Bruno Marchal wrote:

> It just means that I (Bruno) believes that Bruno (I) is not so
> important in the sense that if I die, a perfect number will still
> either exist or not exist. I do interpret Penrose's mathematical
> platonism in that way, and I agree with him (on that), like I think
> david Deutsch and other physicists (but not all!).

> This should suits "centrality of first person notion", but with comp,
> as I try to explain, even that first person will emerge from more
> primitive non personal notion (like numbers ...), and this
> independently of the fact you like to recall and with which I agree
> which is that I have only access to a personal view on numbers.

I feel I must press you on this. I think using 'exists' in this sense
is playing with words. I'm asking that whatever you posit as
fundamental (even when it's in the spirit of seeing where it leads -
which of course I respect and support) you are prepared to defend as
'real' in as strong a sense as 'indexical 1st person' (i.e. our sole
experiential/ existential point of departure). This IMO is crucial.
Without this sense, I genuinely can't see what 'a perfect number will
either exist or not exist' can possibly *mean* - i.e. do any conceptual
or other kind of work. What is 'meaning' but a metaphorisation,
analogising, or mapping of some observation in terms of another? e.g.
'5' is the 'cardinality' of the fingers of my hand. And the 'arena' in
which this 'meaning' is instantiated is always the 'indexical 1st
person'.

So, I can give 'meaning' to an 'indexical 1st-person Bruno'
instantiating the *idea* of 'a perfect number', because its 'indexical
existence' is part of this 'Bruno'. But the only way I could assign an
analogous existence to 'a perfect number' by itself, in the absence of
this instantiation, is to assign 'indexical existence' to the number
realm itself. This realm is then your posited 'medium of instantiation'
(or 'fundamental reality') But isn't this '1st-person primacy'? Or
maybe it's just 'indexical primacy'.  Either way it's OK by me, but why
not you?

> It is important to distinuish some "theory on numbers" (always
> incomplete), and the number realm or truth, which is complete by
> definition, but never effectively axiomatizable.

Yes, and so the 'indexically reality/ completeness' of your number
realm would be the basis of the 'indexical reality/ completeness' of
everything it instantiates. Theories are something else. The
'unreasonable effectiveness' of mathematics lies in its abstraction
from the truly-complete 'indexical number realm'. But all attempts at
reflexive self-axiomatisation of the number realm inevitably lead to
recursive paradoxes of self-reference, and hence 'incompleteness'.

> Le 12-août-06, à 03:00, David Nyman a écrit :
>
> >
> > Bruno Marchal wrote:
> >
> >> If grandmother asks for recalling the main difference between Plato
> >> and
> >> Aristotle's theories of matter, I would just say that in Plato, the
> >> visible (observable, measurable) realm is taken as appearances or
> >> shadows related to a deeper unknown reality.
> >
> > A question from grandma:
> >
> > Since this deeper, unknown reality must forever be inaccessible to our
> > direct probing, I agree when you suggest that this may better be
> > thought of as theology, or at least metaphysics. This grandma, for one,
> > can't find any *literal* meaning in the independent existence of Number
> > in a Platonic realm (though Penrose believes in something of the sort,
> > as did Popper), but it does convey a metaphorical or poetic sense.
>
> Perhaps the grandma put to much sense in "Number exists in a platonic
> realm".
> As I explained to 1Z, Arithmetical realism (part of comp) needs only
> the belief in the independence of some truth (independence with respect
> to me, you, ...). It only mean that "there is a perfect number (which
> are sum of their proper divisor)" is either true or false independently
> of me.
> It just means that I (Bruno) believes that Bruno (I) is not so
> important in the sense that if I die, a perfect number will still
> either exist or not exist. I do interpret Penrose's mathematical
> platonism in that way, and I agree with him (on that), like I think
> david Deutsch and other physicists (but not all!).
>
>
> >
> > Would it be possible to put it more like this:
> >
> > The effectiveness of mathematics may be demonstrable by comp to be so
> > 'unreasonable' as in fact to provide a basis for modelling 'relational
> > reality' that is effectively complete.
>
> The effectiveness of math is an easy consequence of comp because comp
> makes the whole of reality "mathematical".
> The price then is more the efffectiveness of physics. And in our
> context, this question can be tranformed into "how white rabbits are
> eliminated?"
> This should suits "centrality of first person notion", but with comp,
> as I try to explain, even that first person will emerge from more
> primitive non personal notion (like numbers ...), and this
> independently of the fact you like to recall and with which I agree
> which is that I have only access to a personal view on numbers.
> It is important to distinuish some "theory on numbers" (always
> incomplete), and the number realm or truth, which is complete by
> definition, but never effectively axiomatizable.
> physicists are not always aware of that, but concerning numbers the
> dream of having a *complete* TOE has to be abandoned (unless Church
> thesis is false of course ...).
>
>
> > This would be true even if one
> > regarded mathematics not as emanating from an independent realm, but
> > being inferred in its totality from the study of the relata to whose
> > behaviour it is then reflexively applied.
>
> All right (assuming 1-person centrality). But with comp, "inferred"
> should be applied to observers which are eventually described by
> (perhaps unknown) machines, themselves described by "platonic" relation
> between numbers.
>
>
>
> > The metaphysical payoff of
> > taking it to be 'primitive' is to render superfluous further fruitless
> > speculation about 'primitivity', thereafter consigned to Wittgenstein's
> > resounding silence.
>
> I will probably explain more on this in an answer I must give to
> Stathis. To me, we can explain why we have to remain silent on some
> question. This looks like a paradox, and it can be explained by the
> difference between truth and provability. More later.
>
>
> >
> > I would still have to ask what this then has to say about the
> > non-relational - 1st-persons as experienced - as opposed to the
> > inference of relational 1st-persons from comp (I won't resort to my
> > acronyms, but I think by now you know what I mean).
>
> I just hope that you will get the point after the description (in term
> of number relations) of all n-person povs.
> 
> Bruno
> 
> http://iridia.ulb.ac.be/~marchal/


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