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...

I am having trouble understanding how the idea of qualia and p-zombies is logically coherent. If philosophical zombies are conceivable, and behave exactly the same as human beings, then zombies would also claim that they possess conscious experience / qualia, even though they do not. Doesn't it then follow that our conviction that we have qualia cannot be DUE to us actually having qualia, since zombies would hold the same conviction? Thanks.

No, it doesn't follow. Compare: If an evil demon were thoroughly deceiving me right now about my surroundings, then my current perceptual experience would -- unbeknownst to me -- be unreliable. But the truth of that conditional doesn't imply that my current perceptual experience is -- unbeknownst to me -- unreliable. Likewise, if zombies are possible, and if they claim that they have conscious experience, then it follows that claiming to have conscious experience doesn't imply having conscious experience. But we knew that already.

Recently I read a comment on an online debating site where someone stated “ Every deductive statement regarding the real world relies on induction” to me that does not sound correct am I missing something?

One reason it doesn't sound right to me is that I don't know what could be meant by a "deductive statement." I know what a deductive argument is, but it always contains more than one token statement. Did the site say, instead, "every declarative statement" (i.e., every declarative sentence)? In any case, consider the statement "There are no colorless red cars." It's a declarative statement. Does it regard the real world? Arguably, yes: it's at least partly about cars. But knowing its truth doesn't require induction -- it's analytically true. On the other hand, maybe despite appearances it's not a statement even partly about cars but only about the logic of the concepts red and color . We'd need an agreed-on criterion of "aboutness" in order to decide.

My friends and I have gotten into an argument over whether or not there is/are opposites to a circle. Both sides have some valid points, but the main idea is whether or not there are opposite shapes.

I can't think of any ordinary sense of "opposite" that allows for the existence of opposite shapes (i.e., closed plane figures). But you and your friends could invent a technical sense of "opposite" that allows for opposite shapes. Maybe the opposite of a shape is the mirror image of the shape along the vertical axis, or along the horizontal axis, or along some oblique axis, provided that opposite shapes never look the same. On that definition, a circle wouldn't have an opposite shape, but a triangle could. In any case, there's nothing to disagree about until you have a suitably precise definition of "opposite shape," which again I think you'll have to stipulate, because ordinary language doesn't supply one.

I have a strong conviction. It's about free will. I don't think we have it. Here goes: 1. We don't choose our preferences. - I can't say we do, looking into myself and others I've talked to... Which ofcourse makes my basis for this assertion quite limited. So how is it? Do we choose our preferences? 2. We can't make choices outside of our preferences. - Looking into myself and my choices, they're always dictated by my preferences. No matter how banale or how life changing the choice was. I chose as I preferred to choose. (I call it choice even if I don't believe there ever was a choice per se, because there are options at hand, objectively speaking.) Conclusion: We don't have free will. We can't choose any other way than we in fact choose. Does this hold up as it stands? Thanks in advance.

Your comment runs together two things that ought to be kept distinct: (1) Can we choose our preferences? (2) Could we have chosen otherwise than we in fact chose? I'll take them up in turn. I'm not a psychologist, but I take it as common knowledge that we do have some long-term control over at least some of our preferences. Even if you now prefer Bieber to Beethoven, you can choose a program of listening and study that will fairly reliably end up reversing that preference. But the more important point is this: You needn't have chosen your preferences in order to choose freely in light of them. I prefer Beethoven to Bieber, and on that basis I can choose to listen to an hour of Beethoven's music rather than an hour of Bieber's if given those options. I would be unfree if I couldn't choose according to my preferences. Moreover, in some cases we form strong preferences -- e.g., for one job-offer rather than another -- as a result of careful deliberation, and it would be silly to think "Even though my...

Could necessary truths like "red is a color" turn out to be wrong?

Not if they really are necessary truths. By definition, any necessary truth couldn't possibly have been false. It takes some care to state propositions in such a way that they really are necessarily true. For instance, Red is a color asserts the existence of something -- red, or redness -- that arguably doesn't exist in every possible world. If there are possible worlds in which nothing physical ever exists, then nothing is red or (arguably) even could be red in such worlds, making it unclear whether there is a color red in such worlds. By contrast, the necessarily true proposition Whatever is red is colored doesn't assert the existence of anything, so it comes out (vacuously) true even in worlds lacking any red or colored things.