Fred is 14. Would you agree that Fred isn't in the set of people aged less than 15 because he's 14, he's in the set of people aged less than 15 because he's less than 15? (It doesn't matter what his age is, as long as he's less than 15.)

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.

No two sets can have the same conditions for membership, so if Miss X is in the set of young girls because she's a young girl, then she cannot be in the set of female humans because she's a young girl. Paradox?

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.

I wonder about the nature of modal concepts such as necessity and possibility. When I say "It is possible that this page is white" or "it is necessary that two plus two equals four" I use modal words in my speech. Where do these concepts belong to? Are they in my mind or I receive them from the objects themselves?

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...

What purpose does humanity as a whole serve? Considering that the majority of people in this world struggle just to survive on a day-to-day basis, and that those in developed countries struggle to maintain the status quo or at best to improve their lot in life, what purpose do we serve? Very few of us have our needs met in such a way that we can devote all our time to pursuits of thought and charity, and of those few who meet the criteria, fewer still can be bothered to devote their time to the betterment of humanity. I see no useful purpose to humanity as a whole and in fact see humanity as a blight & plague upon the world. We can't survive with the nature around us, in terms of food, but nature can not only survive without humans, but would actually be better off without us; so what use is humanity to the world around us, and what, if any, purpose does humanity serve? #InquirinMindsWannaKnow

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'm interested in the nature of truth. Truth is said to be a quality and sometimes referred to as a property, other times as a 'relation'. Is truth a primary or secondary property? I'm having trouble fitting truth into a category. Thanks.

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.

I am reading a by book by the great logician Raymond Smullyan. In this book he says that any statement of the form, "All As are Bs" are true if there are no "As". That is, these statements are vacuously true. He gives the following example, "All Unicorns have 5 legs" is true since there are no unicorns. So is "All unicorns have 6 legs", and "All unicorns are purple", etc. But this strikes me as obviously false. For example, "All unicorns have two horns" and "All unicorns are necessarily existing" are false statements. The first is false in virtue of the fact that unicorns are by definition one-horned. The second is false in virtue by the fact that it is impossible for something to be both necessarily existing and nonexistent. Am I missing something here or misreading Smullyan? Or are these counterexamples sufficient in refuting the claim that any statement of the form "All As are Bs" is vacuously true if there are no "As"? For reference the book is, "Logical Labyrinths" from pages 99-101. Thanks...

I don't know that book in particular, but I can give you a standard explanation that at least makes sense of the view you find puzzling. In Aristotle's logic, any statement of the form "All S are P" implies that at least one S is P, so the statement comes out false (rather than vacuously true) if nothing is S. By contrast, in contemporary logic, "All S are P" is interpreted as saying "For anything at all, if it is S, then it is P": it is interpreted as a universal quantification applied to a conditional statement. Crucially, the conditional statement "If it is S, then it is P" is standardly treated as a truth-functional conditional that is equivalent to the disjunction "It is not S, or it is P." Now suppose that nothing is S, so that "It is not S" is true of everything. Then the disjunction "It is not S, or it is P" will come out true no matter what we substitute for "it," because a true disjunction needs only one true disjunct. In that case, the truth-functional conditionals "If it is S, then it...

You can't create something out of nothing can you! And yet, here we exist. Is this not the most relevant question we can't answer?

@ Jonathan: If I may, I think Leibniz's analogy is faulty. The constraints on what counts as a good explanation of why there have been any books at all (or any books bearing a particular title) need not be constraints on what counts as a good explanation of why there have been any states of the universe at all. I try to explain why in this brief article .

Is there any way to escape an endless loop of "why"? Like when I was a kid I constantly asked my parents how something works and then it went to why something works. After they responded then it went to another why that went deeper and so on and so on. Similarily we can endlessly ask 'why' on matters like oughts of with what hand should I hold fork or on which hand should I wear a watch etc. So is there a way to escape it? Something like fact about ourselves comes to mind (i.e. because I want to do so) but that seems trivial or problematic in some areas (morality).

With matters of etiquette, such as which hand to use for the fork, or matters of personal preference, such as which wrist to use for one's watch, I don't think "Why?" questions are intellectually substantial enough to be worth asking more than once or twice. But philosophical and scientific questions are intellectually much more substantial, much deeper. There it makes excellent sense to keep asking "Why?" questions for as long as those questions remain well-posed. You're right that we don't want a loop -- a circle -- of "Why?" questions, because in that case a question reappears after it has already been adequately answered. But a loop is different from a regress of questions, which may be finitely long or indefinitely long. On whether an indefinitely long regress is always something to avoid, see this SEP entry .

I still have problems understanding why external world skepticism is a thing in philosophy. I've heard so many hypotheses and they all seem to revolve around the idea that consciousness is a "simulatable". Here's what I don't understand: The keywords are: Consciousness: the state of being aware of and responsive to one's surroundings. Simulation: imitation of something else. Simulation, by definition, is the imitation of something else. The "something else" in this case is consciousness. If it's the imitation of consciousness then it cannot be the real one. How on earth can consciousness not be real? It seems to me that by simulation they are trying to say that there is "illusory simulated consciousness" and "real non-simulated consciousness". How on earth can consciousness be illusory/simulated? A lot of people then say: external world skepticism is skepticism about perception not consciousness. It seems to me that perception and consciousness are more or less the same thing. Consciousness is...

I think that you and those you see as your opponents may simply be talking past each other. You define consciousness so that being conscious logically guarantees being aware of your surroundings. In arguments about external-world skepticism, consciousness has traditionally been given a weaker definition, a definition that doesn't logically guarantee being aware of your surroundings. In the classic evil demon scenario, your conscious mental states are caused by the evil demon and not by your surroundings (not even indirectly). You're conscious -- that is, you're not in the midst of an experiential blank -- but your conscious states are unreliable indicators of your surroundings. Sometimes the term "perception" is used to distinguish conscious states that reliably represent the environment from conscious states that represent it unreliably . I hasten to add that it takes a lot of argument to get from (1) the admission that consciousness can be inaccurate to (2) the conclusion that we never achieve...

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