Ruth Barcan Marcus

Ruth Barcan Marcus

Ruth Barcan Marcus

Ruth Barcan Marcus (August 2, 1921 – February 19, 2012) was an American philosopher and logician who developed the Barcan formula. She was a pioneering figure in the quantification of modal logic and the theory of direct reference. She wrote seminal papers on identity, essentialism, possibilia, belief, moral conflict as well as some critical historical studies.[1] 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."[2]


  • Education 1
  • Academic appointments 2
  • Professional offices and service (partial list) 3
  • Philosophy 4
    • Quantified Modal Logic 4.1
    • Direct Reference 4.2
    • Necessity of Identity 4.3
    • Semantics of QML 4.4
    • Moral Conflict 4.5
    • Belief 4.6
    • Essentialism 4.7
    • Substitutional Quantification 4.8
  • Awards and recognitions 5
  • Books (written or edited) 6
  • See also 7
  • References and notes 8
  • External links 9


Academic appointments

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.

Direct Reference

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 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.[3]

The philosopher of language Stephen Neale has also argued against Professor Smith's claim in the Times Literary Supplement.[4]

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 (See below). 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). T

Moral Conflict

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.[5]


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.[6]


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.[7]

Substitutional Quantification

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

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)

See also

References and notes

  1. ^ [2]
  2. ^
  3. ^ 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.
  4. ^
  5. ^ See "Moral Dilemmas and Consistency" (Journal of Philosophy, 1980)(and frequently published elsewhere)
  6. ^ 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).
  7. ^ Philosophical Review, 78 (1969).
  8. ^ "Book of Members, 1780–2010: Chapter M" (PDF). American Academy of Arts and Sciences. Retrieved July 29, 2014. 

External links

  • Yale University philosophy department biography: Ruth Barcan Marcus
  • Encyclopedia of Jewish Women: Ruth Barcan Marcus
  • Ruth Barcan Marcus, Philosopher-Logician, Dies at 90NY Times