A contrast originally introduced by Kant between types of proposition. An analytic proposition is one where the concept of the predicate is ‘contained in’ the concept of the subject. ‘All brothers are male’ is an example. A synthetic proposition is one where this is not so, and which is therefore apt for providing substantial information. Kant's definition is only preliminary, in that not all propositions are of subject-predicate form, and the notion of ‘containment’ is left metaphorical. But his goal of defining a class of propositions that are importantly trivial can be pursued in ways drawing on modern logic. Thus we might define a proposition to be analytic if it has the form of a tautology, or valid formula of elementary logic, or can be represented as having that form by substitution of synonyms for synonyms. For example, if we substititue ‘male and sibling’ for ‘brother’, then ‘all brothers are male’ is of the form ‘all things that are F and G are F’, and this is a valid formula of the predicate calculus.
The point of Kant's division is that we might not be too disturbed, philosophically, if everything that can be known a priori is analytic: analytic truths are so trivial as barely to count as knowledge at all. But if we can know synthetic propositions a priori the question of how such knowledge is possible becomes urgent. Part of the programme of logical positivism was to show that all a priori propositions are, at bottom, analytic. The entire distinction was queried in one of the most famous papers of modern philosophy, Quine's ‘Two Dogmas of Empiricism’ (1950), which attacks the idea that we have a reasonable criterion for synonymy, on which the definition depends.