I could come up with an argument that you don't exist, but it would be harder for you to. Descartes' point is that even in doubting that I exist, I seem to presuppose that I actually do. Descartes claimed that in any moment when I reflect on it, I know for sure that I exist.

That said, this shows much less than it might seem to. In particular, it doesn't show that there is any unified "self" that has a continued, coherent existence over time. The existence of that sort of "I" has been doubted by many thinkers, going back at least to the Buddha, but also, famously, by David Hume and more recently by Derek Parfit. Views of this sort are sometimes called "bundle theories" because they replace the idea of a unified self with a picture according to which we are an ever-changing bundle of sensations and thoughts.

Here's a link to the section of Hume's Treatise in which he sets forth his views on the self. Enjoy!

http://www.mnstate.edu/gracyk/courses/web%20publishing/TreatiseI.iv.vi.htm

It is a requirement for something to be genuinely known to be true that it is true. So knowledge implies truth (in the sense that if X knows that so-and-so, then it is the case that so-and-so).

But that doesn't make knowledge the same as truth. The implication the other way around doesn't hold. There are truths that you don't know, that I don't know, and indeed that no one right now knows (maybe because nobody has bothered to find them out, maybe because the time has past when anyone could check, or because the truths are about far-off events like meteorite strikes on the far side of the moon, or for other kinds of reason).

Leaving ominiscient deities out of it, not every truth is known. But we might wonder whether every truth is knowable, in principle, e.g. by a suitably placed and sufficiently smart observer. The trouble with that idea is in spelling out the "in principle".

It's worth saying something first about Descartes (as it wasn't his view that he couldn't prove he wasn't dreaming).

Descartes is troubled that, as he sees it, the then dominant systematic story of the world is in deep error, and is getting in the way of the growth of the revolutionary new science of the day. He has a diagnosis, too, of the source of error -- he sees Aristotelianism as springing from some deeply embedded childhood habits of thought. Radical measures are required to prise us out of such deep-rooted error. The ‘Method of Doubt’ provides the once-in-a-lifetime jolt needed to shift us out of certain childish thought-habits and to get us adopt better intellectual methods and open the way to improved science. Faced with even the most reasonable-seeming presumptions, Descartes suggests, "I must withhold my assent from these former beliefs just as carefully as I would from obvious falsehoods, if I want to discover any certainty in the sciences." So for Descartes, it is not that our former beliefs are all unreasonable: but rather we are to play along with fantasies about dreams and evil demons as an instrumental step to help us sort out the safe beliefs from the contaminated dross.

Descartes’s hope and belief is that, after a temporary strategic retreat from received views and common sense, he will still be left with enough indubitable foundational beliefs to provide a secure bridgehead from which he can fight back and recover those common-sense beliefs that don’t carry the baggage of disputable theory -- including of course his common-sense belief that he is sitting by the fire, wide awake. And he can then go on to ground a secure corpuscularian science.

Of course , notoriously, Descartes's fightback is problematic in all kinds of ways. But he certainly thought he could establish on firm grounds the general reliability of the senses and the security of our ordinary knowledge that we are not dreaming.

But that's history, you might say. Descartes might have raised the thought that he might be dreaming just as a methodological tool rather than as a hypothesis about how things really might be to be seriously entertained. But now the doubt has entered in, it (as it were) takes on a life of its own: so how do I prove I'm not dreaming?

Well, speaking for myself, I’m all for a cheerfully resolute response. We have every good reason to suppose that in ordinary life, when our usual criteria indicate that we are wide awake and not dreaming, we are wide awake and not dreaming. And what if the sceptic asks me how I rule out the possibility that, for all that, my whole ordinary ‘waking’ life is in fact just one big coherent dream (unlike any ordinary dream, of course, perhaps being a put-up job engineered by an evil demon)? I just riposte that I have been given not the slightest reason that to suppose that that is a live possibility. As the questioner puts it, it is difficult for me to take the suggestion seriously. Why should I? It is one thing to use the evil demon fantasy as Descartes does, as an imaginative tool in trying to locate some core of infallible beliefs: it is something else entirely to imagine that the honest enquirer needs to rule out the evil demon scenario before he can regard science (broadly conceived) as a reasonable enterprise. The scientist just doesn’t have to waste her time ruling out myriads of daft hypotheses she hasn’t the slightest reason to suppose are true. And for me, that’s pretty much the end of the story.

Of course, in saying that, I'm just relying on our familiar beliefs and best scientific methods for proceeding. But what else am I supposed to do? True, I can’t justify anything without appeal to such familiar beliefs and best scientific methods. But so what? Well, some say (in fact this is a quotation from Barry Stroud),

. . in philosophy we want to understand how any knowledge of an independent world is gained on any of the occasions on which knowledge of the world is gained through sense-perception. So, unlike . . . everyday cases, when we understand the particular case in the way we must understand it for philosophical purposes, we cannot appeal to some piece of knowledge we think we have already got about an independent world.

But what notion of ‘philosophy’ is in play here? I for one just haven’t much grip on what sort of coherent project there could be here, this special ‘philosophical’ enquiry that isn’t part of science broadly conceived. Again quoting Stroud, it seems that

All of my knowledge of the external world is supposed to have been brought into question in one fell swoop . . . I am to focus on my relation to the whole body of beliefs which I take to be knowledge of the external world and to ask, from ‘outside’ as it were . . . whether and how I know it . . .

But that gives the game away. If the ‘philosophical’ project is supposed to involve jumping outside my beliefs and methods, and trying to squint sideways at them from ‘outside’ as it were, to try to justify them as matching up to an external world, then that is just incoherent. If the sceptic is complaining that that project of justifying can’t be pulled off, then he’s quite right the project is impossible, but quite wrong to complain. You can’t be both ‘inside’ and ‘outside’ your own thoughts (thinking them, but squinting at them sideways too).

One thing I know is the difference between the taste of sangiovese and pinot nero -- a bit of wine-wisdom I've acquired over the years. But I certainly would be very hard put to express that knowledge in propositional form, at least in any informative way that could usefully convey my knowledge to you. Is there any proposition I could use to do that?

Of course, I can say -- taking a sip -- "this one is sangiovese", and -- taking another sip -- "that one is pinot nero". But that won't help you, unless you are sipping away from the same wines, and you are attending to the differences.

You need to experience the wines for yourself, and need to pay attention to them and learn to tell them apart. And developing that skill, that know-how, seems to require something other than picking up propositional knowledge-that about the wines.

The idea of a "disembodied spirit" is hardly a clear one. And no doubt some ways of trying to fill out this idea lapse into sheer incoherence. Understood in such a way, there just can't be any such things as "disembodied spirits". And non-existent beings can't do any causing!

But let's suppose we can spell out an internally coherent theory that purports to explain various occurrences by postulating the existence of things that, by the lights of our current scientific beliefs, do look decidedly ghostly. Well, it could in principle turn out that, by our best standards of theory assessment, this surprising theory in the end trumped rival theories. Why not? After all, similar things have happened often enough in the history of science -- meaning that initially whacky looking theories postulating weirdly spooky stuff (action at a distance! photons going through both slits!! many-dimensional strings?!?) can begin, given enough successes, to look to be the best game in town, and even come to be firmly accepted.

Though I think I'd stake my mortgage against a ghost story turning out to be a serious runner ...

All arguments seek premises that most people can agree to without needing further support, and in this sense the appeal to what is "obvious" remains alive and well. What people can agree to without further support often depends on the context, however: in the context of a weekend stroll, it may be obvious that there is a goldfinch nearby, whereas in the context of an official birdcount this may be less obvious.

It is more accurate to call obviousness a criterion of knowledge rather than a criterion of truth, since the obviousness of a certain claim may be part of what makes my state a state of knowledge but it is not a part of what makes it true. The fact that a bird ate the seed will be true (or false) regardless of how obvious it is to me. The fact that is is obvious to me may, however, contribute to my view counting as knowledge.

Note that obviousness may be a criterion of knowledge without being either necessary or sufficient for knowledge. Much of what we know (about the movement of the planets, for example) is not obvious, and some things that are obvious (the bend of the stick in the water) are not known.

A closely related term is "self-evident", and many philosophers think that foundational knowledge, such as the knowledge that is given to us in perception, must be self-evident knowledge -- revealing its truth in the very manner of its appearing. Other philosophers, rejecting the idea that knowledge has foundations, deny that there are any self-evident truths.

Yes. Lots.

That's the easy answer. The hard answer is explaining how we could possibly learn anything true from a series of false statements. One answer is that good works of fiction use false statements to describe deep truths about human nature, emotions, relationships, morality, and the meaning of life. They do so by creating a world of characters and events that does not actually exist but that shares enough common features with our world that we can learn from them. Most importantly, the fictions may share the deep (and general) truths about human nature, etc. with our world, and they may do so because the writer has a deep understanding of these truths.

Fiction also explores the boundaries of the possible and teaches us to think about these possibilities. Philosophy often works in this way. By considering what is possible but not actual we learn something about our world and ourselves. Science fiction and philosophical thought experiments sometimes differ only in that the science fiction tends to be better developed and better written.

Our knowledge of the past derives from perception, memory and inference, in the sense that these are answers to the question, 'How or by what means do you know?' (There are other ways, for example report or testimony). But our knowledge of the future has in it no elements of memory or perception. So as one might therefore expect it is harder to come by knowledge of the future, and we have less of it per hour, if you want. We typically can know more about a past hour than about a future hour, though by no means all of the past hours, for example those in past centuries. If I know p, and p is a proposition about the future, I cannot know it by memory, special cases apart. (A special case would be that I come to know that I am going to Africa next summer - a piece of knowledge about the future - by remembering that I am going to Africa next summer. 'How do you know?' 'I just remembered it . . .' makes sense as a conversation.)

It seems to me, in spite of the assumption you make, however, that in some cases there may not be an element of uncertainty in either knowledge of the past or the future. There is no uncertainty that the cat will be roughly where it is on the sofa in one attosecond - cats don't move that fast - and there is no uncertainty that the cat has been sitting there for the last five minutes, as I have been watching it for the whole time. There is an interesting mistake (I myself think it's a mistake, anyway) to be avoided in this area. Why are there asymmetries in time with respect to knowledge? I am not sure the question put just like that makes sense. Why can we remember the past but not the future, for example? The simple answer is that if I remember something, then it must already have happened, so memory of the future is a contradiction. My own view is that even the alleged logical asymmetries between past and future are much more slippery than they seem at first glance, and we must be careful to get our tenses right. It is certainly true, for example, that the past exists, in the sense that past events have occurred - and what other sense are we considering? But then so does the future exist, in just the same sense: future events will occur.

This doesn't seem at all clear. First of all, the argument assumes that, to know whether we know, on Nozick's account, we would have to know whether a certain counterfactual is true. But this isn't obvious. Water is H2O, but it doesn't follow that, to know whether something is water, you have to know whether it is H2O. Similarly, even if knowledge is (say) Nozick-style tracking, it does not follow that, to know whether you know, you have to know whether you track Nozick-style. That might follow if Nozick's account is construed as providing some kind of conceptual analysis, but even then there are issues that tend to go under the heading "The Paradox of Analysis".

Second, even if the foregoing is waived, I don't see why we can't know "whether the subjunctive condition Nozick deems necessary for knowledge is fulfilled". Surely we do have lots of knowledge about possibility, necessity, and counterfactuals. Of course, the epistemology of modal knowledge is a vexed issue, but so is the epistemology of everything else.

Well spotted! Nozick holds that, in order for you to know p, it must be the case that, if p were false, you wouldn't believe p. This condition is not fulfilled when p is "it is not the case that I am a brain in a vat on Alpha Centauri being stimulated to have my present experiences": if p were false (if I were a brain in a vat on Alpha Centuri being stimulated to have my present experiences), then I would nonetheless be believing p.

But this condition may well be fulfilled when p is "I am typing." It is fulfilled if, were I not typing, I wouldn't believe that I am.

With this move, Nozick takes himself to have shown at least how knowledge is possible: it's possible that I am really typing and that, if I weren't typing, I wouldn't believe that I am. But do I know that I am typing or do I not? Well, according to Nozick, this depends on what I would believe if I weren't typing now. Nozick assumes that there's a definite answer to this question, a fact of the matter. But, even if we grant this, how can we find out what the answer is? How can we examine the possible world in which I am not typing that is closest (whatever this means) to the actual world in order to ascertain whether, in that possible world, I (or "I") believe that I am typing? We cannot find out. More generally, though we may well know many things, in Nozick's sense, and even know that we know them, in his sense, we cannot find out for any belief we might hold whether it constitutes knowledge or not (because, even if we can find out that our belief is true, we cannot find out whether the subjunctive condition Nozick deems necessary for knowledge is fulfilled or not).

So Nozick's showing how knowledge is possible shows the possibility of knowledge in something other than the ordinary sense. We may have knowledge in Nozick's sense, but we can in principle never find out whether we know anything and, if so, what. As you suggest, this isn't much of a victory over scepticism.

(BTW, I wrote up this critique in a termpaper in my first semester at Harvard and got a B+ from Nozick. So there you go.)