Tuesday, March 23, 2010

Ada Lovelace Day: Celebrating Ruth Barcan Marcus

Ruth Barcan Marcus

Ruth Barcan Marcus is a philosopher and logician and pioneering figure in the quantification of modal logic and the theory of direct reference. The Barcan Formula is named after her.


PhD 1946, Yale University

BA 1941, NYU

Academic Appointments

Prior to 1973: Chair of University of Illinois–Chi

cago Philosophy Department, then Professor at Northwestern University.

Since 1973: Halleck Professor at Yale, 1992, and then Senior Research Scholar at Yale and Visiting Distinguished Professor (One term per year) at UC, Irvine

The Barcan Formula is an axiom by Ruth Barcan Marcus, in the first extensions of modal propositional logic to include quantification.

The Barcan Formula is:

The statement reads: If everything is necessarily F, then it is necessary that everything is F. The Barcan formula has generated some controversy because it implies that all objects which exist in every possible world (accessible to the actual world) exist in the actual world. In other words, the domain of any accessible possible world is a subset of the domain of the actual world.

The Converse Barcan Formula is:

If a frame is based on a symmetric accessibility relation, then the Barcan formula will be valid in the frame if, and only if, the converse Barcan formula is valid in the frame.

Personal note: I will never forget the first time I read about Ruth Barcan Marcus' work. It was while I was in graduate school, and was reading an essay by W.V.O. Quine in which he was arguing against modal logic. Quine referred to her as "Miss Barcan" while all the other (male) philosophers were referred to by last names. He had nothing good to say about her views, which seemed to me of a piece with his philosophical program and unsurprising, yet I was bothered. The etiquette seemed completely wrong. Even if, charitably, Ruth Barcan had not yet earned her doctorate, which would explain the reference to her as "Miss," she had nevertheless published work substantial enough that he thought it worth attack in print. Why not just "Barcan"? What did indicating Barcan's unmarried status have to do with intensional logic?

Later on, when I became aware of the controversy surrounding Barcan's work possibly being plagiarized or borrowed from by Kripke, (a controversy described in this article by Jim Holt), it struck me that whatever the reality of the situation, there was a simple fact of the matter at hand. Looking around in the classrooms where I studied philosophy of mind, epistemology, metaphysics and logic, women were scarce. Still. It was not true that women were not capable of the rigors of logic. Pioneers like Ada Lovelace, Grace Hopper (developer of COBOL and pioneer of programming languages) and Ruth Barcan Marcus have been there all along. Under the radar--but why? Under-appreciated? Not any more, not on my watch.

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