[FOM] On Myhill on Gödel on paradoxes

d_obrien d_obrien at telus.net
Tue Aug 23 01:45:13 EDT 2011

I think that by “property theory” is usually meant “property of a certain
subject”, so as to mean that the property belongs as predicate of the whole
of that subject, and where the laws are pretty much governed by Aristotelian
That isn’t a totally extensional theory, so it isn’t the same thing as a set
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of
Frode Bjørdal
Sent: August-22-11 1:52 PM
To: fom at cs.nyu.edu
Subject: [FOM] On Myhill on Gödel on paradoxes
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

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 Oslo
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