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The terms "a priori" and "a posteriori" are used in philosophy to distinguish between deductive and inductive reasoning, respectively. Attempts to define clearly or explain a priori and a posteriori knowledge are part of a central thread in epistemology, the study of knowledge. Since the definitions and usage of the terms have been corrupted over time and therefore vary between fields, it is difficult to provide universal definitions of them. One rough and oversimplified explanation is that a priori knowledge is independent of experience, while a posteriori knowledge is dependent on experience. In other words, statements that are a priori true are tautologies.
Economists sometimes use "a priori" to describe a step in an argument the truth of which can be taken as self-evident. "A posteriori", on the other hand, implies that an argument must be based upon empirical evidence.
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The terms "a priori" and "a posteriori" are primarily used among philosophers to refer to two different types of knowledge. Thus, they are primarily used as adjectives to modify the noun "knowledge", or taken to be compound nouns that refer to types of knowledge (for example, "a priori knowledge"). However, "a priori" is sometimes used as an adjective to modify other nouns, such as "truth". Additionally, philosophers often modify this usage. For example, "apriority" and "aprioricity" are sometimes used as nouns to refer (approximately) to the quality of being a priori. Examples of a priori reasoning include "2+5=7" and "all bachelors are male"; examples of a posteriori reasoning include "Protons are made of quarks" and "Hitler died in 1945".
Although definitions and usage of the terms have varied in the history of philosophy, they have been consistently intended to demarcate two separate epistemological notions. The intuitive distinction between a priori and a posteriori knowledge can be seen in examples of what is supposed to fall under each concept. To borrow from Jerry Fodor (2004), take, for example, the proposition expressed by the sentence, "George V reigned from 1910 to 1936". This is something that one must come to know a posteriori (assuming that it is knowledge), because it expresses an empirical fact that one cannot come to know by reason alone. By contrast, consider the proposition expressed by the sentence, "If George V reigned at all, then he reigned for a while". This is something that one knows a priori, because it expresses a tautological statement that is non-empirical and that one can derive by reason alone.
The phrases "a priori" and "a posteriori" are Latin in origin, and literally mean "from what comes before" and "from what comes later", respectively (or, less literally, "before experience" and "after experience", respectively). An early philosophical use of what might be considered a notion of a priori knowledge is Plato\'s theory of recollection, related in the dialogue Meno (380 B.C.E.), according to which something like a priori knowledge is knowledge inherent in the human mind.
The German philosopher Immanuel Kant (1781) advocated a blend of rationalist and empiricist theories. Kant claims: "That all our knowledge begins with experience there can be no doubt... But... it by no means follows that all arises out of experience."Kant (1781), introduction, §I. According to Kant, a priori knowledge is transcendental, or based on the form of all possible experience, while a posteriori knowledge is empirical, based on the content of experience. Kant states, "... it is quite possible that our empirical knowledge is a compound of that which we receive through impressions, and that which the faculty of cognition supplies from itself (sensuous impressions giving merely the occasion)". Thus, unlike the empiricists, Kant thinks that a priori knowledge is independent of the content of experience; however, unlike the rationalists, Kant thinks that a priori knowledge, in its pure form, that is without the admixture of any empirical content, is knowledge limited to the deduction of the conditions of possible experience. These a priori, or transcendental conditions, are seated in one\'s cognitive faculties, and are not provided by experience in general or any experience in particular. Kant nominated and explored the possibility of a transcendental logic with which to consider the deduction of the a priori in its pure form. Concepts such as time and cause are counted among the list of pure a priori forms. Kant reasoned that the pure a priori forms are established via his transcendental aesthetic and transcendental logic. He claimed that the human subject would not have the kind of experience that she has were these a priori forms not in some way constitutive of her as a human subject. For instance, she would not experience the world as an orderly, rule-governed place unless time and cause were operative in her cognitive faculties. The claim is more formally known as Kant\'s transcendental deduction and it is the central argument of his major work, the Critique of Pure Reason. The transcendental deduction does not avoid the fact or objectivity of time and cause, but does, in its consideration of a possible logic of the a priori, attempt to make the case for the fact of subjectivity, what consititutes subjectivity and what relation it holds with objectivity and the empirical.
For more details on this topic, see Analytic-synthetic distinction.
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".Boghossian (1996), p. 363. One theory, which was especially popular among the logical positivists of the early twentieth 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 Quine put it, the notions of "true by virtue of meanings and independently of fact."Quine (1951), p. 21. 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."Quine (1951), p. 34. 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."Baehr (2006), §3.
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...."Fodor (1998), p. 86. 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",Quine (1951), §1. 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.
However, 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.
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.See Baehr (2006), §2 & §3.
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