There are a couple of ways we might go here. Thinking about the sky, it's a pretty good bet that most people with normal color vision (roughly, people who can pass a color-blindness test like this one ) will say that the sky is blue and will agree that a good many other things are blue, even if they've never seen them before. And so while there is a certain amount of arbitrariness and convention in just where we draw the lines between colors and while the names themselves are certainly matters of convention, there are facts about human physiology here as well. Thus, one way to think about colors is in terms of the responses of "normal" individuals in "normal" conditions (where both of those "normals" are not altogether easy to pin down.) Another way is to think about the physical characteristics of the things we apply the color words to. For example: light with frequency around 450 nanometers is blue light. If the light reflected from a body has this frequency, we call the body blue. But things...

I think the simple answer is that any probabilities we come up with here are pretty much meaningless. Probability calculations ade only as good as the information we feed into them, and it's hard to see what a well-formed question would be like here - not least since it would require some way of quantifying how hard the universe is to understand. Perhaps there's some clever way to come up with a calculation, but let me turn to your other issue - the brain/pancreas thing. To my inexpert eye, brains and pancreases hace a certain superficial resemblance, but neuroscientists will be able to tell you in a good deal of detail why the brain is better suited to computing than the pancreas is. The real point here is that our casual impressions on such matters aren't really worth very much. After all, a casual look at my iPad makes it pretty mysterious that it could be used to write this response, but that's exaclry what it let me do.

Just a footnote on Jonathan's reply on the matter of direction. Length is a measure of a property of things, and it has a natural 'direction' from shorter to longer. As Jonathan suggests, it wouldn't make any sense to say that the difference between one direction and another on the length scale is just a matter of convention. But it may be that position coordinates are closer to your worry. We can assign position coordinate so that heading north from my desk gives us bigger numbers. Or we could do it the other way: going north fives us smaller coordinates. And in this case, we'd say that the choice really is just convention. Nature doesn't favor one direction in space over another. But time seems to be different. There seems to be a real difference between the direction we label with increasing numbers and the opposite direction. As it turns out, physicists and philosophers have written a great deal about this asymmetry. As it also turns out, there isn't a consensus about the best way to think of it. Cups...

Just to continue the conversation - Jonathan and I agree that time is a dimension and not a force. It's just that this still leaves room for interesting questions about the relationship between thermodynamics and fundamental physical laws. We don't agree, it seems, about time travel, but we may agree for "all practical purposes." I'm quite satisfied with David Lewis's treatment of the grandparent paradox. Lewis agrees: you can't travel back in time and kill grandpa or grandma. Any such story is inconsistent, and inconsistent stories are guaranteed to be false. In fact, loosely put, you can't go back in time period unless it's actually a part of the world's history that it happened. Unless it's "already" a fact about the world that an adult Allen Stairs was wondering around the streets of his boyhood home in the 50s and 60s, then we are guaranteed that I will never do any such thing. Lewis's point was that in spite of this, we can tell consistent time travel stories. They just require very...

Counting things is something we actually do to get to the answers to arithmetic problems (who hasn't counted on their fingers at some point?) but we need to be careful. What if you put five drops of water together with five drops of water and count the results? Or what if you put an electron and a positron together? We might say that putting drops of water together or combining electrons and positrons doesn't count as addition. But that's because when when we do, we don't end up with the right answer to the arithmetic question we're supposedly trying to settle empirically. What we see is that arithmetic isn't an hypothesis about what we'll find when we count in various cases. Rather, arithmetic tells us whether an empirical operation is a good model of addition, or whether what we're mumbling under our breath as we flex those fingers really counts as counting.

It's a good idea to start with a distinction. If by "logic" you simply mean something like "correct deductive reasoning," then logic is something mathematicians use -- as do people in any discipline. If by "logic" you mean the study of certain specific kinds of formal systems and their properties -- mathematical logic, as it's often called -- then logic is arguably a branch of mathematics, but also of philosophy (and perhaps also of other disciplines such as computer science; no need for turf wars.) There are people in math departments who specialize in logic, and also people in philosophy departments. Results in mathematical logic, might be published in math journals or in philosophy journals or in computer science journals.

If by "proof" you mean something like "sound a priori " argument, then there are no uncontroversial examples. But then, there are few things that can be shown to exist that way, so lack of proof in that sense doesn't mean much. If you mean something like "purported good argument for the existence of God," there are plenty of those, but people disagree over their merits. The paragraph-length caricatures one sometimes encounters in Phil 101 aren't up to the task, but that's no surprise either. But there are serious people who offer extended defenses of the claim that God exists, as a look at any good Phil of Religion text will make clear. Needless to say, people differ on the question of how good those defenses are. As for what would count as evidence, I take you to be asking what we might observe that could raise the probability of God's existence. Some would say the kind of order we find in the universe -- and others would disagree. Some would say the existence of apparent miracles, but others...

I'd like to offer a rather different take on this than my co-panelist. Many theists don't think that "God exists" is a necessary proposition. However, some famously do. St. Anselm is the most well-known example, but he's not the only one. The contemporary philosopher Alvin Plantinga apparently does as well. Now we can grant that it's not obviously a contradiction to say that the world contains only a single pencil, but people who think God exists necessarily may not think that metaphysical necessity is the same as logical necessity. If I understand Plantinga correctly, he doesn't think it's a contradiction to say "God doesn't exist," though he does think that God's existence is metaphysically necessary. All of that is throat-clearing. We could make a similar point in a different way. Mathematical truths are necessary if true at all, or at least so we'll suppose. But it's famously hard to argue that mathematical truth is the same as logical truth. So the more interesting question is this:...

It might be a good idea to start with a distinction between words and things. The number zero, or 0, is one among an infinity of numbers, special though its algebraic properties may be. As such, it just is and doesn't represent anything. The numeral '0' typically represents the number 0, but doesn't usually represent nothingness, whatever exactly that is. If I write 7 - 7 = 0 I've written something true; if I write 7 - 7 = nothingness I've written something peculiar and not obviously true at all. People sometimes use the word "nothingness" in a way that's fraught with meaning - as in the Existential Void.The number 0 isn't that, and the numeral '0' doesn't normally represent it. That said, we have a very free hand in deciding what represents what. We can and do use '0' to represent all manner of things (or their absence). So whatever you have in mind by your use of the word "nothingness" we no doubt could use '0' to represent it. It's just that this would be something we decide...

Lack of consent isn't the only argument, but I doubt that anyone ever thought it was. Roughly, we think we need consent when we think the person might reasonably object if they only knew about or understood what was being done to them. In the case of pedophilia, there's plenty of reason to think that the child would object if s/he understood. As it happens, I know someone very well who was the victim of a pedophile. When it happened (and it happened more than once), she didn't understand; she was four years old. But if you asked her about it now, she would say that what this man did to her was very wrong and caused her a great deal of torment as she came to terms with it. Though it's hardly the whole story, the phrase "taking advantage of" is entirely apt here.. This man didn't have that young girl's good in mind. He was using her for his own disagreeable reasons. It's a straightforward case of what Kant would call using someone as a mere means. Offhand, I can't think of any cases where...

I think the reason people can't give you a clear answer is that there isn't one. It just seems to be a fact that some people really can love more than one person deeply at the same time, and I'll confess to finding it puzzling that this would puzzle anyone. As for opposition to polygamy, it would be hard to make the case that it's simply wrong. It would be particularly hard to do it a priori, without looking in some detail at polygamous societies. There are some worries one might well have (for example: worries about polygamous arrangements that favor men over women) but that's different from saying that all polygamous arrangements are wrong. None of this is a recommendation for what anyone should do in a society like contemporary America. Marriage and romantic relationships fit into formal and informal social institutions in a complicated way, and not every change we might contemplate is liable to work out well. Once again, there's no saying a priori. I'd add that "falling in love" isn't always...