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?

Brent Meeker

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