Re: Mathematical clarification: Impredicativity in Rosennean parlance

[Torkel Franzen <***>]

Judith Rosen forwards a message from Aloisius Louie concerning the
matter of "formalizable systems". I am interested to learn that
the passage quoted earlier is indeed to be read as applying to
formal systems in the sense of logic. The question considered in
the forwarded message is

>... what Rosen meant by those quantifiers "an
>infinitesimal part", "very little", "almost every", etc.

The answer given is another analogy or metaphor, that of the rational
numbers having measure zero among the real numbers. This analogy isn't
really helpful in coming to grips with the passage in question.
It would be a great deal more illuminating to have a couple of
examples of why questions that can be answered from within the system,
and why questions that cannot be answered from within the system.
This would clarify what sort of poverty of entailment is intended, and
allow readers to judge for themselves the aptness and significance of
"very little", "almost every", and so on.