Excellent synopsis. I think I agree with Professor Taylor's post that the challenge of skepticism cannot be met, and so that our knowledge talk reduces to talk about belief formation strategies tailored to our phenomenal world.
Hume probably gave the only answer to the skeptical challenge one could hope to give, namely, that at the end of the day we all (do and probably should) set aside the assumptive and discriminative problems you've limned and go about "knowing" things about our world (such as it seems to us), with more or less fitting results. I might be trapped in a dream or a simulation, but then if so my best hope for escape would seem to lie in rational belief formation. For what other strategy is there?

The two skeptical arguments above are interesting, but I think Ken
was asking a question in his previous posts that has not
yet been addressed: are there powerful arguments
against rational (or justified or warranted) belief?
For instance, can we modify the above two arguments to produce
compelling arguments that no one can have justified beliefs about
the external world?
This had some plausibility:
H.4 Beliefs that depend for their evidence on an unjustifiable assumption do not count as knowledge.
but what about this?
H.4* Beliefs that depend for their evidence on an unjustifiable assumption do not count as justified.
A similar change for D is changing this
D.1 A person knows that p on the basis of evidence E, only if E rules out alternative possibilities to p.
to this:
D.1* A person is justified in believing that p on the basis of evidence E, only if E rules out alternative possibilities to p.
As far I can see, the reasons given in support of D.1 (on the second
sense of ruling out) support D.1* too. I am unsure about H.4*.

Nice post, Patrick. I think here we need to make a distinction between epistemic and practical justification (this is relevant to Q's comment and Ken Taylor's post as well). I think there is a familiar sense in which an action A or belief B is practically rational if it is my best or only option. But then the skeptic is not challenging the practical rationality of either believing or acting on those beliefs. Rather, he/she is challenging the belief's epistemic standing, and claiming that it is not based on sufficiently good epistemic (truth-indicating) reasons. My point is now this, in favor of H.4*: I can see where it is sometimes practically rational to believe or act on the basis of epistemically unjustified assumptions. But it is much less plausible that one can be epistemically justified in believing on the basis of epistemically unjustified assumptions. If one can be, it should come as a big surprise.

Mike,
I don't think of the skeptical arguments as making knowledge claims themselves. Rather, they take claims that look good to us and show us where they lead. So I am not sympathetic to replies of the form "The skeptical argument assumes we know . . ."
I think your comment about an implict high standard is right. Maybe it is wrong to say we have to rule out every alternative possibility in order to know. But now things get interesting. We would like a principled account of which possibilities need to be ruled out and which do not, and if we can give one I think we will learn something about the nature of knowledge in the process.
I have some ideas about what account to give here:
http://plato.stanford.edu/entries/epistemology-virtue/

Aaron,
I am not sure what your position is regarding the argument. You say it can't be answered, but why not? Because it makes no mistake? But then the conclusion that we lack knowledge is true. If you think we do have knowledge (as the result of context or whatever) then you must think that the argument goes wrong somewhere.
Some contextualists combine the importance of context with Mike's idea above: context determines which possibilities need to be ruled out and which do not. I tend to agree, but I think that backing this up requires us to say interesting and important things about what knowledge is and how it works. And if we can do that, then Hume's argument IS answerable.

Mike,
What makes the arguments interesting, on my view, is not that there is someone who is willing to defend them, and therefore someone who is committed to both the premises and conclusion. What makes them interesting, rather, is that the premises looks good to us, but we want to avoid the conclusion. This is a theoretical problem, not a practical or rhetorical problem, such as asserting something while at the same time denying the sort of knoweldge implied by the assertion.
Look at it this way-- the skeptical arguments would be interesting even if there were no one willing to assert them. We non-skeptics would still have exactly the same problem, i.e. that all the premises seem right whereas the conclusion seems wrong. We still want to know which premise to deny and why.

Does anyone have any philosophical sources that discuss the (obvious)first principle (that "A person knows that p on the basis of evidence E, only if E rules out alternative possibilities to p")? Cheers

Aaron,
You are imagining a debate with a committed skeptic, and you realize that such a person can always raise questions about any claim that is made by his opponent in the debate. You also realize that such a conversation could get nowhere, so long as the skeptic remains consistent in his/her refusal to allow any claim. I entirely agree. If you ever meet such a person, by all means don't get into a conversation with him. But the skeptical arguments I am interested in don't ask questions, and nowhere do they depend on an assumption to the effect that no claims are admissable. So I don't see how your points address those arguments.

Jeremy,
I recommend the following:
DeRose, K. and T. Warfield. Eds. (1999), Skepticism: A Contemporary Reader. New York: Oxford University Press. See especially DeRose's Introduction.
Pritchard, D. (2002a), ?Recent Work on Radical Skepticism.? American Philosophical Quarterly, vol. 39. no. 3, pp. 215-257.

Mike,
I don't find arguments from self-defeat persuasive here, partly for the reasons I have already given. But here is a different point: even if such arguments show that skeptical arguments are mistaken, they don?t show where they are mistaken. That is, they don?t show which assumptions of the arguments are false, and so no lesson is learned from them. Here is another thought: I am already assuming that the skeptical argument is mistaken somewhere. I think I know that I know that here is a hand, and so I don?t need self-defeat arguments to show me or convince me that the skeptical arguments go wrong. The interesting question is WHERE do they go wrong.
I think we can distinguish three grades of success in a response to a skeptical argument, each being more satisfying than the former: a) identify an assumption that we need not accept, b) find a reason for thinking that some assumption is false, and c) find an explanation for why some assumption is false, e.g. come up with a theory of knowledge that explains the mistake. Notice that an objection from self-defeat does not even give us the least satisfying of these grades.

Aaron,
But this sounds like you are simply agreeing with the skeptic-- i.e. that there are various possbilities and they can't be ruled out. Maybe you are saying that they don't need to be ruled out for us to have knowledge.
On my view we have to get clear about what we mean by "rule out." On some readings, I think we can rule out the dream possibility, and so the premise is false. On other readings, I think it turns out false that we need to rule out all the alternative possibilities. But either way, there is something in the argument to deny, and progress to be made by explaining why we can challenge the argument at that point.

Hello there,
Interesting discussion. I want to make a proposal that might perhaps formulate better worries of people like Ken Taylor and others who have made similar points.
As well as justification of beliefs, we might perhaps define another quality: blameworthiness for believing something. (Just bear with me and it will make more sense at the end.)
Despite the moral connotations, the notion of blameworthiness I have here has nothing to do with blameworthiness in that sense. It's "epistemic blameworthiness" if I may so fancy. Suppose that a chess player, without due reflection and calculation, decides upon a move M. The chess player can be "blamed" for his belief that M should be his next move, since he decided upon it without any reflection.
Now suppose that one day you wake up and see a powerful demon who is laughing at all the foolish beliefs you just had and chastising you for not taking skepticism seriously. "But," you say, "there was no EVIDENCE whatsoever for believing in a skeptical hypothesis. True, I may not have had the correct beliefs. Nonetheless, given the evidence I had, these were the BEST beliefs that I could possibly have. Surely, I can't be BLAMED for having them." And this time, you wake up to find yourself in the Matrix.
My point is that even if the skeptic's arguments work for justification and knowledge, there is a sense of blameworthiness for believing that is substantially weaker than both justification and knowledge and for which the skeptics arguments don't work.

Just an addendum.
Here is the distinction between justification and epistemic blameworthiness:
A weak chess player might contemplate over a chess position and after due reflection may decide on a move. The move may be indeed bad and in the light of proper analysis, completely UNJUSTIFIED. Nevertheless, the weak chess player can't be blamed for deciding on that, since he did his "epistemic duty".
I have a feeling that this discussion is likely to spill into the discussion concerning ethics of belief.

To strive above all at holding as many true and as few false beliefs as possible, is not rational. This is one of the valuable points made by Mikael Stenmark in a discussion with Vincent Brümmer about the theism-atheism debate.
Brümmer himself has often argued that since human beings are not merely knowing subjects, but rather actors, the rationality of their decisions as to which view of life to adopt, cannot be adequately judged from a purely epistemological point of view, but should take pragmatic considerations into account. In developing his argument, he draws on the work of Martin Heidegger, but a similar insight might also have been drawn from Ludwig Wittgenstein.
I fact, I think that Hume - unlike Descartes - was, in his own way, trying to make precisely this point when developing his sceptical arguments. He was not trying to convince anyone of scepticism, but rather illustrating the absurdity of a certain kind epistemological approach. The intelligent thing to do, the rational approach, is to get on with living in a way that works for one.
An important contemporary thinker who develops this approach to rationality quite extensively is Wentzel van Huyssteen. He views rationality from an evolutionary perspective, which helps him to see it as an adaptive capacity, something to be used in order to live meaningfully. This links up with perspectives in the philosophy of science that focus on the instrumental value scientific theories, the fact that they are intended to explain, predict and control.
From this kind of perspective the crucial question as far as our basic assumptions about the world is concerned, is not whether we can prove them, but rather whether it is wise to live with them, whether they help us to live well. And perhaps behind it all lies the intuition that if something works, that must be because it has some link with how things really are. And with the question: What does it mean for something to be "real"?
- Gerrit Brand
(Visit my blog at gerritbrand.blogspot.com)

Hello!
I hope no one minds me giving some opinions on this post.
I haven't read through every post above, but I would like to challenge this proposition.
1. A person knows that p on the basis of evidence E, only if E rules out alternative possibilities to p.
This seems ambiguous to me. Intuitively I should have thought if you recognise something, you recognise that thing. If your recognising that thing e.g. your wife consisted in ruling out other possibilities, that would seem highly implausible. How do you know which other possibilities are the ones you need to rule out? And why just these possibilities? On the other hand if you recognise your wife directly, then this as a matter of logic automatically does rule out all other possibilities because they are not your wife. So does this proposition 1) mean a) in order to recognise something (or have a reason for supposing something) this must entail some other possibilities are ruled out, or does it mean b) the nature of having evidence for E consists in ruling out other possibilities?
Even a) might be challenged. For instance it might be argued that if the only thing you ever saw you whole life was one shade of red, then that perceptual experience could never register in your consciousness. We must have at least one other visual experience so that we can contrast one thing with another to register either. This is an argument for a) and it seems plausible. But suppose you experienced just one degree of the most intense agonising pain all your life, does this mean that you could never even have any awareness that there was something wrong somewhere? And how would, or could you set about settling the matter beyond what may seem plausible in an argument?
Justin

An Equation of Truth
Truth is when the subjective = the objective
Or simply: Subject = Object
Or more simply: =
= is truth.
Anything else is only probable or uncertain at best.
Life without measure is equal and equal makes the Universe One.
Equal = "free at last, free at last, free at last..."
"The truth shall set us free."
=
MJA

The old bottom line: Apply the skeptical argument to itself --- things could be another way entirely,we're brains in vats and so on ----and you will be skeptical of skepticism; things could be other than the way skeptics depict them. Skeptics, since they maintain that they know they are correct,cannot admit that things could be other than they say--without contradiction. If the reply is that one cannot apply skeptical argument to itself---why not?
The odd thing is that to make the skeptical argument work skeptics must hold,it seems that the world is a particular way and no other way--otherwise the skeptic could not hold that we cannot know the true state of things. Well the question arises---how does skepticism know there is a true state of things. Where do they get that?

If we'll never know if we know--have the correct thought of-- the true state of things, then I could be wrong in holding that I don't
know the true state of things. But this seems intuitively impossible---how can I not know what thought
arises within me?