[FOM] Parallel to Slater on Numbers

[Hartley Slater]

It may help people to focus on the points I have been making recently 
if I repeat them in connection with the parallel Frege drew between 
what has come to be called 'Hume's Principle' and the definition of 
spatial directions.  We have that d(a)=d(b) iff a || b, where 'a' and 
'b' are straight lines in 2D, and 'd( )' is the function 'the 
direction of'.

So take a paradigm line p in the direction of North, for instance, 
and we can then say that d(a) = N iff a || p.  The first point to 
make (like that about von Neumann ordinals) is that p is not 
identical with the direction North: the relation is that d(p) = N. 
The second point (like that about 'Frege numerals') is that North is 
not {e|e || p}, either.  The relation between N and the Frege set 
{e|e || p} is that {e|d(e) = N} = {e|e || p}.  Maybe d(a) = N iff a 
isin {e|e || p}, but that means N is the value of the function d for 
certain arguments, not the set of those arguments.  In particular 
'd(a)={e|e || p}' and 'a isin N' are ungrammatical.
-- 
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 9380 1246 (W), 9386 4812 (H)
Fax: (08) 9380 1057
Url: http://www.arts.uwa.edu.au/PhilosWWW/Staff/slater.html