Am I a crank?
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From: Han.deBruijn on 31 Aug 2006 15:36 Virgil schreef: > In article <8746c$44f690ea$82a1e228$18104(a)news2.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > Virgil wrote: > > > > > Let's see Zick empirically establish the axiom of infinity, then. > > > > Nobody can. Therefore it does not correspond to (part of an) implicit > > definition of some real world thing. Therefore it will do no harm if > > we throw it out. > > > > Han de Bruijn > > By that argument, it will do no harm to throw out every axiom of every > set theory or geometry theory or any other mathematical theory since > none of them refer to anything that exists in the "real world". Is that so? Lately, I found that if you have ten apples and five people, then you can give everybody two apples. I checked this with the axioms of arithmetic and found that 10 / 5 = 2. > If Han wishes to do entirely without any mathematics, he is free to do > so, but he cannot compel anyone else to join him. No, I'm using mathematics all the time. A few years ago, I had to decide how much wall paper I should buy for my bathroom. Expensive stuff. But almost everything of it was used, thanks to a little bit of mathematics. Han de Bruijn
From: Lester Zick on 31 Aug 2006 15:52 On Thu, 31 Aug 2006 12:49:11 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <m46ef2d4qb8agbn0id2r7efu60ivv2lvcq(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Thu, 31 Aug 2006 02:26:36 -0600, Virgil <virgil(a)comcast.net> wrote: >> >> >In article <8746c$44f690ea$82a1e228$18104(a)news2.tudelft.nl>, >> > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >> > >> >> Virgil wrote: >> >> >> >> > Let's see Zick empirically establish the axiom of infinity, then. >> >> >> >> Nobody can. Therefore it does not correspond to (part of an) implicit >> >> definition of some real world thing. Therefore it will do no harm if >> >> we throw it out. >> >> >> >> Han de Bruijn >> > >> >By that argument, it will do no harm to throw out every axiom of every >> >set theory or geometry theory or any other mathematical theory since >> >none of them refer to anything that exists in the "real world". >> >> Collective angst projection. > >Zick's 'sour grapes' rejection of what he has not the wit to understand. I do understand the collective angst projections of neo platonic mystics however. ~v~~
From: Lester Zick on 31 Aug 2006 15:53 On Thu, 31 Aug 2006 12:52:07 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <v66ef29p15baruaor8s3o848vk04o8prek(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Thu, 31 Aug 2006 09:22:15 +0200, Han de Bruijn >> <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >> >> >Lester Zick wrote: >> > >> >> In physics a hypothesis is either contradictory or not. >> > >> >Likewise, in biology, a piece of fruit is an apple or not. >> >> But apparently not in modern math. > >Zick again attempts to speak authoritatively about modern mathematics >from the depths of his almost total ignorance of it. > >Proclaiming 'sour grapes' about what he cannot have. Clever devil that you are I could scarcely do otherwise. ~v~~
From: Lester Zick on 31 Aug 2006 15:54 On Thu, 31 Aug 2006 12:55:05 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <v76ef2tt99t6kfnltkss0pjl1he46ndppf(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> >Definitions can be false too (i.e. "Let x be an even odd"). >> >> Except that Virgil maintains that definitions in modern math are >> neither true nor false. > >If one had said that there is an odd even, that would be declarative and >a false declaration, bit "Let x be an even odd" is not a declaration of >presumed fact but a request, which can be denied but not falsified. Yes but is that true or false or just an axiom or definition? ~v~~
From: Lester Zick on 31 Aug 2006 15:56
On Thu, 31 Aug 2006 12:57:46 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <5a6ef2t2gn4qosrje5q55uoihf5r76fkmc(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Thu, 31 Aug 2006 09:58:27 -0400, "Jesse F. Hughes" >> <jesse(a)phiwumbda.org> wrote: >> >> >schoenfeld.one(a)gmail.com writes: >> > >> >> Definitions can be false too (i.e. "Let x be an even odd"). >> > >> >That is not what one usually means when he says "mathematical >> >definition". A mathematical definition is a stipulation that a >> >particular phrase means such-and-such. >> > >> >Like: A /group/ is a set S together with a distinguished element e and >> >an operation *:S x S -> S such that blah blah blah >> > >> >But what you're doing is different. You are specifying that a >> >variable should be interpreted as a certain kind of number, namely an >> >even odd. Even though there is no such thing as an even odd, however, >> >this is not false. How could it be false? It's an imperative, >> >telling the reader to do something (namely, assume that x names an >> >even odd). >> > >> >If I tell you to find integers a, b such that a/b = sqrt(2), I haven't >> >said something false. I've given you a command that is impossible to >> >fulfill, but it isn't false. Imperatives don't have truth values. >> > >> >I'm not sure that "Let x be an even odd," is impossible to do in the >> >same sense that finding a rational equal to sqrt(2) is impossible. I >> >think that this imperative just means: Assume that x satisfies certain >> >conditions. And as far as I can see, I can assume impossible facts >> >willy nilly. >> >> So is Virgil right or wrong that definitions in modern math can be >> neither true nor false? > >He is right, in the sense that definitions are requests to let one thing >represent another, and while one can refuse a request, it is silly to >call a request either true or false. So now it's silly to call axioms and definitions in modern math and theorems based on them true? Strangely enough I think I agree. ~v~~ |