A priori and a posteriori

The Latin phrases a priori (lit. 'from the earlier') and a posteriori (lit. 'from the later') are philosophical terms popularized by Immanuel Kant's Critique of Pure Reason (first published in 1781, second edition in 1787), one of the most influential works in the history of philosophy. However, in their Latin forms they appear in Latin translations of Euclid's Elements, of about 300 BC, a work widely considered during the early European modern period as the model for precise thinking. These terms are used with respect to reasoning (epistemology) to distinguish 'necessary conclusions from first premises' (i.e., what must come before sense observation) from 'conclusions based on sense observation' which must follow it. Thus, the two kinds of knowledge, justification, or argument, may be glossed: There are many points of view on these two types of knowledge, and their relationship gives rise to one of the oldest problems in modern philosophy. The terms a priori and a posteriori are primarily used as adjectives to modify the noun 'knowledge' (for example, 'a priori knowledge'). However, 'a priori' is sometimes used to modify other nouns, such as 'truth'. Philosophers also may use 'apriority' and 'aprioricity' as nouns to refer (approximately) to the quality of being 'a priori'. Although definitions and use of the terms have varied in the history of philosophy, they have consistently labeled two separate epistemological notions. See also the related distinctions: deductive/inductive, analytic/synthetic, necessary/contingent. The intuitive distinction between a priori and a posteriori knowledge (or justification) is best seen via examples, as below: Several philosophers reacting to Kant sought to explain a priori knowledge without appealing to, as Paul Boghossian (MD) explains, 'a special faculty ... that has never been described in satisfactory terms.' One theory, popular among the logical positivists of the early 20th century, is what Boghossian calls the 'analytic explanation of the a priori.' 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 the American philosopher W. V. O. Quine put it, the notions of 'true by virtue of meanings and independently of fact.' Analytic propositions are thought to be true in virtue of their meaning alone, while a posteriori 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, Quine argued that the analytic–synthetic distinction is illegitimate. 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.' 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.