There is a simple reasoning. Which is better, bread or love? It seems love is better than nothing. For sure bread is better than nothing. So bread is better than love. Of course this is a wrong reasoning. But I wonder whatever logical mistake is made here?

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...

Sometimes my students want to argue that "my opinion is as good as anyone else's opinion." How do I counter this view with a reasonable philosophical argument? Thanks! Richard in New York

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...

What is the relationship between mathematics and logic?

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.

I was recently having a discussion with someone about the argument from ignorance fallacy, or "absence of evidence is not evidence of absence." We think that the following is a fallacy: 1. Alien spaceships orbiting the earth are observable through a telescope. 2. No one has observed alien spaceships orbiting the earth. 3. Therefore, there are no alien spaceships orbiting the earth. However, what if you changed the premises slightly to this: 1. Alien spaceships orbiting the earth would PROBABLY be observable through a telescope. 2. No one has observed alien spaceships orbiting the earth. 3. Therefore, there are PROBABLY no alien spaceships orbiting the earth. Even though I agree with the conclusion, I think this argument is also a fallacy since it follows the same form as the first one. But then I seemed to remember some kind of rule that the premises of an argument must be absolutes. You can't introduce probabilities, otherwise the laws of logic do not even apply and all bets are off. Or does it not...

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 ...

Is there a problem for atheists to explain, for example, the laws of logic and objective morality. How could we really account for either if the material realm is all that exists?

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...

Hello, If someone proposes an idea, an idea that cannot be objectively proven in no way, as fact, and I ask them what is their education and credentials for them to speak with authority on the subject, could that be considered a fallacy on my part? More specifically is it an appeal to authority?

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.

Presuppositional apologetics arguments attempts to show the logical inconsistencies in non-Christian world views. Is it not the case that, by beginning with the the presupposition that the Christian world view and the bible are the absolute truth, thereby beginning with the desired conclusion as part of the premise, this form of apologetics commits the fallacy of circular reasoning or begging the question?

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.

Is logic ever wrong?

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....

Why is that if P entails not-Q and Q (a contradiction) do we conclude not-P? I understand that this a reductio ad absurdum and that because of the law of bivalence P either has to be true or false so if it entails a contradiction it is proved not true therefore false. But that last step is what I can't seem to justify...why does it become Not-P if it entails a contradiction? If I had to guess it's because contradictions don't exist in real life so if P were true and it entailed something that could never exist then it must be the case that P is not true (and this is true because of modus tollens: not-Q entails not-P). But we are dealing with symbols in the case of formal logic so how does this apply? Is formal logic an analogy of real life? I hope the question is clear after this rant!

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...

I'd like to challenge the validity of the "Ad Hominem" fallacy - it seems to rest on a certain metaphysics. At the very least, this metaphysics should be argued, not assumed, in my view. The separation of a person from his/her ideas strikes me as certainly not obvious. Isn't this the reason why we urge people not to discuss religion and politics with each other? Because their views, expressive of their very identities, can offend us?

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...

Pages