Bloomsbury Encyclopedia of Philosophers - Marcus, Ruth Charlotte Barcan (1921–2012)
The Dictionary of Modern American Philosophers


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Marcus, Ruth Charlotte Barcan (1921–2012)

Marcus, Ruth Charlotte Barcan (1921–2012)
DOI: 10.5040/9781350052444-0636

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Ruth Barcan Marcus, one of the twentieth century’s most important and influential philosopher-logicians, was born Ruth Charlotte Barcan on 2 August 1921 in New York City. She attended New York University (where she was a champion fencer), studying mathematical logic with J. C. C. Mckinsey and graduating with a BA in philosophy and mathematics in 1941. She earned her MA in philosophy in 1942, and PhD in philosophy in 1946, from Yale University. Her doctoral dissertation, supervised by Frederick B. Fitch , introduced predicates and quantifiers into systems of C. I. Lewis ’s propositional modal logic. Three articles in the Journal of Symbolic Logic in 1946 and 1947 – published under the name Ruth C. Barcan before her marriage – established the foundations of quantified modal logic (QML). Following a postdoctoral fellowship taken at the University of Chicago, during which she participated in Rudolf Carnap ’s seminar, she remained in the Chicago area, teaching as a visiting professor of philosophy at Northwestern University (and raising four children), as attention to her published writings grew. Particularly important was “Modalities and Intensional Languages,” which defended quantified modal logic against then-popular objections proposed by W. V. Quine to its legitimacy and intelligibility. First published in 1961, the paper was presented at a famous February 1962 symposium of the Boston Colloquium for the Philosophy of Science that included a formal response by Quine as well as subsequently-published discussion by Marcus, Quine, Dagfinn FøLlesdal , and Saul Kripke .

Marcus was a professor of philosophy at Roosevelt College in Chicago from 1957 to 1963. In 1964 she became the first head of the philosophy department at the University of Illinois, Chicago Circle (now the University of Illinois at Chicago), building it in a period of six years from a faculty of two to a nationally prominent faculty of twenty. After three years at Northwestern University from 1970 to 1973, she went to Yale in 1973 to become Reuben Post Halleck Professor of Philosophy, a position she held until her retirement in 1992. In addition, she has held fellowships from the National Science Foundation (1963–4); the Rockefeller Foundation (1973, 1990); the Stanford University Center for Advanced Studies in the Behavioral Sciences (1979); the University of Edinburgh Institute for Advanced Studies in the Humanities (1983); Wolfson College, Oxford (1985, 1986); Clare Hall, Cambridge (1988); and the National Humanities Center (1992–3). A collection of many of her most important articles, Modalities: Philosophical Essays, appeared in 1993. Since 1994 she has been a visiting distinguished professor at the University of California at Irvine, as well as a senior research scholar at Yale. Marcus did on 19 February 2012 in New Haven, Connecticut.

Throughout her career, Marcus has been remarkably active in professional service. Very few other American philosophers have held as many important national and international professional offices, among them President of the Western Division of the American Philosophical Association (1975–6); Chair of the US National Committee of the International Union of History and Philosophy of Science (1977–9); Chair of the American Philosophical Association Board of Officers (1977–83); President of the Association for Symbolic Logic (1983–6); and President of the Institut International de Philosophie (1989–92). Among the many honors she has received are permanent fellowship in the American Academy of Arts and Sciences (1977); the Medal of the Collège de France (1986); an Honorary Doctor of Humane Letters from the University of Illinois (1995); and the Wilbur Cross Medal of the Yale University Graduate School Alumni Association (2000).

Modal logic is the logic of the modes, such as necessity and possibility, of a proposition’s truth or falsity. While C. I. Lewis (1912, 1932) had developed a series of five axiomatized systems (S1–S5) of modal logic utilizing sentential operators of necessity, possibility, and “strict” (necessary) implication, Marcus was the first to develop modal systems incorporating predicates, relations (including identity), and quantifiers. In doing so, she raised – and in many cases helped ultimately to settle – important issues in the philosophy of language and metaphysics. In her later work, she also made important contributions to the understanding of the consistency of moral codes (with their “deontic” modalities of obligation and permission) and the nature of belief.

One important element of QML as developed by Marcus (1947) is the Necessity of Identity principle, which may be expressed as (∀x)(∀;y)[x=y]⇒□(x, y)], where “∀x” and “∀y” are universal quantifiers, “=” signifies identity, “⇒” is the strict implication operator, and “□” is the necessity operator. This theorem that all identities are necessary is an immediate consequence of the necessity of statements of self-identity, such as “□(x = x)”, given a rule of inference allowing substitution of co-referential terms (e.g., of “x” for “y” in any formula, given x = y). However, it seemed paradoxical to many that a true identity statement such as “Cicero is Tully” should be necessary. It seems paradoxical partly because such names were widely regarded as having different descriptive contents as their meanings, and partly because necessity was often not distinguished from logical truth (truth in virtue of logical form), analyticity (truth in virtue of meaning alone), and a priority (knowability without empirical evidence). Marcus defended the necessity of such identities by arguing that names are purely referential “tags” that designate their objects directly, without any descriptive content that could differ among different names. This response initiated the “direct” theory of reference, to which Saul Kripke and Keith Donnellan later added causal accounts of how directly referring names can preserve their reference over time. The 1990s saw a historical controversy over the extent to which the leading elements of Kripke’s theory of reference and related doctrines were derived from Marcus (see Fetzer and Humphreys 1998).

An additional class of apparently contingent identity statements are those containing definite descriptions, such as “Benjamin Franklin is the first Postmaster General” or “9 = the number of planets”). Quine used such examples to object to the legitimacy and coherence of modal logic by arguing that inferences involving substitution of co-referential expressions into modal contexts based on such identities can fail. For example, assuming that mathematical truths are necessary, we may assert:

  1. □(9>7), where “>” signifies the “greater than” relation; and

  2. 9 = the number of planets; but it does not follow that

  3. □(the number of planets > 7)

for there could have been six planets or even fewer. Unlike names, definite descriptions cannot plausibly be treated as directly referential tags with no descriptive content. However, statements containing them can be analyzed as existential quantifications in accordance with Bertrand Russell’s general theory of definite descriptions. Doing so reveals – as Arthur Smullyan (1948) was the first to argue and as Marcus, citing Smullyan, also emphasized – an ambiguity in the scope of the necessity operator.

Thus, (2) may be analyzed as:

(2’) (∃x){[x numbers the planets & (∀y)(y numbers the planets →y = x)] & x = 9} [where “(∃x)” is an existential quantifier, “&” is the operator conjunction (“and”), and “→” is the operator of material implication (“if then”)]

and (3) is analyzed either as:

(3’) □(∃x){[x numbers the planets & (∀y)(y numbers the planets, →y = x)] & (x>7)]}


(3”) (∃x){[x numbers the planets & (∀y)(y numbers the planets →y = x)] &□ (x>7)]}

Statement (3”) is false but is not a legitimate inference in QML from (1) and (2); (3”) is a legitimate inference from (1) and (2) in QML, but it is true. Following Kripke’s careful distinction of necessity from logical truth, analyticity, and a priority (Kripke 1972), it is now widely accepted that all true statements of identity are necessary.

A second popular objection made by Quine to QML was that it carried with it an objectionable commitment to essentialism, the view that objects have some of their properties necessarily and others only contingently (Quine 1960). He argued that the apparent modal truths that “mathematicians are necessarily rational and not necessarily two-legged” and “bicyclists are necessarily two-legged and not necessarily rational,” together with the proposition “a is a mathematician and a bicyclist,” entail the contradictory conclusion that “a is and is not necessarily rational, and a is and is not necessarily two-legged.” Thus, he concluded, modal logic cannot properly concern individual objects per se, but only concepts of objects or objects considered in a certain way. Marcus noted in response that, while quantified modal logic allows the formulation and hence intelligibility of sentences (such as ‘□Fx’) asserting that an object possesses a property necessarily, there are (as demonstrated in Parson 1969) systems of QML consistent with the falsehood of all such sentences except those attributing necessary possession of “logical” attributes such as self-identity (which are not plausibly regarded as “essentialist” in the Aristotelian tradition of essential properties). Furthermore, she argued, statements attributing to an individual membership in a “natural kind,” such as “h is a horse,” are very plausibly and commonly regarded as necessary and essential. The contradictory conclusion about rationality and two-leggedness, she showed, can be avoided by drawing a scope distinction (rather as in the case of 9 and “the number of planets”) between two interpretations of the initial premises. The first is:

□(x is a mathematician → x is rational) & ~□(x is a mathematician →x is two-legged) [where “~” is the negation operator (“not”)] ? (x is a bicyclist →x is two-legged) & ~□(x is a bicyclist →x is rational)

While the second is:

□x is a mathematician → (□x is rational & ~□x is two-legged)

x is a bicyclist → (□x is two-legged & ~□x is rational)

On the first interpretation, the premises are true but are not sufficient in QML to generate the contradictory conclusion. On the second interpretation, the premises are sufficient (given that a is a mathematician and a bicyclist) to generate the contradictory conclusion, but are not plausible. It is now widely agreed that QML is not committed to essentialism in any objectionable way.

In addition to the Necessity of Identity, Marcus adopted, in her original development of QML, an axiom that soon came to be known as the Barcan Formula:

□(∃x)a fi (∃x)□a [where ‘□’ is the possibility operator, “(∃x)” is an existential quantifier, “a” represents any well-formed formula, and “⇒” is the operator of strict implication]

She also proved the converse: (∃x)□α ⇒ □(∃x)α. But whereas the converse of the Barcan Formula only allows inferences from what is actual (namely, something possibly satisfying the condition specified by “α”) to a possibility (namely, that of something satisfying the condition specified by “α”), the Barcan Formula allows inferences from what is merely possible to what is actual – a seemingly more suspect procedure from an ontological or metaphysical point of view. Acceptance of the Barcan Formula seems to require that the domain of possible things not exceed the domain of actual things, for only then does the possibility of something satisfying a given condition guarantee that it is something actual that accounts for this possibility.

One approach to rendering plausible this limitation on the domain of the possible, subsequently proposed and discussed by Marcus (1972) lies in a substitutional interpretation of quantification. On this interpretation, “(∃x)a,” for example, is true if and only if there is (or can be) a name the substitution of which into the formula “α” results in a true sentence. Such an interpretation potentially leaves open the question of whether all names actually refer; and it provides support for the Barcan Formula insofar as it is reasonable to suppose that the stock of names available for substitution is the same in modal and non-modal contexts. In a later writing (1985), she defended the Barcan Formula by rejecting possibilia, merely possible but non-actual objects, on the grounds that the identity required for objecthood applies only to actual things and that genuine reference to non-actual things is in any case impossible in consequence of the causal requirements for successful naming. This rejection of possibilia guarantees that the domain of the possible does not exceed that of the actual, and it allows for a standard objectual interpretation of quantification (as ranging over objects rather than names), although Marcus continued to maintain that substitutional interpretations are defensible and particularly useful for such purposes as formalizing fictional discourse. Kripke’s approach to modal logic, in contrast, allows the domain of possible worlds to include non-actual objects and thereby permits rejection of the Barcan Formula. The correctness of the Barcan Formula remains controversial.

Marcus’s contribution to ethics lies primarily in her groundbreaking work on moral dilemmas: cases in which one has an obligation to do x and an obligation to do y, even though it is not possible to do both x and y (1980). Using a standard account of consistency, she rejected the then-prevailing view that any moral code that does not rule out the possibility of moral dilemmas is thereby inconsistent. She showed that moral dilemmas may arise even in moral codes based on a single principle, and she defined the consistency of a moral code as there being at least one possible set of circumstances in which all of its requirements or obligations are jointly obeyable. From the consistency of a moral code, then, it does not follow that all of its moral requirements are jointly obeyable in the actual world. On the contrary, Marcus argues, real moral dilemmas often arise; for example, when one promise can be kept only by violating another. In such cases, neither obligation is erased or canceled by the existence of the other; rather, one is “damned if one does, and damned if one doesn’t.” Indeed, it is morally important that conflicting obligations do not merely erase each other, for the possibility of genuine moral dilemmas provides one with a powerful moral motive to do one’s best to prevent them from arising.

Marcus (1981, 1983, 1990) also offered a comprehensive theory of the nature of belief, according to which: x believes that S just in case, under certain agent-centered circumstances including x’s desires and needs, as well as external circumstances, x is disposed to act as if S, that actual or non-actual state of affairs, obtains. This is a largely behavioral rather than language-centered conception of belief, for it treats belief as a relation between a believer and a state of affairs, where states of affairs are understood not as linguistic or quasi-linguistic entities, but rather as possible structures of actual objects, properties, and relations. Thus, since Hesperus and Phosphorus are the same object, the belief that Hesperus is rising is the same belief as the belief that Phosphorus is rising. This view accords well with Marcus’s treatment of proper names as directly referential tags. Similarly, the limitation of states of affairs to structures involving actual objects accords well with the Barcan Formula. One consequence of the proposal is that one cannot literally believe anything impossible. Although one may assent to sentences that express impossibilities, assent is only speech behavior and is not always a final measure of believing.


“A Functional Calculus of First Order Based on Strict Implication,” Journal of Symbolic Logic 11 (1946): 1–16.

“The Deduction Theorem in a Functional Calculus of First Order Based on Strict Implication,” Journal of Symbolic Logic 11 (1946): 12–16.

“The Identity of Individuals in a Strict Functional Calculus of Second Order,” Journal of Symbolic Logic 12 (1947): 12–15.

“The Elimination of Contextually Defined Predicates in the Modal System,” Journal of Symbolic Logic 15 (1950): 92–3.

“Extensionality,” Mind 69 (1960): 55–62.

“Modalities and Intensional Languages,” Synthese 13 (1961): 303–22.

“Iterated Deontic Modalities,” Mind 75 (1966): 580–82.

“Essentialism in Modal Logic,” Noûs 1 (1967): 91–6.

“Essential Attribution,” Journal of Philosophy 67 (1971): 187–202.

“Quantification and Ontology,” Noûs 6 (1972): 240–50.

“Classes, Collections, and Individuals,” American Philosophical Quarterly 11 (1974): 227–32.

“Moral Dilemmas and Consistency,” Journal of Philosophy 77 (1980): 121–35.

“A Proposed Solution to a Puzzle about Belief,” Midwest Studies in Philosophy 6 (1981): 501–10.

“Rationality and Believing the Impossible,” Journal of Philosophy 75 (1983): 321–37.

“Possibilia and Possible Worlds,” Grazer philosophische Studien 25/26 (1985–86): 107–32.

“Some Revisionary Proposals about Belief and Believing,” Philosophy and Phenomenological Research suppl. 50 (1990): 133–54.

Modalities: Philosophical Essays (Oxford, 1993).

Other Relevant Works

“Interpreting Quantification,” Inquiry 5 (1962): 252–9.

“Classes and Attributes in Extended Modal Systems,” Proceedings of the Colloquium in Modal and Many Valued Logic, Acta philosophica fennica 16 (1963): 123–36.

Ed. with Alan Anderson and R. M. Martin, The Logical Enterprise (New Haven, Conn., 1975).

“Dispensing with Possibilia,” Proceedings of the American Philosophical Association 49 (1976): 39–51.

Ed. with George Dorn and Paul Weingartner, Logic, Methodology, and Philosophy of Science (Amsterdam, 1986).

“The Anti-Naturalism of Some Language Centered Accounts of Belief,” Dialectica 49 (1995): 113–29.

“A Philosophers Calling,” Proceedings and Addresses of the American Philosophical Association 84 (2010): 75–92.

Further Reading

Bio 20thC Phils, Blackwell Analytic Phil, Oxford Comp Phil, Pres Addr of APA v8, Women Phils

“Festschrift on Ruth Barcan Marcus,” Dialectica 55 no. 3/4 (1999).

Fetzer, James, and Paul Humphreys, eds. The New Theory of Reference: Kripke, Marcus and Its Origins (Dordrecht, 1998).

Hintikka, Jaakko, and Gabriel Sandu. “The Fallacies of the New Theory of Reference,” Synthese 104 (1995): 245–83.

Kripke, Saul. “Naming and Necessity,” in Semantics of Natural Language , ed. Donald Davidson and Gilbert Harman (Dordrecht, 1972): 253–325, 763–9.

Lambert, Karel. “Quantification and Existence,” Inquiry 6 (1963): 319–24.

Lewis, C. I. “Implication and the Algebra of Logic,” Mind 21 (1912): 522–33.

Lewis, C. I., and C. H. Langford. Symbolic Logic (New York, 1932).

Parsons, Terence. “Essentialism and Quantified Modal Logic,” Philosophical Review 78 (1969): 35–52.

Quine, W. V. Word and Object (Cambridge, Mass., 1960).

Quine, W. V., “Reply to Professor Marcus’ ‘Modalities and Intensional Languages’,” Synthese 13 (1961): 323–30.

Sinnott-Armstrong, Walter, Diana Raffman, and Nicholas Asher, eds. Modality, Morality, and Belief: Essays in Honor of Ruth Barcan Marcus (Cambridge, UK, 1995).

Smith, Quentin. “Marcus and the New Theory of Reference: A Reply to Scott Soames,” Synthese 104 (1995): 217–44.

Smullyan, Arthur. “Modality and Description,” Journal of Symbolic Logic 13 (1948): 31–7.

Williamson, Arthur. “In Memoriam: Ruth Barcan Marcus 1921–2012 ,” Bulletin of Symbolic Logic 19 (2013): 123–126.