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?"
Note also that, with or without comp, we can no more model reality in
any way which would be both effective and complete.
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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Received on Mon Aug 14 2006 - 09:36:32 PDT