Definition:
The phrase a priori is a Latin term which literally means before (the fact). When used in reference to knowledge questions, it means a type of knowledge which is derived without experience or observation. Many consider mathematical truths to be a priori, because they are true regardless of experiment or observation. For example:
2 + 2 = 4
The above is a statement which can be known a priori.
When used in reference to arguments, it means an argument which argues solely from general principles and through logical inferences.
The term a posteriori literally mean after (the fact). When used in reference to knowledge questions, it means a type of knowledge which is derived through experience or observation. Today, the term empirical has generally replaced this. Many empiricists, like Locke and Hume, have argued that all knowledge is essentially a posteriori and that a priori knowledge simply isn't possible.
The distinction between a priori and a posteriori is closely related to the distinctions between analytic / synthetic and necessary / contingent.
Analyticity and necessity
Several philosophers reacting to Kant sought to explain a priori knowledge without appealing to, as Paul Boghossian explains, "a special faculty...that has never been described in satisfactory terms."[3] One theory, popular among the logical positivists of the early twentieth century, is what Boghossian calls the "analytic explanation of the a priori."[3] The distinction between analytic and synthetic propositions was first introduced by Kant. While Kant's original distinction was primarily drawn in terms of conceptual containment, the contemporary version of the distinction primarily involves, as Quine put it, the notions of "true by virtue of meanings and independently of fact."[4] Analytic propositions are thought to be true in virtue of their meaning alone, while a priori synthetic propositions are thought to be true in virtue of their meaning and certain facts about the world. According to the analytic explanation of the a priori, all a priori knowledge is analytic; so a priori knowledge need not require a special faculty of pure intuition, since it can be accounted for simply by one's ability to understand the meaning of the proposition in question. In short, proponents of this explanation claimed to have reduced a dubious metaphysical faculty of pure reason to a legitimate linguistic notion of analyticity.
However, the analytic explanation of a priori knowledge has undergone several criticisms. Most notably, the American philosopher W. V. O. Quine (1951) argued that the analytic-synthetic distinction is illegitimate (see Quine's rejection of the analytic-synthetic distinction). Quine states: "But for all its a priori reasonableness, a boundary between analytic and synthetic statements simply has not been drawn. That there is such a distinction to be drawn at all is an unempirical dogma of empiricists, a metaphysical article of faith."[5] While the soundness of Quine's critique is highly disputed, it had a powerful effect on the project of explaining the a priori in terms of the analytic.
The metaphysical distinction between necessary and contingent truths has also been related to a priori and a posteriori knowledge. A proposition that is necessarily true is one whose negation is self-contradictory (thus, it is said to be true in every possible world). Consider the proposition that all bachelors are unmarried. Theoretically, its negation, the proposition that some bachelors are married, is incoherent, because the concept of being unmarried (or the meaning of the word "unmarried") is part of the concept of being a bachelor (or part of the definition of the word "bachelor"). To the extent that contradictions are impossible, self-contradictory propositions are necessarily false, because it is impossible for them to be true. Thus, the negation of a self-contradictory proposition is supposed to be necessarily true. By contrast, a proposition that is contingently true is one whose negation is not self-contradictory (thus, it is said that it is not true in every possible world). As Jason Baehr states, it seems plausible that all necessary propositions are known a priori, because "[s]ense experience can tell us only about the actual world and hence about what is the case; it can say nothing about what must or must not be the case."[6]
Following Kant, some philosophers have considered the relationship between aprioricity, analyticity, and necessity to be extremely close. According to Jerry Fodor, "Positivism, in particular, took it for granted that a priori truths must be necessary...."[7] However, since Kant, the distinction between analytic and synthetic propositions had slightly changed. Analytic propositions were largely taken to be "true by virtue of meanings and independently of fact",[8] while synthetic propositions were not—one must conduct some sort of empirical investigation, looking to the world, to determine the truth-value of synthetic propositions.
Aprioricity, analyticity, and necessity have since been more clearly separated from each other. The American philosopher Saul Kripke (1972), for example, provided strong arguments against this position. Kripke argued that there are necessary a posteriori truths, such as the proposition that water is H2O (if it is true). According to Kripke, this statement is necessarily true (since water and H2O are the same thing, they are identical in every possible world, and truths of identity are logically necessary) and a posteriori (since it is known only through empirical investigation). Following such considerations of Kripke and others (such as Hilary Putnam), philosophers tend to distinguish more clearly the notion of aprioricity from that of necessity and analyticity.
Kripke's definitions of these terms, however, diverge in subtle ways from those of Kant. Taking these differences into account, Kripke's controversial analysis of naming as contingent and a priori would best fit into Kant's epistemological framework by calling it "analytic a posteriori".[9]
Thus, the relationship between aprioricity, necessity, and analyticity is not easy to discern. However, most philosophers at least seem to agree that while the various distinctions may overlap, the notions are clearly not identical: the a priori/a posteriori distinction is epistemological, the analytic/synthetic distinction is linguistic, and the necessary/contingent distinction is metaphysical.[10]
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