FOM: ``arbitrary objects"
spector at seattleu.edu
Thu Jan 31 12:48:54 EST 2002
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
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