On 3/15/07, Brent Meeker <[EMAIL PROTECTED]> wrote:

>
> Torgny Tholerus wrote:
> > Stathis Papaioannou skrev:
> >> On 3/14/07, *Torgny Tholerus* <[EMAIL PROTECTED]
> >> <mailto:[EMAIL PROTECTED]>> wrote:
> >>
> >>     Stathis Papaioannou skrev:
> >>>     How can you be sure? Maybe space is discrete.
> >>     Yes, space (and time) is discrete.  Everything in the universe is
> >>     finite, and the universe itself is finite.  Infinity is a
> >>     logically impossible concept.
> >>
> >>
> >> I don't see that "discrete" and "finite" necessarily go together. The
> >> integers are discrete, but not finite.
> > No, the integers are finite.  There exists only a finite numer of
> > integers.  There exists a biggest integer N.  It is true that you can
> > construct the integer N+1, but this integer is not a member of the set
> > of all integers.
>
> This must be computer arithmetic (modulo N?) - not Peano's.  :-)
>
> >
> > Because everything is finite, you can conclude that the space-time is
> > discrete.
>
> That doesn't follow.  The universe could be finite and closed, like the
> interval [0,1] and space could still be a continuum.
>
> But these ideas illustrate a problem with "everything-exists".  Everything
> conceivable, i.e. not self-contradictory is so ill defined it seems
> impossible to assign any measure to it, and without a measure, something to
> pick out this rather than that, the theory is empty.  It just says what is
> possible is possible.  But if there a measure, something picks out this
> rather than that, we can ask why THAT measure?


Isn't that like arguing that there can be no number 17 because there is no
way to assign it a measure and it would get lost among all the other objects
in Platonia?

Stathis Papaioannou

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