Not necessarily. On the one hand, if a world view disagrees with Christianity, then it's obviously inconsistent with Christianity . However, it need not be internally inconsistent. And if it is internally inconsistent, then this can be shown without assuming Christianity. A bit more generally, however: a Christian apologist might have more than one logical goal. One goal might be to show that some rival view is incoherent, thereby eliminating it from contention. Another goal might be to point out some not-so-obvious inconsistency between some claim of a rival view and the core doctrines of Christianity. The second sort of enterprise doesn't beg the question either, though the inconsistency by itself wouldn't have to count in favor of Christianity.

Let's try a related question: is physics ever wrong? The answer is pretty clearly yes in one sense. Physicists can be wrong. And if enough physicists are wrong about the answer to some physics question, then Physics as a discipline is wrong. It's happened before and will no doubt happen again. Nonetheless, it's perfectly natural to say things like "I wonder if we really have the physics of black holes right." When we talk that way, we use the word "physics" to mean "the principles that provide the true descriptions of physical systems." Those principles, of course, can't be wrong because the right principles, whatever they may be, aren't wrong. Same goes for logic. There are logicians. They can make mistakes. And there is a discipline of Logic. It could end up in some collective error about something or other. But there's lots of room for the other sort of usage. Someone might insist that logic dictates a certain conclusion when in fact the conclusion doesn't really follow from the premises....

I'll confess that I'm not sure I have your question right. You've given a pretty good explanation of why P can't be true if it entails a contradiction. I'd rephrase the way you put it, however. Instead of saying "contradictions don't exist in real life," I'd say "contradictory statements are never true." But as you in effect note, if a statement entails a contradiction, then the statemetn could only be true if a contradiction were true. That can't happen, so the statement must be false. So far so good. Your worry has to do with that fact that we are dealing with symbols and formal logic rather than "real life. " But the point of the the symbols is just to let us talk in general. The schema is (roughly) that whenever P entails a contradiction, P is false. That's shorthand for saying that whenever a statement entails a contradiction, the statement can't be true. In other words, Pick any "real life" statement you like that entails a contradiction. Then the statement is false. Notice that...

On the one hand, there is still a real fallacy of the sort we label ad hominem . The fallacy consists in claiming that a person's conclusion should be rejected because they have a bad character or have an ulterior motive. This is a fallacy because I don't have good grounds for saying that the conclusion is false. A bad person can occasionally offer a good argument, and a conclusion can be plausible even if it's argued for by someone of suspect character. Further, in the wild, so to speak, ad hominem arguments are often the last (or first) resort of intellectual scoundrels who want to divert attention from the poverty of their own case. That said, there's a familiar sort of move that all of us make legitimately. Suppose, for example, that I am not an expert on some controversial topic, but I do realize that coming to sound conclusions is hard and that I'm not in a position to sort good arguments from bad. Suppose I come across an argument by someone who has something at stake, and who has a...

Same as they are if God does exist. The idea that God (if such there be) has control over truths of math and logic is one that a few philosophers have argued for (Descartes, for instance, if I'm not mistaken) but even staunch believers in omnipotence typically understand omnipotence in a way that doesn't call for the puzzling idea that God could change the laws of logic. Briefly, the view of many theists would that God can perform any logically possible task. One reason for saying that is that logical "constraints" help us make sense of what omnipotence might mean.Why anyone would want more is hard to fathom. Suppose someone asked God to light up a set of pixels on an infintely high-resolution screen so that these pixels made a figure that was perfectly round and perfectly square. What would count? Is there actually a genuine task to be done here? If not, then it hardly seems to be a limitation on God's power (or anyone else's) that s/he can't complete the task.

Although I think the argument is fraught with difficulties, I don't think it simply begs the question. Suppose this hypothetical theist -- call her Thalia -- is arguing with an agnostic, Agatha, who nonetheless believes that there are objective moral standards. Agatha has real-life counterparts, and some of them are even sophisticated philosophers. Suppose Thalia makes a case for premise one: that moral standards really do presuppose the existence of a divine lawgiver. At that point, Agatha has a choice: give up belief in objective moral standards, or take up theism. Depending on how convinced she is that there really are moral standards, she might well decide that she should opt for theism. Notice that from Agatha's point of view, there's no need for proof that there are objective moral standards. She already believes that. What she'd need to be convinced of is that premise 1 is true. And although I'm personally skeptical of premise 1), I do think there's more to be said here than meets the eye ...

Reformed epistemologists, as I understand them, are saying that we could know that God exists even if we were utterly unable to give a proof. That's because on their view, knowing something isn't a matter of being able to give reasons for believing it. Knowing something is a matter of being connected to it in the right sort of way. A little too simply, suppose there really is a God, and that the reason I believe God exists is because God reliably causes me to believe it. (And if God's causings wouldn't be reliable, then which ones would?) Reformed epistemologists would say that in that case, I know that God exists. This isn't a proof that God exists, and it isn't an argument to convince you that you should believe in God. It's a special case of a general view about knowledge: that we know things when they're true and our beliefs about them are caused in the right sort of way. And notice that this sort of view has some advantages. If there really is a computer in front of me, and if my belief...

I did it, last Tuesday. But actually, I'm a bit puzzled. The distinction between deduction and induction never was a distinction between universal-to-particular and particular-to-universal. Consider: All dogs are mammals; all mammals are animals. So all dogs are animals. We haven't gone from universal to particular, but surely the reasoning is deductive. Or better: If Max is in Cincinnati, then so is Jennifer. But Max is in Cincinnati. So Jennifer is there too. A perfectly good deduction, but not a case of reasoning from universal to particular. On the induction side, suppose that every egg I've eaten has given me hearburn. I'm about to eat an egg. So I infer that this particular egg will (probably) give me heartburn. This is inductive reasoning, but it doesn't go from particular to universal. In a correct deductive argument, the conclusion follows from the premises. Put roughly, it's impossible for the premises to be true and the conclusion simultaneously false, but whether premises or...

People have talked about this. One oft-cited paper is Hilary Putnam's 1968 paper "Is Logic Empirical?" (Reprinted in his Mathematics, Matter and Method as "The Logic of Quantum Mechanics.") Putnam's arguments were of a "web of belief" sort: our beliefs form a web with some more central than others, but all are revisable. Quantum mechanics, Putnam thought, has given us the same sorts of reasons to revise our logical opinions as relativity gave us to revise our geometrical opinions. A large literature (to which I made some contributions) followed in the wake of Putnam's paper. The issues here resist easy summary. In an unpublished talk, Saul Kripke offered some trenchant criticisms of Putnam's approach. My own view is that many of Kripke's criticisms can be met, but the upshot is not exactly that logic is empirical in the way Putnam believed. Rather, it could be, for all Kripke has shown, that there are logical relations found in some worlds that may be absent in others. If that's right, it...

But two qualifications to William's comments. First, not all arguments are susceptible to truth-table analysis. (For example: every horse is an animal. Therefore, every horse's head is an animal's head.) Second, there are plenty of good arguments (inductive arguments, for short) whose premises don't strictly imply their conclusions, but that make their conclusions probable given the premises. At least sometimes, informal fallacies aspire to inductive rather than deductive goodness, and so showing that the conclusion doesn't strictly follow from the premises is beside the point. Peter's point still applies however: we can show that such arguments are bad by showing that they have the same form as arguments that are patently bad. Here's a patently bad argument: most pets are mammals. Kiki is a mammal, and so (probably) Kiki is a pet. Any argument with this form is bad, even though the aim isn't to show that the conclusion strictly follow from the premises.