Torgny Tholerus wrote:
> Stathis Papaioannou skrev:
>> On 3/14/07, *Torgny Tholerus* <torgny.domain.name.hidden
>> <mailto:torgny.domain.name.hidden>> 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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Received on Wed Mar 14 2007 - 13:10:49 PDT