Philosophical Studies

Essays in memory of L. Susan Stebbing

Various

• Éditeur: Routledge
• Année: 2022
• ISBN:
  9781000647211
• Édition: 1
• Sujet: Philosophie
• Sous-sujet: Logik in der Philosophie

First published in 1948, Philosophical Studies presents a collection of essays written by friends and colleagues of Professor L. Susan Stebbing in the Aristotelian Society. Most of these essays do not bear directly on Professor Stebbings' work, but they deal with problems which she discussed time and again at the Society's meetings. It explores themes like moral ends and means; reflections occasioned by ideals and illusions; reason in history; the logic of elucidation; logic and semantics; philosophy of nature; and epistemology and the ego-centric predicament. This book is a must read for students and scholars of Philosophy.

LOGIC AND SEMANTICS

BY MAX BLACK

DOI: 10.4324/9781003273653-9

Sie sprechen eine Sprache

Die ist so reich und schön

Doch keiner der Philologen

Kann diese Sprache verstehen

I Introduction

THE technical language of “semantics”¹ and the wider subject of “semiotic” of which it is a part must be agreed to be both rich and mathematically elegant—if the shade of Heine will pardon this mis-application of his rhyming sentiment. Yet many beside philologists are puzzled today by the new language and the discipline whose instrument it is. We may discount as much as we please the mere technical difficulties of mastering a symbolism which makes the language of Vrincipia Mathematica seem transparently lucid by comparison. There remains, even for those philosophers for whom gothic letters are no impediment, a more serious cause for disquiet. If the interest aroused by the birth and growth of semantics has been tinged with perplexity, the reason is largely the difficulty of understanding the full import of the primitive assumptions which determine the character of the subject and its potential usefulness.

1 The best elementary exposition of semantics is included in Professor R. Carnap’s monograph, Foundations of Logic and Mathematics (Encyclopedia of Unified Science, vol. i, No. 3, Chicago, 1939). Professor Alfred Tarski’s article on “The semantic conception of truth and the foundations of semantics” (Philosophy and Phenomenological Research, vol. 4, pp. 341-37£) is very useful, likewise Professor Charles Morris’s Foundations of the Theory of Signs (Encyclopedia of Unified Science, vol. 1, No. 2, 1938) which provides a general setting for the whole subject. A more exact exposition is Carnap’s Introduction to Semantics (Harvard University Press, 1942). I shall refer to these works by the abbreviations, ‘F.L.M.’, ‘S.C.T.’, ‘F.T.S and ‘I.S.’, respectively. In referring to Carnap’s earlier Logical Syntax of Language (English ed., 1937) 1 shall use ‘1.5.1.’

It is, of course, easy to forget that semantics has many precisely distinguished subdivisions—and, so forgetting, to submit irrelevant criticism.

It would be idle, for instance, to complain that in pure semantics the crucial terms receive no definition, being introduced into the discussion by means of rules or postulates which determine only how the words are to be used in the subsequent deductive elaboration of a system defined by those very same rules; or to lament the fact that in pure semantics the objects under discussion are whatsoever elements may happen to satisfy the axioms—“signs” only by proleptic courtesy. For such abstractness and indefiniteness of reference are necessary in any discipline which aspires to be “pure”; the hopes of positive achievement in semantics, qua formal algebra of meaning, rest upon just such self-imposed limitations; and to charge it, in the mathematical aspects of its work, with lack of empirical reference would be quite to misconstrue its purposes.

But semantics is hardly interesting enough as pure mathematics to be pursued for its own sake; and, but for the wider claims of philosophical relevance which have been made on its behalf, the subject would have aroused little interest outside the ranks of specialists in symbolic logic. When a well-wisher claims that “the recent discovery of semantics is of fundamental philosophical importance”¹ it must be presumed that the reference is to descriptive semantics rather than to a branch of pure mathematics. The department of semantics for which such claims of philosophical relevance are made must then be prepared, like any other empirical discipline, to demonstrate the adequacy of its basic concepts and the fruitfulness of its empirical and analytical procedures in the solution of the problems which define its purposes.

1 A. Hofstadter, “On semantic problems,” Journal of Philosophy, 355 (1938), 232.

A comparison of descriptive semantics with some other empirical subject—the theory of optics, perhaps, or the psychology of sign-using behaviour—leaves an impression of relative poverty of factual data and conceptual analysis. The basis for the three-fold analysis of the sign-using situation into sign-vehicle, designatum, and interpretant (“that which acts as a sign, that which the sign refers to, and that effect on some interpreter in virtue of which the thing in question is a sign to that interpreter”²) seems to be nothing more searching or epistemologically sophisticated than common observation. And this simple conceptual framework becomes still further attenuated in semantics where all reference to the interpretant, the locus of all that is distinctively human in the use of signs, is excluded by definition. When a still more advanced level of abstraction yields the subject of syntax, in which reference is made neither to designata (extra-linguistic entities) nor to interpretants (acts of interpretation) Berkeley’s quip about the “ghosts of departed quantities” takes on a new meaning.

2 Charles Morris, F.T.S., 3.

Initial hesitations such as these—and more specific qualms concerning the usefulness of the blanket application of primitive terms such as “designatum” to a heterogeneous diversity of items—are best resolved by reference to the degree of success of the new subject in the solution of its problems. But what are these problems—apart from the interesting, but for present purposes irrelevant technicalities of pure semantics?

An answer is suggested by Professor Hofstadter’s claim that “with the appearance of semantics as a new scientific discipline, those problems which could not be handled with the apparatus provided for in earlier statements of logical empiricism are now in the way of receiving definite treatment.”¹ For among the most important of such problems I take to be those that have in the past troubled all plausible versions of empiricism; those which arise whenever the attempt is made to account, in a manner consistent with exclusive reliance upon experience as a source of knowledge, for the privileged cognitive status of the so-called “necessary” truths of mathematics, logic, or for that matter, philosophy itself. “Logical empiricists” of the Vienna School, inspired by the stimulatingly oracular pronouncements of the earlier Wittgenstein, have constantly sought some linguistic interpretation of “necessary truth”; the promise offered by semantics of completing what has been called the ‘vindication of analyticality”² accounts for the honoured place of the subject in the affections of those who wish to be consistent empiricists.

1 A. Hofstadter, Ibid. 2 G. Bergmann, Mind, 53, 243.

Instead of making further preliminary comment, while loitering at the entrance to semantics, the more useful procedure suggests itself of tracing in detail the contributions of the new subject to the linguisitic interpretation of necessary truth and more particularly, for the purpose of this paper, to the linguistic interpretation of logic.

But here we meet an initial difficulty. In spite of the philosophical importance of the thesis that logic can be subsumed without remainder under semantics, it is impossible to find either a sufficiently clear statement of the meaning of the thesis or a reasoned defence of its truth.

My first task in this paper should be, then, to try to formulate with reasonable precision a claim of the linguistic character of logic, in a manner conforming to the intentions of logical empiricists. I shall be content, however, to do this for a single illustrative proposition belonging to logic; the aim will be to test the plausibility of “the linguistic thesis” (as I shall say by way of abbreviation) in its application to a particularly simple and perspicuous example. Since the simplification of semantical method which this procedure will require need not involve misrepresentation of the methods applicable to more complex instances, we may hope that the conclusions may also apply to the more general thesis.

The sections which follow are arranged in the following way: First (section 2) I reproduce some statements made by Professor Carnap (to whose views the discussion will be confined) in order to establish significant variations in the linguistic thesis according as logic is identified either with syntax or with semantics. Next (section 3) I describe the simple proposition that is to serve as a test-case for the validity of the linguistic thesis, and meet some preliminary objections. In section 4, a syntactical version of the linguistic thesis is described in a presentation free from all unnecessary technicalities. Section £ outlines criticisms of the syntactical version. Finally, in section 6, I try to show that the semantical version of the linguistic thesis is, in certain essential respects, identical in import with the syntactical version, and needs, therefore, to answer the same objections.

In view of the restriction of the discussion to a particular application of semantics, it may be as well to say explicitly that I have no wish to belittle the value of a mathematical approach to the morphology of linguistic systems. Some of the methods already developed (for instance by Godel and Tarski) have considerable interest in the study of the structure of deductive systems. But we are here concerned with the philosophical value of semantics—which has yet to be established.

II Carnap’s formulations of the linguistic thesis

It will be convenient to assemble a number of alternative statements of the type of position to be further examined in this paper; I have chosen passages from books written by Professor Carnap¹ at different stages in the development of his opinions concerning the functions of “scientific philosophy” and its methods of “logical analysis.”

1 Carnap has written the most fully and explicitly upon these topics. But his views are, of course, shared by many logical empiricists and others.

“…we must acknowledge,” says Carnap, “that all questions of logic (taking this word in a very wide sense, but excluding all empirical and therewith all psychological reference) belong to syntax. As soon as logic is formulated in an exact manner, it turns out to be nothing other than the syntax either of a particular language or of languages in general.” (L.S.L., 233; italics in original).

“… ‘non-formal logic’ is a contradictio in adjecto. Logic is syntax.” (1.5.1., 259.)

These quotations are typical of many statements in the Logical Syntax of Language in which logic is summarily identified with syntax. A related insistence, common to positivists from Hume onwards, is that logic is non-factual; or, as Carnap more explicitly says, logical and mathematical theorems

“…do not possess any factual content. If we call them true, then another kind of truth is meant, one not dependent upon facts”² (F.L.M., 2.)

2 The further arguments of the monograph make it clear that Carnap intends to establish the “theorems of logic and mathematics” as what is technically described as “L-true statements of semantics.” (Cf. F.L.M., 15.)

In Carnap’s more recent work, reference to semantics almost, but not quite, replaces the earlier reference to syntax:

“… logic, in the sense of a theory of logical deduction and thereby of logical truth, is a special part of semantics.” (I.S., £6.)

“…. logic is a special branch of semantics… logical deducibility and logical truth are semantical concepts. They belong to a special kind of semantical concepts which we shall call L-concepts.” (I.S., 56.)

But we are also told, in a similar context, that the equation of logic with semantics

“… does not contradict the possibility of dealing with logical deduction in syntax also.” (I.S., 60.)

As syntax is a special branch of semantics (distinguished by the absence of explicit reference to designata) there need be no inconsistency between the later and the earlier formulations. The earlier statements were made at a time when Carnap did not yet hold reference to extra-linguistic designata, which is characteristic of semantics, to be an acceptable part of the new disciplines which were to replace “the inextricable tangle of problems which is known as philosophy”¹ (L.S.L., 279). His gradual relaxation of the methodological restrictions necessitated by earlier positivist criteria of meaningfulness of utterance has clearly not shaken his acceptance of some form of what I am calling a “linguistic interpretation” of logic; the “theory of logical deduction” is still, as in the earlier days, regarded as “not dependent upon facts” because it deals, at least in part, with the consequences of linguistic rules. The intelligibility and plausibility of such a doctrine clearly depend upon the extent to which its advocates can make precise the senses of logic, language and dependence upon language to which they are committed; and for this purpose of mere clarification of the linguistic thesis, the shift of emphasis from semantics to syntax is no less significant than the constancy of the general mode of approach. It will be a major concern of this paper to discover what addition is made to the plausibility of the linguistic thesis by the admission of semantics into the company of reputable philosophical disciplines.

1 Cf. the characteristic early statement “… all theses and questions of logical analysis and therefore all theses and questions of philosophy (in our sense of this word) belong to logical syntax. The method of logical syntax, that is, the analysis of the formal structure of language as a system of rules, is the only method of philosophy.’5 (Philosophy and Logical Syntax, 99.)

First, however, let us pause to ask what Carnap means by logic.

It seems that he wishes the term to be used so broadly as to cover not only the theory of valid deduction and the construction of “modal” logics but even questions, more commonly assigned to metamathematics, concerning the structural relations between axiom systems (I.S.I., 233). But in any case, in presenting an analysis of propositions belonging to wha...