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Re: [ontolog-forum] [ontology-summit] FW: [ontolog-invitation] Invitatio

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Fri, 17 Dec 2010 12:46:02 -0600
Message-id: <1EA3F12E-4E4C-4244-8852-EFD5DBD2C638@xxxxxxxx>
On Dec 17, 2010, at 10:16 AM, Matthew West wrote:
Therefore, I assume a class might be set-like, but it's not a set.

MW: Well that begs the question: What is it to be a set?


And by the way, Common Logic manages to avoid contradictions
by a method similar to what I just described:  the examples
that create paradoxes in some versions of logic just produce
CL statements in which the paradoxical entity doesn't exist.

MW: And what do you call that version of set theory?

It is not a version of set theory at all; there are no specialized set theoretic axioms in CL.  CL (without row variables) is simply a generalized form of first-order logic; specifically, it is the result of generalizing the syntax and semantics of standard first-order logic to permit (among other things) self-predication (a.k.a. self-membership (if predicates are taken to denote classes) or self-exemplifation (if predicates are taken to denote properties)).  Interested readers might consult this paper, forthcoming in Synthese but freely available (for some, at least) online.  If you don't have access to the Springer site, a preprint is available here.

Chris Menzel

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