[FOM] On Myhill on Gödel on paradoxes

Frode Bjørdal frode.bjordal at ifikk.uio.no
Fri Sep 2 05:59:15 EDT 2011

Bill Greenberg wgreenb at gmail.com WROTE

"According to Myhill (p. 130), property theories which embrace *Frege’s
Principle*—the principle that “every formula with one free variable
determines a *property *… which holds of all and only those things which
satisfy the formula”—prove the property-theoretic version of Russell’s

Q(P) iff NOT(P(P))

Might this not be one of the property-theoretic paradoxes that Goedel had in

The postings earlier in this thread seem to have established that
Gödel was questing for a "concept theory". Your Russellian example
would be one such that *Myhill* would have thought that Gödel would
have thought it of as a property theoretic paradox. Hao Wang at the
bottom of page 278 of A Logical Journey explicitly renders this as a
concept theoretic paradox in the Gödelian vernacular.

Frode Bjørdal
Professor i filosofi
IFIKK, Universitetet i Oslo

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