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.[1] 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.

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".[4][not in citation given]

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.

Examples

The intuitive distinction between a priori and a posteriori knowledge (or justification) is best seen via examples, as below:

A priori
Consider the proposition, "If George V reigned at least four days, then he reigned more than three days." This is something that one knows a priori, because it expresses a statement that one can derive by reason alone.
A posteriori
Compare this with the proposition expressed by the sentence, "George V reigned from 1910 to 1936." This is something that (if true) one must come to know a posteriori, because it expresses an empirical fact unknowable by reason alone.
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