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?


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