[FOM] historical question about the axiomatisation of identity

Hartley Slater slaterbh at cyllene.uwa.edu.au
Tue Sep 20 23:50:11 EDT 2005

Richard Heck writes:

>A reconstruction of Frege's system that does without the identification
>of sentences as names could thus simply take identity to be axiomatized
>by (IIIa) and (III*), that is, basically, by (III'). Of course, this
>treatment is ineliminably second-order.

He is too kind, or at least he does not see what an immense amount of 
further work would need to be done to make plausible such a 
reconstruction, even supposing it could be done.

If one separates out identity from equivalence, as Heck suggests, 
then what is to become of the idea that concepts are functions, for a 
start?  This idea arises from the attempt to see, for instance, what 
might be put 'Fa <-> T', where 'T" is a tautology, as like 'f (a)=T' 
where 'T' is a referring phrase.  In addition, truth is a property of 
thoughts so in connection with *truth* one has properly neither an 
equivalence, nor an identity but a simple predication 'T---Fa' where 
'T' is 'is true', and '---' is (a bit like) Frege's horizontal. 
Frege was also confused in this latter area too - see my recent 
paper 'Choice and Logic' in JPL (2205) 34, 207-216, especially p214f. 
- so all in all it is much the best to trace accurate historical 
definitions of identity elsewhere.
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) 6488 1246 (W), 9386 4812 (H)
Fax: (08) 6488 1057
Url: http://www.philosophy.uwa.edu.au/staff/slater

More information about the FOM mailing list