Analytic proposition

An analytic proposition is one whose truth depends on relations of concepts or ideas, and not on what it says about the world. This has been expressed in a number of different ways. Gottfried Wilhelm Leibniz distinguished between what he called truths of reason and truths of fact. English-Scottish philosopher David Hume distinguished between what he called relations of ideas and matters of fact. In the twentieth century, American Philosopher C.I. Lewis, for one, held that analytic truth comes from linguistic convention. Analytic truth and analytic propositions were central notions to the Logical Positivists and members of the Vienna Circle.

Kant's Analytic-Synthetic Distinction

At the beginning of German philosopher Immanuel Kant's Critique of Pure Reason he wrote:

In all judgments in which the relation of a subject to the predicate is thought (if I only consider affirmative judgments, since the application to negative ones is easy) this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it. In the first case, I call the judgment analytic, in the second synthetic. (A:6-7)

As an example of an analytic judgment, Kant gave ‘All bodies are extended.’ He seems to mean that we cannot think of a body without also thinking of an extension in space. He contrasts this example with “All bodies are heavy,” where the predicate (‘is heavy’) “is something entirely different from that which I think in the mere concept of body in general”

Following Leibniz, Kant made a fourfold distinction: analytic vs. synthetic propositions or statements, and a priori vs. a posteriori ones. Analytic statements are those in which, Kant claimed, the predicate is contained in the subject, whereas in synthetic ones it is not. An example frequently given for an analytic statement is "All bachelors are unmarried males." If the definition of 'bachelor' is known, then the predicate 'is an unmarried male' follows from that definition. A priori statements are ones whose truth can be known before any experience with the world, whereas the truth of a posteriori ones is discovered through experience of the world.

These two distinctions made for four possbilities: Analytic a priori, analytic a posteriori, synthetic a priori, and synthetic a posteriori.

Two of those were, until recently, accepted by everyone as noncontroversial: analytic a priori and synthetic a posteriori. Everyone agreed that there are no analytic a posteriori statements because analytic implies a priori, i.e. analytic implies that the truth of the statement is not derived from experience of the world.

The controversial category was synthetic a priori statements. Kant held that this category is not empty; he claimed that there are some synthetic a priori statements, i.e. there are some statements in which the predicate is not contained in the subject — the predicate tells us some new information beyond what is in the subject or what an analysis of the subject would reveal — but the truth of the statement is known a priori, emaning that we do not require empirical experience of the world in order to ascertain their truth. Kant offered the statements of simple srithmetic, such as 4+3=7, and certain statements of philosophy, as examples of synthetic a priori propositions, and he then went on to investigate how synthetic a priori propositions are possible.

The formalists in mathematics — Frege especially, and all who followed in his wake — rejected that claim about arithmetic, and the empiricists, especially Hume and the Logical Positivists and their followers (most of whom considered themselves to be intellectual descendants of Hume) rejected the claim that there are any possible statements of any form that are synthetic a priori. So for the empiricists and logical positivists, there are only two kinds of statements, analytic ones and synthetic ones; moreover, they claimed, all analytic statements are a priori and all synthetic statements are a posteriori, so analytic = a priori, and synthetic = a posteriori.

Quine's Attack on the Analytic-Synthetic Distinction

In his seminal essay, Two Dogmas of Empiricism," (1951) American philodopher-logician Willard Van Orman Quine