Give me ONE digit position of any real that isn't computable up to that digit position!
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From: Leland McInnes on 9 Jun 2010 16:04 On Jun 8, 3:57 pm, Transfer Principle <lwal...(a)lausd.net> wrote: ... <snip> ... > This reminds me of another type of grouping that I > may mention since another poster (Chandler???) > mentioned it earlier. Instead of those who "adhere" > to ZFC, there are those who _understand_ ZFC vs. > those who don't. > > MoeBlee implies this above as well. Herc objects to > ZFC because he doesn't _understand_ ZFC or how the > diagonal argument works. > > But I don't like this idea that the only people (on > sci.math, at least) who attack ZFC are those who > don't _understand_ it, and everyone who does > understand ZFC defends Cantor. > > What I'd love to see is a poster who _fully_ > understands ZFC, perhaps as much or even more than > MoeBlee understands the theory -- yet still doesn't > believe that ZFC is the best theory. I would hardly consider myself an expert, and am certainly not as knowledgeable as MoeBlee, but I believe I have a decent understanding of ZFC. Also, I'm rather partial to topos theory myself. I might even suggest that there are potentially philosophical reasons to like it more than ZFC (a pluralistic view of mathematics, and, if you're partial to it (and I am to a degree) things like synthetic differential geometry with its rather different notion of the continuum). I would say that's a matter of taste however, and neither is "better" than the other (unless you want to qualify "better for what" in a fairly precise way). That's still not what you want, of course, even though it's all you're asking for above. I think you should ask yourself rather more carefully exactly what you're looking for this mysterious poster to say, and then I think you'll start to understand why, despite finding plenty of people who meet your stated criteria, none of them actually meet your desired criteria.
From: FredJeffries on 9 Jun 2010 16:16 On Jun 8, 10:20 am, Transfer Principle <lwal...(a)lausd.net> wrote: Alas, you have not deemed it worthwhile to address that actual issues that I brought up but instead, go off on one of your tirades... > > If Jeffries is allowed to choose alternate theories > based on how well they model situations, then Herc > should be allowed to as well. If Herc believes that > "Cantor is false" models the real world, then he > should be allowed to hold that belief. > You changed verbs in mid-paragraph: There's a big difference between "a system models a situation" and "BELIEVING that a system models a situation". The former is subject to empirical testing and falsification. The latter is not. The assertion that a certain theory is a good model for a given situation must (in order to be science) allow criticism and possible refutation. The right to hold a certain belief is in the USA guaranteed by the Bill of Rights. > But that's not how things work here at sci.math. Indeed not. Herc receives hundreds of replies, many of which contain interesting and helpful suggestions. I receive almost none. > > When Cooper contradicts ZFC, he is then criticized > for not conforming to ZFC. When Jeffries contradicts > ZFC, he isn't so villified. I said nothing to contradict ZFC. I merely object to your claim that "one can prove in the real world that 2+2 = 4, not 5". > > When Herc says, "Cantor is wrong," he is called an > anti-Cantor "kook." When Jeffries says, "6+4+8 = 26 > in bowling," he isn't called an anti-Peano "kook." Yah. I can't even get you guys to call me an anti-anti-cantorian crank. About your other request about why ZFC is not the best theory, I remember something about: For a given set T find a set Y such that T x Y = Y (cartesian product) not having the obvious answer Y = T x T x T x ...
From: Transfer Principle on 9 Jun 2010 19:50 On Jun 9, 1:04 pm, Leland McInnes <leland.mcin...(a)gmail.com> wrote: > On Jun 8, 3:57 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > What I'd love to see is a poster who _fully_ > > understands ZFC, perhaps as much or even more than > > MoeBlee understands the theory -- yet still doesn't > > believe that ZFC is the best theory. > I think you > should ask yourself rather more carefully exactly what you're looking > for this mysterious poster to say, and then I think you'll start to > understand why, despite finding plenty of people who meet your stated > criteria, none of them actually meet your desired criteria.- Hide quoted text - OK then. Here's what I'd like to see. In short, I want to see a counterexample to Little's statement that: "The vast majority of posts arguing against ZFC or its theorems in sci.math are actually from incompetent cranks." Thus, I want to see a post arguing against ZFC that's from a competent poster. I want to see a thread which starts with a poster discussing a theory other than ZF(C), but I don't want the responses to have the air of "You're wrong and everyone else here is right." I don't want the OP to be called by a five-letter insult, or to be accused of not understanding ZFC. I don't want the OP to be accused of having an IQ below 90. I want to see a peaceful discussion in which the OP discusses why they work in the alternate theory, while the others post why they prefer ZFC to the theory, and so on. The closest that I've seen to such a poster is Nam Nguyen, who does appear to be respected more than most posters challenging standard theory. But still, the Nguyen threads do still have a slight feeling of "Nguyen is wrong and everyone else is right." What would I do if I actually saw such a post? I might try to contribute to such a thread, but if it appears that I'm getting in the way, then I'll just stand back and lurk. Indeed, I am doing so in the Nguyen thread, since Nguyen is IMO holding his own in his thread and doesn't need me to interfere.
From: MoeBlee on 10 Jun 2010 12:42 On Jun 9, 6:50 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > Nam > Nguyen is overwhelmingly confused about some of the most basic matters in mathematical logic, and worse, (with rare exception) he will not allow himself to be corrected, educated, or enlightened by the many quite informed posters who try. It is usually a dead end trying to have a rational discussion with Nguyen. This is shown over and over again in thread after thread. And it's definitely not a matter of "a new theory" but rather that he purports to represent a correct understanding of standard, ordinary mathematical logic while yet he's horribly mixed up about it. MoeBlee
From: Aatu Koskensilta on 10 Jun 2010 12:45
Nam Nguyen <namducnguyen(a)shaw.ca> writes: > I'll make an explanation on this as soon as I could. But what did you > mean by "also"? What else did you have in mind that would need > clarification? The notion of "a formula that can't be model theoretically truth definable", which you yourself said "would require a close inspection of our current knowledge about the foundation of reasoning via FOL". -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |