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...

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...

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...