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Mathematics
Science

I am often confused by the rhetorics of physicists that their theory "came from mathematics". I remember the physicist, Brian greence tell the story of paul dirac discovery of anti-matter by pure a priori manipulation of mathematics. I see this to be very confusing, because i often imagine mathematics as being a priori, and necessary without any connection to the real world. That is, i can always imagine possible worlds( or universes) governed by different mathematical expressions, or descriptions. Does it follow that every mathematical expression/description describes our universe? Obviously not. With paper, and pencil, we could probable describe any universe with any arbitrary number of dimension of space, but does it follow that our universe has arbitrary number of spatial dimension? Obviously not. The use of mathematics seems to be good in formulating regularities of nature( laws of nature), and to extract the implication of those laws. It makes me wonder why physicists would say their theory comes...

You are reasoning correctly--mathematics deals with possibilities and physics with actualities (even though in quantum mechanics these are probabilistic). Theory in physics is often expressed mathematically, but that does not make it mathematical knowledge. Some theoretical advances in physics can come from working in an armchair and extending the mathematical implications of (already accepted and contingently true) theory. The actual status of mathematics (a priori or not) is debatable (Quine etc claiming that mathematics is an empirical theory like any other). But you are correct that physics is not mathematics, and the sort of evidence that confirms physical theory is not (or perhaps, not entirely) the evidence (or other considerations) needed to confirm mathematics.
Language
Sex

Is the definition of marriage changing?

There never was a "definition of marriage." Marriage is an ancient human institution that occurs in multiple forms (temporary, permanent, monogamous or open, polygamous or polyandrous) with several possible functions (parenting, property rights, companionship, politics, possession). I don't think that even in our (pluralistic) society, at this time, it has a single meaning, function or definition. One of the things about marriage that does seem to be changing right now is the idea that it has to be between a woman and a man (this idea has been stable in Western society for some time, although it is probably not a human universal). One of the benefits of this wide range of possibilities is that individuals have some freedom to create their own meanings of marriage (whether or not they marry).
Emotion
Philosophy

I believe it was Hume who made the point that reason cannot motivate us, only our feelings can. Supposing that's true, I have a far-flung conclusion that seems to follow from that: when the panelists on this site choose which questions to answer, they're motivated by some emotion, not by reason. But doesn't this corrupt the purity of the logic of the answer? Perhaps not necessarily so, but isn't it likely that of the 2,600+ questions a good number have been tainted? How is it not the case?

In writing this answer I am motivated by the desire to help non-professional philosophers with their philosophical questions. That desire does not influence the answer that I give, it just motivates me to give some answer or another. Or: in writing this answer I am motivated by the desire to point out that emotions should not be thought of as ipso facto "irrational" or "unreasonable." That desire is connected with the answer I give, but may or may not have influenced it. Or: in writing this answer I am motivated by the desire to appear on this website. Again, that desire does not influence the answer that I give. Or: in writing this answer I am motivated by the desire to attack the philosophy of David Hume. That desire is connected with the answer I give, but may or may not have influenced it.
Abortion
Ethics

While I don't have a firm opinion on the issue, I never understand many pro-life positions that state they are against abortion except in the case of rape or incest. Life is life. These babies are as innocent as others. The situation in which they were conceived should have no bearing on whether they should be allowed to be aborted. It is illogical.

If the moral objection to abortion is that it kills innocent persons, then you are right, the circumstances of conception should be irrelevant. An important philosophical article by Judith Jarvis Thomson, "A Defense of Abortion" (originally published in Philosophy and Public Affairs in 1971 and widely reprinted) argues that in some circumstances, killing innocent persons is permissible. Those special circumstances are when the life of another is dependent on some huge personal sacrifice of an individual who did not voluntarily take on that responsibility. Thomson argues that when pregnancy occurs against the will of the pregnant woman (rape is clearly an instance of this, and Thomson argues that contraceptive failure is also an instance) it is morally permissible to abort (although it would be morally admirable to go through with the pregnancy).
Rationality

Can somebody oppose physical pain (felt by other people) and be indifferent to other kinds of suffering without being irrational? I'm affraid that the answer is "yes": you can hate or dislike anything without hating or disliking anything else, and these are perhaps the best grounds for opposing something. But on the other hand I can't help seeing here some kind of contradiction... What do you say?

What is it to "oppose physical pain" as you put it? Do you mean try to prevent physical pain? But why would you do that? Usually the answer is something like "because it causes suffering". So the reason for trying to prevent physical pain will also be a reason for trying to prevent other forms of suffering. So I think the answer to your question is "no." (Unless you have some grounds for "opposing physical pain" that is different from this usual answer.)
Philosophy

Hi, this may seem very strange but what do you love about philosophy (not specific areas, I mean essentially)? What is it to you? Please answer! Oooh I'd be so interested. I'm not trying to waste anyone's time!

What I have always loved about philosophy is its openness to questions, including foundational questions. It's where you can take all the "deep" questions from other disciplines that active practitioners sometimes don't have time for, unless their discipline is at a sticking point. I don't love all of philosophy, but I continue to enjoy the points where it engages with other disciplines and can make a difference to them.
Ethics
Science

I'm a scientist. The results of my research may generate technologies that could potentially be used in both and offensive and defensive military applications. These same technologies could potentially help people as well. Here are two examples: (1) My work could potentially create odor-sensing devices to target "enemies" and blow them up, but the same work could aid land-mine detection and removal. (2) My work could help build warrior robots, but it could also help build better prosthetics for amputees. For any given project, I have to decide which agency(ies) my lab will take money from. I do not want to decide based on the name of the agency alone: DARPA has funded projects that helped amputees and killed no one, while I would bet (but do not know for sure) that some work sponsored by the NSF has ultimately been used in military operations. So I'd like to base my decision on something more than the agency acronym. How can I start to get my head around this? What sorts of questions should I...

These are terrific questions and I hope someone else on the panel can also respond to them. The philosophy of science literature, and even the literature on values in science (Hugh Lacey, Helen Longino, Lynn Hankinson Nelson and others) is rather general and not sufficiently applied to give quick answers. I think you are going to have to do a good deal of the thinking yourself. But here are some questions and considerations. The agency acronym is, indeed, not an infallible guide to the nature of the research. However, it is a rough guide and perhaps more important, it is *perceived* as affecting the content of the research done. The funding agency will influence who chooses to work with you (science is after all not an individual enterprise) and how people evaluate your research. On the other hand, DARPA money is easier to come by than NSF money (or so I hear) and you might prefer to do research with DARPA money than not do it at all (that is a question to ask yourself). The issue here is whether...
Happiness

When I get sad and depressed I am often told to "wise up" and stop moaning because people in Africa suffer far more than I do. Is this a logically valid point? Does the existence of vast quanities of human suffering in Africa necessarily negate my suffering?

I love this question and have often pondered it myself. I don't think sufferings need to be compared with one another. All human pain is of moral concern and deserves unique respect. Utilitarians like to quantify pain. Even if one does this, and thereby compares different pains, it does not follow that we need to devote our psychological attention to the place/person with the greatest quantity of pain. Utilitarians, do, however, think that our moral concern (but not our psychological attention) should be directed to where we can relieve the most pain or bring about the most happiness. Perhaps the audience to your suffering is telling you that they are more obligated to relieve suffering in African than to help you feel better. (I hope for your sake that your friends are not such utilitarians. Care ethics is a better moral framework for this kind of case.) As for "stop moaning," I think this is often psychological advice. Often, we feel better when we consider others who are in much...
Freedom
Science

What kind of scientific evidence, if any, could prove that free-will does not exist?

Let me turn the tables on you and ask, "What is free will?" When people use this concept, they may have any of several different ideas in mind. Some people think of free will as freedom from external factors such as bribery or threats, some think of it as freedom from acting in accordance with one's own baser urges, some think of it as lack of determination (by the laws of nature/brain processes etc.) I think different sciences are relevant to each of these questions and that we can have evidence supporting or disconfirming claims about free will. Another way for you to think about your question: if there is no free will, what would you have lost?
Science

I have a question about “ghosts” that I am wondering whether a philosopher or two could help me explain. I know it sounds ridiculous even to bring up the topic, which is why I do so only under the cover of anonymity. Let me preface this by saying, as a law student in New Haven with heavily atheist leanings, I don’t think I’m a particularly stupid or superstitious person. But a few years ago I had an experience it is difficult to reconcile with my worldview. On a lark, a friend and I spent the night in a hotel room in Savannah that was reputed to be “haunted.” Naturally, we were expecting nothing to happen there. But curiously, every time we left the room, something inside it moved. (We would go in the hallway, wait a minute or two, and then re-enter.) A banana from the fruit bowl and a tub of shampoo from the bathroom were placed on the bed; my friend’s underwear moved from one corner of the room to a trash can in the other; my friend’s student ID was removed from his wallet and placed on the floor; the...

Clearly this experience at the Savannah inn is haunting you, if you are perplexed about it several years later! I'm answering as an empiricist (rather than as a dogmatic materialist/physicalist). I'm willing to believe in ghosts if that's where the evidence points. If you really expected nothing to happen--why did you leave for a couple of minutes, wait in the hallway (watching the door?) and then go back in? Who is this friend anyway and could he have tricked you? If the hotel advertises this room as haunted perhaps they have a hidden entry to the room and yes, they regularly break the law (but who can catch them at it?) If all you say is true--that is, no-one entered the room when you and your friend were absent, and your video camera would have captured e.g. an animal in the room or a hidden entryway then maybe, yes, you experienced something currently unexplained by science (no reason to give up your atheism, though!). In my experience, however, magic (good old fashioned trickery) can be more...

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