Like you, I'm puzzled by the form of the conditional "Only if A, then B." It doesn't seem to be idiomatic English. One might say "Only if you go to the party will I go," but one wouldn't say "Only if you go to the party, then I will go." That would be unidiomatic. So I presume that the conditional form you're learning is "Only if A, B" rather than "Only if A, then B." I would interpret "Only if A, B" as stating that A is a necessary condition for B, and therefore implying that B is a sufficient condition for A. If one wants to say that A is both necessary and sufficient for B, then one can say "If and only if A, B" -- although "A if and only if B" would be a smoother way of saying it. In any case, make sure that your logic teacher really did say "Only if A, then B" and, if so, ask if he/she meant to say "Only if A, B."

Interesting question! I think you're right that there's something peculiar about this disjunctive syllogism: (1) B v ~ B (2) ~ B (3) ~ B You say that (2) must be the negation of (1)'s left disjunct rather than the assertion of (1)'s right disjunct, even though both of those are syntactically the same. You may find allies in those who distinguish between (i) denying or rejecting a proposition and (ii) asserting the proposition's negation. See Section 2.5 of this SEP entry . But here's a different diagnosis. Although (1)-(3) is a valid argument, and even a valid instance of disjunctive syllogism, the argument is informally defective because premise (1) is superfluous: (1) isn't needed for the argument's validity. Furthermore, anyone justified in asserting (2) is thereby justified in asserting (3) without need of (1). This argument is similar: (4) ~ B v B (5) ~ ~ B (6) B The claim that (5) is the negation of (4)'s left disjunct is at least as plausible as the claim that (2) is the negation of (1...

I assume that there's some nonzero minimum time, however brief, that you require to perform each step of addition. In that case, you will never produce an infinite sequence of numbers: that is, there is no finite time at which you will have produced an infinite sequence of numbers. That fact doesn't imply that the positive integers aren't an infinite sequence of numbers -- only that you can't produce them in the described way in a finite amount of time.

You wrote, "The determinist states: Our decisions are bound to causation, and thus we are not truly free." In the context of free will, what you say describes not determinists in general but only hard determinists, i.e., those determinists who also say that determinism rules out free will. The other kind of determinists -- soft determinists -- accept determinism but say that it doesn't rule out free will and may indeed be essential to acting freely. Unlike hard determinists, soft determinists allow for the combination of determinism, free will, and moral responsibility. You'll find details in this SEP entry .

In this context, it sounds as though "qua" is being used to mean "considered as." So, for example, qua sentient being (i.e., considered as a sentient being) you have particular rights, while qua adult citizen (i.e., considered as an adult citizen) you have those rights plus additional rights, such as the right to vote. I see no contradiction here.

I doubt that "because" is as finicky as you seem to be suggesting it is. I think it's perfectly true that Fred belongs to the set because he is only 14, and it's perfectly true that Fred belongs to the set because he is less than 15. I'm not familiar with any explanatory concept according to which one of those facts about Fred, but not the other, explains Fred's membership in the set. In any case, I'm confident that "because" does not stand for any such concept.

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...

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...

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.