On 11/25/2012 9:22 AM, Bruno Marchal wrote:


On 24 Nov 2012, at 14:00, Roger Clough wrote:

Hi Bruno Marchal
Poincare had a lot to say on intuition vs logic in mathematics.
For one thing, the idea of continuity is an intuition.
http://www-history.mcs.st-and.ac.uk/Extras/Poincare_Intuition.html

Poincaré, like Kronecker were intuitionist before and after Brouwer (the founder of intuitionism).

It is the philosophy of the first person of the machine, but it is an error to extrapolate it to reality (at least in the comp theory). It is epistemologically correct, but ontologically disastrous, as it leads to different form of solipsism.

Bruno



Dear Bruno,

Please elaborate in these remarks as to how intuitionism is, among other things, 'ontologically disastrous'. It seems to me that intuitionism is a more general logical framework that can, if constructed carefully, allow us to make correct predictions when we are considering finite approximations to the 'perfect' Platonic notions. It is one thing to have ontological theories that are based on 'ideal' conditions and it is another thing to have the means to make local calculations and approximations. Let us never make Perfection the enemy of the effective.

--
Onward!

Stephen

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