Cantor Confusion
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From: Virgil on 31 Oct 2006 17:26 In article <1162304049.375352.231390(a)i42g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > It is impossible to consistently do mathematics with infinite sets. See > the vase or the tree. Therefore we need not ponder whether a well order > does exist or not. What WMueckenheim declares himself unable to do others do quite easily. It is a shame he passes on his incapacities to others.
From: Virgil on 31 Oct 2006 17:30 In article <bdc92$45476e9e$82a1e228$30478(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > It's easy to come up with a correct physical problem and > solve it with the wrong mathematics. As you did. HdB has come up with a mathematical problem which he claims can end the world: HdB claimed that a discontinuity in a mathematical function of time causes time to stop. And he claimed this followed from physics. Thus, if HdB is right, the vase problem will cause the end of the world.
From: Lester Zick on 31 Oct 2006 18:08 On 30 Oct 2006 15:21:01 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Lester Zick wrote: >> My mistake, Moe. It's just that you keep snipping all these posts. > >I snip so that the posts are not ridiculously long. If I ever leave out >context that you feel needs to be included, then you may reinstate that >context in your reply. I do not snip to materially distort context, >though I recognize that even judicious snipping by its very nature >omits context that, in some aspect, may be considered needed. Well if I previously indicated that converstations with you were short and to the point, I plead guilty but didn't imagine that was a license to truncate and then complain about what was said in the material truncated. Otherwise I have no intention of trying to reconstruct the conversation or arguing the subject further especially since David has taken to whining about it in your behalf. >I disagree strongly with many things you say, but of course I do not >begrudge your prerogative to say whatever you like about these subjects >as I reply and say what I disagree with in what you've said (which is >not generous of me, but rather is, to me, just a reflection of the >basic premise that everyone gets to speak his or her mind)...except I >ask you please not to claim I've said things that I have not said >through your incorrect paraphrases of what I said. I don't recall quoting you directly and literally but of extrapolating the implications of what you said whether you agree with those implications and my inferences or not. The problem I noted directly concerned your ideas and claims of standard mathematical definition which were not employed by Stephen. ~v~~
From: Lester Zick on 31 Oct 2006 18:17 On 30 Oct 2006 15:30:42 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >Lester Zick wrote: >> On 30 Oct 2006 12:12:00 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >> >> >mueckenh(a)rz.fh-augsburg.de wrote: >> >> Get it right: It is nonsense to talk about infinite sets if there is no >> >> axiom of infinity and, therefore, no possible definition of infinity. >> > >> >No, YOU need to get it right. You have it completely wrong. We don't >> >need the axiom of infinity to define the predicate 'is infinite'. >> >> But you certainly need something you ain't got besides the adjective >> "infinite" to define the predicate "infinity". > >I never proposed considering 'infinity' as a predicate nor defining >'infinity' as a predicate or a noun. Obviously since you can't do it. > So since the other poster >mentioned the impossibility of defining 'infinity', your point is well >taken if it is that I should be clear that I am not responding to the >poster's exact point about 'infinity' but rather that I am commenting >upon the fact that we do have definitions of 'is infinite' without >having to adopt the axiom of infinity. I have no idea what the axiom of infinity may be and don't especially care since all mathematikers want to talk about is infinite(x) and not infinity. >This boils down to the fact that set theory defiines 'is infinite' but >there need not be any pretension on the part of set theory to define >'infinity'. Pretension??? See, Moe, we're right back to the same old bullshit. Modern mathematikers want to use the idea of "infinity" without having to define it by referring to the "infinity of x" instead. Fact is that modern mathematikers want to have their cake and eat it too. They use the terms "truth" and "infinity" all the time but when they're called on it they pretend they're using "truth(x)" and "infinite(x)" instead. That's what I call pretentious. > What the theory NEEDS in order to do the math that it >expresses is to define 'is infnite'; while it is not needed to define >'infinity'. Whatever need there is to define 'infinity' is a need that >is extra to the usual mathematical purposes of devising a set theory >and definitions in it. > >Do you see what am saying? Yeah, Moe, I see exactly what you're saying. You're saying that if you get enough particular definitions of "infinite(x)" and "true(x)" you might someday wind up with some idea what "infinity" and "truth" are. ~v~~
From: Lester Zick on 31 Oct 2006 18:23
On 30 Oct 2006 22:32:49 -0800, imaginatorium(a)despammed.com wrote: > >David Marcus wrote: >> Lester Zick wrote: >> > On Mon, 30 Oct 2006 16:43:03 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >> > >Han de Bruijn wrote: >> > >> David Marcus wrote: >> > >> > Han.deBruijn(a)DTO.TUDelft.NL wrote: >> >> > >> >>And add this to the fact that noon and beyond cannot exist >> > >> >>in this problem. >> > >> > >> > >> > Are you still doing physics, water, and a finite number of molecules? >> > >> > Let us know when you switch to mathematics. >> > >> >> > >> I'm DOING mathematics. Mathematics is NOT independent of Physics. >> > > >> > >I guess your definition of "mathematics" is different from mine. >> > >> > I think the only relevant question is whether your definition of >> > "mathematics" is demonstrably true? If not I don't see that any >> > definition of mathematics is more virtuous one way or the other. >> >> That would depend on what your definition of "demonstrably true" is. My >> definition of "mathematics" agrees with what mathematicians do. >> >> Is it "demonstrably true" that "noon... cannot exist"? > >Be careful not to mix up your interlocutors - this is Lester, and I >expect he will only be interested in whether noon is true or not. Actually I'm only interested in whether mathematikers can be true or not, Brian. And it seems pretty much the latter. ~v~~ |