Cantor Confusion
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From: Virgil on 17 Oct 2006 16:01 In article <3aada$4534cbd6$82a1e228$21528(a)news1.tudelft.nl>, 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 according to HdB, what ever we think it is, it isn't. At least not exactly.
From: Virgil on 17 Oct 2006 16:02 In article <7d12f$4534cca1$82a1e228$21528(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <1161029391.305685.141910(a)b28g2000cwb.googlegroups.com>, > > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > >>Sure, theories. Can't you talk about something else but "theories"? > > > > Isn't the point of physics to come up with theories? > > AND experiments. All physical theories are judged by experiments. > > > And now a physicist wants to outen them? > > Han de Bruijn Does HdB suggest that there are no standards by which to judge mental theories?
From: Virgil on 17 Oct 2006 16:03 In article <3832b$4534cd83$82a1e228$21528(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > 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 No.
From: Virgil on 17 Oct 2006 16:10 In article <a6ef5$4534d5fa$82a1e228$26144(a)news1.tudelft.nl>, 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: > > > >>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. > > > > 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? > > The scientific attitude: thy shall not believe what thy cannot measure. > > Han de Bruijn Does HdB mean "Thou shalt not believe what thou cannot measure? "Thy" is possessive, as in "my" or "your" or "his" or "her". The nominative is "thou", accusative is "thee"
From: Virgil on 17 Oct 2006 16:11
In article <1161103769.338793.195850(a)i42g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > William Hughes schrieb: > > > > > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > William Hughes schrieb: > > > > > > > > > > > > But the end time of the problem (noon) does not correspond to > > > > > > an integer (neither in standard mathematics, nor in your > > > > > > system, whether or not you interpret the problem as dealing > > > > > > with infinite integers as well as finite integers). So the > > > > > > function > > > > > > 9n does not have a value at noon. There is no way > > > > > > it can be continuous at noon. And since there is no > > > > > > value of n that corresponds to noon, 9n cannot be used > > > > > > to determine the number of balls in the vase at noon. > > > > > > > > > > But the function n can be used to determine the number of balls > > > > > removed > > > > > from the vase at noon? > > > > > > > > > > > > > Nope. [There are no balls removed from the vase at noon] > > > > > > Arbitrary misunderstanding? > > > > > > > The function 9n has nothing to do with the number of > > > > balls in the vase at noon. > > > > > > But the function n can be used to determine the number of balls having > > > been removed > > > from the vase at noon? > > > > > > No. There are no balls removed from the vase at noon. > > > > Note, that there is no time "just before noon". At any time > > before noon there remain an infinite number of steps. > > > > So no value of n is close to the end. > > > > The balls are removed during an infinite number of > > steps. > > Please read carefully: But the function n can be used to determine the > number of balls *having been* removed from the vase at noon? (That > means up to noon.) Yes. All of them are. |