Quentin Anciaux skrev:
> Hi,
>
> Le Wednesday 28 November 2007 09:56:17 Torgny Tholerus, vous avez écrit :
>
>>
>> You only need models of cellular automata. If you have a model and
>> rules for that model, then one event will follow after another event,
>> according to the rules. And after that event will follow another more
>> event, and so on unlimited. The events will follow after eachother even
>> if you will not have any implementation of this model. Any physics is
>> not needed. You don't need any geometric properties.
>>
>>
> Sure, but you can't be ultrafinitist and saying things like "And after that
> event will follow another more event, and so on unlimited".
>
There is a difference between "unlimited" and "infinite". "Unlimited"
just says that it has no limit, but everything is still finite. If you
add something to a finite set, then the new set will always be finite.
It is not possible to create an infinite set.
So it is OK to use the word "unlimited". But it is not OK to use the
word "infinite". Is this clear?
Another important word is the word "all". You can talk about "all
events". But in that case the number of events will be finite, and you
can then talk about "the last event". But you can't deduce any
contradiction from that, because that is forbidden by the type theory.
And there will be more events after "the last event", because the number
of events is "unlimited". As soon as you use the word "all", you will
introduce a limit - all up to this limit. And you must then think of
only doing conclusions that are legal according to type theory.
So the best thing is to avoid the word "all" (and all synonyms of that
word).
--
Torgny
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Received on Thu Nov 29 2007 - 11:23:20 PST