I believe that Williams' approach has proven to be plausibly anti-sceptical. We were initially challenged by Humean and Cartesian style scepticism, which took a best case scenario, such as sitting in at your desk next the fireplace, and showed that our standards of knowledge show that even in this case we do not have knowledge of the external world. For we may be dreaming, and if we are dreaming then we do not have any knowledge from what the sensations deliver us; and since we do not know whether or not we are dreaming, we do not know anything about the external world.

The difficulty posed by this sort of radical scepticism was that it seemed to be straightforwardly intuitive; even those inexperienced with philosophy and its theories and nuances are struck by its persuasiveness. Many of us find scepticism's conclusions unpalatable and even ridiculous, but we cannot simply discount it for its absurd conclusions. Instead, its intuitive nature means we must somehow square it against our everyday notions of knowledge, or end up accepting that we have no knowledge at all. It is not enough to say, as Moore did, that scepticism is wrong because it conflicts with our everyday usages of knowledge claims and attributions; for scepticism comes from our everyday knowledge claims.

Next we studied the intuitive nature of scepticism, in the hopes of showing that scepticism is not intuitive at all, but rather presupposes some contentious epistemological theory. We had a prima facie reason for doing this, because of the way scepticism clashes so badly with our everyday knowledge practices: radical scepticism is supposed to be intuitive, in that it comes from our everyday practices, yet its conclusions seem to have no bearing on our everyday practices. Our everyday practices tell us we do have knowledge, while scepticism, despite its claim to be rooted in our common concepts of knowledge, tells us we have none; there seems to be reason to look into the supposedly intuitive backing of scepticism.

By looking at best-case-style sceptical scenarios we discovered that radical scepticism seems to require tacit presuppositions to get off the ground. Specifically, it requires the epistemologically realist doctrine of foundationalism, which holds that propositions and beliefs have intrinsic epistemic status if they are perceptual in nature. This is of course a contentious theory and one we need not accept, especially if it brings radical scepticism in tow.

But the sceptic had a response: foundationalism is not presupposed by skepticism; rather foundationalism is a discovery that comes out of sceptical considerations. Once we discover that we need to adopt foundationalism due to sceptical considerations, we show that foundationalism cannot bring us any knowledge of the external world, and we have radical scepticism all over again. But in studying the sceptic's arguments we found no reason to accept that foundationalism falls out of skepticism. Rather, we found more reason to believe that foundationalism must be presupposed by skepticism in order for it to reflect badly on our knowledge; otherwise we just have an argument from error. Having shown that scepticism most likely requires the contentious philosophical doctrine of foundationalism, we moved on to rejecting foundationalism in favour of another epistemological theory. Coherentism did not seem to fit the bill; for it too held implicit foundationalist premises in its criteria of coherence, which have intrinsic priority over other beliefs. So despite its appearance of radically rejecting all of foundationalism's principles, coherentism is ultimately fundamentally foundationalist in its own way.

Thus Williams' contextualism was put forth as an anti-sceptical candidate. Contextualism holds that no belief or proposition has any intrinsic content or epistemic priority outside of any context. According to contextualism, in a particular context certain beliefs will be held as presuppositions that shape the direction of inquiry and allow or disallow certain objections, so that some beliefs and propositions are fixed from criticisms in a particular context. Further, it is methodologically necessary that certain beliefs be fixed in a context if we are to proceed with inquiry at all; the logic of inquiry requires that some beliefs be out of question for inquiry to take place at all. What we find out of Williams' contextualism is that the sceptic may still make sceptical arguments, but only within a context of foundationalism; all of our other contexts are safe from epistemological scepticism because they hold different presuppositions, so that scepticism's authority is restricted, and it cannot damage all of our knowledge at once.

Finally, in responding to Williams' critics we addressed the issue of whether Williams tackled all the most important sceptical arguments, and from there we were led to a discussion of how well contextualism represented our normative practices compared to foundationalism. We found that contextualism does represent our normative practices well. Next we broached the subject of epistemological realism, and found, as Stroud suggested and Graham explained, that epistemological realism is not always sceptical, only a certain branch of it, so that there are anti-sceptical epistemologically realist theories.

In the end, I believe we have made a strong case for avoiding scepticism: we began with the idea that scepticism must be doing something behind the scenes to get such radical conclusions that clash with our everyday ideas so badly, and we found that this was the case; radical scepticism presupposes foundationalism, and so is only effective in foundationalist contexts.