<logic, epistemology> a sentence, proposition, thought or judgement is a priori (literally "before") if its truth is not dependent on how our actual experience (experiment and observation) happens to turn out. Some a priori truths (axiomsor first principles) are held to be directly intuited; the rest are supposed to be deducible from these. Euclid's geometry provides the model for this traditional conception. With a posteriori knowledge or statements, on the other hand, justification does invoke sensory experience either directly via perception or indirectly via induction. Many have thought that the truths of logic and mathematics are a priori, though J. S. Mill and W. V. O. Quine might be thought to maintain the contrary position. Some equate a priori and analytic. The ontological argument for the existence of God is deemed a priori.
based on [A Philosophical Glossary], [Philosophical Glossary]
distinction among judgments, propositions, ideas, arguments, or kinds of knowledge. In each case, the a priori is taken to be independent of experience, which the a posteriori presupposes. An a priori argument, then, is taken to reason deductively from abstract general premises, while an a posteriori argument relies upon specific information derived from sense perception. The necessary truth of an a priori proposition can be determined by reason alone, but the contingent truth of an a posteriori proposition can be discovered only by reference to some matter of fact. Thus, for example: "3 + 4 = 7" is known a priori. "Chicago is on Lake Michigan." is known a posteriori. Rationalists typically emphasize the importance of a priori ideas and arguments as the foundation of all knowledge. Kant held that synthetic a priori judgments are preconditions of experience and form the basis for mathematics and science. Empiricists, on the other hand, usually hold that all a priori propositions are merely analytic, so that we must rely on a posteriori propositions for significant knowledge of the world. Kripke challenges even the identification of this distinction with that between the necessary and the contingent. Recommended Reading: Immanuel Kant, Prolegomena to Any Future Metaphysic (Hackett, 1977); New Essays on the A Priori, ed. by Paul Boghossian and Christopher Peacocke (Oxford, 2000); A Priori Knowledge, ed. by Albert Casullo (Dartmouth, 1999); Robert Greenberg, Kant's Theory of a Priori Knowledge (Penn. State, 2001).
[A Dictionary of Philosophical Terms and Names]
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