Ruth Barcan Marcus, Philosopher and Logician, Dies at 90 Ruth Barcan Marcus, a philosopher esteemed for her advances in logic, a traditionally male-dominated subset of a traditionally male-dominated field, died on Feb. 19 at her home in New Haven. She was 90. Her death was announced by Yale University, from which she retired in 1992 as the Reuben Post Halleck professor of philosophy. Because of its affinities with mathematics and the hard sciences - disciplines historically unwelcoming to women - logic had long been one of philosophy's most swaggering strains. For a woman of Professor Marcus's generation to elbow her way into the field, then dominated by titans like Willard Van Orman Quine, Rudolf Carnap and Kurt Gödel, was almost unheard of. "The rest of philosophy became less male dominated, less macho, more quickly than logic," Stephen Neale, distinguished professor of philosophy at the City University of New York Graduate Center, said in a telephone interview. She was working in a field which was really run by these giants. Professor Marcus was hailed by colleagues for her work in quantified modal logic. The field was born of the marriage of two existing systems, classical quantified logic and modal logic - a marriage she helped bring about. Quantified logic centers on the roles of words of quantification, like "all," "every" and "some," in logical statements. An example of a quantified statement is the sentence "All humans are mortal." Modal logic, by contrast, is concerned with different "modes" of truth - possibility, impossibility, necessity and the like - and the words that convey them. The sentence "Necessarily, humans are mortal" is an example of a modal statement. In the early 1940s, Professor Quine, who taught at Harvard, argued that combining quantifiers and modals produced unintelligible results. Later observers also noted the potential for ambiguity. "Once you combine "necessarily" with "All humans are mortal," " Professor Neale explained, "there are actually two ways of doing it: "Necessarily, all humans are mortal" and "All humans are necessarily mortal." They sound the same, and a grammarian would say, "What's the difference?" But in logic they're quite different. The difference hinges on how much of the sentence the modal word modifies. In Sentence 1, "Necessarily, all humans are mortal," the word "necessarily" casts a wide semantic net: it takes into account not only the real world, but also any hypothetical ones. "The comma is a giveaway," Professor Neale said. "You're saying, "In every possible world, everything that's a human in that world is mortal." " In Sentence 2, "All humans are necessarily mortal," "necessarily" has a narrower scope: it ignores the merely possible and attends only to what actually exists. This sentence means, roughly, "Every human (who actually exists in this world) has the property of being mortal (in every world)." Such issues may seem of small consequence, but the need to talk about them is necessarily the meat of philosophical logic. In the literary arena, questions like these are played out masterfully in the work of Lewis Carroll and Jorge Luis Borges. But philosophy itself lacked a formal framework that would make rigorous discussion possible. Working independently in the mid-1940s, both Professor Marcus and Professor Carnap, who taught at the University of Chicago, devised such frameworks by combining classical quantified logic and modal logic. Professor Carnap's system was rooted primarily in semantics, Professor Marcus's primarily in formal logic. "She was the first person to lay down in rigorous fashion a precisely defined system of rules for reasoning with modal and quantificational notions," said Kit Fine, Silver professor of philosophy and mathematics at New York University. Professor Marcus's system, first published under her maiden name, included what came to be known as the Barcan formula. Where Professor Quine had argued that sentences like No. 2 above were unintelligible, the Barcan formula (together with its converse) renders the first and second sentences logically equivalent. Under her formula, "the second one entails the first one," Professor Neale explained. That is, if all humans are necessarily mortal, then necessarily, all humans are mortal. Like much else in logic, however, the plausibility of the Barcan formula remains the subject of continuing debate. In other work, Professor Marcus examined the philosophical arguments underpinning moral dilemmas. Ruth Charlotte Barcan was born in the Bronx on Aug. 21, 1921, into a satisfying atmosphere of questioning and debate. Her father was a typesetter at The Jewish Daily Forward; a bust of the Barcan household saint, the labor leader Eugene V. Debs, presided over the living room. She earned a bachelor's degree in mathematics and philosophy from New York University, where she was a champion fencer, followed by master's and doctoral degrees in philosophy from Yale. An outspoken advocate for women in philosophy, she taught at what is now the University of Illinois at Chicago and at Northwestern University before joining the Yale faculty in 1973. In retirement, Professor Marcus also taught at the University of California, Irvine. Professor Marcus's marriage to Jules Marcus, a physicist, ended in divorce. She is survived by two sons, James and Peter; two daughters, Katherine Marcus and Libby Marcus; a sister, Hilda Fishback; and three grandchildren.