Cantor Confusion
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From: MoeBlee on 16 Oct 2006 14:10 Han de Bruijn wrote: > Sigh! Start digging into my website. I've said more about mathematics > than anybody else in 'sci.math'. That's hilarious! I didn't even have dig at all to find you proposing an inconsistent set of axioms and blaming not yourself but set theory for the inconsistency - on the very first page I saw at that web site! MoeBlee
From: cbrown on 16 Oct 2006 14:12 Han de Bruijn wrote: > stephen(a)nomail.com wrote: > > > Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > > > >>Dik T. Winter wrote: > > > >>>In article <1160857746.680029.319340(a)m7g2000cwm.googlegroups.com> > >>>Han.deBruijn(a)DTO.TUDelft.NL writes: > >>> > Virgil schreef: > >>>... > >>> > > I do not object to the constraints of the mathematics of physics when > >>> > > doing physics, but why should I be so constrained when not doing physics? > >>> > > >>> > Because (empirical) physics is an absolute guarantee for consistency? > >>> > >>>Can you prove that? > > > >>Is it possible to live in a (physical) world that is inconsistent? > > > > Perhaps. How could we know? > > How can we know, heh? Can things in the real world be true AND false > (: definition of inconsistency) at the same time? > The cat in the box is dead; and the cat in the box is not dead. Cheers - Chas
From: MoeBlee on 16 Oct 2006 14:14 mueckenh(a)rz.fh-augsburg.de wrote: > David Marcus schrieb: > > ZFC does not talk about "vases". If you say that ZFC is inconsistent, > > please give a statement using the language of ZFC. > > All mathematics is built on ZFC and derived from it. From ZFC we can > derive the result of the vase-balls problem too. Hence we can criticize > ZFC if its results are contradictory. Mathematics based on ZFC says > that the vase at noon is empty or not empty (by the way, what was your > result V(12)?). > > But whatever your result may be: Both statemets are in contradiction > with the foundations of ZFC. If the vase is empty then mathematics of > limits as derived from ZFC is wrong. If the vase is not empty then the > assumption is wrong all natural numbers could be put into a bijection > with each other. You have an interpretation of a thought experiment that differs from the interpretation of other people. That doesn't make set theory inconsistent. It just makes set theory not suitable for your intuitions regarding the thought experiment. MoeBlee
From: Virgil on 16 Oct 2006 15:01 In article <78866$45333919$82a1e228$8559(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <1160933229.072292.316580(a)e3g2000cwe.googlegroups.com>, > > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > >>Dik T. Winter schreef: > >> > >>>In article <1160856895.115824.134080(a)b28g2000cwb.googlegroups.com> > >>>Han.deBruijn(a)DTO.TUDelft.NL writes: > >>> > stephen(a)nomail.com schreef: > >>> > > Dik T. Winter <Dik.Winter(a)cwi.nl> wrote: > >>>... > >>> > > > Pray warn me when 2 has changed sufficiently to be the square of a > >>> > > > rational. > >>> > > > I would not like to miss that moment. > >>> > > > >>> > > The day the circle is squared cannot be to far behind. > >>> > > >>> > Come on, guys! You all know that, in the world of approximations, > >>> > 2 _is_ the square of a rational and the circle _is_ squared. > >>> > >>>I thought you were talking mathematics? > >> > >>I thought approximations were a part of mathematics? > > > > But approximations are not all of mathematics in the way that HdB > > preaches, and "approximately equal" is still mathematically > > distinguishable from "exactly equal". > > How? By allowing a possibly non-zero distance between approximately equal values, but not allowing it for exactly equal values, of course! Note that, starting with any rational number, x_0, the sequence of rationals defined recursively by x_{n+1} = (x_n + 2/x_n)/2 eventually approximates sqrt(2) to any desired degree of accuracy short of exactness, but no member of that sequence is ever exactly equal to sqrt(2).
From: Virgil on 16 Oct 2006 15:05
In article <28c1b$45333aa0$82a1e228$8769(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <1160933968.829143.108720(a)f16g2000cwb.googlegroups.com>, > > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > >>imaginatorium(a)despammed.com schreef: > >> > >>>You have been told, probably hundreds of times now: mathematics is the > >>>study of consistent abstract systems. If you don't like that, push off > >>>to sci.physics, or alt.crystal-gazing. > >> > >>The funny thing is that you are not in the position to DICTATE what > >>mathematics is, especially not in a FREE forum like 'sci.math'. If you > >>don't like that, push off to a censored forum like 'sci.math.research'. > > > > He does not have to dictate what is common knowledge among > > mathematicians. > > Cantorians/Hilbertian mathematicians, as distinguished from intuitionist > and constructivist mathematicians. Not to speak of the many more people > who find their employment in Applied Mathematics (e.g. Computer Science) Does HbD claim that intuitionists, constructive mathematicians or applied mathematicians, even including those who work in computer science hold that mathematical systems are not consistent or not abstract? |