[FOM] Semantical realism without ontological realism in mathematics

[Neil Tennant]

On Mon, 26 May 2003, Gianluigi Oliveri wrote:

> This is extraordinary! The argument offered by Tennant for the
> independence of what he calls 'semantical realism' from 'ontological
> realism' is the same as I offer in a book I have submitted for
> publication to various publishing companies last August. In my book I
> speak of 'metaphysical realism' and 'realism about truth'.       
> 
> Another case of quasi-simultaneous intuitions?

I don't think so. The point of view put forward in my email was argued for
in more detail in my book "Anti-Realism and Logic" (OUP, 1987). So "quasi"
here means "to within a temporal epsilon (of about, say, 16 years)".

But never mind!---you will be in exceedingly distinguished company in
not having read the book. I'd love to know (privately) what you think of
it once you have read it, if you can find time to do so. The main thing in
the book that might interest you, as a member of fom, is the account of
"constructive logicism" towards the end. I derived the Peano-Dedekind
axioms using a weakly second-order, free, intuitionistic relevant logic,
with meaning-determining natural-deduction rules for zero, successor and
#xF(x) [the number of Fs]. By means of these rules one can eschew "Hume's
Principle" and the huge ontological commitments that HP incurs within a
non-free logic.

For a thorough comparison of constructive logicism with Wright's
neo-Fregean treatment based on HP and full second-order, unfree, classical
logic, see my forthcoming review essay, in the June 2003 issue of
Philosophia Mathematica, of the recent collection of essays by Bob Hale
and Crispin Wright titled "The Reason's Proper Study".

Best regards,
Neil Tennant