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

[Torkel Franzen <***>]

"glen e. p. ropella" writes:

>Your definition of the term: "a definition that defines an object by 
>means of quantification over a totality to which that object itself 
>belongs" contains a kind of circularity (X is used to define X).

  As commented on by Calvin (and some sixty years ago by Gödel),
impredicative definitions are circular only if we put them forward as
constructions rather than specifications. Otherwise, they are no more
circular than a specification such as "the tallest man in Tulsa".

>I am unclear on why B&M would want to swap out the FA for what they call 
>the "Anti-Foundation Axiom" in order to avoid the situation obtained in 
>prop 2.6.

  Because they are writing about the specific subject of non-well-founded
set theory. It's not a matter of "avoiding a situation", but one of
pointing out the differences between set theory with foundation and
with anti-foundation.