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A priori ('from the earlier') and a posteriori ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. A priori knowledge is independent from any experience. Examples include mathematics, [i] tautologies and deduction from pure reason.
a posteriori: from the latter: Based on observation, i. e., empirical evidence. Opposite of a priori. Used in mathematics and logic to denote something that is known after a proof has been carried out. In philosophy, used to denote something known from experience. a priori: from the former: Presupposed independent of experience; the reverse of ...
A posteriori necessity existing would make the distinction between a prioricity, analyticity, and necessity harder to discern because they were previously thought to be largely separated from the a posteriori, the synthetic, and the contingent. [3] (a) P is a priori iff P is necessary. (b) P is a posteriori iff P is contingent.
In the Introduction to the Critique of Pure Reason, Kant contrasts his distinction between analytic and synthetic propositions with another distinction, the distinction between a priori and a posteriori propositions. He defines these terms as follows: a priori proposition: a proposition whose justification does not rely upon experience ...
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By combining Frege's thesis that all mathematical truths are logical with the early Wittgenstein's idea that all logical truths are mere linguistic tautologies, they arrived at a twofold classification of all propositions: the "analytic" (a priori) and the "synthetic" (a posteriori). [41]
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A priori and a posteriori knowledge – these terms are used with respect to reasoning (epistemology) to distinguish necessary conclusions from first premises.. A priori knowledge or justification – knowledge that is independent of experience, as with mathematics, tautologies ("All bachelors are unmarried"), and deduction from pure reason (e.g., ontological proofs).