Bruno, 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 "unreasonableness"paper)!! 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). Cheers, -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] Harvard-Smithsonian Center for Astrophysics 1815 Massachussetts Av. , Cambridge MA 02140 Work Phone: (617)-496-7990 extension 124 VoIP Phone: (617)=384-6679 Cell-Phone: (617)-817-1800 ---------------------------------------------- "All generalizations are abusive (specially this one!)" -------------------------------------------------------
