Friday, February 24, 2012

Ruth Barcan Marcus

Ruth Barcan Marcus died on February 19, and I have been thinking about what to say on the subject. It's difficult to know where to begin; she was one of the true greats. Quine and Kripke get more press, but she was easily as great a logician as they. She is most famous for her work in modal logic; the Barcan Formula is named after her. The Barcan Formula is:

∀x□Fx → □∀xFx

Or, roughly, whatever F may be: if it is posited for everything that it is necessary that it is F, it follows that it is necessary to posit for everything that it is F. The Barcan Formula has a converse, imaginatively called the Converse Barcan Formula. It is:

□∀xFx → ∀x□Fx

Or, roughly, whatever F may be: if it is necessary to posit for everything that it is F, it can be posited for everything that it is necessary that it is F. Both of them can be formulated in terms of ◊, i.e., possibility, instead of necessity, if one prefers; for instance, what the possibilistic form of the Barcan Formula tells us is that when it is possible that something is posited to be a unicorn, something is posited for which it is possible that it is a unicorn. The debates about what is required for either of these principles to be true are quite complicated.

Barcan had many other interesting contributions; she argued, for instance, that it is impossible to believe impossibilities, just as it is impossible to know impossibilities. If you thought you believed something, but discover that it is not just false but really impossible, you were simply mistaken in thinking that you ever believed it at all. (This is not a very popular view, but as she notes, it is not unknown in the history of philosophy, and needs at least to be considered fairly.) She also argued both that consistent moral principles would not rule out moral dilemmas and that the existence of moral dilemmas need not be due to any inconsistency in moral principles. (Consider, for instance, a situation in which you have to decide which of two identical twins to save from drowning, where it is simply unclear which twin you are in a better position to save.) She also argued, in an argument that I think should be considered more widely than it is, that the existential quantifier does not always indicate that something exists.

Barcan was involved in two well-known professional controversies. One had to do with Derrida; she was one of the major philosophers protesting Cambridge's awarding of an honorary doctorate to him, arguing that where Derrida was coherent at all, his claims were either false or trivial. And even before that she had written a letter to the French government protesting his appointment as Director of the College International. The second big controversy was actually more about her than by her: Quentin Smith argued in 1995 that certain key parts of Saul Kripke's philosophy of language were actually taken, without acknowledgement, from prior work by her (she herself had never suggested such a thing). This led to a big, big blow-up. I don't think Smith fully made his case but, frankly, the fawning over Kripke that his defenders often engaged in makes much of the dispute utterly nauseating to read.

I find my disagreements with her positions to be quite considerable, but she was in every way a remarkable philosopher.


  1. awatkins691:41 AM

    Thanks for this summary. Do you know where she argues that the existential quantifier doesn't necessarily imply something exists?

  2. branemrys9:18 AM

    It's presented in a couple of essays in her book Modalities; I think it was first proposed in "Modalities and Intensional Languages"; but she discusses further implications in "Nominalism and the Substitutional Quantifier."


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