[FOM] what is predicativity?/again

Harvey Friedman friedman at math.ohio-state.edu
Thu May 4 17:25:44 EDT 2006

Evidently from the two recent Weaver postings, there are several notions of
"predicativity" that have to be carefully sorted out before a fruitful
discussion can take place.

I wrote already in 

"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

I presented this challenge to Weaver and also, more recently, to Avron.

So far, they have not taken up the challenge. Perhaps they, or someone else,
will take up this crucial challenge, and we can go from there.

It would also be helpful if the word "refute" could be retracted, as applied
to Feferman/Schutte.

Harvey Friedman 

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