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/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---