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 “Everything is physical.”
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, Plato was human” 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 ‘Everything is physical,’ ” Professor Neale explained, “there are actually two ways of doing it: ‘Necessarily, everything is physical’ and ‘Everything is necessarily physical.’ They sound as if they mean the same, and a grammarian might 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, everything is physical,” 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 is physical.’ ”
In Sentence 2, “Everything is necessarily physical,” “necessarily” has a narrower scope: it ignores the merely possible and attends only to what actually exists. This sentence means, roughly, “Everything existing in this world has the property of being physical 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 everything is necessarily physical, then necessarily, everything is physical.”
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. 2, 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 Roosevelt University in Chicago; 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.Continue reading the main story
An earlier version misstated Professor Marcus’s date of birth, based on information supplied by her family. It is Aug. 2, 1921, not Aug. 21.
|Ruth Barcan Marcus|
|Born||(1921-08-02)August 2, 1921|
New York City
|Died||February 19, 2012(2012-02-19) (aged 90)|
New Haven, Connecticut
|Education||New York University (B.A. 1941)|
Yale University (M.A. 1942)
Yale University (Ph.D. 1946)
|Awards||Medal of the Collège de France (1986)|
Doctor of Humane Letters, honoris causa, University of Illinois at Chicago (1995)
Wilbur Cross Medal, Yale University (2000)
Lauener Prize (2007–08)
Permanent Member of the Common Room, Clare Hall (1986-)
Phi Beta Kappa (1941)
Membre, Institut International de Philosophie, Presidente 1989–92, President Honoraire 1992-
Quinn Prize (2007)
|Quantified modal logic,Barcan formula|
Ruth Barcan Marcus (; born Ruth C. Barcan; August 2, 1921 – February 19, 2012) was an American philosopher and logician who developed the Barcan formula. She was a pioneer in the quantification of modal logic and the theory of direct reference, and conducted seminal research on identity, essentialism, possibilia, belief, moral conflict as well as some critical historical studies.Timothy Williamson, the Wykeham Professor of Logic at Oxford University, sums up his celebration of Professor Marcus's career by stating that many of her "main ideas are not just original, and clever, and beautiful, and fascinating, and influential, and way ahead of their time, but actually — I believe — true."
Professional offices and service (partial list)
Quantified modal logic
Ruth Barcan Marcus' earliest published work was the publication of the first axiomatic study of modal logic with quantifiers. These three ground-breaking articles were "A Functional Calculus of First Order Based on Strict Implication", Journal of Symbolic Logic (JSL, 1946), "The Deduction Theorem in a Functional Calculus of First Order Based on Strict Implication" (JSL, 1946), "The Identity of Individuals in a Strict Functional Calculus of Second Order", (JSL, 1947). The three articles are published under Marcus' maiden name: Ruth C. Barcan. The widely discussed Barcan formula is introduced as an axiom in QML. The papers of 1946 and 1947, were the first systems of quantified modal logic, which extended some propositional modal systems of Clarence Irving Lewis to first and second order; a major accomplishment in the development of 20th century logic. Lewis gives Marcus special recognition in his "Notes on the Logic of Intension", originally printed in Structure, Method, and Meaning: Essays in Honor of Henry M. Sheffer (New York, 1951). Here Lewis recognizes Barcan Marcus as the first logician to extend propositional logic as a higher order intensional logic.
Ruth Barcan Marcus proposed the view in the philosophy of language according to which proper names are what Marcus termed mere "tags". ("Modalities and Intensional Languages" (Synthese, 1961) and elsewhere). These "tags" are used to refer to an object, which is the bearer of the name. The meaning of the name is regarded as exhausted by this referential function. This view contrasts for example with late Bertrand Russell's description theory of proper names as well as John Searle's cluster description theory of names which prevailed at the time. This view of proper names (presented in 1962 with Willard Van Orman Quine as commentator) has been identified by Quentin Smith with the theory of reference given in Saul Kripke's Naming and Necessity. However, in a recent laudatio to Ruth Barcan Marcus, Professor Timothy Williamson says:
One of the ideas in them that resonates most with current philosophy of language is that of proper names as mere tags, without descriptive content. This is not Kripke's idea of names as rigid designators, designating the same object with respect to all relevant worlds, for ‘rigidified’ definite descriptions are rigid designators but still have descriptive content. Rather, it is the idea, later developed by David Kaplan and others, that proper names are directly referential, in the sense that they contribute only their bearer to the propositions expressed by sentences in which they occur.
The philosopher of language Stephen Neale has also argued against Professor Smith's claim in the Times Literary Supplement.
Necessity of identity
Marcus formally proved the necessity of identity in 1946 and informally argued for it in 1961 and thereafter thus rejecting the possibility of contingent identity. See Journal of Symbolic Logic, (1947) 12: pp 12–15
Semantics of QML
Marcus prefers an interpretation where the domain of the interpretation comprises individual entities in the actual world. She also suggests that for some uses an alternative substitutional semantics is warranted. She provides arguments against possibilia. See "Dispensing with Possibilia" (Proceedings of the American Philosophical Association, 1975–76); "Possibilia and Possible Worlds" (Grazer Philosophische Studien, 1985–86).
Marcus defines a consistent set of moral principles as one in which there is some "possible world " in which they are all obeyable. That they may conflict in the actual world is not a mark of inconsistency. As in the case of necessity of identity, there was a resistance to this interpretation of moral conflict. Her argument counts against a widely received view that systems of moral rules are inevitably inconsistent.
It is proposed that believing is a relationship of an agent to a possible state of affairs under specified internal and external circumstances. Assenting to a quoted sentence (the disquotation account of belief) is only one behavioral marker of believing. Betting behavior is another. The wholly language centered account of belief (e.g. Davidson) is rejected. Where an agent would traditionally be described as believing an impossibility until its impossibility was disclosed, Marcus proposes that under those circumstances the agent should say that she only claimed to believe an impossibility. In much the same way, when a mathematician discovers that one of his conjectures is false, and since if it is mathematically false it is impossible, he would say he only claimed that the conjecture was true. Odd as this proposal is, it is analogous to the widely accepted principle about knowing: if we claim to know P, and P turns out false, we do not say we used to know it, we say we were mistaken in so claiming.
Aristotelian Essentialism is concerned with properties which Marcus defines in the context of a modal framework. One proposal is that a property is essential if something has it, not everything has it, if something has it then it has it necessarily, and it is not wholly individuating e.g. a natural kind property. It is otherwise claimed by Quine and others that modal logic or semantics is committed to essentialist truths. Marcus argues informally that there are interpretations of some modal systems in which all essentialist claims are false. Terence Parsons later formally proved this result.
An alternative to Tarskian (model theoretic) semantics is proposed for some uses where "the truth conditions for quantified formuli are given purely in terms of truth with no appeal to domains of interpretation". (Later called by others "truth value semantics".) She shows that the claim that such a semantics leads to contradictions is false. Such a semantics may be of interest for mathematics e.g. Hartry Field, or for fictional discourse. Objectual quantification is required for interpretation of identity and other metaphysical categories.
Awards and recognitions
- Guggenheim Fellow (1952)
- National Science Foundation Fellow (1963)
- Rockefeller Foundation Residency (Bellagio, 1973 and 1990)
- Center for Advanced Study in the Behavioral Sciences (1979)
- University of Edinburgh Fellow, Humanities Institute (1983)
- Wolfson College of Oxford University, Visiting Fellow (1985 and 1986)
- Clare Hall of Cambridge University, Visiting Fellow (1988)
- National Humanities Center, Mellon Fellow (1992–93)
- Fellow of the American Academy of Arts and Sciences(1977)
- Medal of the Collège de France (1986)
- Doctor of Humane Letters, honoris causa, University of Illinois at Chicago (1995)
- Wilbur Cross Medal, Yale University (2000)
- Lauener Prize in Analytic Philosophy, Lauener Foundation, 2007–08.
- Permanent Member of the Common Room, Clare Hall (1986-)
- Phi Beta Kappa (1941)
- Membre, Institut International de Philosophie, Presidente 1989–92, President Honoraire 1992-
- Quinn Prize, American Philosophical Association 2007, for service to the profession
- Dewey Lecture, APA, Dec 2009.
Books (written or edited)
- The Logical Enterprise, ed. with A. Anderson, R. Martin, Yale, 1995
- Logic, Methodology and Philosophy of Science, VII, eds. R. Barcan Marcus et al., North Holland, 1986
- Modalities: Philosophical Essays, Oxford University Press, 1993. Paperback; 1995 (contains many of Marcus's important papers)
References and notes
- ^Dagfinn Føllesdal, Referential Opacity and Modal Logic, Routledge, 2014, p. 19.
- ^Ruth Barcan Marcus, Modalities: Philosophical Essays, Oxford University Press, 1993, p. x.
- ^"Ruth Barcan Marcus | Jewish Women's Archive". jwa.org. Retrieved August 19, 2016.
- ^"Leiter Reports: A Philosophy Blog: Timothy Williamson's Tribute to Ruth Barcan Marcus on the Occasion of Her Receipt of the Lauener Prize". leiterreports.typepad.com. Retrieved August 19, 2016.
- ^Timothy Williamson's Tribute to Ruth Barcan Marcus on the Occasion of Her Receipt of the Lauener Prize, Leiter Reports: A Philosophical Blog, October 14, 2008.
- ^"Neale Kripke | Stephen Neale - Academia.edu". academia.edu. Retrieved August 19, 2016.
- ^See "Moral Dilemmas and Consistency" (Journal of Philosophy, 1980).
- ^See "A Proposed Solution to The Puzzle About Belief" (Foundations of Analytic Philosophy in Midwest Studies, 1981) and "Rationality and Believing the Impossible" (The Journal of Philosophy, 1983 and elsewhere).
- ^Philosophical Review, 78 (1969).
- ^"Book of Members, 1780–2010: Chapter M"(PDF). American Academy of Arts and Sciences. Retrieved July 29, 2014.