Hi Georges,
I got that mail before. And I did answer it. Are you sure you send the
right mail?
see
http://www.escribe.com/science/theory/m5026.html
Bruno
At 10:14 13/01/04 +0100, Georges Quenot wrote:
>Bruno Marchal wrote:
> >
> > 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.
>
>I don't think this is very different. I could argue that even if
>natural numbers were not out there, as soon as anybody consider
>them, their properties automatically come with and impose themselves.
>Even this seemingly weaker statement can be contested and it is not
>actually weaker but equivalent since there might be no other way than
>this one for natural numbers to be out there.
>
>Some people do argue that there is no arithmetical property
>independent of us because there is no thing on which they would
>apply independentkly of us. What we would call their arithmetical
>properties is simply a set of tautologies that do come with them
>when they are considered but exist no more than them when they
>are not considered.
>
> > Do you think those people believe that the proposition
> > "17 is prime" is meaningless without a human in the neighborhood?
>
>" "17 is prime" is meaningless without a human in the neighborhood"
>is exactly the kind of claim these people make (possibly generalizing
>the concept of human to aliens and Gods). After discussing with some
>of them I think they actually believe what they claim. I am not sure
>however that we always fully understand each other and that you or I
>would exactly understand such a claim in the same way as they do.
>
> > 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.
>
>And certainly vice versa. Though it is difficult to have them saying
>it explicitely I have the feeling that the reason why they do not
>want the natural numbers to be out there and even as not possibly
>being considered as out there is that they do not accept that the
>complex human be understood from something simpler (number property).
>They do not even accept the idea being considered, were it as a mere
>conjecture or working hypothesis. Their more official argument is
>that such a view would prevent the foundation of human dignity.
>
> > Also, I would take (without added explanations) an expression
> > like "numbers are a production of God" as equivalent to
> > arithmetical realism.
>
>Yes and there are several ways to understand this.
>
> > >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?
>
>I have not met any of them physically but I had discussion with
>some of them via Internet. There might not be so many of them but
>there are. You will find, at least in the US, a lot of people
>considering the views of evolution and/or of the big-bang as evil.
>If they finally have to abandon these positions due to the amount
>of evidence in favor of it, the last line of defence for their
>conception of a personal God and for a significant role for Him
>could be at the level of artihmetical realism. Artihmetical
>realism by itself (not from a distinct personal God) is therefore
>seen as evil by them. As I mentionned, they usually do not put it
>that way. Rather they argue that such a view would prevent the
>foundation of human dignity and the like.
>
>Georges Quénot.
Received on Wed Jan 14 2004 - 05:55:38 PST