Unfortunately MOST of the following is not about a priori and a posterori knowlege at all, so I'm moving it here, and replacing it with a less controvercial, and more consise stub. Perhaps we'll be able to find a home for all of this, but I don't think this page is it MRC
Then, Mark, please move it to an appropriately-named page; don't just leave nothing on the page. --LMS
Sorry. I accidentally hit enter, and the page was saved before I pasted in a new edited stub text. MRC I'll be adding to that stub some more this afternoon as I have time, but I'll not be including the very controversial claim that sense perception, and memory are ultimate justifiers of belief, and the notion that a priori knowledge doesn't exist. (Though I will mention that most contemporary philosophers have doubts about the existence of a priori knowledge
<The following is a portion of Larrys Text, wikification is encouraged>
We've just finished discussing, in a very introductory way, the first part of my definition of "epistemology." So we just finished discussing "what the epistemic features of belief, such as justification and rationality, each are (e.g., what justified belief is)." Next we are going to discuss, much more briefly, "the origin or sources of such [epistemic] features (and thus the sources of knowledge)." So to phrase it as a question, we are next going to ask: What are the ultimate origins or sources of justified belief? Now look, we've just got done discussing justification, and in our discussion of it we found that justified beliefs have justifiers. So we could rephrase the question like this: What are the ultimate justifiers of belief?
Well, that's what we were talking about just a few minutes ago, isn't it? Sense-perception, for example, is one of the ultimate justifiers of belief; memory is another. And now just ask yourself something. Is there any mental process -- remember our list of mental processes -- that does not contribute any justification to any belief? Just for fun let's consult that list of cognitive processes that I gave you when we talked about the philosophy of mind. Here it is again: "perception, introspection, memory, imagination, conception, belief, reasoning, volition, and emotion." Are there any of those which do not, in any way, contribute to your justification, your intellectual right to believe something or not believe?
Perhaps. Maybe belief, volition, and emotion have little to do with knowledge. What could I learn, or be justified in believing, on account of my simply accepting something, or using my will, or merely feeling some way? Perhaps there are some things: use your imagination.
But whether or not volition and emotion can justify beliefs at all, what about the other processes? Some of them can obviously justify our beliefs; such as perception, introspection, memory, imagination, conception, reasoning. Those processes can all definitely contribute to the justification of beliefs. Even introspection? How so? Well, introspection is just awareness of your own mental states. So say you belief you are in great pain. What justifies you in the belief? That you introspect, or consider your own mental states; and when you do that you discover that you've got a pain. You can do that, right -- discover that you're in pain? Well, the process you're engaged in, in making the discovery, is introspection. "Gosh, I've been working all day long at this computer and I've just realized I've got an enormous pain in my neck" -- for example!
The process of reasoning is extremely important for human knowledge. It is by reasoning -- which means, using arguments of various sorts -- that we build up knowledge from basic beliefs. If we couldn't reason, then we couldn't get beyond the level of raw perception, unvarnished memory, and so for; we would be like children. And indeed until children learn the ability to reason, they may hold lots of beliefs about religion and politics and so forth, but they have just learned those beliefs from their parents and elders. Those childhood beliefs are not justified, though, because they are merely accepted on authority, not on any reasoning.
Now I want you to consider another kind of belief, in particular beliefs that have to be true. You can call them beliefs in necessary truths, because they must be true. Such as the following: 2+2=4; yellow is a color; a single point of light cannot be both red and blue at the same time; all bachelors are men; a part of a thing is never greater than the whole. There are many examples. The question now is: Given that we believe those claims, and given that those beliefs are justified, then what are the justifiers for those claims?
Some people think that they are justified totally independently of any sense-perception or other kind of experience; so their justifiers do not include perception or introspection (those are the two kinds of "experience," I guess). In other words, those beliefs are justified a priori -- "prior" to experience, if you will. Here is a definition of that term:
A belief is justified a priori iff its ultimate justifiers do not include sense-perception or introspection.
For example, what justifies you in believing that 2+2=4? I mean, surely you are justified in that belief; the question is what justifies the belief. If you accept that there is priori justification, you'd say: it's not by sense-perception or introspection. So it's not as though you see two things, and then two more things, and then count out four. That's not how you're justified in believing that 2+2=4. So how are we justified in the belief?
The advocates of the a priori are not always perfectly clear. But they often speak of something like "intuition," or "rational insight," or a faculty of "pure reason." Exactly what such "intuition" amounts to is a little mysterious, I guess. But plainly there are supposed to be lots of examples of its use: it is by intuition that we understand, and are justified in believing, that 2+2=4. It's by intuition that we understand and are justified in believing that the whole is greater than its parts. And so forth. But not by experience.
So another definition of a priori would be:
A belief is justified a priori iff its ultimate justifiers are only from the use of intuition (rational insight, pure reason).
A priori justification is contrasted by a posteriori justification. What is justified a posteriori is justified "after" (think "posterior" to) experience. So we can define a posteriori justification as follows:
A belief is justified a posteriori iff its ultimate justifiers include sense-perception or introspection.
So just any ordinary belief about your surroundings, about things you see, hear, feel, and so forth, is going to be a posteriori. Moreover, any introspective belief about your mental states is also going to be a posteriori. Then beyond that, any belief that is ultimately grounded in such experience, in perception or introspection, is also going to be justified a posteriori. So you might have some complex theory about gamma rays and galaxies and the origin of the universe; even though it's the result of lots of complex scientific reasoning, since that reasoning starts with observations that you make with scientific instruments, it's still a posteriori. Its ultimate justifiers include sense-perception.
The big question that epistemologists ask about this topic is: Are there any a priori justified beliefs? In the history of philosophy, some people have thought so; they tended to be called rationalists. There is more to rationalism than that, but the view that was really basic to rationalism is the belief in the a priori. Contrasted with rationalism was empiricism, the essential part of which is the rejection of the a priori, and the view that the justification of all beliefs ultimately depends on experience -- that there is only a posteriori justified beliefs, not a priori justified beliefs.
I suspect that you won't be surprised if I tell you that most philosophers these days are empiricists, and that they deny the existence of a priori justified beliefs. They think everything must ultimately be justified based on experience; experience is all we have, in the long run.