Re: defn of impredicativity (was Re: goals and language?)

[Torkel Franzen <***>]

glen e. p. ropella writes:

>I have to paraphrase this to see if I understand.  An impredicative 
>definition (of an object, set, predicate, whatever) is one that relies 
>on multiple collections of objects, including the object being defined, 
>where all those collections relate in some way.

  No, an impredicative definition is quite specifically a definition
that uses quantification (the phrases "for all X", "for some X") over
a collection containing the object being defined. There are
problematic aspects of this explanation, but they haven't been touched
on in our exchange. It's unclear to me what you intend by "that
definition depends on some R such that aRb, xRa, and xRb, for
collections x, a, and b".

  As regards your further remarks, I can only reiterate that Kercel's
supposed explanation is useless if you're interested in what "impredicative"
means in logic and philosophy. Such comments as

>Given the foundation axiom, for 
>all a, a is not a member of a.  (apparently prohibiting impredicative 
>definitions)

are grossly incorrect.