[FOM] Slater - Hazen - Holmes exchange

Dean Buckner Dean.Buckner at btopenworld.com
Mon Oct 6 16:25:09 EDT 2003

Isn't the problem we started with, that whatever language we use to express
mathematical truths, we are expressing the same thing?  Whereas none of the
available stories show how it can be the same thing at all?  For example,
there is some fact expressed by all these statements

(a)  5+7=12
(b) if there are exactly 5 things in box A, and exactly 7 things in box B,
there are exactly 12 things in box-A-or-box-B
(c) Same fact expressed in FOL: (E5x) Fx & E7x Gx implies E12x F-or-Gx
(d) Same fact expressed in Von Neumann
(e) Same fact expressed in Zermelo
(f) whatever else you like

and whatever it is, it seems to be the same fact.  What bothers
philosophers, or at least what bothers me, is that if they express the same
thing, their meaning must be the same.  Yet their meaning clearly can't be
the same, since in case (d) and (f) there are certain objects involved in
the meaning, which are different, and there are no such objects required in
(b) or (c) at all.

You may want to escape this by arguing that the Von Neumann and Zermelo
objects are irrelevant to the meaning.  But then what use are they at all?
If they are of some use, they are connected with what the sentences say, and
the problem remains.  If they are not connected with what the sentences say,
then how are they of use?


Dean Buckner

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