These Latin terms mean literally “from what comes before” and “from what comes after.” Both terms relate to how one acquires knowledge of the truth of a proposition.
An a priori proposition can be known to be true or false without reference to the evidence of experience, while the truth or falsity of an a posteriori proposition depends upon such evidence.
Examples of propositions commonly held to be known a priori include:
a bachelor is an unmarried male; 2 + 3 = 5; if you know something, then what you believe is true; if A is greater than B, and B is greater than C, then A is greater than C; no object can be red and green all over at the same time; the shortest distance between two points is a straight line; no object can be wholly in two different places at the same time; it is wrong to torture infants to death just for the fun of it; and it is unjust to punish an innocent person.
On the other hand, a proposition such as “some bachelors are very happy” can only be decided as true or false a posteriori – as a result of empirical investigation.
Ontological arguments for God’s existence are a priori, while an argument, for example, for Jesus’ resurrection from the dead is a posteriori.