On 10/31/2012 11:52 AM, Bruno Marchal wrote:
I don't see why denying mathematical realism would entail saying no to the 

It implies not saying "yes" qua computatio. It implies NOT understanding what Church thesis is about, as to show it consistent you need the diagonalization, which use the excluded middle principle.
You can still say "yes", but only by using some magic.

The doctor isn't proposing to replace part of you brain with a piece of Platonia, he has a real physical device to implant.

This is not related. That will follow step 8.

Here, you have to be arithmetical realist to get an idea of what a computer is, and how it functions, as the physical one will approximate it, well enough, it is hoped.

Of course you can say "yes" to the doctor, just because you trust him. But comp is not "saying yes" to the doctor. Comp is the doctrine that saying yes will indeed work, once the artificial brain is a *computer*. The definition of computer makes no sense with arithmetical realism.

?? If I'm a materialist I could say yes because I think the artificial brain produces the same input/output signals. I don't see why I would have believe in Platonia. I may believe that only some computations are instantiated and there are no infinities.


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