Le 23-oct.-06, à 14:29, 1Z a écrit :

> Bruno Marchal wrote:
>> Le 20-oct.-06, à 17:04, 1Z a écrit :
>>> As usual, the truth of a mathematical existence-claim does not
>>> prove Platonism.
>> By Platonism, or better "arithmetical realism" I just mean the belief
>> by many mathematician in the non constructive proof of "OR" 
>> statements.
> So where is the UD running? If Platonia doesn't exist,
> how can I be in it?

You miss the point. For asserting that the UD exists,  I don't even 
need to use the non-constructive OR. The UD exists for an intuitionist 
as well.
("exists" in the same sense that it exists a number which is not the 
sum of three squares (x = 7 for example).

I think that in many of your last posts you are begging the point. You 
seem to assume the existence of a physical universe, then you define 
"existence" by existing in the physical universe. I don't assume a 
physical universe. I define existence by the arithmetical truth of 
existential sentences. Then I explain in all (technical thus) details 
why immaterial machines/numbers come to feel, perceive, know, believe 
in sharable quanta and unsharable qualia.

You say somewhere that we see matter. I think that this is the main 
difference between you and me, and I would say between Aristotle and 
Plato: Aristotle (like St-Thomas) argues indeed in his metaphysics that 
what we see and measure is what really exist (so that we can sleep in 
peace). Plato and actually most (rational) mystics (from Pythagorus to 
St-Augustin) try to explain that what we see could as well be only the 
shadows of the shadows of the shadows of the shadows ... of what 
perhaps is (so that we have to keep our vigilance and our skepticism or 
our doubting abilities in front of *all* theories (especially including 
those who could have been built in by long evolutionary processes).

All what I say is that (standard) computationalism is epistemologically 
incompatible with materialism. It *is* a necessary-redundancy argument: 
even if matter exists, standard comp makes it impossible to use for 
justifying any stable belief. That is the conclusion of the UDA. The 
AUDA makes it constructive and can generate the physical laws 
completely (making comp or acomp 100% scientific (popper-testable).
It remain possible that the translation of UDA in arithmetic is to 
rough, and that is why I say "comp or acomp". But until now, empirical 
physics seems to confirm all the "weird" prediction of (a)comp.



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