Le Thursday 29 November 2007 17:22:59 Torgny Tholerus, vous avez écrit :
> 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.

I'm sorry I don't get it... The set N as an infinite numbers of elements still 
every element in the set is finite. Maybe it is an english subtility that I'm 
not aware of... but in french I don't see a clear difference between "infini" 
and "illimité".

> So it is OK to use the word "unlimited".  But it is not OK to use the
> word "infinite".  Is this clear?

No, I don't see how a set which have not limit get a finite number of 

> 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".  

If there are events after the last one, how can the last one be the last ?

> 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.

o_O... could you explain what is type theory ?

> So the best thing is to avoid the word "all" (and all synonyms of that
> word).

like everything ?

Quentin Anciaux

All those moments will be lost in time, like tears in the rain.

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