[FOM] impredicative definitions/paper announcement

[Nik Weaver]

Daniel Mehkeri wrote:

> Kleene's O was mentioned, but it is constructed from below in a
> sense. It is common especially in constructive mathematics to call
> that predicative

Yes, Michael Rathjen calls this kind of thing "generalized predicative".
I would use the term "pseudo-predicative".  Generally you're talking
about constructive reasoning which is genuinely predicative augmented
by one or two axioms which are not (most notably, full set induction).

Incidentally, I have a new survey paper on predicativism (and it does
discuss this point).  It's called "What is predicativism?" and can be
found at

http://www.math.wustl.edu/~nweaver/what.pdf

or among my other papers at

http://www.math.wustl.edu/~nweaver/conceptualism.html


Nik Weaver
Math Dept.
Washington University
St. Louis, MO 63130 USA
nweaver at math.wustl.edu