Re: Mathematical clarification: Impredicativity in Rosennean parlance

["glen e. p. ropella" <***>]

Torkel Franzen wrote:
> 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.

Perhaps B&M might help, here.  In chapter 9 of "vicious circles", they 
state:

  "We have asserted more than once that the universe of hypersets is 
richer than the universe of wellfounded sets, richer in that you can 
think of the former as an enlargement of the latter obtained by 
'throwing in' solutions to systems of equations.  This chapter makes 
this claim precise and proves it."

Now, I can't pretend to understand the details of their proof.  But, I 
can get the basic point, I think.  Basically, B&M are saying that 
allowing the circularity that results from ZFA as opposed to ZFC gives 
us a richer formal space in which to work.

From this 50,000 ft perspective, it seems that RR is saying something 
very similar, regardless of whether he is (or I am) using the right 
terms or can see a clear path from circularity in formal systems to 
circularity in organisms.

It would be a great boon if you guys could help iron out these issues. 
The inadequacies you find and work to correct will help continue what RR 
started.

--
glen e. p. ropella              =><=                Hail Eris!
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