Synonymy in Natural Languages

41

4. INTENSIONS IN THE LANGUAGE OF SCIENCE

The discussions in this paper concern in general a simple, pre-scientific language, and the predicates considered designate observable properties of material bodies. Let us now briefly take a look at the LANGUAGE OF SCIENCE. It is today still mainly a natural language (except for its mathematical part), with only a few explicitly made conventions for some special words or symbols. It is a variant of the pre-scientific language, caused by special professional needs. The degree of precision is here in general considerably higher (i.e. the degree of vagueness is lower) than in the every day language, and this degree is continually increasing. It is important to note that this increase holds not only for extensional but also for intensional precision; that is to say that not only the extensional intermediate zones (i.e. those of actual occurrences) but also the intensional ones (i.e. those of possible occurrences) are shrinking. In consequence of this development, also the intension concepts become applicable with increasing clarity. In the oldest books on chemistry, for example, there were a great number of statements describing the properties of a given substance, say water or sulphuric acid, including its reactions with other substances. There was no clear indication as to which of these numerous properties were to be taken as essential or definitory for the substance. Therefore, at least on the basis of the book alone, we cannot determine which of the statements made in the book were analytic and which synthetic for its author. The situation was similar with books on zoology, even at a much later time; we find a lot of statements, e.g. on the lion, without a clear separation of the definitory properties. But in chemistry there was an early development from the state described to states of greater and greater intensional precision. On the basis of the theory of chemical elements, slowly with increasing explicitness certain properties were selected as essential. For a compound, the molecular formula (e.g. *H 2 0') was taken as definitory, and later the molecular structure tionnaires, and gives examples of statistical results found with these questionnaires. The practical difficulties and sources of possible errors are carefully investigated. The procedures concern the responses of the test persons, not to observed objects as in the present paper, but to pairs of sentences within specified contexts. Therefore the questions are formulated in the metalanguage, e.g. "Do the two given sentences in the given context express the same assertion to you?" Although there may be different opinions concerning some features of the various procedures, it seems to me that the book marks an important progress in the methodology of empirical meaning analysis for natural languages. Some of the questions used refer also to possible kinds of cases, e.g. "Can you imagine circumstances (conditions, situations) in which you would accept the one sentence and reject the other, or vice versa?" (p. 368). The book, both in its methodological discussions and in its reports on experiences with the questionnaires, seems to me to provide abundant evidence in support of the intensionalist thesis (in the sense explained in §3 above).

42

R. Carnap

diagram. For the elementary substances, first certain experimental properties were more and more clearly selected as definitory, for example the atomic weight, later the position in Mendeleev's system. Still later, with a differentiation of the various isotopes, the nuclear composition was regarded as definitory, say characterized by the number of protons (atomic number) and the number of neutrons. We can at the present time observe the advantages already obtained by the explicit conventions which have been made, though only to a very limited extent, in the language of empirical science, and the very great advantages effected by the moderate measure of formalization in the language of mathematics. Let us suppose — as I indeed believe, but that is outside of our present discussion — that this trend toward explicit rules will continue. Then the practical question arises whether rules of extension are sufficient or whether it would be advisable to lay down also rules of intension. In my view, it follows from the previous discussion that rules of intension are required, because otherwise intensional vagueness would remain, and this would prevent clear mutual understanding and effective communication.

5. THE GENERAL CONCEPT OF THE INTENSION OF A PREDICATE

We have seen that there is an empirical procedure for testing, by observations of linguistic behavior, a hypothesis concerning the intension of a predicate, say 'Pferd', for a speaker, say Karl. Since a procedure of this kind is applicable to any hypothesis of intension, the general concept of the intension of any predicate in any language for any person at any time has a clear, empirically testable sense. This general concept of intension may be characterized roughly as follows, leaving subtleties aside: the intension of a predicate '£)' for a speaker X is the general condition which an object y must fulfil in order for X to be willing to ascribe the predicate 'Q' to y. (We omit, for simplicity, the reference to a time t.) Let us try to make this general characterization more explicit. That X is able to use a language L means that X has a certain system of interconnected dispositions for certain linguistic responses. That a predicate 'Q' in a language L has the property F as its intension for X, means that among the dispositions of X constituting the language L there is the disposition of ascribing the predicate 'Q' to any object y if and only if y has the property F. (F is here always assumed to be an observable property, i.e., either directly observable or explicitly definable in terms of directly observable properties.) (The given formulation is oversimplified, neglecting vagueness. In order to take vagueness into account, a pair of intensions Flt F2 must be stated: X has the disposition of ascribing affirmatively the predicate 'Q' to an

Meaning and Synonymy in Natural Languages

43

object y if and only if y has Ft; and the disposition of denying 'Q' for y if and only if y has F2. Thus, if y has neither F1 nor F2, X will give neither an affirmative nor a negative response; the property of having neither Fx nor F2 constitutes the zone of vagueness, which may possibly be empty.) The concept of intension has here been characterized only for thingpredicates. The characterization for expressions of other types, including sentences, can be given in an analogous way. The other concepts of the theory of intension can then be defined in the usual way; we shall state only those for 'synonymous' and 'analytic' in a simple form without claim to exactness. Two expressions are SYNONYMOUS in the language L for X at time t if they have the same intension in L for X at t. A sentence is ANALYTIC in L for X at t if its intension (or range or truthcondition) in L for X at t comprehends all possible cases. A language L was characterized above as a system of certain dispositions for the use of expressions. I shall now make some remarks on the METHODOLOGY OF DISPOSITIONAL CONCEPTS. This will help to a clearer understanding of the nature of linguistic concepts in general and of the concept of intension in particular. Let D be the disposition of X t o react to a condition C by the characteristic response R. There are in principle, although not always in practice, two ways for ascertaining whether a given thing or person X has the disposition D (at a given time t). The first method may be called BEHAVIORISTIC (in a very wide sense); it consists in producing the condition C and then determining whether or not the response R occurs. The second way may be called the METHOD OF STRUCTURE ANALYSIS. It consists in investigating the state of X (at t) in sufficient detail such that it is possible to derive from the obtained description of the state with the help of relevant general laws (say of physics, physiology, etc.) the responses which X would make to any specified circumstances in the environment. Then it will be possible to predict, in particular, whether, under the condition C, X would make the response R or not; if so, X has the disposition D, otherwise not. For example, let X be an automobile and D be the ability for a specified acceleration on a horizontal road at a speed of 10 miles per hour. The hypothesis that the automobile has this ability D may be tested by either of the following two procedures. The behavioristic method consists in driving the car and observing its performance under the specified conditions. The second method consists in studying the internal structure of the car, especially the motor, and calculating with the help of physical laws the acceleration which would result under the specified conditions. With respect to a psychological disposition and, in particular, a linguistic disposition of a person X, there is first the familiar behavioristic method and second, at least theoretically, the method of a micro-physiological investigation of the

44

R. Carnap

body of X, especially the central nervous system. At the present state of physiological knowledge of the human organism and especially the central nervous system, the second method is, of course, not practicable.

6. THE CONCEPT OF INTENSION FOR A ROBOT

In order to make the method of structure analysis applicable, let us now consider the pragmatical investigation of the language of a robot rather than that of a human being. In this case we may assume that we possess much more detailed knowledge of the internal structure. The logical nature of the pragmatical concepts remains just the same. Suppose that we have a sufficiently detailed blueprint according to which the robot X was constructed and that X has abilities of observation and of use of language. Let us assume that X has three input organs A, B, and C, and an output organ. A and B are used alternatively, never simultaneously. A is an organ of visual observation of objects presented. B can receive a general description of a kind of object (a predicate expression) in the language L of X, which may consist of written marks or of holes punched in a card. C receives a predicate. These inputs constitute the question whether the object presented at A or any object satisfying the description presented at B is denoted in L for X by the predicate presented at C. The output organ may then supply one of three responses of X, for affirmation, denial, or abstention; the latter response would be given, e.g., if the observation of the object at A or the description at B is not sufficient to determine a definite answer. Just as the linguist investigating Karl begins with pointing to objects, but later, after having determined the interpretation of some words, asks questions formulated by these words, the investigator of A"s language L begins with presenting objects at A, but later, on the basis of tentative results concerning the intensions of some signs of L, proceeds to present predicate expressions at B which use only those interpreted signs and not the predicate presented at C. Instead of using this behavioristic method, the investigator may here use the method of structure analysis. On the basis of the given blueprint of X, he may be able to calculate the responses which X would make to various possible inputs. In particular, he may be able to derive from the given blueprint, with the help of those laws of physics which determine the functioning of the organs of X, the following result with respect to a given predicate 'Q' of the language L of Zand specified properties Fi and F2 (observable for X): If the predicate 'Q' is presented at C, then X gives an affirmative response if and only if an object having the property Fl is presented at A and a negative response if and only if an object with F2 is presented at A. This result indicates that the boundary of the intension of 'Q'

Meaning and Synonymy in Natural Languages

45

is somewhere between the boundary of Ft and that of F2- For some predicates the zone of indeterminateness between F1 and F2 may be fairly small and hence this preliminary determination of the intension fairly precise. This might be the case, for example, for color predicates if the investigator has a sufficient number of color specimens. After this preliminary determination of the intensions of some predicates constituting a restricted vocabulary V by calculations concerning input A, the investigator will proceed to make calculations concerning descriptions containing the predicates of V to be presented at B. He may be able to derive from the blueprint the following result: If the predicate ' P ' is presented at C, and any description D in terms of the vocabulary V is presented at B, X gives an affirmative response if and only if D (as interpreted by the preliminary results) logically implies Gu and a negative response if and only if D logically implies G2- This result indicates that the boundary of the intension o f ' P ' is between the boundary of Gy and that of G2- In this way more precise determinations for a more comprehensive part of L and finally for the whole of L may be obtained. (Here again we assume that the predicates of L designate observable properties of things.) It is clear that the method of structure analysis, if applicable, is more powerful than the behavioristic method, because it can supply a general answer and, under favorable circumstances, even a complete answer to the question of the intension of a given predicate. Note that the procedure described for input A can include empty kinds of objects and the procedure for input B even causally impossible kinds. Thus, for example, though we cannot present a unicorn at A, we can nevertheless calculate which response X would make if a unicorn were presented at A. This calculation is obviously in no way affected by any zoological fact concerning the existence or nonexistence of unicorns. The situation is different for a kind of objects excluded by a law of physics, especially, a law needed in the calculations about the robot. Take the law ly : "Any iron body at 60° F is solid". The investigator needs this law in his calculation of the functioning of X, in order to ascertain that some iron cogwheels do not melt. If now he were to take as a premise for his derivation the statement "A liquid iron body having the temperature of 60° F is presented at A", then, since the law lt belongs also to his premises, he would obtain a contradiction; hence every statement concerning X's response would be derivable, and thus the method would break down. But even for this case the method still works with respect to B. He may take as premise "The description 'liquid iron body with the temperature of 60° F ' (that is, the translation of this into L) is presented at B". Then no contradiction arises either in the derivation made by the investigator or in that made by X. THE DERIVATION CARRIED OUT BY THE INVESTIGATOR contains the premise just mentioned, which does not refer to an iron body

46

R. Carnap

but to a description, say a card punched in a certain way; thus there is no contradiction, although the law l t occurs also as a premise. On the other h a n d , in THE DERIVATION MADE BY THE ROBOT X, t h e c a r d p r e s e n t e d a t B

supplies, as it were, a premise of the form "y is a liquid iron body at 60° F " ; but here the law does not occur as a premise, and thus no contradiction occurs. X makes merely logical deductions from the one premise stated and, if the predicate l R ' is presented at C, tries to come either to the conclusion "y is R" or "y is not R". Suppose the investigator's calculation leads to the result that X would derive the conclusion "y is R" and hence that X would give an affirmative response. This result would show that the (causally impossible) kind of liquid iron bodies at 60° F is included in the range of the intension o f ' R ' for X. I have tried to show in this paper that in a pragmatical investigation of a natural language there is not only, as generally agreed, an empirical method for ascertaining which objects are denoted by a given predicate and thus for determining the extension of the predicate, but also a method for testing a hypothesis concerning its intension (designative meaning).6 The intension of a predicate for a speaker X is, roughly speaking, the general condition which an object must fulfil for X to be willing to apply the predicate to it. For the determination of intension, not only actually given cases must be taken into consideration, but also possible cases, i.e., kinds of objects which can be described without self-contradiction, irrespective of the question whether there are any objects of the kinds described. The intension of a predicate can be determined for a robot just as well as for a human speaker, and even more completely if the internal structure of the robot is sufficiently known to predict how it will function under various conditions. On the basis of the concept of intension, other pragmatical concepts with respect to natural languages can be defined, synonymy, analyticity, and the like. The existence of scientifically sound pragmatical concepts of this kind provides a practical motivation and justification for the introduction of corresponding concepts in pure semantics with respect to constructed language systems.

Y. Bar-Hillel in a recent paper (1954) defends the concept of meaning against those contemporary linguists who wish to ban it from linguistics. He explains this tendency by the fact that in the first quarter of this century the concept of meaning was indeed in a bad methodological state; the usual explanations of the concept involved psychologistic connotations, which were correctly criticized by Bloomfield and others. BarHillel points out that the semantical theory of meaning developed recently by logicians is free of these drawbacks. He appeals to the linguists to construct in an analogous way the theory of meaning needed in their empirical investigations. The present paper indicates the possibility of such a construction. The fact that the concept of intension can be applied even to a robot shows that it does not have the psychologistic character of the traditional concept of meaning.

6

Meaning and Synonymy in Natural Languages

47

BIBLIOGRAPHY Bar-Hillel, Y. 1954 "Logical Syntax and Semantics", Language 30, 230-237. Carnap, R. 1942 Introduction to Semantics (Cambridge, Mass.). 1952 "Meaning Postulates", Phil. Studies 3, 65-73. Naess, A. 1953 Interpretation and Preciseness (Oslo). Quine, W. V. O. 1951 "Two Dogmas of Empiricism", Philos. Review 60, 20-43. 1953 From a Logical Point of View (Cambridge, Mass.). White, M. G. 1950 "The Analytic and the Synthetic", in S. Hook, ed., John Dewey (New York).

Robert Rogers

A SURVEY OF FORMAL SEMANTICS

My purpose in this paper is to present an account of certain of the principal results that have been obtained in the field of formal semantics. These results will be stated in what from the logician's point of view is an informal way; that is, in stating them there will be little or no use of a precisely formalized language (though we shall of course speak about such languages). These results will, however, be stated as precisely as is possible within a non-formalized language. Taken together, my statements of these results will constitute what I believe to be a representative survey of what has been accomplished within the field of formal semantics. The paper will be divided into the following four parts: First, an introductory section in which I give a definition of the term 'formal semantics', together with a statement of certain of the leading concepts and distinctions within formal semantics. Second, I shall give statements of two diiferent basic concepts in terms of which much of semantical theory can be developed, and show how the concept of truth can be defined in terms of each of these concepts. These will be the concept of satisfaction, as developed by Alfred Tarski, and the concept of multiple denotation, as recently developed by Richard Martin. Third, I shall present two further concepts in terms of which the so-called ¿-CONCEPTS, viz., analyticity and its related concepts, can be defined. These will be the concept of a state-description, as developed by Rudolf Carnap, and the concept of an interpretation, as developed by John G. Kemeny. Fourth, and finally, I shall present what certain writers have taken to be the significance of formal semantics for problems of ontology. Reprinted from: Synthese 15 (1963), 17-56.

A Survey of Formal Semantics

49

I As the term 'formal semantics' is understood by those writers I am directing my attention to in this paper, it is the name of a certain kind of systematic inquiry into the problems of meaning and interpretation. More specifically, it is concerned with the problems of meaning in the sense of COGNITIVE, or DECLARATIVE meaning, as contrasted with such other types of meaning as emotive or exhortative meaning. Roughly speaking, a SEMANTICAL THEORY is a theory that provides us with a set of concepts by means of which we can give an account of the meaning of statements, or whole bodies of statements, and of the terms appearing within them. Now a FORMALIZED SEMANTICAL THEORY is one that proceeds with respect to a formalized language. Within such a theory, the semantical problems and concepts being dealt with are relativized to some well-defined language, called the OBJECT-LANGUAGE. A distinction is made between this language and the language in which the semantical analyses are being carried out, this latter language being called the META-LANGUAGE with respect to that given object-language. The object-language is always an example of what is called a FORMALIZED LANGUAGE, while the meta-language may or may not itself be a formalized language. Before I give an account of the nature of formalized languages, let me state why it is that formal semantics has come to use such languages. Principally, it is because of the clarity and precision that are made possible once one relativizes the problems of semantics to such languages. There is about them, and results based upon the use of them, a kind of definiteness which it is impossible to obtain when one is working with an ordinary language. And because, though formalized, such languages have much in common with ordinary languages, and can be made successively to approximate such languages in power of expression, semantic analyses carried out with respect to formalized languages are of interest not only to students of such languages, but also to those who are especially interested in the semantics of ordinary, unformalized languages. There is in addition a technical type of consideration which argues strongly for the use of formalized languages. This concerns the so-called SEMANTICAL PARADOXES. There are a number of such paradoxes known, each of which seems to lead to the impossible conclusion that a contradiction is true. These paradoxes seem to be forced upon us once we decide to carry out semantical investigations within an ordinary language. By carefully setting up a distinction between a formalized object-language and its meta-language, however, we can avoid the known paradoxes. Let me briefly state one such paradox, a version of the well-known paradox of the liar.

50

Robert Rogers

Consider the following sentence: The sentence on page 50, line 2, is not true. Clearly this sentence is true if and only if the sentence on page 50, line 2, is not true. But the sentence on page 50, line 2, is just this sentence itself. Thus we conclude that the sentence in question is true if and only if it is not true; that is, that it is both true and not true, both true and false. But this is a contradiction. Yet it seems that every step in the above argument is an admissible step within the logic of the ordinary English language. Until that language is more precisely specified than it has been heretofore, the conclusion seems inescapable that anyone who wishes to develop semantical theory within it is committed to this type of contradiction. As we shall illustrate later, however, the semantical paradoxes known to date can be successfully avoided if one has recourse to properly developed formalized languages. Let us now give an account of what a formalized language is. In order to do this, we make use of the distinction between an OBJECT-LANGUAGE and a META-LANGUAGE. The language being formalized, and thus being TALKED ABOUT, is called the OBJECT-LANGUAGE; the language within which we formalize this language, that is, the language we use for this purpose, is called the META-LANGUAGE. Let us call the object-language iL\ and the meta-language 'Af'. In order to formalize L, within M we first lay down rules which determine the SYNTAX of L; and then rules which determine the SEMANTICS of L, and thus provide an interpretation of L. As the first of our syntactical rules, we give a full specification of the PRIMITIVE SIGNS of L, that is, its alphabet and punctuation signs. Such a rule provides first for those signs that are to be used as punctuation signs and logical connectives; e.g. parentheses, a comma, a sign to play the role of negation, and a sign to play the role of material implication. This rule also specifies which signs are to be used as subject matter variables and constants. Then a FORMATION RULE is introduced, for the purpose of defining which combinations of these primitive signs of L are accepted as well-formed formulas of L. Usually this rule is in the form of a recursive definition. When it takes this form, first the most elementary or atomic types of wffs (we use 'wff' as an abbreviation of 'well-formed formula') are given a general characterization, and then the various means by which the more complex types of wffs are built up out of simpler wffs are enumerated. Next, definitions of bound and free occurrences of variables are given, and those wffs of L (if any) which contain no free occurrences of variables are identified as the SENTENCES of L. Finally, among one's list of rules determining the syntax of L one may include a characterization of certain of the wffs of L as AXIOMS, and then specify RULES OF INFERENCE by means of which one may legitimately infer certain wffs from others. And one

A Survey of Formal Semantics

51

may also include rules which permit us to abbreviate certain wfifs in certain ways. If we add no more rules than these syntactical rules, our language L is not yet really a language at all, but merely what is called a 'calculus', or an uninterpreted system. In order that L be truly a LANGUAGE, we shall have to provide an interpretation for L. This we do by laying down certain SEMANTICAL RULES for L in our meta-language M. There are various ways of doing this, and I shall examine a number of them later, in our next section. Still, each of these ways presupposes that our meta-language M has a number of certain well-defined features, and I specify these now. Within M we are to give an interpretation of L. To do this, within M we must first be able to talk about any and all expressions of L. We must therefore have within M a way of forming NAMES for any and all expressions of L. The usual means of accomplishing this end is to include within M specific names for each of the primitive symbols of L, together with an operation sign for concatenation. By putting the concatenation sign between any two signs of M which stand for given expressions a and b of L, we form an expression in M which stands for the result in L of putting the two expressions a and b together. For example, let ' P ' and *x' be two primitive symbols of L; let 'pee' and lex' be their respective names in M; and let ' such that for all xeAa, all pel1, and all iel,f(x) (p) (/) = 1 if and only ifp(i) = 0. (3h) G s (""necessarily"") is that function / in ((2 J ) 2l ) Aa such that for all xeAm, all pel1, and all iel, f(x) (p) (i) = 1 if and only i f p ( J ) = 1 for all jel. (We thus employ STANDARD, or UNIVERSAL, or LEIBNIZIAN necessity, amounting to truth in all possible worlds.)

Richard Montague

100

It is because the categories of basic expressions overlap that we must have separate functions G0,..., G8, rather than a single function assigning denotation functions to all basic expressions.

5. SYNTACTIC CATEGORIES

In this section we shall extend the basic syntactic categories B0, B1,..., Be to the full syntactic categories C 0 (or the set of name phrases), C x (or the set of formulas), ..., C 8 (or the set of adjective phrases). These sets will be 'introduced', in a sense that will be made precise below, by the following SYNTACTICAL (or GRAMMATICAL) rules, S1-S17; let it only be said that C0,...,CS will be defined in such a way as to make S1-S17 true. (I use '&' as an abbreviation of 'and' and as an abbreviation 'if... then'). Rule of basic expressions: 51. Bo £

£ C8.

Rules corresponding to functional application: 52. SeC2 & aeC0 & id, a,