A priori and a posteriori
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 A priori
A priori (literally "from before") is a Latin term used in formal logic (and philosophy) to mean a fact that is assumed to be true prior to any empirical research. A priori conclusions are usually reached through reasoning rather than observation and are the centerpiece of (philosophical) rationalism. It is opposed to so-called a posteriori knowledge, which is gained through observation and forms the basis for empiricism.
At the most solipsistic level, the only a priori statement that a tough skeptic can be assured of is "I think, therefore I am" ("cogito ergo sum"), although it can be argued that even Descartes' thought experiment had the a priori assumption that a thought requires a thinker.
 A posteriori
A posteriori ("From the later") is a Latin phrase used in formal logic (and philosophy) to denote knowledge that is derived from empirical observation (experience). While it has nothing to do with one's posterior, some people manage to extract "knowledge" from their posteriors. As the logical basis for induction, it is extensively used in the scientific method and in most courtrooms. In philosophy, a posteriori knowledge is contrasted with a priori knowledge, which is the backbone of deduction and rationalism.