a posteriori: from the latter; a description of inductive reasoning that moves from effect to cause, from the specific instance to the general principle; specifically, a term applied to those proofs of the existence of God that begin with the finite order and ascend toward the first cause (prima causa, q.v.), or first mover (primum movens, q.v.). SEE causa.
a priori: from the former; a description of deductive reasoning that moves from cause to effect, from the general or principle to the specific; a term applied particularly to the so-called ontological proof of God’s existence developed by Anselm, which moves from the idea of God to the actual existence of God. The term can also be applied, although less precisely, to the order of those systems of theology that begin with foundation principles (principia theologiae, q.v.), Scripture and GOd, and then move more or less deductively through the works of God (opera Dei, q.v.) to the doctrine of the last day (dies novissimus, q.v.) to the doctrine of the last day (dies novissimus, q.v.). The term is not applied with absolute precision to these systems since they are not purely deductive in structure but frequently pattern themselves consciously on the Apostles’ Creed.
Taken from Richard Muller’s Dictionary of Latin and Greek Theological Terms: Drawn Principally from Protestant Scholastic Theology (1985, 1995 paper back edition, Baker Book House Company)