The Logic Quine Tried to Bury

In 1946, a 24-year-old named Ruth Barcan published a paper in the Journal of Symbolic Logic that did something nobody had done in print before: it built a formal system that mixed quantifiers ("there exists," "for all") with modal operators ("necessarily," "possibly"). The schema at the heart of it now bears her name.

The Barcan formula, in plain English, says that if it's possible something has a property, then there's something that possibly has that property. In symbols: if it is possible that there exists an x such that Fx, then there exists an x such that it is possible Fx. The converse goes the other way. Together they fix a relationship between two questions philosophers had been mixing up for centuries: what is possible, and what there is.

The consequence is awkward. The formula implies that the domain of objects can't grow when you cross from the actual world to a merely possible one. Whatever could exist already does. There are no merely possible people waiting in the wings.

W. V. O. Quine spent the next thirty years arguing the whole enterprise was incoherent. Modal contexts, he said, broke the substitution of co-referring terms; they smuggled in "Aristotelian essentialism," the idea that objects have properties necessarily and others only contingently. He treated this as a reductio.

Marcus answered that Quine's worry depended on treating proper names like definite descriptions. Names, she argued, refer directly — they tag the same object across every possible world they appear in — so the substitution problem dissolves. As for essentialism: yes, and so what?

She went to Yale in 1973 and stayed until she died in 2012. The view of names she defended in the 1960s is now usually credited to Saul Kripke, who heard her give it at a Boston colloquium in 1962. She lived long enough to see the record corrected, slowly.