FOM: ``arbitrary objects"

[Mitchell Spector]

On Thursday, January 31, 2002, at 04:07  AM, Arnon Avron wrote:
> I should say that I find the discussion about "arbitrary objects"
> (or "arbitrary numbers") rather embarrassing, especially that
> it is made by logicans. When I read it I got the feeling that
> Gentzen (and his analysis of Natural Deduction) and Tarski
> (with his semantical analysis of formulas, using structures
> and assignments) had never existed, and that
> variables and their correct use are still a mystery...
>
> Arnon Avron

Well, that was, more or less, my immediate reaction as well.  But then I 
thought of "definite descriptions," which were given a specific logical 
analysis by Russell but which tend to be explained away in most modern 
mathematical treatments of logic.  Just because something _can_ be 
explained away doesn't mean that it _should_ be explained away; if 
mathematicians find a concept useful in practice, maybe it's worth 
analyzing.  In the particular case of definite descriptions, the idea 
turned out to be useful, in modified form, in the so-called abstraction 
terms of set theory (and particularly in the development of the notion 
of forcing).

Mitchell Spector
Seattle University