FOM: sterility?

[Charles Silver]

On Tue, 23 Mar 1999, Randall Holmes wrote:

> Dear Dr. Kanovei,
> 
> I reply to your letter point by point.
> 
> You said,
> 
> a) 2nd order logic axiomatizes N caregorically 
> through appeal to subsets of N. 
> 
> I reply:
> 
> This is not the best way to see it.  I prefer to say that one appeals
> to properties rather than sets (because of the "topic-neutral" character
> required of a logic).

	One thing that bothers me about talking of properties is that
there don't seem to be desirable, *extensional* identity conditions for
them. For example, two sets are equal if they have all their elements in
common.  I don't know of any such conditions for properties.  Take the
property of being under ten feet tall and the property of being under nine
feet tall.  Every human that has one property has the other.  But, are the
properties themselves the same?  I don't think so.  I would be more
comfortable talking of properties if I knew some nonintensional way of
identifying them.  A long time ago, I fiddled with this a little, but
nothing seemed satisfactory.  Does anyone know of such conditions? 

(I tend to think attaching possible-world considerations would only make
matters worse, but maybe I'm wrong.) 

Charlie Silver