<P> The Latin phrases a priori (lit. "from the earlier") and a posteriori (lit. "from the latter") are philosophical terms of art 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 BCE, a work widely considered during the early European modern period as the model for precise thinking . </P> <P> 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: </P> <Ul> <Li> A priori knowledge or justification is independent of experience, as with mathematics (3 + 2 = 5), tautologies ("All bachelors are unmarried"), and deduction from pure reason (e.g., ontological proofs). </Li> <Li> A posteriori knowledge or justification depends on experience or empirical evidence, as with most aspects of science and personal knowledge . </Li> </Ul>

Science begins with the premise that knowledge should first be acquired through observation