Galileo's Paradox
in [Math]
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From: Virgil on 30 Nov 2006 18:46 In article <jack-B2A9F2.15210830112006(a)newsclstr02.news.prodigy.com>, Michael Press <jack(a)abc.net> wrote: > In article > <1164888031.386857.96190(a)j72g2000cwa.googlegroups.com>, > "Tonico" <Tonicopm(a)yahoo.com> wrote: > > > Ps Have you, and anyone else, noted how all the anticantorian cranks > > are NEVER mathematicians? But Internet welcomes all, and google's > > sci.math is an uncensored group, so anyone can offer his piece to > > all...and you know what? I think this is just fine. I'm convinced that > > also from the most stupid, dense and even annoying crank/troll we all > > can learn. > > I too conduct my affairs in accord with this conviction. Even the worst of them can serve as bad examples!
From: Tonico on 1 Dec 2006 02:55 Lester Zick ha escrito: ......................................................... > >> >What sort of evidence? Surely not empirical evidence. Mathematics done > >> >abstractly has no empirical content whatsoever. > >> > >> Except apparently for axioms and definitions. > >****************************************************************** > >What axioms of what part of maths have "empirical" evidence in the > >sense Eckard is tryuing to convey?!? > > I don't know what sense Eckard is trying to convey. My response was in > reply to Bob not Eckard. ****************************************************************** Bob was answering Eckard's ranting, and you got in the middle talking something about axioms...and you don't know what Eckard was trying to convey? ****************************************************************** > > For him, and for other trolls, > >Cantor "not having evidence" for his idea (what stupid this sounds!) > >means that he (cantor) never foiund an aleph_null under his bed, or > >that so far no one can buy aleph_beith apples out there. > > Well empirical evidence would certainly be one criterion for the truth > of what one claims. **************************************************************** "Truth"?? Who gets to define what "truth" is, except religious fundamentalists and other cuckoos of the kind? And what do we care of that in maths? The basic questioning for a mathematical set of axioms is, imo, whether it is a consistent such set...and whether it is interesting to deal with, of course. If you mean this by "truth" then fine. **************************************************************** Otherwise one is forced to rely on analytical > criteria for the the truth of infinities which no modern mathematikers > appear willing to assert and demonstrate. **************************************************************** Again: what does "the truth of infinities" in the mathematical world mean? And again: I don't think any mathematician is interested at all in assert and demonstrate whatever about "truths" (whatever the meaning of that is for you), UNLESS you're referring to consistency of axioms, relevance, interest....and all this has been widely done the last 130 years or so. *************************************************************** > >What "empirical evidence" are there in group theory's axioms? Or in > >Topology? > > The axioms and definitions themselves are empirical. **************************************************************** Perhaps it is that we don't really understand what each other means by "empirical". For example, what empirical evidence (of what, where, when...?) does the axiom stating the existence of a unit element in group theory have? Or the axiom in Topology that states that the empty set is part of the set of open sets? Regards Tonio ****************************************************************
From: Eckard Blumschein on 1 Dec 2006 03:48 On 11/30/2006 1:32 PM, Bob Kolker wrote: > Eckard Blumschein wrote: > >> >> Uncountable means: Counting is impossible. This property obviously >> belongs to fictitious elements of continuum. There is simply too much of >> them. So counting is not feasible. As long as one looks at a finite, >> just potentially infinite heap of single integers, one has to do with >> individuals. The set of all integers is something else. It is a fiction. >> It is to be thought constituted of an uncountable amount of >> non-elementary elements. Well this looks nonsensical. There is indeed a >> selfcontradiction within the notion of an infinite set. >> Non-elementary means not having a distinct numerical address. Element >> means "exactly defined by an impossible task". > > Have you forgotten to take your meds again? Element should read "element of IR"
From: Eckard Blumschein on 1 Dec 2006 03:59 On 11/30/2006 1:32 PM, Bob Kolker wrote: > Eckard Blumschein wrote: > >> >> >> I consider Dedekind wrong, and he admitted to have no evidence in order >> to justify his basic idea. > > What sort of evidence? Surely not empirical evidence. Mathematics done > abstractly has no empirical content whatsoever. > > Bob Kolker Serious mathematicans have to know the pertaining confession. Dedekind wrote: "bin ausserstande irgendeinen Beweis f�r seine Richtigkeit beizubringen". In other words, he admitted being unable to furnish any mathematical proof which could substantiate his basic assumption. Consequently, any further conclusion does not have a sound basis. Dedekind's cuts are based on guesswork.
From: Tonico on 1 Dec 2006 04:27
Eckard Blumschein wrote: > On 11/30/2006 1:32 PM, Bob Kolker wrote: > > Eckard Blumschein wrote: > > > >> > >> > >> I consider Dedekind wrong, and he admitted to have no evidence in order > >> to justify his basic idea. > > > > What sort of evidence? Surely not empirical evidence. Mathematics done > > abstractly has no empirical content whatsoever. > > > > Bob Kolker > > Serious mathematicans have to know the pertaining confession. Dedekind > wrote: "bin ausserstande irgendeinen Beweis für seine Richtigkeit > beizubringen". In other words, he admitted being unable to furnish any > mathematical proof which could substantiate his basic assumption. > Consequently, any further conclusion does not have a sound basis. > Dedekind's cuts are based on guesswork. ****************************************************** The "engineer" decides what serious mathematicians have to know....haha! Anyway, the german phrase above means, more or less literally: " [ I ] am unable to provide any evidence for [somebody's....perhaps his own] accuracy (or correctness)"....what was Dedekind talking about here? From where in that rather short, given-without-context sentence, does Eckard boy deduces the nonsense he wrote? "Serious"....(1) Provide proper references; (2) provide AT LEAST the complete context from which the above sentence was taken...**sigh**....and we (or I, at least) keep on learning. Tonio |