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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Received on Tue May 12 2009 - 17:26:11 PDT