Bruno Marchal wrote:
> Le 12-août-06, à 03:00, David Nyman a écrit :
>>Bruno Marchal wrote:
>>>If grandmother asks for recalling the main difference between Plato 
>>>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!).

But how must the perfect number exist or not exist?  You say you only mean 
it must be true that there is a number equal to the sum of its divsors 
independent of you.  Do you mean independent only in the sense that others 
will know 6 is perfect after you're gone, or do you mean 6 is perfect 
independent of all humans, all intelligent beings, the whole world?

Brent Meeker

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