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Color
Mind

Is there any objective, scientific way to prove that we all see colours the same? I know it's one thing for two people to point at an object and agree on its colour, even the particular shade, but there's no way that I can tell whether or not the next person in line sees everything in shades of greys, or in negative. We can even study how light interacts with objects and enters our eyes, without truly knowing if one person would see everything the same if he suddenly were able to see though another's eyes. So, is there any proof that we all do see colours the same? Maybe even proof or evidence to the contrary? If that's so, I must say that you're all missing something great from where I can see.

This is a much discussed question, which often appears in the guise of the " inverted spectrum hypothesis ": One might wonder whether some other person sees what you see as red the way you see green, etc. It turns out it can't be quite that simple, but one might nonetheless wonder whether we do all see colors the same way. In fact, Ned Block has argued that there is some empirical evidence that we don't all see colors the same way. (See this paper .) It goes without saying that this is very controversial.
Mind

If a person were to be a created, a virtual reality person (such as a character in a Sims game, that "reacts" and "grows"), and this person was "downloaded" into an actual body, is that person considered "real?" Were they real before the download, or is a physical body part of the conception of real? Would you even be considered a legitimate person, since all of your "memories" could be considered "fake"?

I have no views about this question at all. But I did recently hear the philosophy David Velleman read a paper on a very similar question. I think it's this one .
Knowledge
Mathematics

As commonly understood and reinforced here, 2 + 2 = 4 is taken as meeting the test for absolute certainty. This appears to be true in a formal or symbolic sense but is it true in reality? When we count two things as being the same and add them to two other same things do we really get four identical things? Perhaps, perhaps not; it may depend on one's identity theory. Do we know with absolute certainty when we have one thing and not two? What am I missing?

I don't myself have a view on whether 2+2=4 is absolutely certain. I suppose it's as certain as anything is or could be. But the question here is different. It's whether that certainty is undermined by doubts about what happens empirically. As Gottlob Frege would quickly have pointed out, however, the mathematical truth that 2+2=4 has nothing particular to do with what happens empirically. It might have been, for example, that whenver you tried to put two things together with two other things, one of them disappeared. (Or perhaps they were like rabbits, and another one appeared!) But mathematics says nothing of this. That 2+2=4 does not tell you what will happen when you put things together. It only tells you that, if there are two of these things and two of those things, and if none of these is one of those, then there are four things that are among these and those. It's hard to see how one's theory of identity could affect that.
Abortion
Ethics

One of the most common justifications I hear for abortion is "a woman should have control over her body." If humans reproduced oviparously, would that change the debate? Let's say a woman conceives a child, and then immediately lays an egg. The egg would still need incubation and maintenance, though this could be performed by any party, not just the mother. After nine months of development, the egg would hatch into a baby human. Would a woman be justified in crushing this egg? This mimics the abortion debate, except that in this case the fetus cannot be addressed as part of the woman's body. Would that invalidate any abortion arguments?

There are several different questions here. The first is whether, in the circumstances imagined, one would have a right to kill the developing ovum, or whatever. The second is whether a negative answer to this question would invalidate arguments in favor of the the permissibility of abortion. Let me answer the second question first. I think the answer here is "No": At least, I don't see that there are any very plausible arguments it would undermine. If you consider, for example, the central argument of Judith Jarvis Thomson's famous paper "A Defense of Abortion", it depends crucially upon the fact that the developing fetus is dependent upon the woman's body and that the woman's body is affected by the presence of the fetus. Thomson then argues, largely by analogy, that a woman is not morally obligated to carry a fetus under those circumstances. It's this kind of argument that I take to be summed up by "a woman should have control over what happens in and to her body". Thomson actually does...
Ethics
Religion

Why is it that very religious people tend to be kinder and more compassionate (with a few notable exceptions to people they deem unworthy i.e.: homosexuals) than secular people? Is this evidence that we need religion/should be religious?

Are we entirely sure that religious people do tend to be kinder and more compassionate than secular people? And are we sure of this, especially, when we do not set aside the notable exceptions?
Race

Abraham Lincoln once made this argument that white people have no right to enslave black people: "You say A. is white, and B. is black. It is color, then; the lighter, having the right to enslave the darker? Take care. By this rule, you are to be slave to the first man you meet, with a fairer skin than your own." If I understand Lincoln correctly, he is arguing that because some white people have darker skin than other white people, skin color is not sufficient justification for slavery. Isn't this a fallacious conceptual slippery slope argument? Let's say we have three men. The first has only a few dollars, the second is a multi-millionaire, and the third is a billionaire. The third one is richer than the second. But that does not change the fact the the first and second are both rich and the first is not. In the same way, it might be true that some white people have darker skin than others. But this doesn't change the fact that there are white people and black people (as well as borderline cases.) ...

First, I need to applaud your engagement with this argument. Many people would hesitate to criticize, simply because they agree with Lincoln's conclusion. But, as you implicitly note, whether we agree with the conclusion is quite independent of whether the argument is any good. The question worth asking, I take it, is why Lincoln thinks the justification for slavery rests upon the claim that "the lighter [have] the right to enslave the darker". Certainly you are right that this does not, and need not, follow from the thought that whites have the right to enslave blacks. But, on the other hand, it is so obvious that it doesn't follow that it seems uncharitable to Lincoln to suppose he thought it did---which is not, of course, to say he didn't think it did. What it means is that we ought now to search for some other reason he might have thought that the justification involved "lightness" rather than whiteness. That's an historical question, and I'm in no position to answer it. But here's one...
Mathematics

When young children perform long division or multiplication, are they constructing a proof?

So I asked my brother about this, and he tells me that this kind of question is much discussed in the literature on mathematics education. Here's what he had to say: "Good thing to think about. A related idea I've been considering for some time---and maybe the difference is just a matter of cognitive development---is whether solving an equation algebraically is a proof. "Another spin on the idea---which is what got me thinking about it in the first place---is whether solving equations ought to be taught as proof, since every step one takes in algebraic solutions can be mathematically/logically justified through some equivalence that leads to the solution set. What most kids end up learning to do is to conduct the procedures of solving without any real understanding (or caring) of why what they are doing is mathematically justified. I have a sense that if solving were taught as proof, then it would be more natural for kids to pay attention to why certain steps that seem OK actually introduce...

Sure, why not? What they construct---I take it we mean, "write down"---is the very same proof you or I might construct. So they've constructed the same thing we would, so it's a proof. But there is a different question you might ask, namely, do they understand it as a proof? And that, I take it, is an empirical question. Let me ask my brother, who works on mathematics education, and see what he has to say....
Mathematics

What are numbers? Are they unquestionably EVERYTHING? Let's take 17 and 18 for example: Isn't there an infinite amount of numbers that exist between 17 and 18? There is no such thing as the smallest number, and there is no such thing as the largest number. WHY?!

Well, there are a lot of questions there. I won't try to answer the first one: That's a topic for a book, not an internet posting. And I'm not sure I understand the second one. But regarding the next two, yes, of course there are infinitely many numbers between 17 and 18. Here are some of them: 17.1; 17.11; 17.111; 17.1111; etc. And between any two of those, there are infinitely many more. But if you want something that will really make your head spin: Consider all the rational numbers, that is, all the numbers that can be written as fractions m/n. There are no more of those numbers than there are "natural numbers", like 0, 1, 2, etc., and that is true even though there are infinitely many rational numbers in between any two natural numbers. The proof of this is not terribly difficult. The point is that we can order all the rational numbers like this: 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, .... (What's the pattern?) Some rational numbers occur more than once, of course, but they can be...
Mathematics

We generally hold that a mathematical proposition such as "2 + 2 = 4" is necessarily true; it is difficult to imagine a possible world in which it is false. However, is it possible that "2 + 2 = 4" is not a statement that expresses a mathematical necessity (or an operation involving numeric values that must provide a certain result), but rather presents an inductive inference based on how people currently "define" the number "2", and the operator "+"? We could, for example, someday come to discover that "2" does not represent "2 things or ideas"; what we call 2 things may turn out to be 3 things, or 1 thing, etc. If this is possible then it would seem that "2 + 2 = 4" is an empirical, not a rational truth. Is this intelligible? I realize that this last statement, that we could discover 2 to refer to 3 things, etc., entails a theory of what a number is, i.e. a number "represents a quantity or amount of something". It seems, though, that in order to conclude that "2 + 2 = 4" is a necessary truth we must...

Perhaps the first thing to say here is that we need to distinguish the question whether it is necessary that 2+2=4 from the question whether the sentence "2+2=4" is necessarily true. It seems to me that no sentence is necessarily true. Any sentence might have been false, simply because that sentence might have meant something other than what it in fact means. For example, "2+2=4" might have meant that 3+3=4, and then it would have been false. And that is what it would have meant had "2" meant 3 rather than what it does mean, namely, 2. So I agree absolutely the whether "2+2=4" is true depends upon how we what "2" and "+" and "4" and "=" all mean, not to mention the grammatical rules that govern the significance of combining them in a certain way. And if you want to put that by saying that the truth of this sentence depends upon how we "define" the numeral "2", I won't object. Not too strongly, anyway. But it is an entirely different question whether it is necessary that 2+2=4. That is not at...
Mathematics

Are the infinitely small and the infinitely large the same thing?

It would help to be told why one might think they were. But in mathematics, no, they are not. Something that is infinitely small---a so-called infinitesimal---is something that is smaller than anything of finite size. Something that is infinitely large is something that is larger than anything of finite size. So if they were the same, something would have to be both larger and smaller than anything of finite size. And that ain't gonna happen.

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