THE HOLY GRAIL ~ CANTOR DISPROOF
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From: Transfer Principle on 28 May 2010 22:57 On May 27, 3:31 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "Transfer Principle" <lwal...(a)lausd.net> wrote .. > > I definitely do _not_ accept Herc/Cooper's claim that > > he is Genesis Adam, since, to say the least, Adam is > > _dead_ according to Genesis (for having eaten the > > forbidden fruit). How can someone be a specific > > person mentioned in a book if according to that book, > > that person is dead? (Unless that book is wrong, of > > course but Herc/Cooper also states belief that the > > book is true.) > Well that's it for me and sci math you have your wish. When people stop blatantly lying in my face I'll check again in 100 years. And this is exactly what I was trying to avoid. In another thread, there was a long discussion about how I should stop being so quick to defend the so-called "cranks" and start allowing for the possibility that what they are saying might be "wrong." Jim Burns, Jesse Hughes, and others convinced me that I am more likely to be respected (and less likely to be killfiled) by posters, if only I would consider the possibility that the "cranks" are "wrong." So what happens? I decide to consider the possibility that Herc might be wrong. And then Herc becomes offended and decides to stop posting. One word that I told myself that I'd try to use less often is "bully" -- in particular, I wanted to stop referring to other posters as "bullies." But right now, I need to call _myself_ (and only _myself_) a "bully." For that's exactly what I just did. I just "bullied" Herc out of sci.math. What did I do to offend Herc? First, when he made a mathematical claim, I told him that ZFC refutes his claim and gave him a proof of this. I avoided assuming that ZFC is the only possible theory or only theory worth considering, but merely told him that ZFC refutes his claim. Herc's response? > Translation, "No because I told you so". Next, I tried to show Herc a specific counterexample to his claim, still working in ZFC. Herc's response? > You are selecting specific diagonals based on the list. reminding me that his claim was probabilistic in nature. But the straw that broke the camel's back wasn't even mathematical in nature. It was a discussion about Genesis Adam, which I was trying to avoid. But I had to say in passing to Aatu (who had just criticized me for trying to defend Herc) that I don't consider Herc to be Genesis Adam, and do reiterate that I consider all discussion about Adam to be off-topic for sci.math in the first place. Herc's response? > ps that's the dumbest [expletive] rebuttal of Genesis possible And then he leaves, because I have just "bullied" him away. It's threads like these that make me want to go back to my habit of defending "cranks" at all costs. I'd much rather be overly accommodating to Herc than be the poster who is responsible for scaring Herc away. If galathaea were still here, I bet she'd be pointing her finger directly at me for being the "bully" who "scared" Herc away. And it was all because Aatu criticized me for defending Herc, and I had to react to his criticism. What I want to be able to do is speak to posters like Herc in such a way as not to be a "bully" to them, yet avoid drawing criticism from others, like Aatu in this thread. And so the next time someone posts a claim refuted by ZFC, I defend their claim, and someone criticizes me for doing so, then I'll be sure to remember this thread, the thread in which I bullied and scared Herc away.
From: Transfer Principle on 28 May 2010 23:34 On May 27, 7:32 am, William Hughes <wpihug...(a)hotmail.com> wrote: > On May 27, 1:10 am, Transfer Principle <lwal...(a)lausd.net> wrote: > > Probability? Random? > It is true that the set of counterexamples may have measure > 0 in the usual Lebesgue measure. Indeed, I suspect > this, though I cannot see a simple way of demonstrating it. > However, the set of counterexamples is non-empty and uncountable. Thanks. > [Note that the idea that an infinite number of reals can have > Lebesgue measure 1 already requires uncountability. If you insist on > trying to make Herc's statements consistent you will need a > theory of probability in which a countable infinity of elements, > each with the same probability, has a probability of 1.] Yes, I've heard of the proof that any countable set must have measure zero (since we can cover the first real on the list by an interval less than epsilon/2, the second real by an interval less than epsilon/4, the third less than epsilon/8, and so on). This idea has also come up in the tommy1729 threads. In particular, tommy1729 was trying to discredit the Axiom of Choice, which is used in the proof of the existence of a non-Lebesgue-measurable set. The usual proof entails using AC to come up with a set such that the countable disjoint union of images of the set under rigid motions is the entire unit interval. Now tommy1729 pointed out that the only way for this to work would be to assign a nonzero infinitesimal as its measure. Since standard analysis does not permit nonzero infinitesimals, this is not done, and instead the set is declared to be nonmeasurable. Of course, it would be pointless to attempt to come up with such a theory for Herc since it's unlikely that Herc, who appears to doubt the existence of uncomputable reals, would suddenly accept nonzero infinitesimals instead. And even if he did, Herc isn't cuurently active in this thread. It might be worth coming up with a theory of noninfinitesimal measure for tommy1729. But we must remember that tommy1729 rejects ZFC and instead proposes an alternate theory, which he calls TST. Although it might be an interesting exercise for me to attempt to axiomatize TST, we must recall that TST is completely different from ZFC as it's based on mereology and three-valued logic. So we would be required to come up with the three-valued logic (including new rules of inference), then the mereology, then sets. Only then could we come up with reals, sets of reals, and their measures. But I'm likely to be stuck at the three-valued logic, trying to come up with laws of inference that both tommy1729 and the others are willing to accept. Most posters would have abandoned the thread by the time I even reached mereology, much less measures of sets of reals. At this point, I do wish to consider a single poster to defend, and work on a theory for just that one poster. But I'm still stuck on which poster to choose. I was earlier considering AP, but I fear that it will be difficult to separate AP-reals from Atom Totality, just as the posters in this thread had trouble separating computable reals from Genesis Adam. So AP is out. As I already mentioned, tommy1729 is out.
From: George Greene on 29 May 2010 03:06 On May 28, 11:34 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > So AP is out. As I already mentioned, tommy1729 is out. You, too, are pretty much out.
From: George Greene on 29 May 2010 03:07 On May 28, 10:57 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > What I want to be able to do is speak to posters like Herc in > such a way as not to be a "bully" to them, Why? What makes you think that this is a constructive (or even defensible) behavior on YOUR part??
From: George Greene on 29 May 2010 03:13
On May 28, 11:45 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > Then what should I do the next time someone makes a claim > that is refuted by ZFC? You should ask him whether he "believes" the axioms of ZFC, or, more specifically, ask him which axiom he disbelieves. Logic in general is not even about "claims": FIRST, you HAVE to have AXIOMS (and zeroth, you have to have rules of inference, but people in general are far less likely to insist on variations-away-from-the-usual on those, with maybe the possible exception of constructivism). The most irritating of the cranks will refuse to specify their axioms, or attack the legitimacy of "the" axiomatic "method". |