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Empirical or a posteriori knowledge is propositional knowledge obtained by experience. It is contrasted with a priori knowledge, or knowledge that is gained through the apprehension of innate ideas, "intuition," "pure reason," or other non-experiential sources.
The natural and social sciences are usually considered a posteriori, literally "after the fact," disciplines. Mathematics and logic are usually considered a priori, "before the fact," disciplines.
For example, "all things fall down" would be an empirical proposition about gravity that many of us believe we know; therefore we would regard it as an example of empirical knowledge. It is "empirical" because we have generally observed that things fall down, so there is no reason to believe this will change. This example also shows the difficulty of formulating knowledge claims. Outside of the Earth's gravitational field, for example, things do not "fall down", as there is no "down".
The vast bulk of the empirical knowledge that ordinary people possess is gained via a mixture of direct experience and the testimony of others about what they have experienced—iterated in an interesting way that is studied in the field of social epistemology as well as other fields. More complicated and organized methods of gaining empirical knowledge are the methods of science—see scientific method—which results in perhaps the best examples of rigorously codified, scientific empirical knowledge, namely, physics.
A priori and a posteriori in terms of constructed languages are specific jargon: the latter means that a conlang is explicitly based in whole or in part upon existing languages (for instance, Esperanto), whereas the former indicates that it is completely invented and based only upon the desires of the creator (for instance, Klingon).