Ever since Wittgenstein and his theory of family resemblance, philosophers have mainly abandoned the attempt to define concepts in terms of their "necessary and sufficient conditions" originally made famous by none other than Socrates. Still, the attempt is great practice in critical and creative thinking, and it can be incredibly helpful in illustrating what it is precisely that we mean when we deploy certain words in our discourse.
Now, one of the concepts that has been central to most philosophical discussions for the past few thousand years has been the concept of knowledge. What exactly does it mean to 'know' something? I hope you can immediately see why this is a theoretically and practically important question, but believe it or not, it turns out to be an exceedingly difficult concept, especially if we think of it in terms of wanting to defeat a global skeptic.
In the following fascinating lecture, Professor Millican demonstrates philosophy at work as he shows how philosophers wrestle with these conceptual issues. As you'll notice, each attempt at a definition will seem to encapsulate an intuitive conception of knowledge that captures most of what we might ordinarily mean by it, but its implications might produce new problems, which are usually shown with the deployment of thought experiments and counterexamples (like Gettier's). A new definition will be proposed to solve the previous problems, but new ones will arise. Lather, rinse, repeat, and you might think that this is going nowhere. I disagree. At the very least, we continue to learn the mistakes we are no longer entitled to make, and although slow, I think it does constitute a progress of sorts.
Click here to see the course slides