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Philosophy

If there IS philosophical progress, is it worthwhile to read philosophy that was written before you were born? Isn't the most current understanding of philosophy the most valid? For example, we now know Newtonian physics is false at the quantum level; wouldn't it stand to reason that after two hundred years Kant's moral philosophy has been refined or superceded and should not be followed in its entirety? If there is NOT any philosophical progress and philosophical questions are inherently unresolvable, then is the entire field of philosophy futile? If philosophers can't even agree on what the aims of philosophy are, then does that mean Marx's philosophy is as equally valid for people to follow as that of Aristotle's?

I agree with Ian for similar reasons (see my Unsolvable Problems and Philosophical Progress ) So, because we both agree that there is philosophical progress, is it worthwhile to read philosophy that was written before you were born? Yes, for at least two reasons: First, of course, some of that philosophy might consist of good reasoning that has not been improved upon. Saying that philosophy progresses doesn't mean that old philosophy is "wrong" in any way (any more than saying that science progresses doesn't mean that old science is "wrong"). Second, philosophy is best thought of as a conversation that has been going on for at least 2500 years. One of the best ways of joining that conversation is to read "transcripts" of its earlier stages.
Mind

When I look at the room I'm sitting in, I am consciously aware of it as existing outside my body and head. So, for example, I can walk towards the opposite wall and I appear to get closer to it until I reach out and touch it. Now I understand that light is being reflected off a wall, travelling across a room, entering my eyes and this process creates nervous impulses. (In fact a physics would correctly point out that the photons that hit my retina are not even the same as the photons 'reflected' by any object). I understand that these impulses are processed in various parts of my brain, some unconsciously but eventually a mental "schema" representing the room is created. I also understand that there are other processes going on in my brain that create my awareness of different types of "self"s, that continually shift my awareness and that attempt to always produce a self-consistent view of myself and the world. However, my question is not about these (well not directly!). My question is simply how does...

I don't have a good answer for you, but I can point you to a very readable book that discusses this issue among many others: O'R egan, J. Kevin (2011), Why Red Doesn't Sound Like a Bell: Understanding the Feel of Consciousness (Oxford: Oxford University Press). The book's supplementary website has an answer to your question at Other Twisted Issues, and there's an article-length version of the book in: O'R egan, J. Kevin (2012), "How to Build a Robot that Is Conscious and Feels", Minds and Machines 22(2) (Summer): 117-136, as well as a video and a transcript of the author's talk. I don't agree with everything O'R egan says, but he fully understands the issues and has interesting things to say.
Mathematics

Are 3 and √9 the same mathematical object (in light of the fact that they have the same numerical value), or are they distinct mathematical objects? In other words, are the expressions '3' and '√9' co-referential names (both referring to the number 3), or do they refer to different objects?

Using Gottlob Frege's theory of sense and reference, you might say that '3' is the name of the natural number that is the third successor of 0, and that 'the (positive) square root of 9' is a (definite) description of that very same number. The name and the description have different senses, but the same referent; the senses "get at" the same mathematical object in two different ways.
Mind

If we assume that both computers and the human mind are merely physical, does it follow that a sufficiently advanced computer could do anything that a human brain could do?

As Richard points out, logically, no, it does not follow. Just because two things are both (merely) physical, it does not follow that one of them can do anything that the other can do, not even if both of the (merely) physical things are brains. My pencil is a physical thing, but it can't do everything that my brain can. A cat's brain is physical, but it can't do everything that mine can. (Of course, mine can't do everything a cat's brain can either: I don't usually land on my feet when I jump from a height, and I'm pretty bad at catching mice.) But I think your question really is simply whether a sufficiently advanced computer can do anything that a human brain can. Even so, we need to be a bit more precise. By "anything", I'm guessing that you really mean "anything cognitive"; so, I think your real question is a version of: Can computers think? Philosophers, cognitive scientists, and computer scientists disagree on the answer to that question. I think that one of the best ways to think...
Education
Philosophy

What would you say is the best resource for learning philosophy at the level of an absolute beginner? I have tried MIT OCW, reading articles on the Stanford Encyclopedia of Philosophy, and taking out books from the library -- none of it makes total sense to me. Usually I get the general idea, but I feel like I'm missing something. Should I continue using the Stanford Encyclopedia/will I gain enough from it for it to be effective? Are there other, better ways? Thanks for replying ^_^

My favorite for beginners (although the author is somewhat out of favor with some professional philosophers these days) is Thomas Nagel's What Does It All Mean?: A Very Short Introduction to Philosophy . It raises all of the interesting questions in a readable fashion, but leaves the answers to the reader. (And the author of The Story of Philosophy , by the way, spelled his name "Will Durant".)
Logic

Is it true that anything can be concluded from a contradiction? Can you explain? It's seems like its a tautology if taken figuratively because we can indeed conclude anything if we suspend the rules of reasoning, but there is nothing especially interesting in that fact in my humble opinion.

It's not just that disjunctive syllogism breaks down, but that the conclusion Q is, in general, irrelevant to the premise, which only talks about P (and Not-P). So, in Bertrand Russell's famous version, given a contradiction about, say, arithmetic ("2+2=4 & 2+2=5"), you can use the derivation given by Maitzen to prove that Russell (a famous atheist) is the Pope. For interesting (and amusing) arguments in favor of the importance of relevance, see the early chapters of Anderson, Alan Ross, & Belnap, Nuel D., Jr. (eds.) (1975), Entailment: The Logic of Relevance and Necessity, Vol. I (Princeton, NJ: Princeton University Press). Relevance logics, a form of paraconsistent logic, have found important applications in artificial intelligence, where it is desirable, in devising a computational model of a mind, to have it use a system of logic that does not lead to irrelevancies. For discussion on that topic, see Shapiro, Stuart C. & Wand, Mitchell (1976), 'The Relevance of Relevance' , ...
Logic

If the sentence "q because p" is true, must the sentence "If p then q" also be true? For example, "the streets are wet because it is raining," and the sentence "if it is raining, then the streets are wet." Are there any counter-examples where "q because p" could be true while "If p then q" could be false?

Suppose that "q because p" is true. I would say that it follows that both q and p have to be true. But, in that case, "if p then q" is also true (assuming that the English "if...then..." expression is interpreted as the material conditional). However, "if q then p" is also true! So, there doesn't seem to be much of an interesting connection between the causal sentence and the conditional sentence.
Logic

If the sentence "If p then q" is true, must the sentence "q because p" also be true? For example, "if it is raining, then the streets are wet" and the sentence "The streets are wet because it is raining." Are there any counter-examples where "If p then q" could be true while "q because p" could be false?

The answer to your first question is: No. Let's take your example: Suppose that it is true that it is raining. And suppose that it is true that the streets are wet. Then, by the truth table for the material conditional (which is the default interpretation of the English "if…then…" locution), the sentence "If it is raining, then the streets are wet" is true, because both antecedent and consequent are true. But it might have been the case that the reason that the streets are wet is that someone was cleaning the street with water before the rain began, so that it is false that the streets are wet because it is raining. And there's your counterexample. The one possible piece of wiggle room would be for someone to claim that the material conditional is not the correct interpretation of "if…then…" in this case.
Philosophers

What did Descartes mean by saying "I think, therefore I am?"

Here's a simple (maybe even simplistic!) answer: "I think" is Descartes's first axiom. "I am" is his first theorem. Descartes was seeking propositions that could not be doubted. He determined that the most indubitable one was "I think", on the grounds that, even if he were being deceived and was not really thinking—if, that is, he only thought that he was thinking—then he was still thinking! (Either I am really thinking or I only think that I am thinking; in either case, I am thinking.) He then decided that he could derive from that starting point (that axiom) the proposition that he, who was thinking, must exist in order to think. Some of his critics have suggested that a more cautious "theorem" to derive from "I think" is: thinking is going on (not necessarily that he is thinking or that he who thinks exists).
Education

I have done B.Tech in Computer Science, and Masters in Humanities (specialization in Ontology). Can you kindly suggest me some places where I can do a Ph.D which combines both these fields?

I don't know what you mean by "ontology", which can refer to either the branch of philosophy (metaphysics) that is concerned with existence or the branch of artificial intelligence that is concerned with knowledge representation techniques for organizing information (both of those characterizations are very, very rough, of course). In the latter case, you might want to look into doctoral programs in either philosophy or computer science departments where there are researchers specializing in that, such as the (SUNY) Buffalo Center for Ontological Research (disclaimer: that's my institution!). For more information on this kind of ontology, see http://aitopics.net/Ontologies

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