Cantor Confusion
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From: Han de Bruijn on 17 Oct 2006 08:31 MoeBlee wrote: > Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>MoeBlee schreef: >> >>>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! >> >>Dig deeper! > > "Dig deeper." It has the sound of a punchline to a joke. http://huizen.dto.tudelft.nl/deBruijn/sunall.htm Han de Bruijn
From: Han de Bruijn on 17 Oct 2006 08:33 MoeBlee wrote: > Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>David Marcus schreef: >> >>>Han de Bruijn wrote: >>> >>>>How can we know, heh? Can things in the real world be true AND false >>>>(: definition of inconsistency) at the same time? >>> >>>That is not the definition of "inconsistency" in Mathematics. On the >>>other hand, I don't know of any statements in Mathematics that are both >>>true and false. If you have one, please state it. >> >>What then is the precise definition of "inconsistency" in Mathematics? > > How many times does it have to be posted? > > G is inconsistent <-> G is a set of formulas such that there exists a > formula P such that P and its negation are both members of G. Isn't that exactly the same as: P is at the same time true AND false? Han de Bruijn
From: Han de Bruijn on 17 Oct 2006 08:36 David Marcus wrote: > Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>David Marcus schreef: >> >>>stephen(a)nomail.com wrote: >>> >>>>Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> 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? >>>> >>>>What does it mean for a thing in the real world to be true? >>>>How do you know if a thing in the real world is true? >>>> >>>>Consider the twin slit experiment. Is the fact that none of >>>>the following accurately describe the situation an inconsistency? >>>> a) the photon goes through one slit >>>> b) the photon goes through both slits >>>> c) the photon goes through neither slit >>> >>>In Bohmian Mechanics (and similar theories), the photon goes through >>>only one slit. Physicists could learn something about logical thinking >>>from mathematicians. >> >>Sure, theories. Can't you talk about something else but "theories"? > > In the real world, the photon undoubtedly goes through one slit. Not in my real world of physics. > However, discussing physics with you is undoubtedly even more useless > than discussing mathematics. BTW. Are you a physicist? Han de Bruijn
From: stephen on 17 Oct 2006 08:40 Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > stephen(a)nomail.com wrote: >> Han.deBruijn(a)dto.tudelft.nl wrote: >> >>>Virgil schreef: >> >>>>In article <290c1$45333e14$82a1e228$8972(a)news2.tudelft.nl>, >>>> 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? >>>> >>>>The consistency of the physical world did not guarantee the consistency >>>>of the Phlogiston theory of combustion. Being a physicist is not a >>>>guarantee of being right, or of being consistent. Every physical theory >>>>must be, at least in theory, falsifiable, so that none of them can be >>>>held to be infallibly consistent. >> >>>I'm not talking about a theory. I'm talking about the world as it IS. >> >> And exactly how IS the world? > The secret is in the word "exactly". >> We have nothing but theories about the world. We do not, >> and cannot, know the world as it IS. > On the contrary. We CAN know the world as IS, because it IS NOT EXACTLY. > Han de Bruijn So the world is not exact? But it is consistent? Sounds strange to me. Anyway, how NOT EXACTLY IS the world? Is there an aether? Do photons have mass? Share your secrets. Stephen
From: stephen on 17 Oct 2006 08:44
Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > stephen(a)nomail.com wrote: >> You have not answered the question about how one determines >> if a thing in the real world is true. I can guess you >> will say something about measurements, but how does one >> know that your measurements are "true", or that they truly >> correspond to "a thing in the real world", and so on. >> It is a big ugly kettle of philosophical fish. > Not only philosophical fish. Also religious fish. And political fish. > And scientific fish. Actually everyday's life fish. You are right! >> I agree that it is sensible to assume that the Universe >> is consistent, but given how strange and unintuitive >> the Universe can be, who knows. > I think we agree on the above. But it doesn't mean that we cannot answer > _part_ of the question: do INFINITIES exist or not. Are they true or are > they false? And IMO _that_ can be decided _now_, without rocket science. > Han de Bruijn No, I do not see how we can decide that. We cannot observe infinities, but that does not mean they do not exist. Unless of course that is some axiom of yours, but again, you cannot know that that axiom is "true". There are people who are convinced that the Universe is truly eternal, that is always has been, and always will be. I suppose their arguments have convinced them that an infinity does exist. What irrefutable evidence do you have that the Universe has not always existed? Stephen |