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I know that this might be common but I just got interested in philosophy...

I know that this might be common but I just got interested in philosophy... So here it goes, How do we really know if we are Dreaming or Awake right now?

It is indeed a common question, at least in the sense that almost everyone has considered it at some point in life. And yet, as common as it is, it leads directly to some of the most difficult, profound ideas. As Strawson once wrote, there is no shallow end in the philosophical pool. So, it needn't bother us that the question is a common one. However, the question is also a HUGE one, as philosophers have had many, many different ideas about it. I can't possibly summarize all of it here (not that I know all of it!). But I can offer a few different ideas about what direction one might take in thinking about this question.
One idea is that we can somehow tell, given the content and character of our current experiences, that we are awake. Dreams, according to this idea, are seldom if ever this coherent, this consistent, and this integrated with our accessible memories. And experiences in dreams are never this "stable" or lucid. So, we have empirical evidence, or evidence based on our present experience, that we are not now dreaming. One problem with this idea is that we've been convinced before that we are awake and then discover that we were dreaming. And as correct as the idea sounds to us right now, the impression that we were awake during previous dreams have also convinced us of their "correctness." But, perhaps more troubling, we might ask: how do we know that this isn't a dream unlike any we've had before, in that it is more vivid and apparently coherent than any other dream we remember?
Another, second idea in response to the question is that the what we mean by terms like "table," "chair," "body," and even "dreaming" are just whatever we are actually confronted with at this moment. It would follow (though it takes lots more theorizing to get there) that I cannot possibly mean something true by "I am now dreaming" or "this apparent table in front of me is dreamed, and not a real table." However, one may well doubt that this theory of meaning (not that I've given it its most subtle, effective formulation) is true. Couldn't you truly assert, while dreaming, that you are dreaming? Isn't this what sometimes happens when you have a lucid dream (a well-documented phenomenon)? Furthermore, and perhaps more telling, this response to the question doesn't seem to satisfy us even if we grant it is correct. Even if we grant that whatever we mean by "I am dreaming" is false, all this seems to show is that we cannot formulate some troubling hypothesis. That is, we seem to be able to describe a possible situation in which reality is not as it currently seems (notice I didn't exactly use the term 'dream'), and we apparently can't rule that out, even if we can't use our ordinary terms to express the possibility. We are left with a feeling that something inexpressible could be true, and if it were true, reality would be disturbingly disconnected from how things seem to us.
A third way to answer to the question is to suggest that, though it might be the case that I am now dreaming, the best, or simplest explanation of my present experiences is that I am awake. This may sound like the first response, and in some ways it is. But it adds a crucial element: explanatory considerations. By thinking about my experiences and the way they are now unfolding, I conclude--according to this idea anyway--that the simplest explanation for them is that I am now awake. In the first idea, I read my awakeness, as it were, directly off of my experiences. So, does this explanatory addition help? It might, but it all depends on how the many details are filled in. I don't know how to fill all of those details in, and even if I did, it'd be a very long story. We'd need to specify in what sense, exactly, is the awakeness explanation better, or simpler, and why it is that, in this instance, the simpler explanation is the more likely, or rational, one. And, I noticed you asked how we "really know" whether we are awake. Does noticing that an hypothesis is the simplest explanation suffice for KNOWING that that explanation is true? REALLY KNOWING? These are some pretty controversial questions, but anyway that's one direction to explore.
Let me suggest a final sort of reply to you question: we cannot really know whether we are dreaming or awake. This is the "skeptical" reply. From here, things could go in various directions. You might think that therefore you don't know anything at all about the world around you! After all, if you don't know that you're not dreaming, how could you know that there is a table, a poodle, and a computer in your room (as there seems to be, let us suppose)? But you might question that. You might think that, even if you don't know the very large-scale claim that you are not dreaming, you still somehow know that there is a table in front of you. In fact, this is one way to use some of the insights of the second reply, above, in a more skeptical spirit. Tables, for example, are just whatever THIS is (point to the apparent table). But who knows if this is all a dream or not? Another direction to go is to think that you don't know whether you are dreaming this, but that's just because you never really know anything at all. This is just a particular instance of not knowing, or ignorance, which is everywhere. Sure, I don't know whether I'm dreaming. But I don't really know anything, so that's not big news. Knowledge is an impossible standard.
What a strange situation we find ourselves in! It is such a remarkable and yet, as you say, "common" and perhaps obvious thought that this might all be a dream. And it's not at all obvious how we could know whether that is the case. Is this bad news? That's another, related question. Does it matter? Here's a thought: if this is a dream, it doesn't matter whether this is a dream. So it couldn't be a dream while it matters whether it is a dream. I'm not sure that's right, but it can be a tempting thought.
As you can see, there's just so much to say. Great question! As Descartes once observed, consideration of whether you are dreaming makes you feel a little dazed, which makes it seem all the more plausible that you are in fact dreaming. Just don't try this while driving or operating other heavy machinery.

I've heard many philosophers promote skepticism. But it seems that skepticism is

I've heard many philosophers promote skepticism. But it seems that skepticism is self-defeating, since the skeptics would have to be skeptic about their own doubts. Therefore, by virtue of that, they should not be skeptic. Is this argument valid?

Whether this argument is valid really depends on what you mean by some of the key terms (this happens a lot in philosophy). But first: I don't think that a lot of philosophers promote skepticism. Most philosophers aren't skeptics, in the sense that they don't think that we have no knowledge about the world, or that we should doubt everything. But this gets us to the first term that needs to be clarified: what is skepticism? I gather from what you say later in your question that you take it to be something like the view that one should doubt everything. But then what does it mean to be a skeptic "about your own doubts?" One guess is that it means to doubt whether you should doubt, or to doubt that doubting is the right thing to do. If skeptics are people who doubt everything, that seems compatible with their also doubting whether they should doubt. There doesn't seem to be any contradiction there. We have doubts about what we think, and do, all the time. This would just be another instance of that: I doubt, and also I doubt whether I should doubt. This is especially clear if what we mean by "doubt" is just withholding belief (though I think you didn't mean just that by "doubt"). You can withhold a belief and also withhold the belief that you should withhold belief. This happens sometimes when you just have no idea what to think about some issue at all. So far, no contradiction. If a skeptic is one who doubts everything, then, it seems there is no problem here, with regard to having doubts even about one's doubts. Let's assume, then, that you meant to be talking about those skeptics who hold a theory, the theory that we should doubt everything. So if, instead, a skeptic is someone who believes that we should doubt everything, then that skeptic seems to be in an unstable situation: she believes something, and also believes that she should doubt that thing which she believes (since she believes that she should doubt everything). That seems problematic, as you point out. But you should also appreciate that most sorts of skepticism, at least as they are discussed today, are about a particular subject matter. Two prominent examples are skepticism about the external world and skepticism about morality. In both of those cases, the skeptic (the one who believes that we should doubt everything on such matters) is not in any trouble. She believes that she should have doubts about the external world and morality. But notice that this belief, that she should have doubts about the external world and morality, is not itself about the external world or morality (unless we unnaturally interpret "should" as a moral, rather than an epistemic "should" that concerns our intellectual, rather than our practical, conduct). So, her belief in skepticism is not something that her skepticism requires her to doubt instead.

In the light of the current state in philosophy, do skeptics still get an upper

In the light of the current state in philosophy, do skeptics still get an upper hand? Can we really know anything with certainty?

I'm going to refer you to two websites. At the PhilPapers Survey, you'll discover that only 4.8% of "target faculty" said that they accept or lean toward skepticism. Among specialists in epistemology (the theory of knowledge), that figure increases to 9.4%, but it's still small enough to suggest that philosophers in general don't think of skepticism as having the upper hand once the reasons for and against it are examined carefully.

For detailed discussion of your second question, you might start with the SEP entry on "Certainty". I hope you find these resources helpful.

I admit that my knowledge of philosophy is very limited; not advanced, yet it is

I admit that my knowledge of philosophy is very limited; not advanced, yet it is my overall second favorite subject after science. If one accepts the proposition, "I do not know anything with absolute certainty," then is it actually self-refuting or logically contradictory? The reason, is that, if one accepts it, then one must know something with absolute certainty, which is the proposition itself. Therefore, one knows with absolute certainty that one does not know anything with absolute certainty. However, it seems to become infinitely (pun intended) problematic if one thinks about it deeply enough. For instance, if one knows with absolute certainty that one does not know anything with absolute certainty, then one must also know with absolute certainty that one knows with absolute certainty that one does not know anything with absolute certainty. I think that one knows where I am going with this. It could be extended ad infinitum. If one, however, accepts that one does not know with absolute certainty...

Nice question! It's one with a long history, as something like what you're saying was one of the main objections to the ancient skeptics and their intellectual decedents. Let me just say a couple of things. First, to answer your question, I don't think your observation would show that skepticism is contradictory or self-refuting, at least not technically. The observation is that some skeptics take themselves to know for certain that nothing can be known with certainty. The view that they take themselves to know with certainty, namely that nothing can be known with certainty, is not thereby shown to be contradictory. It is compatible with that view that some people take themselves to know something for certain. To see this, just notice that it is compatible with the view that no one knows anything that some people, who unlike skeptics don't accept that view, take themselves to know some things. So the mere fact that people take themselves to know (or "accept" that they know) does not show that the view that no one knows is false or contradictory. Nor is the view that nothing can be known for certain thereby shown to be self-refuting, though that may depend on exactly how we understand "self-refuting." A view or position that is self-refuting is one such that, if it is true or correct, then it is false or incorrect. But the view or *position* that nothing can be known for certain does not entail that something can be known for certain. For, that view doesn't say that it (the view) can be known for certain. (Consider the statement "this statement can't be known for certain." That's a weird statement, but it is not self-refuting or a contradiction.) So, it doesn't seem we've found the skeptical view, or claim, to be a contradiction or self-refuting. The key is that what a view, or claim, or position, states need not include that it itself can be known. If the skeptical claim were, instead, that it can be known for certain that nothing can be known for certain, then that would be a contradictory view. However, we must distinguish one's being certain about claim C and the claim that C can be known with certainty. That is, we must distinguish the attitude one has towards a claim or view and the content of that claim or view. As you note, one might also form a further thought: I know for certain that skepticism (the view that nothing can be known for certain) is true. But, the content of that further thought is not skepticism. It is a thought about what one's attitude about skepticism is. This further thought contradicts skepticism, but it is not entailed by skepticism (skepticism, the view, does not imply that this further thought is true). So, that one might have this further thought does not show that skepticism is contradictory, either.
Secondly, now that I've suggested that the view skepticism, is not a contradiction or self-refuting, we should ask whether skeptics, or those who accept skepticism are doing anything irrational. Of course, there does seem to be something incoherent, inconsistent, and perhaps hypocritical with someone who takes herself to know for certain that nothing can be known for certain. Does "acceptance" require taking oneself to know for certain? I doubt it. But let's grant that for a moment. Such a person has contradictory or inconsistent attitudes. Does skepticism, the claim that nothing can be known for certain (at least as you have formulated it) entail that we should accept or take ourselves to know skepticism for certain? I don't see any reason to think that it does. So, even if skeptics are being inconsistent, this doesn't seem to reflect badly on skepticism, the view. Consider a slightly different sort of skepticism though: you should suspend judgment about everything. That view does seem to imply that you should suspend judgment even about it. So anyone who holds that view is doing something that their view says not to do. To hold such a view is, perhaps, irrational, or at least not ideally rational, because such a person has inconsistent or incoherent attitudes. It doesn't, though, seem to show that the view is false. Couldn't it be true, fully coherently, that nothing should be believed at all, not even that nothing should be believed? That could be true, but no one could ever believe it coherently, or while being rational. It seems we accept, generally, that there are truths that are unknowable and not rationally believable (think of all the insanely complex mathematical truths that no one with a human mind ever has good reason to believe). So maybe this skepticism is just another one of those truths. If so, then here is what we can conclude: believing such a skeptical view is irrational.
Ok, where are we? Skepticism, the view, is not contradictory or self-refuting. But, perhaps, being a skeptic, or believing skepticism, may be irrational. This may not be so bad if one specifies how exactly it is irrational: it is irrational only because it is a view that is believed, or a position, not because the content of the view has not been well argued for or has been shown to be false or contradictory. Maybe that takes some sting out of the objection. Skeptics are irrational, but not in the same way that, say, astrologists are irrational. Astrologist believe something on the basis of bad arguments. But nothing of the sort has been shown about skepticism. Skepticism of this sort says that no one should believe anything, not even skepticism. So while skeptics, or those who believe it, are being irrational (though, as I just said, not for the reasons that philosophical or superstitious positions are usually said to be irrational), skepticism as a view may still be true, supported by the best arguments, and so on.
I haven't answered the question, what would the most radical skeptics claim. But maybe they'd point out something like I just did.

what are the requirements for knowledge?

what are the requirements for knowledge?

Isn't prejudice just common sense? If it's reasonable to assume that since every

Isn't prejudice just common sense? If it's reasonable to assume that since every dog I've ever met has four paws and a snout, then, until proven otherwise, every dog I will meet with have four paws and a snout, then why isn't it reasonable to assume, if every American I've ever met is foolish, unless proven otherwise, that every American I will meet will be foolish?

It seems to me that you have at least three classes of judgement in your question. 1. Prejudice. 2. Common Sense. 3. Informal definitions. 4. Inductive generalisation.

Let's start with the latter: if all the Xs I have come across are Ys, and if I have no reason to believe that the Xs I have come across are exceptional or otherwise not representative, then I have some confidence that Xs are Ys. Americans are foolish.

What I am calling an informal definition is a way of describing an identifying feature of something: dogs have four paws. Now, this is different from the above because you very likely learned about dogs in part by having the number of paws pointed out to you, whereas probably you didn't learn what an American is by having their foolishness pointed out.

Continuing backwards, I would claim that the first two categories have something social or cultural about them, that the second two do not necessarily have. Common sense is called 'common' to indicate that it belongs to a particular social group at a particular time. What is common sense to an 18th Century French farmer is a very different set of beliefs than common sense to a Google employee in 2015. Prejudice is similar.

However, if we wanted to attempt to differentiate between common sense and prejudice, we might start with the following. First, common sense usually means something positive (a good thing, tending to be accurate), whereas prejudice something negative (a bad thing and a mistake). However, insisting on that difference would beg the question. Further, common sense can be quite practical (particular ways of doing things, such as how to store grain, for the farmer; or good practice in coding software), whereas the things we call prejudices do not. Again, prejudice is value-laden towards its object ("any application written by Microsoft will be rubbish"; people from X are lazy and criminal) whereas common sense, where it is value laden, tends to be so towards the person who claims or denies it ("he has no common sense"). Finally, prejudices tend to form a system (someone who is prejudiced against nationality X is likely to be so towards other nationalities), whereas common sense does not. This may have something to do with why prejudice is more difficult to change than some specific bit of common sense: common sense resists new evidence to be sure, but yields more easily than prejudice because of this systematic quality.

Quantum mechanics seems to suggest that there really is such a thing as a random

Quantum mechanics seems to suggest that there really is such a thing as a random number, yet all of philosophy and logic point to a reason or cause for everything, perhaps beyond our understanding. Is this notion of a random number just another demonstration of limited human understanding?

I guess I'd have to disagree with the idea that "all of philosophy and logic point to a reason or cause for everything." There's certainly no argument from logic as such; it's perfectly consistent to say that some events are genuinely random. Some philosophers have held that there's a reason (not necessarily a cause in the physical sense, BTW) for everything, but the arguments are not very good.

On the other hand... quantum mechanics is a remarkably well-confirmed physical theory that, at least as standardly interpreted, gives us excellent reason to think that some things happen one way rather than another with no reason or cause for which way they turned out.

An example: suppose we send a photon (a quantum of light) through a polarizing filter pointed in the vertical direction. We let the photon travel to a second polarizing filter, oriented at 45 degrees to the vertical. Quantum theory as usually understood says that there's a 50% chance that the photon will pass this filter and a 50% chance that it won't. But quantum theory itself provides no account whatsoever of which will actually happen. And on the usual interpretation, there is no reason or cause; it's really random.

Now the usual interpretation of quantum mechanics could be wrong. There are deterministic interpretations, most notably "many worlds" or Everettian quantum mechanics, and Bohmian mechanics. No one is in a position to rule either of those out; all I can say is that neither of those approaches is to my taste. But even though both of them restore determinism, that's not really their motivation. Most people who work in foundations of physics are not bothered by the very idea of indeterminism and in fact, indeterminism wasn't by any means Einstein's biggest issue with quantum mechanics.

So to sum up: I don't think there are any good general arguments against randomness. I think the concept is coherent, and that it's a plausible fit for our best physical theory. It also happens to suit my own prejudices about quantum mechanics, but that's just icing on the cake. ;-)

Is it possible to disprove or refute the seemingly indubitable Cogito ergo sum?

Is it possible to disprove or refute the seemingly indubitable Cogito ergo sum? Is it possible for even that to be doubted? Is it possible for something to think, but it does not exist? In my opinion, I think that the only "thing" of which anything that "thinks" could be certain, is that, "there is something," "it is," "there is," or "it is." I feel that for one even to doubt that "there is something," there has to be "something," or one could not doubt at all, or that there could not even have been a "one" in the first place to do anything let alone "doubt." I have just confused myself now, and I apologize for not explaining this much better. I am trying to go beyond René Descartes, and "truly" find "something" that could not be doubted at all, or is it possible to doubt anything or everything, even that statement itself, ad infinitum, and even that?

There are two questions here: first, can Descartes' cogito be doubted—is it open to doubt that "I" exist? Second, more generally, is there anything that's not open to legitimate or reasonable or rational doubt? (What people are psychologically capable of doubting maybe another matter.)

On the first, may philosophers would say yes. Even if it's certain that there's thinking going on, it doesn't follow that there's some one or some thing doing the thinking. Consider the Buddhist/ Humean "no self" view. On that way of understanding things, there's no substantial self. There is, as the Humean might say, just a bundle of perceptions. "I think," on this account, is just a manner of speaking. We can't get from "there is thinking" to "I exist."

So maybe it's open to doubt that I exist. Is it open to doubt that there's thinking going on when it seems that there is? Maybe not, though I don't doubt that some clever philosopher could offer an interesting argument to the contrary. What else? Can it be rationally doubted that anything that exists is self-identical? Some might say it depends on whether there are "things" to be self-identical.

At this point, however, I feel more like a philistine than a philosopher; I'm not sure I care. Maybe there's something beyond all possibility of rational doubt, or maybe there's not. But even if there isn't, real epistemic life will go on as it always has. We'll continue to believe things, reasonably in my view, and, I'm willing to say, we'll even know some of them. Here my sympathies are broadly with G. E. Moore. The arguments that one has to come up with to adopt wholesale skepticism are a lot more fragile and open to doubt than the innocuous thought that we actually know some stuff, even if we're not entirely sure just what.

As technology develops, do you think it will ever make sense to say that a

As technology develops, do you think it will ever make sense to say that a computer "knows" things?

That depends, of course, on what you mean by "know".

On one well-known, though flawed, definition, to know that P is to have a justified true belief that P. Suppose that you are willing to say that a computer believes-true a proposition P if P is true and the computer has (a representation of) P stored in its database. And suppose that a computer would be justified in such a belief if it deduced it from axioms (also stored in its database). Because some computers can deduce propositions according to rules of logic, such a computer could, on this definition of "know", know that P.

Sometimes, people feel that to know something is also to be aware that one knows it, or that one knows that one knows it. So, could a computer know something in this sense? That, of course, depends on what might be meant by "aware". But it is certainly possible for a computer to believe that it believes something (for example, in the sense that it not only has P stored in its database, but also has something like "I have P stored in my database" stored in its database). So it's surely plausible that such a computer could be "aware" that it knows that P.

My colleagues and I investigated some of these possibilities with a computer system that could represent and reason about beliefs, including its own beliefs. One of our papers on this topic is:

Rapaport, William J.; Shapiro, Stuart C.; & Wiebe, Janyce M. (1997), "Quasi-Indexicals and Knowledge Reports", Cognitive Science 21: 63-107.

online here.