Torkel Franzen on truth
in [Logic]
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From: Daryl McCullough on 28 Dec 2007 09:25 Nam D. Nguyen says... >tchow(a)lsa.umich.edu wrote: >> Your remarks here are even more absurd than your remark that belief is not >> relevant. Daryl McCullough is not asserting that >> >> the negation of Goldbach's conjecture is not true >> >> He asserts only that >> >> we have no reason to believe that the negation of Goldbach's conjecture >> is true Well, Tim is exactly right. I am no asserting that the negation of Goldbach's conjecture is not true, I am asserting that we have no reason to believe that the negation of Goldbach's conjecture is true. >I'm giving you one clue: had he only said exactly no more than that sentence, >then what you've said would have been true; What he said is true. >and in fact I would have not involved in this conversation at all! And we'd all be happier. >He did use the words "_for example_", "_because_" >didn't he? Yes, the negation of Goldbach's conjecture is an example of a statement that we have no reason to believe. >The point being is he was making an (meta level) *assertion*/*argument* >with a hypothesis that would lead to a conclusion, however informal his whole >statement may have sounded. And since his " we have no reason to believe... >is true" is a *supporting hypothesis*, one would have no choice but >interpreting it as the assertion "the negation of Goldbach's conjecture >is not true". I don't know why you say that you have no choice but to interpret it that way. Nobody made you interpret it that way, and that interpretation is wrong. >One of the things I'd complain about his whole statement is the >absurdity that *any* proof of ~GC in PA would be not convincing, I didn't suggest any such thing. You are being ridiculous. There *is* no proof of the negation of GC (as far as I know). That's why I said that there is no reason to believe the negation of GC. -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 28 Dec 2007 09:27 Nam D. Nguyen says... >In fact, DMC's whole statement above is a religion statement, dressed in >formalism! You are a very strange person. -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 28 Dec 2007 09:46 Nam D. Nguyen says... >At this point in time, when there's no proof, the belief that the negation of >Goldbach's conjecture is not true is of the nature of religion belief, which is >quite irrelevant to reasoning: reasoning requires proof not belief. Wouldn't you >think so? I think that you are very confused. Belief in general has nothing to do religion. Religion is a particular *kind* of belief. So you are mixed up about that. When I agree to fly in an airplane, I am tacitly proclaiming that I believe that it is reasonably safe to do so. That has nothing to do with religion. When you claim "Reasoning requires proof not belief" you are espousing a *belief*. It's not a religious belief, but it is a belief. But also, you don't understand reasoning very well, either. Reasoning is certainly not the same thing as theorem proving. Outside of the limited domain of pure mathematics, reasoning is ultimately about trying to make the best decisions. Do I take this drug to prevent that disease? Is it safe to ride in this car or that airplane? What is the best shape for a bridge? You can work out the consequences of this or that theory, or of this or that assumption, but ultimately, when you make a decision, there will be unproved assumptions that will go into your decision. Refusing to make assumptions without proof is not reasoning, it is irrationality. We can weed out some assumptions as false because they are contradictory. Other assumptions we can prove are true. But at some point, you have to make a decision that depends on hypotheses that are not proven to be true. You can weigh the evidence for and against such a hypothesis, but conclusions are always uncertain. In the case of Goldbach's Conjecture, nothing much rides on its truth or falsity (as far as I know). It's not *necessary* to have any opinion either way about its truth value. However, it doesn't *hurt* anything, either. You are allowed to have a belief about anything. It's very bizarre for you to have such a strong reaction to my beliefs. I don't even have a very strong belief about -- Daryl McCullough Ithaca, NY
From: Nam D. Nguyen on 29 Dec 2007 14:51 Daryl McCullough wrote: > Nam D. Nguyen says... > >> So his hypothesis is: >> >> H = "we have no reason to believe that the negation of Goldbach's >> conjecture is true." >> >> His (reasoning) conclusion based on H is: >> >> C = "a proof in PA + the negation of Goldbach's conjecture would not >> be very convincing". >> >> Independent of what he actually intended to say, taken on face value his >> statement's conclusion is, after being stripped from its informality: >> >> C' = "(PA + ~GC) is an inconsistent theory due to ~GC" > > No, I never suggested that C' is an inconsistent theory. I said > that it is possibly an unsound theory. That is, it can prove false > claims. Unsound does not imply inconsistent, as PA + ~Con(PA) shows. As I've explained recently to PS, what you've now said (or clarified) is not what you stated before. You've now stated a different statement! > > -- > Daryl McCullough > Ithaca, NY >
From: Nam D. Nguyen on 29 Dec 2007 14:53
Daryl McCullough wrote: > Nam D. Nguyen says... > >> and in fact I would have not involved in this conversation at all! > > And we'd all be happier. Somewhere I think I've heard: to kill a dog we would just label it a "mad" dog! |