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 could not 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.

Intentionally false speech isn't completely free. Lying under oath is against the law. So are slander and libel. So is providing false information on your tax forms. And so on. It would be odd to think these laws should be abandoned.

But not all deliberately false speech is illegal. If you tell me that my ridiculous new hat is just dandy because you don't want to hurt my feelings, it's legal and should be. Less happily, politicians can lie when they make campaign promises or stand up in the Senate and say that there's no such thing as global warming even when they know damn well that it's real.

Of course being legal isn't the same as being cost-free. If you come to be known as a liar, you're likely to pay a social price, and that seems more or less right. Politicians may also pay if they can't persuade voters to believe them or if they get caught in a lie. The justice is rough, but it's not nonexistent.

It's hard to say anything precise here. Wrongdoing shouldn't be cost-free, and deliberate lying is usually wrong. (Kant seemed to have thought that it's always wrong, but most of us would say that it's fine to lie to the Nazi at the door.) There's a point to reminding ourselves that we shouldn't become indifferent to bad acts, though we also shouldn't let ourselves become zealots. But these days is seems that truth is fighting a losing battle; the lies have been costly and they're getting costlier. This makes your question a timely one; a reason to remember that there's an election coming up.

Are most philosophers of religion theists? You may be right, but I don't actually know. And I also don't know whether most philosophers of religion are theists before they study philosophy of religion. I also don't know how many philosophers change their minds after they study philosophy of religion.

My sense is that what you're really interested in is how much influence philosophical arguments have on people's religious beliefs—at least, if the people are people who study philosophy. It's an interesting question and all I have to offer are personal impressions, which may well be wrong.

I'd guess that there are lots of philosophers who stopped believing partly because they studied various arguments for the existence of God and found them to be inadequate. I'd guess that because it fits a fair number of people I've known, but as they say: the plural of "anecdote" is not "data." I'd also guess that there are far fewer philosophers who started out as non-believers and became theists because of their study of philosophy of religion. The main reason I'd make that guess is that I haven't met many (if any) theists who became believers on account of the arguments, but once again, anecdotes don't add up to data.

A bit more "philosophically," my sense is that there aren't many, if any, good "proofs" for the existence of God. I say that having given many of them quite a bit of thought, and having co-authored a textbook on philosophy of religion. Further, the highly anthropomorphic idea of God that many believers have in mind strikes me as not even wrong, to borrow a phrase attributed to Wolfgang Pauli. My sense is that for many philosophers, that's the end of the discussion, but I don't think it should be.

One reason is that highly anthropomorphic notions of God aren't the only ones on offer. Another is that sophisticated theological claims may not be your cup of tea, but they don't strike me as a whole lot stranger than some of the ideas that get taken seriously by serious philosophers or, for that matter, serious physicists. But perhaps the main reason is that religious belief isn't, never was, and mostly doesn't pretend to be a purely intellectual matter. The outlook of many believers is much more a matter of how the world feels to them or strikes them in a hard-to-articulate way, rather than a matter of proofs. To see religious commitment as mainly about arguments and reasons is a bit like thinking one has to have good arguments for loving the ones one loves.

This is not to say that religious beliefs are beyond critique; religion can be at least as toxic as love can. Still, the fact that there's bad love doesn't prove that love is bad. Quite apart from that, however, philosophy of religion that doesn't stray beyond arguments for and against metaphysical theses is ignoring the biggest part of the picture. Not clear why a philosopher would want to do that.

I tend not to distinguish between a property and a quality. I would say that truth is a property (or quality) of propositions primarily and sentences derivatively: sentences are true when and only when they express true propositions, but propositions can be true without ever being expressed by sentences.

It seems odd to me to classify truth as a relation: it would be a relation between what and what else? Some theories of truth say that a proposition's being true depends on a relation, such as a "correspondence" relation between the proposition and a state of affairs in the world. But depending on a relation is different from being a relation.

I'm not sure that Locke's distinction between primary and secondary qualities straightforwardly applies to the property (quality) of truth. But I do think that the truth of any proposition is independent of anyone's believing it to be true -- which I suppose makes truth more like a primary than a secondary quality.

The problem here, I think, is that there's no one answer to the question "What are the fundamental laws of logic?" We can do things in different ways, and things which are fundamental on some accountings will be derived on others.

Let's assume that there is a definite answer to the question "What are the logical truths of classical logic?" (I'm using this as a proxy for "logical statements." If we want to expand it to include principles of inference, like modus ponens, that's okay too.) Note that the set of all such truths will be infinite, but that's okay. And to make "classical logic" well-defined, let's assume we mean truth-functional and first-order predicate logic, in which our first assumption is indeed correct. Then there are sets of rules and/or axiom schemes that provably allow the derivation of every logical truth thus understood. As just noted, there is no one way to so this, and the different ways won't contain the same axioms and/or rules. Even "the law of non-contradiction" will show up differently in different systems. For example: if by "the law of non-contradiction" you mean statements of the form "not-(P & not-P)," then such statements will be derived rather than basic in typical systems, but in all systems capable of capturing the logical truths, "not-(P & -P)" will come out true.

Logic isn't special in this regard, by the way. There are different ways to axiomatize pretty much any theory that can be axiomatized at all. Whatever fundamentality amounts to in these cases, it's not rigid and fixed.