Bruno Marchal skrev:
> On 08 May 2009, at 19:15, Torgny Tholerus wrote:
>> Bruno Marchal skrev:
>>> On 07 May 2009, at 18:29, Torgny Tholerus wrote:
>>>> Yes it is right.  There is no infinity of natural numbers.  But the
>>>> natural numbers are UNLIMITED, you can construct as many natural
>>>> numbers as you want.  But how many numbers you construct, the  
>>>> number of
>>>> numbers will always be finite.  You can never construct an  
>>>> infinite number of
>>>> natural numbers.
>>> This is no more ultrafinitism. Just the usal finitism or  
>>> intuitionism.
>>> It seems I recall you have had a stronger view on this point.
>>> Ontologically I am neutral on this question. With comp I don't need
>>> any actual infinity in the third person ontology. Infinities are not
>>> avoidable from inside, at least when the inside view begins some  
>>> self-reflexion studies.
>> I was an ultrafinitist before, but I have changed my mind.
> Excellent. The ability of changing its mind is a wonderful gift.

It was the Mathematical Universe that made me change my mind:

Earlier I was convinced that the number of time steps in the universe 
was explicitely finite, that time goes in a circle.

But the Mathematical Universe says that all mathematically possible 
universes exists.  And it is possible to construct an EXPANDING 
universe, where you have a simple rule stating that the status of a 
space-time point is a combination of the statuses of the neighboring 
space-time points in the previous time point.  In this universe there 
will never happen that the same space will be repeated at a later time, 
because the space consists of more space points at the later time.  So 
in that case the universe is UNLIMITED, it will never stop, but continue 
for ever...

Torgny Tholerus

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