Before we get all academic in this beezy, lets take a quick look at some of the main problems epistemologists have tried to solve/argue incessantly about. Some of the problems are best illustrated by an example, which I will shamelessly steal from my prof., Dr. Creath:
Imagine you have two beakers (I love that word). The first beaker (ha!) has 1 cup of water and the second has 1 cup of sugar. What will happen if you pour one beaker into the other? Give up? Well, you'll get some sweet water. But how much? 2 cups? Actually the solution will only measure about 1 1/2 cups. So what? The problem is that the basic laws of algebra tell us that 1+1=2. Nevertheless, nobody in their right mind is going to suggest that this experiment disproves the laws of basic algebra.
The experiment does, however, point to some very important philosophical and philosophy of science issues. Basically this experiment demonstrates that different forms of reasoning about the same phenomenon can yield different results. Which form of reasoning should we follow? Should some forms of reasoning supersede others? Should quantity of demonstrations count? (i.e. if I show you 1 000 ways that 1+1 does not equal 2, then will you relinquish the belief in the rules of arithmetic?) If we redo the experiment with 1 cup of water in each beaker, most people will say that this confirms 1+1=2. But why only consider the conformational evidence? Doesn't evidence that disconfirms a hypothesis count too?
There is another related issue concerning how we justify claims about knowledge. It is known as the "infinite regress" problem". Generally, when we want to support a claim as true, we point to reasons why it is true. But each of these reasons are themselves claims about objective truth and themselves need to be justified, and so on and so on until...you throw your hands up in the air, and wave 'em like you just don't care. Or you can take an approach some philosophers have taken (most famously Descartes of the "I think therefore I am" fame ) and claim there are some fundamental objective truths about the world and all other facts about the world can be derived/deduced from these truths (some of which will be very very long explanations).
So...we have a problem concerning how to justify claims (as true). Another solution is to say that some claims can be justified through observation. There are however problems with this method of justification beyond the practical problem that sometimes our senses deceive us and we that have no way reliable way of distinguishing between when our senses deceive us and when they don't. (As an aside, it is my humble opinion that most claims of paranormal experiences stem from this inability to distinguish). The philosophical problem is, how do we prove that observation is a reliable method of justifying claims? The only tool we have for this undertaking is observation itself (i.e. we can run experiments to determine if observation is reliable but experiments rely on observational data to confirm/disconfirm hypothese). When you presuppose what you are trying to prove, this, as most people know, is called circular logic and is not particularly helpful in our dilemma.
Ok, so there you have it. A quick overview of the problems in epistemology and philosophy of science. Mainly, what constitutes knowledge? how do we derive knowledge? what methods of obtaining knowledge are reliable? and what do we do in cases where different methods of obtaining knowledge lead to contradictory or incongruous results?
Actually, I was kidding, there is another family of problems, and it has to do with something called apriori knowledge (I'm such a kidder!). Apriori literally means "prior to" and it is in reference to experience. In everyday English it means, "things that you can/do know without having to have empirical (observational) evidence". The typical example is truths by definition, such as: all bachelors are unmarried. You don't have to go around and interview every bachelor in the world to know that this is true. There are other things, usually matters that don't have correspond to anything in the physical world like math and logic. You don't need to go measure every equilateral triangle in the world to know that the Pythagorean theorem is true. It's truth is derived by the understanding of the principles of geometry. Also, principles of geometry like, the shortest distance between 2 points is a straight line, don't need you to do anything more than reflect in your mind to verify it's truth (later we will contend this, but for now, lets say that the Euclidian geometric axiom is true).
Most people, will agree that we do not need experiential knowledge to verify the examples i've given. So where does this knowledge come from? If we don't acquire it from the external world then it must be part of the structure of our brain....hmmm But the story doesn't end here because sometimes we discover that what we thought were absolute truths in logic or math (apriori knowledge), turn out to have alternative explanations or are wrong. Doh! So now we are in trouble. We need a hero who can lift us out of this mess. I present to you....
Actually, I'm going to let that stew in your head for a bit (cuz I've got other stuff to study). Hopefully you'll lose some sleep over it, then when your appetite for knowledge reaches levels unknown to any man hence, you will beg me to reveal, in all it's philosophical glory, Rudolf Carnap's ideas on how to reconcile some of these problems. Ta!ta!