[FOM] Tangential to Slater and Numbers

[Peter Smith]

On Oct 7 2003, Hartley Slater wrote:

> If one expresses 'there are exactly two Fs' as
>          (Ex1)(Ex2)(y)(Fy <-> y=x1 v y=x2)
> then the counting of the variables is explicit, and so the number is 
> referred to in the expression.

That claim seems crucial to him. But if I express the symmetry of identity 
(for example) by
             (Ax1)(Ax2)(x1 = x2 <-> x2 = x1) where the counting of the 
variables is explicit, have I in fact referred to the number two? If I 
write our old friend
             (Ex1)((Ax2)(KFx2 <-> x1 = x2) & Bx1) have I failed to refer to 
a bald king of france but managed to refer to the number two instead?? That 
seems an extraordinary claim to me. But if there is not numerical reference 
in these claims, why is there in Hartley's?

Peter S.
-- 
Dr Peter Smith
Faculty of Philosophy, University of Cambridge
www.logicbook.net
www.phil.cam.ac.uk/Smith