As I mentioned, I've been working on Williamson's Knowledge and its Limits. It's a great book and one that really makes one think. It does presume a fair familiarity with epistemology. But those with even a little background in philosophy will be quite rewarded for checking it out. It does careful arguing as well as careful concept analysis. The basic thesis of the book is that, unlike what was traditionally claimed, knowledge should not be considered justified true belief.
Now the problem with knowledge as justified true belief goes back a fair ways. At least back to Edmund Gettier in the 1960's who came up with what became known as the Gettier examples. These were examples where a proposition is true, a person believes the proposition, the belief is justified, and yet where it seems incorrect to say the person knows the proposition. The general idea is that of luck. Consider for example a clock that normally works but which happens to have stopped. You look at the clock coincidentally at the same time it shows. Clearly you don't know what time it is based upon looking at the clock.
This threw some people for a loop and the next forty years or so involved additional complexities to epistemology to maintain something like the traditional view, followed by ever more complex counter-examples.
I'll not go through all of William's examples. But he deals fairly completely with most of the recent literature, based upon what I can see. (I must confess that being only an amateur philosopher, there was a lot I wasn't that familiar with) What is most interesting though is how Williams considers knowledge a basic mental state. This has far reaching metaphysical implications, I think, although from what I can see Williams doesn't really look at those. Certainly his view is an externalist epistemology. (Meaning that ones knowledge depends upon things external to the self or ones introspection - Alston being one of the classic examples of an externalist with his position of reliabilism) Yet by making knowledge a fundamental mental state it seems like the mental state as a state is a state dependent not just upon the state of the person but on the state of the person's environment. In a way the state is the state of the brain of the knower and the state of what is known.
While I may well be wrong, it seems like this points towards considering minds as far broader in terms of composition than merely the brain. Indeed it seems to support if not suggest a more general semiotic approach in which facts can be part of the makeup of ones minds. And by facts I don't merely mean the representation of the fact but the fact itself. Of course I fully admit this is all me jumping the gun and I really ought to finish reading the book and considering it more before leaping where angels fear to tread. Still it seems like Williamson, if his arguments become influential, may significantly affect philosophy of mind a fair bit.
As well as considering knowledge a mental state it becomes one of the foundational mental states for many processes. Allow me to quote Williamson.
To know is not merely to believe while various other conditions are met; it is to be in a new kind of state, a factive one. What matters is not acceptance of a disjunctive account of believing but rejection of a conjunctive account of knowing. Furthermore, the claim that belief is what aims at knowledge is constonant with the suggestion in disjunctive accounts that illusion is somehow parasitic on veridical perception. Properly developed, the insight behind disjunctive theories leads to a non-conjunctive account of knowledge and a non-disjunctive account of belief.
While belief aims at knowledge, various mental processes aim at more specific mental states. Perception aims at perceiving that something is so. Memory aims at remembering that something is so. Since knowing is the most general factive state, all such processes aim at kinds of knowledge. If a creature could not engage in such processes without some capacity for success, we may conjecture that nothing could have a mind without having a capacity for knowledge.
The book is fairly exciting in making one consider many things. I think it may have numerous philosophical implications for Mormon theology as well. However I'll hold off making any of those claims until I've digested the book more. I'm still at that point where one recognizes that ones excitement isn't the result of careful consideration.
Just a brief note that there's a fairly good paper that is a response to Williamson. It's called "Reflections on Knowledge and Its Limits." While I'd still say the book is one of those "must read" sorts of things, the article by Harmon probably is a good way to get an idea of what Williamson is doing, as well as some criticisms.
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