[FOM] stopping at ACA_0

Nik Weaver nweaver at math.wustl.edu
Fri Feb 17 01:07:01 EST 2006

Harvey Friedman wrote:

> On can stop a lot earlier than "predicativity", say, stop at
> ACA0 or RCA0, or one can stop somewhat higher than "predicativity",
> say at one inductive definition, or Pi11-CA0. Or one can stop even
> higher at, say, the theory of a recursively inaccessible, or what
> have you.
> All of these stopping places, and many more, have very "nice"
> stories. All of these stories have advantages and disadvantages.
> These advantages and disadvantages make sense and have their
> proponents, both mathematically and philosophically.

In response I asked

> I have to admit I've never heard of anyone advocating ACA_0 as
> a basic philosophical stance.  Yet you tell me there is a "nice
> story" in its favor, which "has proponents both mathematically
> and philosophically".  Can you say who some of those proponents
> are, and what that nice story is, in the case of ACA_0?

and got the non-answers

> Child's play to come up with one that looks as attractive as
> tortuous involved controversial ones for predicativity.


> Any story you can make about some precise stopping place for
> predicativity, and I can make a much better story about stopping
> at ACA_0.

These sound like evasions.  I like ACA_0 and am genuinely interested
in knowing whether it really has a "nice story" so I'll ask again.
(I gather that there are no proponents, either mathematically or
philosophically, so I'll drop that part of the question.)


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