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What's the difference between saying that the burden of proof is on one's opponent, and simply saying that they are likely wrong? The idiom of "burden of proof" is used in a way that suggests that it's somehow different from ordinary, straightforward evaluations of evidence and arguments, but I can't think of what that difference could be.

You often do hear people in philosophy say that the 'burden of proof' is on their opponent. And you sometimes hear people argue about who has the 'burden of proof'. I think that what this usually is about is which position is antecedently more plausible, or which position presently has the best arguments in favor of it. It's kind of like the game "King of the Hill". Whoever's on top of the hill is king, and someone else has to knock them off. Personally, I don't find this way of thinking about philosophical arguments very helpful. It's not that I don't think there is a 'truth' to these matters, but philosophical progress tends not to happen in a linear manner. The fact that something seems plausible today may not be a very good guide to whether it is true. More generally, I tend to think that understanding an issue is in a way more important than knowing how to solve it, so telling me that you've given an argument and now someone else has the 'burden of proof' just sounds gratuitous. You gave an...

On April 10, 2014, in response to a question, Stephen Maitzen wrote: "I can't see how there could be any law more fundamental than the law of non-contradiction (LNC)." I thought that there were entire logical systems developed in which the law of non-contradiction was assumed not to be valid, and it also seems like "real life" suggests that the law of non-contradiction does not necessarily apply to physical systems. Perhaps I am not understanding the law correctly? Is it that at most one of these statements is true? Either "P is true" or "P is not true"? or is it that at most one of theses statements is true? Either "P is true" or "~P is true"? In physics, if you take filters that polarize light, and place two at right angles to each other, no light gets through. Yet if you take a third filter at a 45 degree angle to the first two, and insert it between the two existing filters, then some light gets through. Based on this experiment, it seems like the law of non-contradiction cannot be true in...

Just for clarity, and not that Prof Rapaport needs me to tell him this, but it is important to distinguish the question whether contradictions can be true from the question whether one can get oneself into a situation in which one was believed . I rather suspect that we most or even all of us have contradictory beliefs of one sort or another, and that might motivate the view that classical logic is not a good theory of how we ought always to reason . But as Gilbert Harman famously pointed out, it isn't obvious that logic should be in the business of formulating norms of reasoning. Maybe what it does is simply study the notion of truth-preservation. So classical logic might be a good theory of validity, but not a good theory of how to reason, and maybe paraconsistent or relevance logics (or probabilistic analogues thereof) are better theories of the latter. For what it's worth, my own view is that Harman's point, though fundamentally correct, needs very careful handling and that, even in the...
I won't address the issue about physics, but yes: There are plenty of logical systems that allow for the possibility of true contradictions. For the most part, these are motivated by various sorts of paradoxes, such as the liar paradox (which has to do with truth) or the Sorities paradox (vagueness) or Russell's paradox (set theory). But there can be, and have been, deeper motivations, connected with questions about the limitations of human thought, and even Buddhist notions about the nature of ultimate reality. If you're interested in that sort of issue, have a look at Graham Priest's book In Contradiction or his more recent book Towards Non-Being , which is on a slightly different but related topic. I'll add that my own view is that contradictions cannot be true and that, even if they could, that would not help us solve the sorts of paradoxes I mentioned. But that doesn't mean such views aren't worth taking seriously. I could be wrong!!!

Suppose I have never played a game of chess. If I now make the claim that I've won all the games of chess I've ever played, is that claim true, false, or undefined? A group of friends had an argument over this, and I figured that philosophers are deeply logical thinkers that can give us the answer and also to get a proper understanding of why the answer is what it is.

The claim is true. There is no game of chess that you have ever played and lost. That said, if you say that every game of chess you have ever played you have won, then you have said something very misleading . But that is different from saying something false. H.P. Grice started the development of a theory that would explain that difference.

Is it possible for two tautologies to not be logically equivalent?

The term "tautology" has no established technical usage. Indeed, most logicians would avoid it nowadays, at least in technical writing. But when the term is used informally, it usually means: sentence (or formula) that is valid in virtue of its sentential (as opposed to predicate, or modal) structure. I.e., the term tends to be restricted to sentential (or propositional) logic. It is clear that Rapaport is assuming the sort of usage just mentioned: "a tautology is a 'molecular' sentence...that, when evaluated by truth tables , comes out true no matter what truth values are assigned to its 'atomic' constituents". Hence, on this definition, "Every man is a man" would not be a "tautology". Which is fine. It's logically valid, but not because of sentential structure. It is all but trivial to prove, as Rapaport does, that all tautologies are logically equivalent. In fact, however, it is easy to see that Rapaport's proof does not depend upon the restriction to sentential logic. One can prove ...

Are there any philosophers who deny that the principle of explosion is a valid principle while at the same time both being not accepting of a paraconsistent logic and being accepting of the Law of Non Contradiction?

According to the article on paraconsistent logic at the Stanford Encyclopedia of Philosophy : "A logical consequence relation, ⊨, is said to be paraconsistent if it is not explosive." So denying explosion just is accepting a paraconsistent logic.

How does one determine which side in an argument must shoulder the burden of proof?

The other guy has the burden of proof. And yes, I'm serious. It's that bad. But, to elaborate a little bit, I despise burden of proof type arguments. I do not know of any reasonable way of telling who "ought" to have the burden of proof, and I'm not sure I understand what is supposed to follow from someone's having it. People often end arguments saying something like, "Since they have the burden of proof and haven't met it, it is reasonable for us to believe my view". But this seems to me an odd way of thinking about philosophy. I mean, I do hope that some of the philosophical views I hold will have some influence and help us understand certain sorts of things better than we do. But whether any of my views might actually be true I very much doubt. And the fact that the other guy hasn't been able to knock my view down doesn't seem like good reason to believe it, even if my view is more common-sensical than his (a common test). Philosophy seems to me to be much more a hunt for understanding than...

If the sentence "If p then q" is true, must the sentence "q because p" also be true? For example, "if it is raining, then the streets are wet" and the sentence "The streets are wet because it is raining." Are there any counter-examples where "If p then q" could be true while "q because p" could be false?

Even if the conditional isn't material, it's clear that this kind of inference has to fail. Suppose my roof leaks whenever it rains. Then it seems true to say: If my roof is leaking, then the streets are wet. But the streets aren't wet because my roof is leaking. Rather, there is a third cause of both these events. Even if there has to be a "link" between them for the conditional to be true, then, the link needn't be directly causal.

Me and my professor are disagreeing about the nature of logic. He claims that logic is prescribes norms for correct reasoning, and is thus normative. I claim that logic is governed by a few axioms (just like any in any other discipline, i.e. science) that one is asked to accept, and then follows deductively, free of any normative claims. My question is: which side is more sound? Thank you.

Without disagreeing with Stephen's fine response, let me point out one other issue. You say that " logic is governed by a few axioms...and then follows deductively, without any normative claims". But t here is no "following deductively" without logic: logic is about the correct norms of deductive reasoning. So this conception is flatly circular: a point made a long time ago by Quine in his paper "Truth by Convention". I should say that there are philosophers who deny that logic is about reasoning at all. On this view, logic is about a certain relation between propositions, implication, that it aims to characterize. But then the dispute just shifts to whatever one thinks does characterize the norms of reasoning, e.g, decision theory. And, for what it's worth, my own view has always been that these philosophers have too simplistic a conception of what sorts of norms logic articulates. But that is a larger issue.

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