Bruno Marchal wrote:
> At 09:45 09/01/04 +0100, Georges Quenot wrote:
> >Bruno Marchal wrote:
> > >
> > > At 11:34 08/01/04 +0100, Georges Quenot wrote:
> > >
> > > >I am very willing (maybe too much, that's part of the
> > > >problem) to accept a "Platonic existence" for *the* integers.
> > > >I am far from sure however that this does not involve a
> > > >significant amount of faith.
> > >
> > > Indeed. It needs an infinite act of faith. But I have no problem
> > > with that ...
> >
> >Unfortunately, it seems that some people do.
> 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.
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.

> You know an ultrafinitist cannot assert that he is an "ultrafinitist"
> without going beyong ultrafinitism. So perhaps only animals do not do
> that infinite act of faith, but IMO, most mammals does it in a sort of
> passive and implicit way. If you pretend to understand a statement
> like:
>                  N   =    {1, 2, 3 ...},  or  N =  {l, ll, lll, llll,
> lllll, llllll, lllllll, ...},
> then you do it. Words like "never", "always", "more", "until", "while", etc.
> have intuitive meaning relying on it. I have worked  with highly mentally
> disabled people, and only with a few of them I have concluded that there
> was perhaps some evidence in their *non grasping* of the "simple"
> potential infinite. All finitist and all intuitionnist accept it. Second order
> logic and any piece of mathematics rely on it.
> Some people would like to doubt it but I think they confuse Arithmetical
> Realism with some substancialist view of number which of course I reject.
> (I reject substancialism even in physics, actually I showed it logically
> incompatible with the comp hyp).

I would not say "infinite act of faith" but rather "act of faith
in infinity". I don't know the work of the mathematician you think
of neither of any other such kind of work but I flatly consider
that we only manipulate infinity formally within obviously finite
formalisms. I am not sure that it is necessary that any infinite
exists (let's say by itself in some platonic sense) for that
everything that we are talking abour within this kind of finite
formalism makes sense (and exists in some platonic sense).

> Fearing the death in the long run (as opposed of fearing some near catastroph)
> also rely on that faith in the infinite, at least implicitly.
> Some people believe that human are religious because they fear death, but
> it is the reverse which seems to me much more plausible: it is because
> we are religious (i.e. we believe in some infinite) that we are fearing death.

I do not share all of Dawkins' views (especially from the social
point of view) but I have a Dawkins' view of religion. I would
say that human are religious simply because this induces among
themselves a behavior that increases their fitness (at the level
of communities). The corresponding set of memes interact in various
ways with other aspects like fear of death in complex networks
from which it might be vain to try to isolate simple one-way causal

> >I am not sure how much I share that faith. As I mentionned,
> >I am willing to but since I could not find some ground to
> >support that willingness, I might be a bit agnostic too.
> No problem. The point is that it is a nice and deep hypothesis
> which makes comp fun and extremely powerful. It is definitely
> among my working hypotheses.

I think I can consider both this one and some alternatives
(not simulatneously, of course). However I do not find the
alternatives very fecund currently (and I am even more
agnostic about them).

> > > Why there is no FAQ? Because we are still discussing the meaning of
> > > a lot of terms ....
> >
> >I saw some posts on tentative glossaries of acronyms. Maybe
> >before complex terms, we should focus on "basic" ones like
> >"universe". I would not be upset to encounter definitions
> >for several possible senses of that word.
> I don't think the word "universe" is a basic term. It is a sort
> of deity for atheist.

I guess this would be called "pantheism" (the difference might
lie in the level of worship involved rather than in the level
of faith).

> All my work can be seen as an attempt to mak
> it more palatable in the comp frame.

I think we can only produce tautologies, were they formulated
in a mathematical way or not. This certainly does not mean that
these tautologies are vain or meaningless. Rather, their interest
might come from the "level of resonance" they induce within the
various people who devise or consider them. This might even be
the case for any concept and we might actually have no other
way to communicate anything. The global level of resonance of
"the universe" here appears quite low...

> Tegmark, imo, goes in the right direction, but seems unaware
> of the difficulties mathematicians discovered when just trying to
> define the or even a "mathematical universe".  Of course tremendous
> progress has been made (in set theory, in category theory) giving
> tools to provide some *approximation*, but the big mathematical
> whole seems really inaccessible. With comp it can be shown
> (first person) inaccessible, even unnameable ...
> Bon week-end,

A toi aussi.


Reply via email to