No.

There is a set of even numbers. There is also a set of numbers that are even or prime. (Note, by the way: something can be even and prime: the number 2.) The number 8 is in the first set because it's even. It's also in the second set because it's even, hence even or prime.

Not all good paintings are beautiful, but for present purposes, we can still assume that all beautiful paintings are good paintings. A beautiful painting clearly fits the membership condition for the set of beautiful paintings. But it also fits the membership condition for being in the set of paintings that are beautiful or good and it fits it by virtue of being beautiful.

There's nothing peculiar here at all. If X and Y are both sets, their union is also a set. That's elementary set theory, and it's so whether or not X and Y are mutually exclusive.

Some theologians and philosophers would say that religious devotion to anything less than a perfect being amounts to idolatry, and a less-than-omniscient or less than omnibenevolent or less-than-omnipotent being would be less than a perfect being.

My own view is that this is a view that only someone in the grip of a theory could love. I rather doubt that most believers give much thought at all to the difference between omni-God, as it's sometimes put, and a being so far beyond us that, perfect or not, deserves their profoundest devotion. (Whether there actually is such a being is a separate matter, and not the subject of these comments.)

Perhaps there's one exception. Perhaps a being that was less than morally perfect couldn't be the object of a non-idolatrous religious devotion. That's a subject for an interesting conversation, but I'm not convinced that even this is right. So I think your question is a good one, and I"m inclined to think you're right.

One of the philosophical roots for identifying divine attributes is the idea that God (if there is a God) is maximally excellent or (in language going back to St. Anselm) God is a being greater than which cannot be conceived. Advocates of this way of thinking are sometimes described as advancing perfect being theology. They ask: what would be more excellent a being that knows a great deal or an omniscient being? a being that is very powerful or one that is omnipotent? It is through this line of reasoning, that it is held that God (if God exists) exists necessarily (rather than contingently), God is maximally good (rather than sort of good) or worthy of worship (rather than worthy of admiration). Interesting disputes arise over different attributes. For example, some philosophers think that a maximally excellent being would be eternal in the sense of not being temporal (on this view, temporality may be a creation of God) versus everlasting (God is in time, but without a temporal beginning or end).

A technical term that these philosophers use about God is that God has the greatest or maximal com-possible set of attributes. "Com-possible" means that the attributes can be had (or be exemplified) of the same being at the same time. Philosophers in the perfect being tradition include Jews, Christians, and Muslims (and some theistic Hindus). If interested, the work of T.V. Morris is quite accessible.

Perhaps you are very gifted and your mother was humorously commending humility. Maybe you won an award and she did not want you to think you were the best and could therefore retire. In any case, on the matter at hand: if your mother told every (to use your example) artist that there was always somebody better than that artist, then there would indeed have to be infinitely many artists --just as there cannot be a greatest possible number, there could not be a greatest possible artist. Going further, if we have reason to believe there are finitely many artists (which we do), it would be hard to argue that there must be a single best artist. There might be many equally talented artists. Also "if person A was the best person at art in the world" there might be many artists who can POSSIBLY be better at art than them, but they never try to be.

PS: I suggest that you may be good at something and nobody could be better: being you.

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.