Scott put in a conditional request: To name my favorite argument for foundationalism, but only if I'm not a foundationalist. Luckily, I'm not a foundationalist.
This post is a brief introduction to the foundationalism/coherentism debate for non-epistemologists. I'll get into more detail in subsequent installments.
Epistemologists study knowledge: what it is, where it comes from, how we get it, how we transmit it, and so on. Knowledge is justified true belief.* You don't know something unless you've got good reasons for believing it. True beliefs generated by accident or by faulty reasoning aren't knowledge.
Most of our beliefs are justified by other beliefs. For example, I believe that koala bears eat eucalyptus leaves. What's my justification? Well, I believe that National Geographic wouldn't just make up a thing like that. How do I know they wouldn't? And so on, and so on.
Foundationalists and coherentists disagree about where this chain of "how do you know" questions will end. The stakes are high because if we can't deal with the regress satisfactorily, it will turn out that we don't know anything at all.
Foundationalists insist that there must be some beliefs that are directly or immediately justified, as opposed to being justified by inferences from other beliefs. They maintain these special non-inferentially beliefs form the foundation all knowledge and that all the rest of our beliefs are ultimately justified in relation to the foundational beliefs.
What sort of beliefs are at the foundation? Foundationalists differ on the details, but they agree that order to provide a firm foundation, these beliefs must be ones that we couldn't possibly be wrong about. Some philosophers place immediate experience at the base of the pyramid. Others emphasize our grasp of logical or mathematical principles.
My favorite argument for foundationalism is the argument from the regress. It does seem that justification must come to an end somewhere. If it doesn't, it's hard to see how we can have knowledge. The biggest challenge for foundationalism is not so much in identifying a few items of certain knowledge, but rather in showing how our everyday knowledge can be derived from these truths. So far, no one has been able to pull it off.
Coherentists argue that justification is more like a raft than a pyramid. They argue that our beliefs justified in relation to each other. On their view, a belief is justified if it is firmly enmeshed in a network of justifications. But what if your beliefs are totally consistent and totally wrong? At this point, coherentists usually remind us of how much foundationalism sucks. Sure, it would be nice to base all our knowledge on indubitable first principles, but it can't be done. Unless we want to embrace radical skepticism, we've got to rethink our preconceptions about what knowledge must be.
*That definition isn't quite right, but it's close enough.