Cantor Confusion
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From: stephen on 16 Oct 2006 16:32 Han.deBruijn(a)dto.tudelft.nl wrote: > stephen(a)nomail.com schreef: >> 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? > Start studying something else but mathematics. A _science_, perhaps? >> 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 > Of course not. Is the "fact" that heat is phlogiston an inconsistency? > Han de Bruijn 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. 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. Stephen Stephen
From: stephen on 16 Oct 2006 16:36 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? We have nothing but theories about the world. We do not, and cannot, know the world as it IS. Stephen
From: Virgil on 16 Oct 2006 16:46 In article <1161027429.194776.277830(a)m73g2000cwd.googlegroups.com>, 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? Not even that.
From: Virgil on 16 Oct 2006 16:49 In article <1161027538.870754.34000(a)k70g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > The connection between finite paths and partial sums of edges > leads to > (1-(1/2)^n+1)/(1 - 1/2) edges per path. Which, as written, is negative for all positive naturals n.
From: Virgil on 16 Oct 2006 16:51
In article <1161027684.800946.299570(a)m73g2000cwd.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > There are no infinite n, whatever terminology you coose. No one except TO has calimed any infinite members of N or of aleph_0. > And aleph_0 is > considered larger than any finite n. That is simply impossible. Not in my world. |