[FOM] what is predicativity?/yet again

[Harvey Friedman]

On 5/4/06 11:58 PM, "Nik Weaver" <nweaver at math.wustl.edu> wrote:

> 
> I hadn't intended to write anything more for now about the
> Feferman-Schutte analysis of predicativity, but looking at
> Harvey Friedman's message # 010471 I realized there is one
> more thing I'd like to say.
> 
> Friedman wrote:
> 
>> That still allows for a system S with infinitely many axioms,
>> written down by someone who is acting at least a bit beyond
>> predicatively, with a claim that the predicativist can come
>> to accept any finite number of the axioms, but cannot come to
>> accept all at once - e.g., because the predicativist cannot
>> formulate a suitably meaningful predicate to which to apply
>> induction. This appears to be the approach of Feferman/Schutte.
> 
> Such an approach is highly unlikely to succeed.

You have already made this point several times. On the contrary, it
certainly can be expected to succeed, provided one is definite enough about
what notion of "predicativity" one is analyzing.

I have been trying to channel the discussion into something productive,
hence the subject line "what is predicativity"?

I repeat my challenge of posting
http://www.cs.nyu.edu/pipermail/fom/2006-May/010503.html

This will likely flesh out the real issues. Readers will likely come to the
conclusion that this whole thread came about because of insufficient clarity
concerning what "predicativity" means, and in particular, a failure to
distinguish between several notions of "predicativity".

Can you or Avron meet this basic challenge?

Without meeting this basic challenge concerning "what is predicativity", the
claims you have been making concerning "refuting" longstanding works of
others would appear to be empty.

Harvey Friedman