[FOM] Feferman/Schutte unfazed

[Harvey Friedman]

On 4/14/06 3:53 PM, "Nik Weaver" <nweaver at math.wustl.edu> wrote:

>I leave it to interested readers to decide for themselves whether
>the above, if successful, constitutes a "refutation" of the F-S
>analysis.

My answer is that it unequivocally does NOT constitute a "refutation" of the
Feferman/Schutte analysis of predicativity. Because I am under the
impression that no one except Weaver is questioning my answer, I doubt if
there is interest among the readers to continue with the detailed discussion
with Weaver along the lines that it has been going.

In fact, I prepared a detailed response, since I do not believe that there
are any productive matters to be resolved in connection with this exchange,
I have thrown it away.

So I will now attempt to throw the discussion into productive channels.

Let us START SLOWLY, at FIRST PRINCIPLES. Let's crawl before we start
running and fighting.

CHALLENGE. Present an entirely transparent nontechnical informal/semiformal
explanation of "predicativity" that is really powerful enough to determine
the status of basic assertions.

TEST CASE. Consider

"the truth predicate for arithmetic exists"

Can your presentation of predicativity clearly establish this? Let us go
thru, SLOWLY, why the above is true, predicatively, on the basis of your
presentation.

Harvey Friedman