Analytic and Synthetic Statements

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The distinction between analytic and synthetic judgments was first made by Immanuel Kant in the introduction to his Critique of Pure Reason. According to him, all judgments could be exhaustively divided into these two kinds. The subject of both kinds of judgment was taken to be some thing or things, not concepts. Synthetic judgments are informative; they tell something about the subject by connecting or synthesizing two different concepts under which the subject is subsumed. Analytic judgments are uninformative; they serve merely to elucidate or analyze the concept under which the subject falls. There is a prima facie difficulty as to how a judgment can be simultaneously about an object, uninformative in relation to it, and explicative of the concepts involved, but this question will be examined later.

Kant associated this distinction with the distinction between a priori and a posteriori judgments. The one distinction was taken to cut across the other, except that there are no analytic a posteriori judgments. The remaining three classifications were, in Kant's opinion, filled; there are analytic a priori judgments, synthetic a posteriori judgments, and synthetic a priori judgments. Since Kant there has been little argument concerning the first two of these, but considerable argument and opposition, chiefly from empiricists, about the last. Analytic a priori and synthetic a posteriori judgments correspond roughly to logically and empirically true or false judgments. In distinguishing them, Kant was following in the steps of Gottfried Wilhelm Leibniz and David Hume, both of whom had made a similar distinction, although in different terms. Leibniz had distinguished between truths of fact, guaranteed by the principle of sufficient reason, and truths of reason, guaranteed by the principle of contradiction. The latter were such that their denial involved a contradiction; they could indeed be reduced to identical propositions via chains of definitions of their terms. Hume had likewise distinguished between matters of fact and relations of ideas. The former were merely contingent, while the latter were necessary and such that their denial involved a contradiction. Kant's innovation was to connect this distinction with the two further distinctions between the analytic and the synthetic and the a priori and the a posteriori.

It should be noted that Kant's distinction between the analytic and the synthetic was made in terms of judgments and concepts. This gave it a psychological flavor for which it has been criticized by many modern philosophers. The notion of judgment is ambiguous between the act of judging and what is judged. One problem is how to extend what Kant said so that it applies only to what is judged or to propositions. Furthermore, an implication of Kant's formal account of the distinction was that it is limited in its application to subject-predicate judgments (although it was also one of Kant's doctrines that existential judgments are always synthetic).

Kant's Criteria and Use of the Analytic/Synthetic Distinction


Apart from the general distinction, Kant offered two criteria for it. According to the first criterion, an analytic judgment is one in which the concept of the predicate is contained (although covertly) in the concept of the subject, while in a synthetic judgment the concept of the predicate stands outside the concept of the subject. According to the second criterion, analytic judgments are such that their denial involves a contradiction, while this is not true of synthetic judgments of any kind. Kant was here following his predecessors, although, with Leibniz, he did not suggest that analytic truths can be reduced to simple identities. This criterion can scarcely be said to suffice as a definition of an analytic statement, although it may provide grounds for saying whether a judgment is analytic or not. It will do the latter if it can be assumed that all analytic judgments are logically necessary, since reference to the principle of contradiction may provide the basis of logical necessity.

The first criterion seems on firmer ground in this respect, since it offers what seems to be a formal characteristic of all analytic judgments. It specifies what we must be doing in making an analytic judgment, in terms of the relations between the concepts involved. It has been objected that the idea of one concept being contained in another is also a psychological one, but this was certainly not Kant's intention. The point may perhaps be expressed in terms of meaning. When we make an analytic judgment, what we mean when we invoke the predicate concept is already included in what we mean by the subject concept. Just as the notion of a judgment is ambiguous, so a concept can mean either the act of conceiving or what is conceived, and it is the latter which is relevant here. By this criterion, therefore, a judgment is analytic when, in judging about something, what we judge about it is already included in what is meant by the term under which we subsume the subject. Kant assumed that all judgments of this kind are a priori, presumably on the grounds that their truth can be ascertained merely by considering the concepts involved, without further reference to the facts of experience.

characteristics of analytic statements

Kant's criterion could be applied only to statements of subject-predicate form, and could not, therefore, be used to make an exhaustive distinction between all statements. If Kant's distinction is to be of use, however, it must be extended to cover propositions or statements and, moreover, statements of any form, not just those of subject-predicate form. If an analytic judgment is of an object, an analytic statement must similarly be about the object or objects referred to by the subject expression. Analytic statements cannot, therefore, be equated with definitions, for the latter are surely about words, not things. It has sometimes been said (for instance, by A. J. Ayer in his Language, Truth and Logic ) that analytic statements make clear our determination to use words in a certain way. Apart from the fact that the use of words cannot be a simple matter of choice, what Ayer says cannot be the main function of analytic statements, since this would be to identify them with (possibly prescriptive) definitions. If we learn something about the use of words from analytic statements, this must at most be indirect.

Analyticity, a property of statements

We have seen that Kant's point of view might be represented as saying that only the meaning of the terms involved, the nature of the corresponding concepts, makes the judgment true. It might, therefore, seem feasible that an analytic statement could be characterized as a statement about something which says nothing about the thing but is such that the meanings of the words involved make it true. To be more exact, it would be the meanings of the words involved in a sentenceany sentence that expresses the statementthat make that statement true. It is important to stress the words "any sentence," for analytic truth can be a feature only of statements. It cannot be a feature of sentences per se, nor can it be limited to sentences in a given language (as Rudolf Carnap in effect supposes). Truth is a property of statements, not sentences, and the same must be the case with analytic truth. No account of analyticity which explains it in terms of what is the case with regard to sentences in any one language will do. If someone who says "All bodies are extended" makes an analytic statement, so will anyone who says the same thing in any other language.

Analyticity as a function of the meanings of words

What is meant by saying that the meanings of the terms involved make a statement true? Are analytic truths those which follow from the meanings of the words involved; that is, from their definitions? This cannot be so, since all that can follow from a definition is another definition, and how, in any case, can a statement about things follow directly from one about words? If analyticity is connected with meaning, it must be more indirectly. Friedrich Waismann has suggested that an analytic truth is one which is so in virtue of the meanings of the words involved. But the words "in virtue of" are themselves vague. It has been held by certain empiricists that "All bodies are extended" is analytic if and only if we use "body" in exactly the same way we use "extended thing"; that is, if we attach the same meaning to each expression. Nevertheless, the truth of "All bodies are extended" does not follow simply from the fact that the expressions "body" and "extended thing" have the same meaning, for the substitution of expressions equivalent in meaning leaves one with a statement corresponding in form to the law of identity. Hence, the original statement will be true only if the law of identity holds. In other words, an analytic statement will be one whose truth depends not only on the meanings of the words involved but also on the laws of logic. This raises the question of the status of these laws themselves. It is sometimes claimed that they, too, are analytic; but this cannot be so if a definition of analyticity involves reference to the laws of logic.

Analyticity as a function of the laws of logic

The necessity of referring to the laws of logic in any account of analyticity has been noted in modern times by many philosophers. Waismann, for example, eventually defines an analytic statement as one which reduces to a logical truism when substitution of definitional equivalents is carried out. Gottlob Frege had much earlier defined an analytic truth as one in whose proof one finds only "general logical laws and definitions," and he had sought to show that arithmetical propositions are analytic in this sense. Both of these accounts make reference to logical truisms or logical laws. Whatever the status of these, it certainly seems that analytic statements must depend for their validity not only on the meanings of the terms involved but also on the validity of the laws of logic; and these laws cannot themselves be analytic.

Objections to the Distinction

the problem of synonymy

Nevertheless, objections to the notion of analyticity have been made, particularly by Willard Quine, on the basis of supposed difficulties about meaning itself, and not merely on those about the status of the truths of logicalthough here, too, Quine has found difficulties. He distinguishes between two classes of analytic statements. There are, first, those which are logically true, such as "No unmarried man is married"; these are statements which are true and which remain true under all reinterpretations of their components other than the logical particles. Second, there are those, such as "No bachelor is married," which can be turned into logical truths by substituting synonyms for synonyms. It is the second kind of analytic statement that raises problems here, and these problems arise from the notion of synonymy or, to be precise, cognitive synonymy; that is, synonymy that depends on words having the same meaning for thought, as opposed to merely applying to the same things. The notion of definition which other philosophers have invoked in this connection rests, Quine maintains, on that of synonymy. How is this to be explained?

Quine's difficulties here are associated with general difficulties about synonymy raised by himself and Nelson Goodman in the effort to embrace a nominalism that does not involve the postulation of so-called meanings, and to push as far as possible the thesis that language is extensional; that is, such that it can be built up from variables and an indefinite set of one and many-place predicates, so that complex sentences are related to atomic sentences by truth-functional relationships and by quantification. In such a language, sameness of meaning might be equivalent to extensional equivalence, such that any two extensionally equivalent expressions are interchangeable salva veritate ; that is, leaving unchanged the truth value of the statements in which they occur, wherever the expressions occur. The outcome of Goodman's argument in this connection is that since there may always be some occurrence in which the two expressions are not interchangeable salva veritate, no two expressions are identical in meaning. Quine himself recognizes something of this and has explored the restrictions which must be put upon the general thesis.

In the present connection, Quine explores the possibility that synonymity might be explained by interchangeability salva veritate except within words. But the interchangeability of, say, "bachelor" and "unmarried man" in this way may be due to accidental factors, as is the case with "creature with a heart" and "creature with kidneys." If it is the case that alland onlycreatures with a heart are creatures with kidneys, this is due simply to the fact that, as it happens, the two expressions always apply to the same things and not to any sameness of meaning. How do we know that the situation is not the same with "bachelor" and "unmarried man"? It is impossible to reply that it is because of the truth of "Necessarily, alland onlybachelors are unmarried men," for the use of "necessarily" presupposes a nonextensional language. Furthermore, a sense has already been given to the kind of necessity involved here: analyticity. Hence, while cognitive synonymy might be explained in terms of analyticity, to try to explain analyticity in terms of cognitive synonymy would involve something like circularity.

Quine argues that similar considerations apply to attempts, such as Carnap's, to deal with the matter in terms of a semantic rule. Quine then considers the further possibility that, given that the truth of statements in general rests upon a linguistic component and a factual component, an analytic statement might be one in which the factual component is null. This, while apparently reasonable, has not, he objects, been explained; and the attempt by positivists to do so by reference to the verification theory of meaning (with its assumption that there are basic propositions in which the factual component is all that matters and, on the other hand, that there are analytic propositions in which the linguistic component is all that matters) involves reductionism, an unjustified dogma.

Synonymy and meaning

A possible objection to Quineone in effect made by H. P. Grice and P. F. Strawsonis that his difficulty over synonymy involves a refusal to understand. There is a family of terms that includes analyticity, necessity, and cognitive synonymy, and Quine will not accept, as explanations of any one of them, accounts that involve reference to other members of the family. On the other hand, to go outside the family in one's explanations, as is involved in having recourse to extensional equivalence, is necessarily an inadequate explanation. This is a situation that frequently occurs in philosophy, wherever one is confronted with families of terms between which and any other family there is a radical or categorical distinction. This is perhaps an oversimplification of the situation, true though it is. It must be remembered that Quine's basic urge is to do without meanings, so as not to introduce unnecessary entities into our ontology. The failure of this particular enterprise of defining synonymy is, however, in fact, a demonstration of its futility. Meaning is a notion which must be presupposed rather than explained away in this connection.

the boundary between analytic and synthetic statements

Quine also has a second thesis in connection with analyticity, a thesis that has been echoed in different forms by other philosophers. It is a quite general thesis, in the sense that it does not depend on considerations about synonymy and is not, therefore, restricted to statements whose truth turns on synonymy. This thesis states that even if a distinction could be drawn between analytic and synthetic statements or between logical and factual truth, it is impossible to draw a sharp boundary between them. The contrary supposal rests on the dogma of reductionism already referred to. On that thesis, there is clearly an absolute distinction to be made. The denial of the dogma entails that there can be, at the most, a relative distinction. Within any particular system it is possible to distinguish those statements, those of logic and mathematics, which we should be extremely reluctant to give up and those, on the other hand, which we should be ready to give up if required to do so. The former are entrenched because of their close connections with other elements of the system. It has often been pointed out that the giving up of some high-grade scientific statements would involve the giving up with them of whole scientific systems. On Quine's view, the situation is worse, but not intrinsically different, with logical statements. There are no statements that depend for their truth on a direct confrontation with experience. The best that can be produced in the way of a distinction between different kinds of statements is a relative distinction between those which are more or less entrenched. No absolute and sharp distinction between analytic and synthetic statements can be drawn. Quine's conventionalism here reflects pragmatist tendencies.

One possible reply to this thesis is that the rejection of the dogma of reductionism does not by itself dispose of an absolute distinction of this kind. Even if it is accepted that there are no statements in which the factual component is everything, it does not follow that there are no statements in which the linguistic component is everything. Despite what Quine says, the thesis that there is a distinction between analytic and synthetic statements is independent of that of reductionism. Grice and Strawson have also attempted to deal with the issue by making a distinction in terms of the responses to attempts to falsify a statement. Analytic statements are those that, in a falsifying situation, demand a revision in our concepts; synthetic statements are those that demand a revision in our view of the facts. It has frequently been pointed out that it is possible to preserve a scientific statement against falsifying circumstances by making it logically true and thus immune to falsification. In doing this, we revise our concepts but not our view of the facts. It is clear that Quine could not accept this suggestion as such, since it presupposes that an answer has been given to the first of his problemsthe definition of analyticityin terms of notions like those of a concept or meaning. But, given that Quine's thesis is untenable in this first respect, there is no reason for denying its untenability in the second.

statements that are neither analytic nor synthetic

Other reasons for dissatisfaction with a sharp distinction between analytic and synthetic statements have been offered by other philosophers. Waismann, for example, has maintained that there are some statements which do not admit of a clear classification; for instance, "I see with my eyes." In this case there are reasons for saying that it is analytic, since whatever I see with might be called "eyes"; on the other hand, it might be said that it is a matter of fact that it is with my eyes that I see. Hence, Waismann maintains, such statements are neither analytic nor synthetic, properly speaking. The objection to this, as has been pointed out by W. H. Walsh, is that Waismann has failed to consider the contexts in which such statements are made. The sentence "I see with my eyes" may be used in one context to express an analytic statement and in another to express a synthetic one. The fact that the same sentence may have different uses and that the analyticity or syntheticity of a statement is a function of those uses (a statement is just the use of a sentence) shows nothing about the necessity of abandoning the analytic-synthetic distinction.

are there any analytic statements?

Emphasis of the point that analyticity is a function of use prompts the question of whether sentences which purport to express analytic statements have a use at all and whether, in consequence, there are any analytic statements. It has been emphasized from Kant onward that analytic statements are trivial, and similar things were said even before Kantby John Locke, for instance. The truth of an analytic statement makes no difference to the world. It is, therefore, difficult to see why anyone should ever make an analytic statement. A possible reply is that such a statement might be made in order to clarify something about the concepts involved. If the statements in question are about concepts, however, rather than about the thing or things referred to by the subject expression, why are they not simply definitions? Definitions are not in themselves analytic statements, whatever their exact status. It could thus be argued that any statement which has a use either provides information about things or about the meanings of words, and in either case the statement would be synthetic, or at least not analytic. The only viable function remaining for the term analytic would be as a term of logical appraisal, not as a classificatory expression. That is to say, the use of the words "That is analytic" would not be to classify the statement in question, but to say, in effect, "You have not said anything."

Whether or not this is plausible in itself, the crucial question remains: How is it possible for a statement both to be about something and to elucidate the concepts involved? (The question is probably more crucial for judgments than for statements, since it might seem obvious what a judgment must be about, while the criteria of "aboutness" are less obvious in the case of statements.) The issues are simple. A statement is one use of a sentence, and an analytic statement is such a use that conforms to certain conditionstwo of which are that it says nothing about its subject and that its truth depends at least in part on the meanings of the words involved. If this is so, it cannot be used to make clear those meanings. If an analytic statement does serve to make clear those meanings to someone, this must be an incidental and unintended consequence of its use, not an essential part of that use. On the other hand, if the triviality of analytic statements is accepted, there can be no argument to show that their use is impossible, for there is no reason why a statement, if it is to be about something, should also say something about that thing. The use of such statements would simply lack point.

A Possible Way of Making the Distinction

Ludwig Josef Johann Wittgenstein pointed out in the Tractatus Logico-Philosophicus (4.4611) that tautologies are senseless but not nonsense. By "senseless" he meant that they do not pick out any determinate state of affairs that makes a difference to our view of the world. They are, in effect, trivial. They are not nonsense, however, because they are part of our symbolism, just as "0" is part of the symbolism of arithmetic, although it is useless for counting. Given a system of symbolism, or a language, it must always be possible to construct sentences that could be used to assert analytic truths or falsehoods (contradictions), whether or not there would be any point in doing so. This possibility is a necessary consequence of the nature of language. A language, however, is not just a system of symbols; it is something whose function is, among other things, to state and communicate facts. Hence, it is possible to say that, given that these sentences have a use, the truth of their uses (or, in the case of contradictions, their falsity)that is, the truth of the relevant statementsis a necessary condition of the employment of the language from which the corresponding sentences are drawn, or of any language in which there are sentences with the same meaning. More briefly, analytic statements will be those whose truth is necessary to the employment, as expressed in language, of the system of concepts on which they depend. Any statement of which this is not true will be synthetic. Of these other statements, many will be such that their truth is not necessary in any way, but there may be others whose truth is necessary in some way other than that of analytic statementsas Kant maintained about the synthetic a priori.

See also A Priori and A Posteriori; Ayer, Alfred Jules; Grice, Herbert Paul; Hume, David; Kant, Immanuel; Locke, John; Quine, Willard Van Orman; Strawson, Peter Frederick; Wittgenstein, Ludwig Josef Johann.



Ayer, A. J. Language, Truth and Logic, 2nd ed. London: V. Gollancz, 1946. Ch. 4.

Carnap, Rudolf. Introduction to Semantics. Cambridge, MA: Harvard University Press, 1942.

Frege, Gottlob. Foundations of Arithmetic. Translated by J. L. Austin. Oxford: Blackwell, 1950.

Hume, David. Treatise of Human Nature. Oxford: Clarendon Press, 1896. I.iii.1.

Kant, Immanuel. Critique of Pure Reason. Translated by Norman Kemp-Smith. London, 1953. Especially the introduction.

Leibniz, G. W., throughout his works. Especially Monadology, 31ff.

Pap, Arthur. Semantics and Necessary Truth. New Haven, CT: Yale University Press, 1958. Useful discussions of general issues.

Quine, W. V. From a Logical Point of View. Cambridge, MA, 1953. Ch. 2.


Goodman, Nelson. "On Likeness of Meaning." Analysis 10 (1) (October 1949): 17.

Grice, H. P., and P. F. Strawson. "On Defence of a Dogma." Philosophical Review 65 (March 1956): 141158.

Hamlyn, D. W. "Analytic Truths." Mind, n.s., 65 (259) (1956): 359367.

Hamlyn, D. W. "On Necessary Truth." Mind, n.s., 70 (280) (1961): 514525.

Putnam, Hilary. "The Analytic and the Synthetic" In Minnesota Studies in the Philosophy of Science. Minneapolis, 1962. Vol. III, pp. 358397.

Waismann, Friedrich. "Analytic and Synthetic." Analysis 10, 11, and 13 (19491952). A series of articles.

Walsh, W. H. "Analytic and Synthetic." PAS 54 (1953/1954): 7796.

White, M. "Analytic-Synthetic: An Untenable Dualism." In John Dewey: Philosopher of Science and Freedom, edited by Sydney Hook, pp. 316330. New York, 1950.

D. W. Hamlyn (1967)