The opening sentence of Roger Myhill's article Paradoxes, in 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.”

What, precisely, were Gödel's property theories. I have for a long time thought that they simply were set theories without the axiom of extensionality. But perhaps there is something more to them, e.g. something stemming from Gödel's ontological argument?

  • $\begingroup$ See here $\endgroup$ Apr 12 at 11:16
  • $\begingroup$ Reference: Frege and Russell and the logicist project based on the idea that the "concept" is a logical concept. $\endgroup$ Apr 12 at 11:18
  • $\begingroup$ See B.Russell letter to Frege (1902) [reprinted into van Heijenoort's Sourcebook, page 125]: "Let w the predicate: to be a predicate that cannot be predicated of itself." And Frege's reply (1902) [page 128]: "it seems to me that the expression 'a predicate is predicated of itself' is not exact. I would prefer to say 'a notion is predicated of its own extension'." $\endgroup$ Apr 12 at 15:19
  • $\begingroup$ I know the history. Recently, the term has been used differently. See e.g. here: dropbox.com/s/npc2xd19b5uaj7f/Property%20THEORY.pdf?dl=0 $\endgroup$ Apr 13 at 20:23


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.