There is an infinite number of words - "ONE", "TWO", "THREE"... etc. Every word has a definition. Every definition consists of letters. There is a finite number of arrangement of letters; thus there is a finite number of definitions. Thus there is at least one word that doesn't have a definition. Paradox?

There is a finite number of arrangements of letters; thus there is a finite number of definitions. Is that true if we're allowed to use each letter an increasing number of times? If our stock of letter tokens increases without limit, then can't the number (and length) of our definitions also increase without limit? Certainly the names of the numbers will tend to get longer as the numbers they name increase, and those names will reuse letters to an ever-increasing degree.

Say I have a sequence of numbers - 1,2,3,4,5,6,7. I add 1 to 7 to create the next number in the sequence,8. The sequence is finite. I add 1 to 8 to get the next number in the sequence, 9. The sequence is finite. I keep on going... At what point does my sequence become infinite? How can my sequence ever become infinite?

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.

Keep in mind I'm a complete novice in philosophy, especially when it comes to the literature. I might misrepresent some positions completely. Please call me out. In short: The determinist states: Our decisions are bound to causation, and thus we are not truly free. This statement implies that the only way for free will to exist would be to detach an agent from causation; as long as some factors affect out motivation to do something, we are not truly free. The determinist thus claims that the only way for a choice to be free is that there would be some force acting above the physical reality, especially when it comes to cognition and decisionmaking. Thus only in a dualistic reality is free will possible. I have a few problems with this: 1. This method of defining free will seems to consequentally destroy the agent. If we were to be able to decide what we want, we'd, at least apparently, fundamentally be nothing. How would it be possible to even assign a different "want" to ourselves without that want...

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 .

Hi, While reading aristotle and aquinas on part whole relationship i often read the phrase "something qua itself and qua something else" as in man qua headed or qua an animal, what do they mean by that ? and how can something be qua itself and at the same time be as something else ? Isnt that a contardiction ? Thanks in advance

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.

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...