By the law excluded middle, an item of knowledge is either inferred from prior items of knowledge or it is not inferred from prior items of knowledge. Items of knowledge that are inferred are called a posteriori
, and items of knowledge that are not inferred are called a priori
. The only way to escape this dichotomy is to deny that there's any such thing as knowledge at all.
The denial of a priori knowledge leads to absurdity. If you deny that it's possible to know something without inferring it from something else, then you would have to say that for everything you know, there is a prior item of knowledge from which you inferred it.
For example, let's say you know that Socrates is mortal. Perhaps you inferred that item of knowledge from these two items of knowledge:
1. All men are mortal.
2. Socrates is a man.
But if each item of knowledge you possess must be inferred from something prior, then there must be further items of knowledge from which you infer 1 and 2. Otherwise, you couldn't know that Socrates is mortal. And then there must be further items of knowledge from which you infer those as well.
If you continue to think this through, you'll quickly see that it leads to an infinite regress. If all of our items of knowledge must be inferred from prior items of knowledge, then the only way it's possible to know anything is if there is a beginningless line of reasoning from prior premises that leads up to your present state of knowledge.
But that is impossible for three reasons. First, none of us know an infinite number of things. Second, because nobody has been around long enough to make an infinite number of inferences. Third, because if there were no beginning, there would be no way to even get started making inferences. You couldn't very well start at the beginning because there's no beginning to get started from!
So it is impossible that all of our knowledge is a posteriori. If we know anything at all, then at least some of our knowledge must be a priori. That means that unless there are some things we know immediately without inferring them from anything else, then knowledge is impossible.
Some people may be willing to bite the bullet and say, "Well, okay, then nobody really knows anything at all, including me." This view is called global skepticism. It is a self-refuting point of view for a couple of reasons.
First, it's self-refuting because if nobody knows anything, then we wouldn't know it. A person who claims not to know anything is stating something he doesn't know to be true.
Second, it's self-refuting because if nobody knows anything, then nobody knows that any of the premises that lead to the conclusion are true, nor that the conclusion follows from those premises.
Besides that, there are plenty of things we obviously know. We each know that we exist. We know that two contradictory statements can't both be true at the same time and in the same sense. I know that I have a sister named Jennifer and a brother named James. There are all kinds of things we know. So there must be a priori knowledge.