[FOM] On Myhill on Gödel on paradoxes

Bill Greenberg wgreenb at gmail.com
Thu Sep 1 22:13:05 EDT 2011

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

2011/8/22 Frode Bjørdal <frode.bjordal at ifikk.uio.no>

> The opening sentence of Roger Myhill's *Paradoxes, *Synthese 60 (1984),
> 129-143, is: “Gödel said to me more than once "There never were any
> set-theoretic paradoxes, but the property-theoretic paradoxes are still
> unresolved"; and he may well have said the same thing in print.”
> This remark seems to have had influence in that some later authors have
> used the term "property-theory" for theories which seek to account for more
> type-free accounts that approximate naive abstraction in dealing with the
> paradoxes.
> Can someone at this stage fill in with more information concerning what
> Gödel may have said or written concerning this? What is the earlies use of
> the term "property-theory" in the area?
> --
> Frode Bjørdal
> Professor i filosofi
> IFIKK, Universitetet i Oslowww.hf.uio.no/ifikk/personer/vit/fbjordal/index.html
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