FOM: North Pole Argument (Frege #1)

[Dean Buckner]

In his thoughtful reply to my posting, Robert Williams questions whether I
have correctly interpreted Jevon's idea of number as "the empty form of
difference", and thus whether my interpretation really was Frege's target.

(PS could replies be made either to me direct, in the 2nd person, no FOM cc,
or direct to FOM, in 3rd person, no cc to me.  Otherwise I am sorting out a
slew of e-mails, most of which are duplicates.  Thanks)

Jevons, (The Principles of Science London 1874, p.156), says that we
abstract the character of _difference_ from which plurality arises.
_retaining merely the fact_.  This is exactly the position I defend, and
also (since he quotes it) the one Frege seems to be attacking

Also, is there no obvious way to relate (1) `the Earth has two poles' to
(2) `the north pole is different from the south pole'?  Surely

    (a) the Earth has a pole x and the Earth has a pole y and
    (b) x is a different thing from y and
    (c) x = the north pole and
    (d) y = the south pole

are together equivalent to (2), and we agreed (a) and (b) are together
equivalent to (1), so (2) actually contains the statement that there are two
poles.

Robbie also asks if I can offer a "coherent alternative" to the Fregean
account of number.  All in good time!  The first step is to question the
series of arguments whereby Frege sets out to show there really is no
alternative to his idea that number is a property of concepts, since all the
arguments for other explanations of number - in particular Mill's idea that
"though numbers must be numbers of something, they may be numbers of
anything" (System, II. vi. 2., 8th ed, p. 167b) - are faulty.

Can I recomend once again the piece by Tait,which is here:

http://home.uchicago.edu/~wwtx/


Dean