Thanks for the Hardy quote: it still reads well, indeed,
But I am afraid I can't agree with your reading of it or
your version of mathematical realism (and physical realism)
which strikes me as quite orthogonal to Hardy's. Nowhere does
he claim or suggest  that "physical reality could be mathematical
reality seen from the inside"!  What he stresses is that "mathematical
reality" is something entirely more precisely known and accessed
than "physical reality" and he is surely correct as the whole EPR
debacle clearly demonstrates. One may add that what little we
know about "physical reality" is what we manage to map to
mathematical reality! In truly Platonic terms "Reality" is
purely mathematical and what Physics is about is better
named "appearance" (or corrupted reality).

By no means does this translate to the identification you
suggest between what is empirical is what is... "incomplete",
If anything physical reality sees mathematical reality "from
the outside", and it is this "map" that is incomplete and likely
to remain so, not because of the sparseness of empirical
data, but due to the limited resources of physicists. As far
as nature is concerned what is weird is not what cannot be
mapped to math but what can (as in Wigner's famous

By the way, Church-Turing and computablity  does not
change this situation in any way! Computations and
measurements are two classically distinct ways to "reach"
(produce, connect) numbers (though quantum computation
may yet suggest otherwise).


-Joao Leao

Bruno Marchal wrote:

> Hi All,
> I have often try to explain what is mathematical realism.
> May I quote the full section 24 of G. H. Hardy's "A Mathematician's
> Apology" which explain so well what I try to say?


> .
> Now, Hardy lacks Church thesis and comp and so seems not aware that
> the physical reality could be mathematical reality "seen from inside",
> in which case, "empiricalness" can be justified by "incompleteness",
> and this, of course makes the distinction between physics and mathematics,
> still more fuzzier.


Joao Pedro Leao  :::  [EMAIL PROTECTED]
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