First, just a terminological point. The phrase "naturalistic fallacy" is usually used to mean the supposed fallacy of defining a moral term such as "good" in terms of non-moral properties. For example, if someone said that "good" means "produces happiness," they would be accused of committing the naturalistic fallacy. (Note, by that way, that even if "good" doesn't mean "produces happiness," it could still turn out that producing happiness is a genuine good.) The worry you have is of a different sort: deciding whether something is right or wrong by deciding whether it's "natural." The most familiar case is probably homosexuality, which is sometimes said to be wrong because homosexuality isn't "natural." You're right to be suspicious of that sort of reasoning. One problem is that what we see as "natural" is often not a matter of how things are in "nature" but of what we're used to. People have claimed that it's "unnatural" for women to perform certain jobs or for people of different...

There are several questions in what you've asked, all of them interesting. I'm going to single out one of them. If I read you correctly, one thing you're asking is why we can describe the universe using math and logic -- why the universe "fits" our rules of math and logic. We can begin our stab at an answer by noticing that this fact -- that the universe can be described using math and logic -- is weaker than it might seem. Imagine a computer screen of 1024 by 768 pixels, for a total of 786,432 pixels. For simplicity, imagine that each pixel is simply ether off or on; ignore color. Then there are 2 786,432 possible patterns that could show up on the screen. Most of those are a jumble -- not "logical" or orderly in any interesting way. However, each can, in principle, be described. An exhaustive list stating for each pixel whether it's off or on would do. So the fact that the screen can be described using math/logic doesn't really constrain things much at all. Some number of pixels will be on...

Of course, in a perfectly good sense of "exist", existence doesn't exist either. Existence isn't a thing, and so there is no such thing as existence, though of course, bears, bells and BMWs exist, to mention but a few. And yes: there is no such thing as non-existence, because "non-existence" isn't way of referring to a thing. But unicorns don't exist. Neither do square circles. And, according to some, neither do free lunches. No fallacy there. Does everything exist? Well, if "everything" means "all the things that exist," then everything exists. (Though of course, this doesn't mean that there is a special thing, namely everything , that exists.) But since, as noted, unicorns don't exist, it's not true that "everything" in the sense of "everything that might have existed" actually exists. It's likewise not true that that every description (e.g., "round square") picks out something that exists. The conclusion of the argument comes partly from trading on ambiguity. Related: ...

Imagine that someone finds it useful to define a new term -- "mimp," say. The newly-defined term is a conjunction, i.e., it's used to link sentences together, and it works this way: "P mimp Q" is false when "P" is true and "Q" is false. Otherwise it's true. With this definition in hand, consider the sentence "New York city has fewer than 150,000 resident mimp the next US president will come from New York." Give our definition, this is true. Our definition of "mimp" guarantees that whenever "P" is false, "P mimp Q" is true. Looking at "→" this way may help with your puzzle. The symbol "→" (alternatively "⊃" ) is one that logicians found useful to define, and its definition is given by the rule above. Whether it matches any connective in natural language is open to doubt, and in particular, it does not mean what we mean by the phrase "logically implies." After all, "New York City has fewer than 150,000 residents" does not logically imply that the next US President will be from New York. It...

There are two problems here. First, let's look at an argument about sports teams that's similar to yours but different in a simple way: The Lions are better than the Tigers The Bears are better than the Tigers. Therefore, the Bears are better than the Lions This is flat-out fallacious. The premises give us no more reason to think the Bears are better than the Lions than that the Lions are better than the Bears. But the structure -- X is better than Z; Y is better than Z; therefore Y is better than X -- is the one I think you were thinking of. I'm guessing that what you really had in mind was some variation on this old chestnut: Bread is better than nothing. Nothing is better than God. Therefore, bread is better than God This at least looks as though it could be valid; the form seems to be: X is better than Y; Y is better than Z; therefore X is better than Z. If we take as given that "better than" is transitive, as logicians would say, then the form will lead us to a true conclusion...

Ah yes. We've all been there. It may be worth helping the students see that if they extend this to all opinions, then they've put themselves in a position of telling us that we have no reason to take their own opinions seriously. In particular, if they're right all that all opinions are equally good, then your opinion that opinions aren't all equally good is just as good as theirs. This is a bullet that most thoughtful people could only pretend to bite . Of course, when people say what your students say, they often have something a little less paradoxical in mind. They may mean that when it comes to certain kinds of questions -- the Olde Chestnuts of philosophy, perhaps, or difficult moral questions -- the fact that consensus is well nigh impossible to come by suggests that one belief on the matter is as good or bad as another. A really good answer to this worry would take up rather more space than this forum allows. But a few things seem to the point. The first is that some arguments are...

It's a good idea to start with a distinction. If by "logic" you simply mean something like "correct deductive reasoning," then logic is something mathematicians use -- as do people in any discipline. If by "logic" you mean the study of certain specific kinds of formal systems and their properties -- mathematical logic, as it's often called -- then logic is arguably a branch of mathematics, but also of philosophy (and perhaps also of other disciplines such as computer science; no need for turf wars.) There are people in math departments who specialize in logic, and also people in philosophy departments. Results in mathematical logic, might be published in math journals or in philosophy journals or in computer science journals.

Arguments can have probabilistic premises. Some such arguments are inductive -- merely be intended to show that their conclusions are likely. Others can be deductive. For example: here's a deductively valid argument with probabilistic premises: 1. It's likely that X 2. If it's likely that X, then it's likely that Y. 3. Therefore, it's likely that Y But this doesn't have a lot to do with your worry. Let's start with the first argument. The problem here, intuitively, is that just because something is observable with a telescope, we can't conclude that it would have been or even likely would have been observed . Put another way: if alien spaceship visitations are rare events, then even if they could be observed, it would be no surprise if they weren't. And so from the mere fact that they could be observed by someone lucky enough to point a telescope in the right direction at the right time, it doesn't follow that they would have been observed, nor even that they ...

Interesting question, but the illusion here is to think that atheists face any special problem. Let's take the issues in turn. On morality: suppose God exists. How would that make morality objective? Someone might think that if God commands something, that makes it morally right. But it's long been pointed out (at least since Plato's Euthyphro ) that this way of thinking about things is problem-ridden. What if God commanded torturing all blue-eyed babies? Would that make it right? Hard to see why anyone should agree. Someone might say that God would never command any such thing. But why not? Presumably because God, if there is one, doesn't command evil deeds. In fact, if the theist wants to make sense of the idea that God is praiseworthy partly because he is good, there will have to be a standard of good and bad, right and wrong, separate from what God happens to will. This may still leave it puzzling how there can be objective moral truths. That's too big an issue to tackle here, but it...

No fallacy that I can see. People have a striking tendency to give their own casual and uniformed opinions a lot more weight than they deserve. Asking someone whether there's good reason to believe what they're saying is perfectly appropriate, though doing it too bluntly may not be the best rhetorical strategy.