Cantor Confusion
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From: David Marcus on 19 Nov 2006 17:53 Lester Zick wrote: > On Sat, 18 Nov 2006 13:44:58 -0500, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > >Lester Zick wrote: > >> I'm saying that you don't understand what a mathematical definition is > >> but nonetheless want to pretend you do. If a mathematical definition > >> were "just" an abbreviation as you claim you wouldn't have any way to > >> tell one mathematical definition from another. > > > >Why not? Suppose I make the following definitions. > > > > Let N denote the set of natural numbers. > > Let R denote the set of real numbers. > > > >Then I can tell N and R are different because their defintions are > >different. If I write > > > > 0.5 is not in N, > > > >then this means the same as > > > > 0.5 is not in the set of natural numbers. > > > >And, it means something different from > > > > 0.5 is not in R. > > But the problem, sport, is you claim mathematical definitions are > "only abbreviations". Granted I suppose even mathematikers can tell > the difference between N and R in typographical terms. I mean they may > be too lazy and stupid to demonstrate the truth of what they say but > even they can see differences in typography. But in terms of > abbreviations alone we can't really say what the difference is between > N and R because you insist their definitions are "only abbreviations" > and not their conceptual content. You said there was no way to tell two definitions apart. The typographical difference suffices to tell the definitions apart (as you just admitted). -- David Marcus
From: Lester Zick on 19 Nov 2006 18:04 On 19 Nov 2006 03:43:04 -0800, imaginatorium(a)despammed.com wrote: > >David Marcus wrote: >> imaginatorium(a)despammed.com wrote: >> > David Marcus wrote: >> > > imaginatorium(a)despammed.com wrote: >> > > > Dik T. Winter wrote: >> > > > > In article <1163602667.089204.113210(a)m73g2000cwd.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: >> > > > > > Dik T. Winter schrieb: >> > > > > ... >> > > > > > > In >> > > > > > > principle no axiom is necessary. But you need a few to have some start >> > > > > > > to work with. >> > > > > > >> > > > > > That's the question. By means of axioms you can produce conditional >> > > > > > truth at most. I am interested in absolute truth. Axioms will not help >> > > > > > us to find it. I don't think we need any axioms. >> > > > > >> > > > > If you want to find absolute truth you should not look at mathematics. >> > > > >> > > > Really? There are two groups of order 4; could any truth be more >> > > > absolute than that? >> > > >> > > I think it depends on what the words mean. If the axioms are correct in >> > > your model, then the theorems are correct in your model. >> > >> > Well, model-schmodel, really. (This stuff is a bit beyond me, >> > actually...) >> > >> > It's not entirely clear what the notion of "absolute truth" refers to. >> > Suppose you think it is a matter of absolute truth that all men are >> > created equal. Then you go to Venus and discover that in their language >> > the word 'All' means flying, 'men' means pigs, 'are' means eat, >> > 'created' means chocolate, and 'equal' means icecream.* Moreover the >> > atmosphere of Venus turns out to be full of flying pigs, but is of such >> > chemical composition that icecream of any flavour self-combusts >> > explosively. Well, has absolute truth varied? I think the reasonable >> > answer is 'No', because a truth is _about_ something, not merely a >> > string of formal symbols. >> > >> > : * Language doesn't work like this - I know, but I haven't time to >> > assemble grammars and whatnot >> > : just to make the same point. Anyway, see the Hilary Putnam stuff >> > about horses and schmorses >> > : (which I have only read secondhand in Dennett). >> > >> > > Why did you pick the statement you did, rather than something like 2 + 2 >> > > = 4? >> > >> > Because as far as I know there is no (normal, sane) interpretation of >> > the _words_ of my statement about groups of order 4 other than the >> > standard one. Whereas, for example, in other contexts 2 + 2 = 1, so >> > while the truth to which "2+2 = 4" refers is absolute, it takes longer >> > to write, because you have to spell out the full context, and in >> > present crank company even saying "integers" may take 2-3 lines. >> > >> > You say this depends on my axioms and my model; but are there such that >> > make my claim about groups of order 4 untrue? >> >> I don't know. > >You claim to have a PhD in mathematics, and you "don't know"? What a >feeble answer. So disappointed was I when I saw it, that I was tempted >to say I begin to understand where Lester gets his "ideas" from, though >mercifully I overcame that temptation, seeing it would probably start >him off again. Well, Brian, the problem is that you and others get into mathematics to find some kind of absolute truth then for answers you get shuffled off into models, axioms, and theorems nonsense. The difficulty is you are asking the wrong people. You're asking the models, axioms, and theorems people and all they can do is engage in a professional recitativo of the status quo. That's all they know. What else could you expect? As far as they're concerned there is no truth. If you really want truth the skip truth police like David and if you really don't want to get me started again try figuring it out for yourself. >I think I see that there could be a set of rather weak axioms that >formed something called groupette theorino, which were simply powerless >to prove the existence of two groups of order 4, but my suggestion is >that no-one would accept such a miniature as being grownup group >theory. > >Brian Chandler >http://imaginatorium.org ~v~~
From: Virgil on 19 Nov 2006 18:05 In article <MPG.1fcaaa61c8ed43a3989964(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > Lester Zick wrote: > > On Sat, 18 Nov 2006 13:44:58 -0500, David Marcus > > <DavidMarcus(a)alumdotmit.edu> wrote: > > >Lester Zick wrote: > > > >> I'm saying that you don't understand what a mathematical definition is > > >> but nonetheless want to pretend you do. If a mathematical definition > > >> were "just" an abbreviation as you claim you wouldn't have any way to > > >> tell one mathematical definition from another. > > > > > >Why not? Suppose I make the following definitions. > > > > > > Let N denote the set of natural numbers. > > > Let R denote the set of real numbers. > > > > > >Then I can tell N and R are different because their defintions are > > >different. If I write > > > > > > 0.5 is not in N, > > > > > >then this means the same as > > > > > > 0.5 is not in the set of natural numbers. > > > > > >And, it means something different from > > > > > > 0.5 is not in R. > > > > But the problem, sport, is you claim mathematical definitions are > > "only abbreviations". Granted I suppose even mathematikers can tell > > the difference between N and R in typographical terms. I mean they may > > be too lazy and stupid to demonstrate the truth of what they say but > > even they can see differences in typography. But in terms of > > abbreviations alone we can't really say what the difference is between > > N and R because you insist their definitions are "only abbreviations" > > and not their conceptual content. > > You said there was no way to tell two definitions apart. The > typographical difference suffices to tell the definitions apart (as you > just admitted). Responding to Zick is a waste. Even reading him is a waste. I found killfiling him to be much more profitable.
From: Michael Press on 19 Nov 2006 18:31 In article <1163857371.306845.100530(a)b28g2000cwb.googlegroups.com> , mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > > I claim case iia: There is a potentially infinite sequence N = > > > 1,2,3,..., such that for any n there is n+1 but we cannot recognize or > > > treat all of its elements. In particular we can never complete this > > > set. We can never put it into a list > > > > OK. Knock yourself out. > > I read this several times from you. What does it mean? It means a fool who persists in his folly will be made wise, with the further implication that the speaker will no longer attempt to dissuade his interlocutor from a declared course of action. -- Michael Press
From: David Marcus on 19 Nov 2006 18:32
Virgil wrote: > Responding to Zick is a waste. > Even reading him is a waste. > I found killfiling him to be much more profitable. I basically agree. He was almost coherent for a little while there. But, now he seems to have reverted back to making inane comments. He's just a heckler. -- David Marcus |