Like your friend, the German Enlightenment philosopher Immanuel Kant in “On a Supposed Right to Lie from Philanthropy” argued that it's categorically wrong to lie, even to a murderer at the door looking for someone inside. Like you, however, I think he's obviously mistaken. It would to my mind obviously be permissible to lie to Nazis at the door looking for Anne Frank, and similarly lying to slave catchers hunting people who had escaped enslavement. There also seem to be harmless, trivial, but nonetheless beneficial lies--call them lies of kindness and social lubrication, just the the sort you mention, for example. Similarly: "So nice to meet you"; and "I'm fine," certainly. Friedrich Nietzsche in a grander but not unrelated way describes in "The Birth of Tragedy" how one of the functions of art is to mask, even lie, to us about the horrifying truths about reality. Elsewhere he maintains that concepts are always bound up with at least poetic lies as well as lies maintaining power relations (an idea later that Michel Foucault would appreciate). Plato argues in "Republic" (Book 3, 414e–15c) that the good ruler may, even should, tell a "noble lie" to the people about their rootedness in the land they occupy for the sake of social cohesion and well being. From the Trojan horse to the Allies deceiving the Nazis about the location of the invasion of France to the US deceiving Iraq during Operation Desert Storm, military forces commonly use deception to advance their plans. Today there are ongoing discussions about whether the government ought to lie to us if the destruction of life on Earth were to become imminent (say because a massive asteroid is about to strike us). I'm not quite sure what I think is proper in that situation, but arguably preventing chaos and panic might be a mercy. Now, of course, there ought to be serious constraints on lying. If social interactions can succeed without white lies, avoid them. Perfidy in military conduct (e.g. by pretending to surrender or lying about the terms of surrender) is unethical. And democracy requires a government that is as transparent and truthful as possible. Remember that even Plato argued that the "lie in one's soul" is the most hateful and repugnant of things (Book 2, 382a-382d).

The argument is valid. That's because in logic, we say that an argument is valid if it's impossible for the premises to be true and the conclusion false at the same time. If two statements A and If A then B really are true, then so is B. If both A and If A then B are false (or better, if at least one of them is), then the conclusion might be true or might be false, but the argument is still valid; the conclusion still follows.

You seem to say that if we have no evidence for something, then it's false. But that's not right. Lots of things are true whether anyone knows them. (How many worms were there in the garden plot at noon yesterday? There's only one right answer, but no one happens to know it or even have evidence.) And things can turn out to be false even if we have serious evidence that they're true. And you seem to be saying that if the premises of an argument are false, the conclusion must be false too. But that's not right, and in particular it's not right even for valid arguments. Consider

All dogs are fish.
All fish are mammals.
Therefore all dogs are mammals.

This is a valid argument. No argument with that structure could have true premises and a false conclusion, and that's what validity amounts to. But the premises are false and the conclusion true.

So your friend is right and isn't committing any fallacy. (By the way: fallacy names are over-rated. Most of the professional logicians I know are not good at remembering those names. But they are very skilled at explaining what makes arguments bad.)

Don't let all this throw you off-balance. Anyone who's taught logic will tell you that you're in good company; understanding logical validity takes a little bit of practice and work. But there are very good reasons why logicians define validity as they do, and in any case, the argument form you offer really is a textbook case of a valid argument form. It even has a name: it's called Modus Ponens and it's a basic rule in just about any logic text.

We have apples and Martian oranges here. Whatever exactly biology means by "species" (and there's a debate about that), it's about what the actual science of biology, with its particular set of concepts, theories and empirical claims, uses the term "species" to mean. And so to imagine the word "human" defined only in terms of psychological and mental properties is to imagine a use of the word "human" that has nothing to do with what biologists mean when they talk about species. Once we get to uploading and matrix-style scenarios, we're not even in the same intellectual universe as biology.

This doesn't mean that we shouldn't use the word "human" in a way that's tied purely to the psychological. We can use words however we like. I'd suggest, however, that there's a better word: person as used by philosophers. And so in that vocabulary, your question becomes: if we discovered alien creatures who fit our psychological notion of what a person is, should we count those creatures as persons?

My impression is that most philosophers would say "Yes" without much hesitation—not all, but most. Also: most philosophers would say that if psychological traits are what really matter in deciding what it is to be a person, then there may very well be non-human persons ."Human" in most contexts is at least partly a biological term. But when it comes to how we should treat beings, whether they are biologically human doesn't seem nearly as important as whether they are psychologically like us. Some non-human creatures feel pain. That's a reason not to treat them in certain ways. Some non-human creatures form emotional attachments to other creatures. That's a reason not to separate them gratuitously. And so on.

So I think what you're really asking about is a perfectly good thing to think about, but I don't think it's about species in the sense that that word is used in science. In fact, the word "speciesism" is a term of relatively recent origin that's meant to remind us: what species a creature is shouldn't be where we focus our attention when we try to decide how a being should be treated. What we should concentrate on is what the being is like—especially what it's like psychologically.

If there is a paradox here, I don't think it will have anything to do with a conflict in the conditions for set membership. Let's leave aside that there may be sorites-style paradoxes arising from the vagueness of the predicates "young girl" and even "female human." I suspect that those paradoxes can be solved in the "epistemicist" way (see this link).

One and the same individual can possess various mutually consistent properties: she can be a young girl (at a specified time t), a female human being (at any time during her existence, including at time t), and so on. So Miss X can belong to the set of girls who are young at t, the set of female human beings, the set of human beings, the set of mammals, the set of things referred to by you in your question above, etc. She would belong to each of those different sets for different but compatible reasons. I don't see anything paradoxical about that.

It's a good idea to distinguish between epistemic uses of modal language (which have to do with our knowledge) and alethic uses (which have to do with truth independently of our knowledge). When you say, "It is possible that this page is white," you might be wearing tinted glasses and simply admitting that, for all you know, the page that looks amber to you is in fact white (i.e., it looks white to normal observers in normal conditions). That use of "possible" would be epistemic. Or, instead, you might be saying that the page, which in fact emerged a mottled gray from the unreliable paper mill, could have been white had the mill done a better job. Or you might simply infer from the fact that the page is white that it's possible that the page is white: what is true is of course also possible. Those uses of "possible" would be alethic.

Where do alethic modal concepts belong? I'd say that they belong to logic, in the sense that they are at the foundation of the concept of logical consequence. To say that some proposition A is a logical consequence of some proposition B is just to say that the conjunction (B and not-A) is not possible, i.e., the conjunction couldn't have been true in any circumstances. Equivalently, it is to say that the disjunction (not-B or A) is necessary, i.e., it must be true in all circumstances.

On one way of seeing it, these modal facts are neither in your mind nor received by you from objects in the physical world. Yes, you can understand and know modal facts. For instance, you can know that possibly the page is white based on your knowledge that the page is in fact white. But modal facts would be facts whether or not your mind, or any mind, or any physical objects existed. In this way, modal facts are like the laws of logic (which depend on them) or the laws of mathematics.

The fallacy of composition is drawing conclusions about the whole from facts about the parts when the facts about the parts don't support the conclusion. Obvious case: every cell in my body weighs less than a pound. But that doesn't support the conclusion that I weigh less than a pound. The fallacy of composition is an informal fallacy: you can't tell whether it's been committed just by looking at the form of the inference while ignoring the content.

In any case, the inference you're considering isn't a conclusion about a particular car—a whole—based on premises about its parts. It's a conclusion about all or most cars of a certain sort based on facts about some cars of that sort. This doesn't count as a part/whole relationship in the sense relevant for potential cases of the fallacy of composition. "Chevy cars" aren't a whole in the relevant sense.

On the other hand, it would be hasty to generalize about Chevies based on a sample of two. So yes: hasty generalization.

A footnote, however: even people who've taught informal logic are often bad at naming fallacies; I certainly am. That's because the names aren't really important. What's important is being able to say what's gone wrong. Saying that an argument commits a petitio principii or the homunculus fallacy (I didn't know what that was either until five minutes ago) won't help most people unless they already know what these terms mean. And most of the time, they won't.

I don't have anything insightful to offer here, but I can say for certain that you're not the first person to be puzzled by the sorts of things you're puzzled by. It's also very hard to articulate your question in a way that would make sense to someone who didn't "get" it.

As for philosophers who might have written about this, I'm going to offer up a long quote from a philosophically-inclined physicist, Hermann Weyl. This passage is from his Philosophy of Mathematics and Natural Science, originally published in 1927. I suspect there's no fully coherent way to make sense of the whole quote, but this passage has stuck with me for a very long time.

"The postulation of the ego, of the 'thou,' and of the external world is without influence upon the cognitive treatment of reality. It is a matter of metaphysics, not a judgment but an act of acknowledgement or belief... Yet this belief is the soul of all knowledge. From the metaphysico-realistic viewpoint, however, egohood remains an enigma. Leibniz... believed he had resolved the conflict of human freedom and divine predestination by letting God (for sufficient reasons) assign existence to certain of the infinitely many possibilities, for instance to the beings Judas and Peter, whose substantial nature determines their entire fate. This solution may objectively be sufficient, but it is shattered by the desperate outcry of Judas, 'Why did I have to be Judas?' The impossibility of an objective formulation of this question is apparent. Therefore no answer in the form of objective thought can ensue. Knowledge is incapable of harmonizing the luminous ego with the dark erring human being that is cast out into an individual fate." —Hermann Weyl

Humans comprise a naturally occurring species, so I would ask, "What purpose could any naturally occurring species serve?" We humans use some naturally occurring species, such as Oncorhynchus nerka (sockeye salmon), as food, but it doesn't follow that the purpose of that species is to be our food. Unless there is a god who created species for this or that purpose, naturally occurring species -- qua species -- have no purposes. Whatever has a purpose must be intentionally given that purpose, and I think that no being exists who could give humanity as a whole a purpose. So I agree with you that humanity as a whole has no purpose. But humans are hardly unique in that way.

Moreover, even if there were a being who created all humans for a purpose, I doubt that any humans (much less all of humanity) would thereby acquire that purpose, as I suggested in my answer to Question 27543. The only way I can see in which humanity as a whole could have a purpose would be if all humans collectively resolved to make some particular thing the purpose of our species, but even then I doubt that our unanimous resolution would do the trick. An organization can require that every member sign on to the purpose of the organization, but a species isn't an organization. No purpose that the existing members of our species might sign on to can bind past or future humans to that purpose, because past and future humans didn't sign on.

While there are some philosophers today, known as "animalists," who identify the human person as their whole body (brain and all). many more philosophers hold that personal identity is a function of brain continuity. On this view, if your brain were transplanted into a different body, you would then be re-embodied in that new body. The way you phrase your question is interesting as you refer to "the body by its name" and refer to "the brain's name." This is rare, as (to take my own case) few would think that "Charles" refers to my brain or my body. I believe most would think "Charles" refers to me as a subject, a substantial individual being who thinks, acts, has feelings, has a past, and so on. It is a further question about what is essential (in bodily terms) for me, Charles, to endure over time. Would I survive if half my brain was removed? There is a recent book on such questions, Are we bodies or souls? by Richard Swinburne. Swinburne argues that reflection on personal identity should lead us to believe that we are more than our brains (and more than our whole animal bodies). Whether you agree with him or not, I commend his methodology: we should begin with a certainty about our own substantial existence as persons who endure over time. After such a beginning, we can then go on to ask whether you and I are brains or our continuity rests on our brain's identity, and so on.

This has been a major concern for many philosophers. Few think that "equality" as an abstract term is ipso facto (by itself) something good; it would not be good, for example, for all people to have the same sickness or ingest equal amounts of poison. But with respect to some domains like moral and legal rights, equality has often been seen as a virtue (you and I should have the same -or an equal-- right to vote, etc). Probably one of the most vexing issues of inequality today --globally but certainly in the USA and Europe-- is the inequality of pay due to gender. There is evidence that men are paid more than women, both in the sense that men have more high paying jobs than women, and in that men are paid more even when they do the same job as women. The American Philosophical Association strongly opposes such inequity and condemns discrimination on the basis of not just gender but sexual orientation, race / ethnicity, religion.

Your focus on the inequality of persons with respect to factors that are beyond our control has concerned some political philosophers like John Rawls and some ethical theorists like Thomas Nagel (one of Rawls's students). Rawls developed a theory of justice that sought to insure that those who are most disadvantaged in a state would receive some compensation; he opposed a libertarian state in which those with natural talents are entitled to maximum benefits without any responsibility for the dispossessed or those worse off. Nagel has spent some time examining what is known as moral luck: cases in which we might praise one person for some talent or virtue or event that was not due to her own free choice but a matter of luck (factors beyond the agent's control).

Unfortunately, there is no consensus on such matters, though I personally commend Rawls's effort to oppose a completely unchecked free market economically and Nagel's effort to distinguish between cases that are and are not under our control. Bernard Williams has also addressed the nature of moral luck. Two other historical, philosophical sources you might look into: Thomas Hobbes's notion that in a state of nature, all persons are equal and Descartes's thesis that all people have an equal ability of use reason. Your last point about the danger of seeking "absolute equality" seems right on. On this point, Medieval philosophers often stressed the good of diversity, diversity of the kinds of creatures that exist and diversity within those kinds. Many many medieval philosophers endorsed a principle of plentitude, arguing that an all good God would not have created a homogenous cosmos, but one in which there are indefinitely many different (and thus unequal) creatures.
See Arthur Lovejoy's The Great Chain of Being for some great references.