Stathis Papaioannou wrote:
> On 3/15/07, *Brent Meeker* <[EMAIL PROTECTED] 
> <mailto:[EMAIL PROTECTED]>> wrote:
>     Torgny Tholerus wrote:
>      > Stathis Papaioannou skrev:
>      >> On 3/14/07, *Torgny Tholerus* < [EMAIL PROTECTED]
>     <mailto:[EMAIL PROTECTED]>
>      >> <mailto:[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

I think it's more like asking why are we aware of 17 and other small numbers 
but no integers greater that say 10^10^20 - i.e. almost all of them.  A theory 
that just says "all integers exist" doesn't help answer that.  But if the 
integers are something we "make up" (or are hardwired by evolution) then it 
makes sense that we are only acquainted with small ones.

Brent Meeker

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