Re: Is the universe computable?

From: Bruno Marchal <>
Date: Mon, 12 Jan 2004 15:50:42 +0100

At 13:36 09/01/04 +0100, Georges Quenot wrote:
>Bruno Marchal wrote:
> > It seems, but it isn't. Well, actually I have known *one* mathematician,
> > (a russian logician) who indeed makes a serious try to develop
> > some mathematics without that infinite act of faith (I don't recall
> > its name for the moment). Such attempt are known as "ultrafinitism".
> > Of course a lot of people (especially during the week-end) *pretend*
> > not doing that infinite act of faith, but do it all the time implicitly.
>This is not what I meant. I did not refer to people not willing
>to accept that natural numbers exist at all but to people not
>wlling to accept that natural numbers exist *by themselves*.
>Rather, they want to see them either as only a production of
>human (or human-like) people or only a production of a God.

What I mean is that their arithmetical property are independent
of us. Do you think those people believe that the proposition
"17 is prime" is meaningless without a human in the neighborhood?
Giving that I hope getting some understanding of the complex human
from something simpler (number property) the approach of those
people will never work, for me.
Also, I would take (without added explanations) an expression
like "numbers are a production of God" as equivalent to
arithmetical realism. Of course if you add that God is a
mathematical-conventionalist and that God could have chose
that only even numbers exist, then I would disagree.
(Despite my training in believing at least five impossible
proposition each day before breakfast ;-)

>And I said "unfortunately" because some not only do not want to
>see natural numbers as existing by themselves but they do not
>want the idea to be simply presented as logically possible and
>even see/designate evil in people working at popularizing it.

OK, but then some want you being dead because of the color of the skin,
or the length of your nose, ... I am not sure it is not premature wanting
to enlighten everyone at once ...
I guess you were only talking about those hard-aristotelians who
like to dismiss Plato's questions as childish. Evil ? Perhaps could you be
more precise on those people. I have not met people seeing evil
in arithmetical platonism, have you?

Received on Mon Jan 12 2004 - 09:51:07 PST

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