FOM: "The unreasonable effectiveness of mathematics"

[Solomon Feferman]

On Mon, 26 Jan 1998, Martin Davis wrote:

> This discussion was in the context of Wigner's question rather than the
> Quine/Putnam indispensibility argument (which, as it happens, I never found
> convincing). I think that faced with your system (assuming Wigner agreed
> that all the mathematics needed for physics was there), he would be led to
> reply that a version of real numbers satisfying at least your weak closure
> conditions could be "actually out there". At least I don't see how the
> conservative extension result rules out that possibility.
> 
I agree; the conservation result does not at all rule out that
possibility.  Nor does it rule out the possibility that sets and functions
of such real numbers are "actually out there".  What it does show is that
the principles of impredicative set theory are not justified by their
scientific applications, whatever the ontological status of the objects
involved (John Steel to the contrary).  

--Sol