analytic–synthetic distinction the distinction, made famous by Kant, according to which an affirmative subject-predicate statement (proposition, judgment) is called analytic if the predicate concept is contained in the subject concept, and synthetic otherwise. The statement ‘All red roses are red’ is analytic, since the concept ‘red’ is contained in the concept ‘red roses’. ‘All roses are red’ is synthetic, since the concept ‘red’ is not contained in the concept ‘roses’. The denial of an affirmative subject-predicate statement entails a contradiction if it is analytic. E.g., ‘Not all red roses are red’ entails ‘Some roses are both red and not red’. One concept may be contained in another, in Kant’s sense, even though the terms used to express them are not related as part to whole. Since ‘biped’ means ‘two-footed animal’, the concept ‘two-footed’ is contained in the concept ‘biped’. It is accordingly analytic that all bipeds are two-footed. The same analytic statement is expressed by the synonymous sentences ‘All bipeds are two-footed’ and ‘All two-footed animals are two-footed’. Unlike statements, sentences cannot be classified as analytic or synthetic except relative to an interpretation. Witness ‘All Russian teachers are Russian’, which in one sense expresses the analytic statement ‘All teachers that are Russian are Russian’, and in another the synthetic statement ‘All teachers of Russian are Russian’.
Kant’s innovation over Leibniz and Hume lay in separating the logicosemantic analytic–synthetic distinction from the epistemological a priori–a posteriori distinction and from the modalmetaphysical necessary–contingent distinction. It seems evident that any analytic statement is a priori (knowable without empirical evidence) and necessary (something that could not be false). The converse is highly controversial. Kant and his rationalist followers maintain that some a priori and necessary statements are synthetic, citing examples from logic (‘Contradictions are impossible’, ‘The identity relation is transitive’), mathematics (‘The sum of 7 and 5 is 12’, ‘The straight line between two points is the shortest’), and metaphysics (‘Every event is caused’). Empiricists like J. S. Mill, Carnap, Ayer, and C. I. Lewis argue that such examples are either synthetic a posteriori or analytic a priori.
Philosophers since Kant have tried to clarify the analytic–synthetic distinction, and generalize it to all statements. On one definition, a sentence is analytic (on a given interpretation) provided it is ‘true solely in virtue of the meaning or definition of its terms.’ The truth of any sentence depends in part on the meanings of its terms. `All emeralds are green’ would be false, e.g., if ’emerald’ meant ‘ruby’. What makes the sentence synthetic, it is claimed, is that its truth also depends on the properties of emeralds, namely, their being green. But the same holds for analytic sentences: the truth of ‘All red roses are red’ depends on the properties of red roses, namely, their being red. Neither is true solely in virtue of meaning.
A more adequate generalization defines an analytic statement as a formal logical truth: one ‘true in virtue of its logical form,’ so that all statements with the same form are true. In terms of sentences under an interpretation, an analytic truth is an explicit logical truth (one whose surface structure represents its logical form) or one that becomes an explicit logical truth when synonyms are substituted. The negative statement that tomorrow is not both Sunday and not Sunday is analytic by this definition, because all statements of the form : (p & — p) are true. Kant’s definition is obtained as a special case by stipulating that the predicate of an affirmative subjectpredicate statement is contained in the subject provided the statement is logically true. On a third generalization, ‘analytic’ denotes any statement whose denial entails a contradiction. Subject S contains predicate P provided being S entails being P. Whether this is broader or narrower than the second generalization depends on how ‘entailment’, ‘logical form’, and ‘contradiction’ are defined. On some construals, ‘Red is a color’ counts as analytic on the third generalization (its denial entails ‘Something is and is not a color’) but not on the second (‘red’ and ‘colored’ are logically unstructured), while the rulings are reversed for a counterfactual conditional like ‘If this were a red rose it would be red’. Following Quine, many have denied any distinction between analytic and synthetic statements. Some arguments presume the problematic ‘true by meaning’ definition. Others are that: (1) the distinction cannot be defined without using related notions like ‘meaning’, ‘concept’, and ‘statement’, which are neither extensional nor definable in terms of behavior; (2) some statements (like ‘All cats are animals’) are hard to classify as analytic or synthetic; and (3) no statement (allegedly) is immune from rejection in the face of new empirical evidence. If these arguments were sound, however, the distinction between logical truths and others would seem equally dubious, a conclusion seldom embraced. Some describe a priori truths, both synthetic and analytic, as conceptual truths, on the theory that they are all true in virtue of the nature of the concepts they contain. Conceptual truths are said to have no ‘factual content’ because they are about concepts rather than things in the actual world. While it is natural to classify a priori truths together, the proffered theory is questionable. As indicated above, all truths hold in part because of the identity of their concepts, and in part because of the nature of the objects they are about. It is a fact that all emeralds are emeralds, and this proposition is about emeralds, not concepts. See also A PRIORI, CONVENTIONALISM , NECESSITY, PHILOSOPHY OF LANGUAGE , QUIN. W.A.D.