The two terms you mention, a priori and a posteriori, are both types of knowledge and are also classifications of argument. They were made significant by the German philosopher Immanuel Kant in the 1800s.
The term a priori can be translated as something like "from that which goes before." An a priori argument is one which does not require scientific or measurable proof; in other words, there is no research or experience required for this kind of knowledge. Instead, this kind of knowledge is based on reasoning which nearly every human being is capable of doing. Examples of a priori argument might include the following:
- If the sun is shining, it is a sunny day.
- Circles are round.
- 1 + 1 = 2
We do not have to know whether the sun is shining now; we can simply reason that if the sun is shining, then today is a sunny day. We do not have to do scientific research to know that one and one is two or that circles are round. Good, logical reasoning leads us to these conclusions.
The term a posteriori can be translated as something like "from that which comes after." An a posteriori argument, on the other hand, is one which requires some kind of observation and experience. This kind of knowledge is based on observable experience and is therefore based on empirical fact or evidence. Examples of this kind of knowledge might include the following:
- The water in the ocean is salty.
- Staying in the sun too long can cause a sunburn.
- A fire produces heat and smoke.
These are all things we cannot know with any certainty unless we experience them. If you taste water from the ocean, you will experience its saltiness. If you stay in the sun too long, you are likely to discover, quite painfully, that you can get sunburned. If you sit near or around a fire, you will quickly be aware that both heat and smoke are produced. You know because you experience.
Both of these terms refer to a different kind of knowing, and they are used in both philosophy and religion as arguments for (and against) faith and God. Undoubtedly you will have a different understanding of and relationship with God if you only have a priori knowledge rather than having the more experiential a posteriori kind of knowledge.