Cantor Confusion
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From: Han de Bruijn on 9 Oct 2006 04:46 Albrecht wrote: > William Hughes schrieb: >>Don't you find it interesting that of all the places you looked, >>the only place where anyone disagreed with the diagonal >>argument was the newsgroups? > > That's really untrue. I had read several books and papers of academics > (who do not post in this or the german math newsgroups) in which they > formulate (very cautious) criticism about ZF, axiomatic set theory or > especially the axiom of infinity. I understand, why they are cautious. > They fear the defamation they must be aware of if they would be very > concrete in criticism. I have experienced this defamation (not for me > but other persons). There are a lot of people who do not abhor from > defamation and denuncation. This people react about criticism as their > sanity or life is threatened. It's really not understandable. It's very much understandable, but not very flattering. Mathematics is a part of our Capitalistic society, whether mathematicians like is or not and whether they deny it or not. So the reason is basically simple: http://groups.google.nl/group/sci.math/msg/19e5174536f49c32?hl=en& Mainstream mathematics doesn't slap the hand by which it's fed. And Set Theory is the _idealization_ of Karl Marx's "ungeheure Waren-sammlung". The latter is most characteristic for our society. Thus the undermining of Set Theory has its mirror in undermining our society as such. Which explains the exceptionally strong emotions accompanying these debates. Han de Bruijn
From: Han de Bruijn on 9 Oct 2006 04:52 Tonico wrote: > On the other side, of course, one has to consider: how could anyone > having a brain virgin of any mathematical education and without any > concern for logic, sound reasoning and intellectual honestity be able > to express herself otherwise? Georgie, I see your point. Show us some of your mathematical abilities, Tonico. Impress us with your publications in refereed journals or some such. I'm breathlessly awaiting ... Han de Bruijn
From: Han de Bruijn on 9 Oct 2006 05:02 Dik T. Winter wrote: > So, if you come here, and simply state: "the axiom of infinity is false, > because no infinite sets do exist", that is just a bald statement of > opinion. Mathematicians have found another name for scientitic facts. They call them "just an opinion". No! The burden is yours. _You_ have to provide arguments why it is admissible to allow for infinite sets. While _all_ eyes and all instrumentation in the cosmos can only make observations of things that are _finite_. Read "The Physics of Infinity" at: http://huizen.dto.tudelft.nl/deBruijn/grondig/natural.htm#oo Han de Bruijn
From: Tonico on 9 Oct 2006 05:09 Han de Bruijn wrote: > Tonico wrote: > > > On the other side, of course, one has to consider: how could anyone > > having a brain virgin of any mathematical education and without any > > concern for logic, sound reasoning and intellectual honestity be able > > to express herself otherwise? Georgie, I see your point. > > Show us some of your mathematical abilities, Tonico. Impress us with > your publications in refereed journals or some such. I'm breathlessly > awaiting ... > > Han de Bruijn **************************************************** Han, Han...ts,ts,ts. My boy, you really are confused, aren't you? So if someone has lots of paper published he's a better mathematician than someone that has less, or none? I wonder where that leave Grigori Perlman, last Field's Medal winner, who hasn't published even close to many others that, imfho, are way less talented than him. Anyway, in that funny quote you post in your last message you write some rather juicy and pretty fantastic nonsenses about maths being a capitalistic thing and stuff...jeje. I wonder what the chinese maths, soviet-era maths or the 17th-18th century maths in many countries were...ALL those were capitalistic, uh? Aha. But leave that alone: you talk of people NOT wanting to hear new ideas....is that so? Can you mention some of them? I mean, worthwhile, well-based and sound ideas, because just simply "ideas" we all can have, and as you surely know many times those are rather stupid ideas....can you? Albrecht, another buffoon besides yourself and Mueck (some good ones have landed in this group from that dutch-deutsch zone lately...interesting: Holland, Germany, Austria, etc produce both very good scientist and very highly-energized rubbish...oh well), that participated in this thread barked a lot about "many mathematicians" opposing Cantor's ideas and/or some other stuff refering to infinity, or something like that. He was urged to share that information with the group....and we still are waiting. Go figure! And now take your breathe back, Han hun, and try to think things...it won't hurt, I hope. Regards Tonio
From: Han de Bruijn on 9 Oct 2006 05:14
Virgil wrote: > In article <1160319212.308670.87550(a)h48g2000cwc.googlegroups.com>, > "Albrecht" <albstorz(a)gmx.de> wrote: > >>Virgil wrote: >> >>>In article <1160223586.604282.269450(a)h48g2000cwc.googlegroups.com>, >>> Han.deBruijn(a)DTO.TUDelft.NL wrote: >>> >>>>Tonico wrotef: >>>> >>>>>Maths, just like the other sciences, isn't grounded on dogma, and >>>>>people forwarding REASONABLE, well-based objections, opinions or ideas >>>>>on whatever are always welcome. >>>> >>>>_There_ is your problem! Ask Virgil, and the other mathematicians here: >>>> >>>> MATHEMATICS IS _NOT_ A SCIENCE >>>> >>>>And therefore there is NO guarantee that it "isn't grounded on dogma". >>> >>>HdB's version of mathematics certainly seems to be grounded in dogma. >>> >>>My mathematics is merely grounded on determining what can be derived >>>from a given set of axioms. >> >>1. The moon exists >>2. The moon consits of green cheese >>3. The man in the moon is a mouse >> >>Now do maths. Else explain why you prefer a special set of axioms. > > Does A.S.S suggest that enough can be derived from his set of axioms, > without any additional assumptions, to be of any interest? > Does that man-in-the-moon-mouse exist or not? > Does he/it, if extant, survive by eating the green cheese? > If so, what does he/it excrete, and for how long has he been doing it? > > A.S.S. needs a more interesting axiom set to interest me. You don't get the message. Do you? Han de Bruijn |