Ruth Barcan Marcus (1921–2012) was one of the most influentialphilosophers of the second half of the twentieth century. Her first1946 publication contains the first published construction of formalsystems of quantified modal logic.^[1] Her pioneering formal work in quantified modal logic contributedcrucially to the initial development of the intensional logics. Italso helped to lay the foundation for the inception and blossoming ofmodal metaphysics, a fertile field of inquiry to which she also madesubstantial philosophical contributions.Marcus’s influential philosophical work extends beyondlogic and metaphysics. She has published significant work inepistemology, on belief and rationality, and in ethics, on moraldilemmas and deontic logic, and has contributed to Spinozian andRussellian scholarship. Her philosophical views—about language,essentialism, belief, and moral dilemmas—are deeply naturalisticand eschew rationalistic idealizations.

Barcan Marcus was an actively engaged and authoritative participant insome of the main and most-heated philosophical debates taking placefrom the 1950s to the end of the last century. In the fifties andsixties, in formidable opposition to Quine, she crucially contributedto establishing the legitimacy of modal logic and thus of modalmetaphysics. Her work bridges two very different philosophical erasand paves the way for the philosophical revolutions, in philosophy oflanguage and metaphysics, of the seventies. As a rare female logicianand philosopher, and of a rare caliber too, she was also a pioneeracademic, an active participant in the life of the profession,determined to reform and improve its institutions.

This entry focuses on Ruth Barcan Marcus’s key contributions toformal logic, metaphysics, epistemology and ethics. It engages withthe controversies in which she was involved only insofar as they arerelevant to her philosophical development. In this entry Ruth BarcanMarcus is sometimes called Barcan, sometimes Marcus, and sometimesBarcan Marcus, mainly according to the temporal context, in a way thatshould sound natural and generate no confusion.

• 1. Life
• 2 Early Formal Work
  • 2.1 Quantified Modal Logic
  • 2.2 Deducibility and the Deduction Theorem
  • 2.3 The Necessity of Identity
• 3 The Dispute with Quine
• 4 Intensionality, Ontology, Names and Quantifiers
  • 4.1 Intensionality and Extensionality
  • 4.2 Ontology: Individuals, Classes and Attributes
  • 4.3 Names
  • 4.4 Quantifiers
• 5 Essentialism
  • 5.1 Quantified Modal Logic and Essentialism
  • 5.2 Genuine Aristotelian Essentialism
• 6 Actualism and the Barcan Formula
• 7 Belief and Rationality
• 8 Moral Dilemmas
• Bibliography
  • Barcan Marcus’s Corpus
    • Published as Ruth C. Barcan
    • Published as Ruth Barcan Marcus
    • Coauthored Work
    • Festschriften
  • Secondary Literature
• Academic Tools
• Other Internet Resources
• Related Entries

1. Life

The main written source of information on Ruth Barcan Marcus’spersonal and professional life is her Dewey Lecture “APhilosopher’s Calling” delivered at the Eastern APAmeeting on December 29, 2009 (Marcus 2010).

Marcus was born Ruth Charlotte Barcan in New York on August 2, 1921 tosecular Jews of Eastern European descent. The third of threedaughters, she grew up in the Bronx in an activist socialisthousehold. She describes 1930 as a catastrophic year when her fatherdied in the midst of the Great Depression, leaving the now all-femalefamily in economic and emotional distress but also freer to followunconventional paths. Marcus emerges from her own recollection as avivacious, unruly, athletic and intelligent child with a voraciousappetite for knowledge. After high-school, she enrolled at New YorkUniversity, instead of attending a college for women as expected. AtNYU she majored in philosophy and mathematics. Of her teachers at thetime, the most influential was J.C.C. McKinsey who, clearly aware ofher talent, tutored her in advanced mathematical logic. She developedan interest in C.I. Lewis’s modal systems, and McKinsey advisedher to continue her studies at Yale under the supervision of F.B.Fitch. She started Yale’s graduate program in 1942 and receivedher PhD in 1946. At Yale, she met her future husband, Jules A. Marcus,at the time a graduate student in physics who was, like her, anaccomplished fencer. They married in 1942, had four children, anddivorced in 1976. At the time Yale accepted women in its graduateschool but not as undergraduates. Marcus recollects the paradoxicalsituation of female graders prohibited from entering the classroomsfor the undergraduate courses they assisted, and the embarrassment ofa library room accessible only to men. In this discriminatoryenvironment she was nonetheless elected president of the philosophystudents’ club. She reports receiving a letter from the chair ofthe department suggesting that she decline as well as having to workaround the logistic difficulties she faced as female president of anassociation used to meeting in a location closed to women. Herattitude in the face of such difficulties seems to have been one ofhealthy disregard. Marcus completed her dissertationA StrictFunctional Calculus in 1946, and that same year she startedpublishing parts of it as articles in theJournal of SymbolicLogic, under Alonzo Church’s editorship.

Starting in 1944 Marcus followed her husband who pursued his academiccareer as a physicist. In 1947 they moved to Chicago where she held apost-doctoral fellowship from the American Association of UniversityWomen and took the opportunity to study with Rudolf Carnap, who inthose years was also working on the modalities and quantification. In1949 her husband was hired at Northwestern University and they movedto Evanston. Marcus reports that at the time Northwestern Universityhad an anti-nepotism policy excluding the regular appointment offaculty spouses and that for some years she did not seek a regularfull-time academic position. She held instead various part-time andvisiting positions, while continuing to work on intensionality and theinterpretation of modal languages. In 1953 she received a GuggenheimFellowship. Beyond Carnap, Marcus recollects philosophically fruitfulexchanges with Leonard Linsky at Chicago University, as well as DavidKaplan who visited Chicago in those years, and Arthur Prior whoseseminar she attended in 1961. That same year, she presented the paper“Modalities and Intensional Languages” at the BostonColloquium in Philosophy of Science, followed by a discussion withQuine, Kripke, Føllesdal and McCarthy. In 1962 she presented apaper on sets and attributes at the famed Helsinki “Colloquiumon Modal and Many-Valued Logics”. In 1964, the University ofIllinois opened its Chicago campus, and Marcus was hired to chair itsnew department of philosophy. For six years, she played a leading rolein building a strong graduate department. From 1970 to 1973 she was aprofessor at Northwestern University.

In 1973 Marcus agreed to join and help rebuild the Yale philosophydepartment, a department she describes as unsettled and uneven, butalso as her academic home, a home she never left despite flatteringcompeting offers and much travel for temporary positions at otherinstitutions. Marcus had by now built a distinguished philosophicalreputation as a leading figure in her field. Throughout the rest ofher career she received numerous awards, fellowships, and honors, likethe Medal of the Collège de France in 1986, an honorarydoctorate of humane letters by the University of Illinois in 1995, andthe Yale Graduate School’s Wilbur Cross Medal in 2000. She wasthe first recipient of the APA Quinn Prize for service to theprofession in 2007, and the first female recipient of the LauenerPrize for an Outstanding Ouevre in Analytical Philosophy in 2008.Marcus retired from Yale in 1992, but remained active in theprofession and held a regular one-term-per-year Distinguished VisitingProfessor position at the University of California, Irvine. Aside fromthe crucial roles she played in building the philosophy departments ofthe University of Illinois Chicago and Yale, throughout her careerMarcus was committed to service to the profession. Notably, startingin 1961 she served for fifteen years in the American PhilosophicalAssociation, first as secretary and then president of its CentralDivision, and finally as chair of its National Board of Officers(1977–1983). She was also vice president (1980–83) andpresident (1983–86) of the Association of Symbolic Logic. Shedied in New Haven on February 19, 2012.

In her Dewey Lecture Marcus recollects fondly the joy of teaching toundergraduates, some of whom, like some of her graduate students, wenton to distinguished philosophical careers. Concerning herphilosophical style, she describes herself as a philosopher not drawnto big philosophical questions, but driven instead by “commonsense observations, couched in our common, ordinary language”.Unfond of philosophical labels, she found herself naturally inclinedto naturalistic views. Despite her active academic life, her collegialattitude and her many philosophical friendships, she ultimatelyregarded herself as “essentially a loner” who was“not driven to publish” unless she thought she hadsomething useful, interesting and clear to say.

On Marcus’s life and work, see also Marcus 1993: ix–xi,Lauener 1999: 173–177, Marcus 2005 which contains an interviewon Marcus’s formal work, Hull 2013, Williamson 2013a, andFrauchiger 2015 which contains a biographical proem by Frauchiger, aLaudatio by Williamson and an interview with Marcus.Cresswell 2001 is a brief summary of the main topics of Marcus’sphilosophy.

Note: For the remainder of the entry, at the beginning ofeach section (or subsection), Marcus’s papers most relevant tothe topic of the section are listed. This does not imply that Marcustreated that topic exclusively in those papers. On the contrary,throughout her published work Marcus often returns to the central,interconnected themes of her philosophy.

This entry examines Barcan Marcus’s work mostly as originallypublished. It does not scrupulously track later revisions and does notattempt to reconstruct whether those revisions simply clarify ormarginally alter the original points.

2. Early Formal Work

This section surveys Marcus’s early formal papers, publishedfrom 1946 to 1953 inThe Journal of Symbolic Logic, andexamines two of their key results: the proofs of the deduction theoremfor S4 and of the necessity of identity. The most relevant papers are:“A Functional Calculus of First Order Based on StrictImplication” (1946a), “The Deduction Theorem in aFunctional Calculus of First Order Based on Strict Implication”(1946b), “The Identity of Individuals in a Strict FunctionalCalculus of Second Order” (1947) and “Strict Implication,Deducibility and the Deduction Theorem” (1953). This is the mosttechnical section of the entry, and may be skipped by readers who areless concerned with Marcus’s achievements in modal logic.

2.1 Quantified Modal Logic

1946 was a good year for modal logic. Barcan’s “AFunctional Calculus of First Order Based on Strict Implication”appeared in the first issue of the 1946 volume ofThe Journal ofSymbolic Logic, soon followed by Carnap’s “Modalitiesand Quantification” in the second, and Barcan’s “TheDeduction Theorem in a Functional Calculus of First Order Based onStrict Implication” in the fourth. Barcan’s first paperextends the propositional system S2, which C.I. Lewis had singled outas the best system for formalizing the notion of deduction in theobject language (Appendix of Lewis & Langford 1932).

For the propositional part, Barcan follows exactly Lewis’saxiomatization of the system, which she supplements with axioms andrules for quantification. Most of the axioms are versions of standardpropositional and quantified axioms, but formulated for strict insteadof material implication.^[2]

Barcan uses Greek letters in the metalanguage: upper case Greekletters represent well-formed formulas (wff’s) and lower caseGreek letters represent (individual, propositional and functional)variables. Axioms are given as schemata, thus eliminating the need forLewis’s rule of uniform substitution. Negation, conjunction, theexistential quantifier and the possibility operator (the diamond\(\modalD\)) are taken as primitive. Disjunction, material implication(the conditional), material equivalence (the biconditional), theuniversal quantifier and the necessity operator (the box \(\modalB\))are defined in their terms. \((A \Rightarrow B)\) is defined as\(\nsim\modalD (A \land \nsim B)\), which is equivalent to \(\modalB(A \rightarrow B)\).

Though formulated for strict implication (\(\Rightarrow\)), mostaxioms, as well as the rules, are standard for non-modal systems. Thepurely modal additions areAxiom 7, the so-called consistency axiom characteristic of S2, andAxiom 11, the Barcan formula, as Prior will later dub it (1956: 60).

The rest of the paper proceeds purely syntactically. Among otherresults, Barcan proves the converse of the Barcan formula:

System S2 is not strong enough to prove BF, which is thus assumed asan axiom. In these early papers, Barcan does not discuss the semanticsignificance of the Barcan formula (BF) and its converse (CBF).

The paper ends with a brief discussion of the stronger system S4 whichextends S2 by the addition of its characteristic axiom\(\vdash\modalD\modalD A \Rightarrow \modalD A\) (axiom 4 in currentterminology) equivalent to \(\vdash\modalB A \Rightarrow\modalB\modalB A\), and includes the proof of a key theorem (XIX*)which together with axiom 4 will be employed to prove the deductiontheorem for S4.

2.2 Deducibility and the Deduction Theorem

In her second 1946 paper, “The Deduction Theorem in a FunctionalCalculus of First Order Based on Strict Implication”, Barcanproves that the deduction theorem fails for S2 both for material andfor strict implication. She proves this for the quantified systemS2¹, but her result holds already for propositional S2, andis independent from quantification.

The deduction theorem holds for a system S if whenever \(A_1, A_2,\ldots , A_n \vdash B\) holds for S, so does \(A_1, A_2, \ldots ,A_{n-1} \vdash A_n \rightarrow B\), andvice versa.Marcus’s focus is on the left-to-right direction (explicitlystated here). The deduction theorem is standardly stated for thematerial conditional, but in her papers Marcus is chiefly concernedwith the deduction theorem for the strict conditional, that is,whether in her modal systems it is the case that given \(A_1, A_2,\ldots , A_n \vdash B\), then \(A_1, A_2, \ldots , A_{n-1} \vdash A_n\Rightarrow B\) also holds. Her interest in the theorem is notproof-theoretical, i.e., it is not related to conditional derivations,which the deduction theorem justifies, and the possibility of devisingnatural deduction systems for modal logics. Rather, her focus is onthe interpretation of strict implication. On the history andsignificance of the deduction theorem, see Franks 2021; on thededuction theorem in modal logic, see Hakli and Negri 2012; on naturaldeduction for modal logic see Fitch 1952: ch. 3; Fitting 2007; Zeman(1973: 197) is critical of the whole idea of a deduction theorem forthe strict conditional.

Barcan’s proof that the deduction theorem does not hold for S2employs a matrix by Parry (1934) which satisfies all the axioms andrules of S2, but not the characteristic axiom of S3:

Parry’s result establishes that S3 is a stronger system than S2.Barcan points out that it also establishes that the deduction theoremfails for S2, given that in S2 the following holds:

but

does not hold.

The failure of the deduction theorem for S2 means that for someformulas \(A_1\), \(A_2\), …, \(A_n\) and \(B\), (1) holds, butneither (2) nor (3) does:

For S4 (S4¹) instead, Barcan proves the full deductiontheorem for the material conditional, i.e., for S4 (2) holds whenever(1) does.

For the strict conditional, Barcan proves the following restricteddeduction theorem for S4:

XXIX*.

If \(A_1, A_2, \ldots , A_n \vdash B\) and if \[\begin{align*}\vdash A_1 & \Leftrightarrow \modalB\Gamma_1,\\ \vdash A_2 & \Leftrightarrow \modalB\Gamma_2,\\ &\;\;\vdots\\ \vdash A_n &\Leftrightarrow \modalB\Gamma_n,\\ \end{align*}\] then\(A_1, A_2, \ldots , A_{n-1} \vdash A_n \Rightarrow B\).

Thus, Barcan concludes that the proof of the deduction theorem forstrict implication goes through only for arguments whose premises areprovably equivalent to necessities.

In her 1953 paper “Strict Implication, Deducibility and theDeduction Theorem” Barcan focuses exclusively on S4 anddistinguishes three forms of the deduction theorem for any notion\(\notionI\) of implication, including the material and strictconditional:

I.

If \(A_1, A_2, \ldots , A_n \vdash B\) then \(A_1, A_2, \ldots ,A_{n-1} \vdash A_n \notionI B\)

II.

If \(A_1, A_2, \ldots , A_n \vdash B\) then \(\vdash (A_1\land A_2\land \ldots \land A_{n-1} \land A_n) \notionI B\)

III.

If \(A_1\vdash B\) then \(\vdash A_1 \notionI B\)

In 1946 her focus was just ontheorem I. She now proves thatII andIII hold unrestrictedly for strict implication too, that is, they holdeven from premises that are not provably equivalent to necessities.The stronger form of the deduction theorem I instead cannot besimilarly proved and the restriction to necessary premises remains inplace.

In her 1953 paper, Barcan also discusses interpretative questions. Inthese early papers she, like Lewis, interprets modal systems asdesigned to represent and formalize a system-independent,proof-theoretic notion of deducibility or entailment. Strictimplication (\(\Rightarrow\)) represents this target notion. In theformal systems, the notion of consistency, represented by the\(\modalD\) sign, is taken as primitive, and strict implication isdefined in its terms: if \((A \land \nsim B)\) is inconsistent, i.e.,\(\neg\modalD (A \land \nsim B)\), then \(A\) strictly implies \(B\),i.e., \((A\Rightarrow B)\). Necessity is similarly defined in terms of(in)consistency: if \(\nsim A\) is inconsistent, i.e.,\(\nsim\modalD\nsim A\), then \(A\) is necessary, i.e., \(\modalB A\).The interpretative focus on strict implication as deducibilityexplains why Lewis and Barcan did not set apart the non-modal basefrom the modal part of the systems, given that deducibility—thenotion the systems aim to formalize—is represented as strictimplication, which is not defined in terms of material implication. Italso explains the focus on the weaker non-normal systems.

In contrast, in his 1946 paper developing a system of quantified modallogic Carnap starts by briefly mentioning that \(\necessityN p\)(where “N” is the necessity operator) can be defined interms of Lewis’s \(\modalD\), but then immediately proceeds todefine all the logical modalities in terms of N and clearly takes theidea of logical necessity as the fundamental one also from aninterpretative point of view. Carnap also distinguishes thepropositional and the functional calculus from the modal calculi“constructed by the addition of ‘N’” (1946:33). This interpretative concern leads Carnap to focus on S5 andpropels his formal semantics. It is fair to say that Barcan and Carnapdeveloped independently the first quantified systems of modal logic inthe early 1940s, but at the time Barcan’s focus was syntacticaland her first published philosophical considerations (in 1953) werestill driven by Lewis’s interpretative concerns aboutdeducibility, itself a syntactic notion. However, in later work Barcanunderlines also Lewis’s informal interpretation of themodalities in terms of possible worlds (see 1968: 88; 1981b: 279;1990a: 232; and Frauchiger 2015: 149–150).

The 1953 paper challenges Lewis’s claim that S2 is the rightsystem to represent deducibility. Lewis had argued that S3 was toostrong and settled on S2. Barcan instead claims that the correctsystem must be such that at least some form of the deduction theoremfor strict implication holds for it. Thus, to be adequate a systemmust be at least as strong as S4. In fact, only a normal system withthe rule of necessitation will have the strength to prove some versionof the deduction theorem for the strict conditional. However, Barcandoes not elaborate on why she thinks that the deduction theorem musthold if deducibility is to be properly represented.

2.3 The Necessity of Identity

In the third paper derived from her dissertation, “The Identityof Individuals in a Strict Functional Calculus of Second Order”(1947), Barcan proves a series of results concerning the necessity ofidentity in S2² and S4², the second orderextensions of S2¹ and S4¹.

The paper starts by extending the previous systems by allowing thequantifiers to bind propositional and first-order functionalvariables. Definitions, axioms and rules are correspondingly extended.The abstraction operator \(\hat{}\) is introduced to abstract termsfor properties and relations from formulas, with this axiom:

\(2.3\)

\(\hat\alpha_1\hat\alpha_2 \ldots \hat\alpha_n A(\beta_1\beta_2\ldots \beta_n) \Leftrightarrow B\) where \(\alpha_1\), \(\alpha_2\),…, \(\alpha_n\) are distinct individual variables occurringfreely in \(A\), no free occurrence of \(\alpha_m (1\leqq m \leqq n)\)in \(A\) is in a wf part of \(A\) of the form \((\beta_m)\Gamma\), and\(B\) results from \(A\) by replacing all free occurrences of\(\alpha_1\) by \(\beta_1\), all free occurrences of \(\alpha_2\) by\(\beta_2\), …, all free occurrences of \(\alpha_n\) by\(\beta_n\) in \(A\). (1947: 13)

If \(A\) and \(B\) are as in2.3, \(\hat\alpha_1\hat\alpha_2 \ldots \hat\alpha_n A\) is the abstract of\(B\). For example, starting from a formula\(A\beta\) (corresponding to \(B\) in2.3), \(\hat\alpha A\alpha\) is its abstract, and \(\hat\alphaA\alpha(\beta)\) is strictly equivalent to \(A\beta\).

Barcan introduces two identity relations (and their negations),material identity and unqualified identity, defined as follows interms of indiscernibility:

From which the following theorems follow:^[3]

and

So, by definition an object \(\beta_2\) is materially identical to\(\beta_1\) just in case it has all the properties of \(\beta_1\); and\(\beta_2\) is identical to \(\beta_1\) just in case for any propertyof \(\beta_1\) it is necessary that \(\beta_2\) bears it too.^[4] From this it follows, given symmetry, that material identity consistsin actually sharing all properties and identity consists innecessarily sharing all properties. Various other theorems are statedwithout proof, including the reflexivity, symmetry and transitivity ofboth material identity and identity.

The following are the S2² results pertaining to (thenecessity of) identity and material identity proved or stated byBarcan.

Barcan does not take identity as primitive, so neither \ref{th2.6} nor\ref{th2.18} are axioms. The proof of \ref{th2.6} must clearly startfrom \(\vdash (\Phi \beta \Leftrightarrow \Phi \beta)\) (recall thatBarcan’s systems are axiomatized for strict implication) andmake use of second-order universal generalization and of theorem\ref{th2.5}. \ref{th2.18} can be similarly derived but using also\(\vdash (\modalB A \Rightarrow A)\) (a theorem of S2 for Barcan, nowstandardly assumed as axiom T) to get \(\vdash (\Phi \beta\leftrightarrow \Phi \beta)\). Finally, \ref{th2.24} can be derivedfrom \ref{th2.6} using this instance of the second-order Barcanformula (not by necessitation of \ref{th2.18} as necessitation is nota valid S2 rule):

Recall that \((\forall \theta) \modalB(\theta(\beta)\rightarrow\theta(\beta))\) is none but \((\forall\theta) (\theta(\beta)\Rightarrow\theta(\beta))\), the definiens of(strict) identity. The consequent is the necessitation of thedefiniens of material identity. Barcan states without proof these‘unexciting’ results. She doesn’t even prove thestrict equivalence of identity to the necessity of materialidentity:

as its proof clearly depends just on the second-order BF and CBF,given that by definition \(\modalB (\beta_1 \mID \beta_2)\) and\((\beta_1 \uID \beta_2)\) are equivalent to \(\modalB (\forall\theta) (\theta(\beta_1)\leftrightarrow \theta(\beta_2))\) and\((\forall \theta) \modalB(\theta(\beta_1)\leftrightarrow\theta(\beta_2))\), respectively. So,by the second-order CBF (the left-to-right direction) if it isnecessary that \(\beta_1\) and \(\beta_2\) are indiscernible, namelythat they share all their properties, then it strictly follows thatall properties are necessarily shared by them, i.e., no property candifferentiate them. And by the second-order BF (the right-to-leftdirection) if no property can differentiate \(\beta_1\) and\(\beta_2\), then it strictly follows that they are necessarilyindiscernible. This result is model-theoretically guaranteed if thesecond-order quantifiers range over an invariant domain of properties(and relations) assigned to all the worlds of a model.

This must have been Barcan’s assumed reading as it matches herreading of the first-order quantifiers (seesection 6 of this entry) and is quite natural in the second-order case. On analternative reading, assigning to each world its domain of propertiesand relations, the result holds if the world-relative domains areconstant: in this case \ref{ex2.23} can be read as stating theequivalence between the possibility that a property distinguishes\(\beta_1\) and \(\beta_2\) and some actual property possiblydistinguishing them.

Barcan’s focus is on the more interesting result that identitycan be proved to be equivalent to material identity (and not just tothe necessity of material identity as in \ref{ex2.23}). Theirequivalence is material (\(\leftrightarrow\)) in S2² andstrict (\(\Leftrightarrow\)) in S4² (1947: 15). Thefollowing is Barcan’s proof of the material equivalence ofmaterial identity and identity in S2².^[5]

Thefirst step of the proof follows from the definition of \(\mID\). If \(\beta_2\) is materiallyidentical to \(\beta_1\), it has all the properties of \(\beta_1\).So, if one of \(\beta_1\)’s properties is to be strictly, thatis, necessarily identical to \(\beta_1\), i.e., \(\hat\alpha(\beta_1\uID \alpha)\), then \(\beta_2\) has that property too. Theabstraction axiom is also needed to transform expressions like\(\hat\alpha(\beta_1 \uID \alpha)(\beta)\) into \((\beta_1 \uID\beta)\). Given \ref{th2.6}, that is \(\vdash \beta_1 \uID \beta_1\),step 2 follows from 1.Step 3 follows from \(\vdash \modalB (\beta_1 \mID \beta_2) \Rightarrow(\beta_1 \mID \beta_2)\) and \ref{ex2.23}, the equivalence of identityto the necessity of material identity: if the necessity of materialidentity strictly and so materially implies material identity so doesidentity, by substitutivity of equivalents.Step 4 combines 2 and 3.

The interesting part of the proof is the first two steps proving theleft-to-right direction, where we move from the statement that\(\beta_1\) and \(\beta_2\) are actually indiscernible to their beingnecessarily indiscernible (as far as actual properties are concerned,if the domain of properties is world-relative). This direction is theone for which in S2² only the material conditional holds.Barcan’s proof of this result will inevitably remind us ofKripke’s proof of the necessity of identity in the opening pagesof “Identity and Necessity” (1971). Barcan’s andKripke’s proofs have a similar structure. We start with (someform of) identity betweenx andy implying theirindiscernibility, and given that one of the properties ofxis to be (in some sense) necessarily identical tox weconclude thaty too bears that property. But there aredifferences too. Kripke’s starting point is primitive identitywhich implies indiscernibility (by Leibniz Law) but is not defined inits terms. So, Kripke derives the unqualified necessity of identity.Barcan’s starting point is material identity defined asindiscernibility, no property differentiates the two objects, fromwhich it is derived that no property can differentiate them. Moreover,Kripke’s proof is not stated in terms of properties at all,rather necessary statements. Barcan’s is in terms of properties,though as referents of abstracts derived from formulas (on this pointsee Wiggins 1976a and 1976b). Also, as far as Barcan’s result isconcerned, the objects may indeed still be two ifI asdefined is still not genuine identity, i.e., should necessaryindiscernibility not suffice for identity.

Next, Barcan proves the following results which hold only in thestronger system S4²: the strict equivalence of identity andthe necessity of identity (theorem \ref{ex2.32}) and the strictequivalence of identity and material identity (theorem\ref{ex2.33}).

Concerning the strict equivalence of identity and the necessity ofidentity, the proof makes use of the characteristic axiom of S4. Giventhe strict equivalence in S4 of \(\modalB A\) and \(\modalB\modalBA\), we have that the necessity of the necessity of material identityis strictly equivalent to the necessity of material identity \(\vdash\modalB \modalB (\beta_1 \mID \beta_2)\Leftrightarrow\modalB(\beta_1\mID \beta_2)\). And since the necessity of material identity isstrictly equivalent to identity (theorem \ref{ex2.23}) \((\beta_1 \uID\beta_2)\) can replace \(\modalB (\beta_1 \mID \beta_2)\) in the aboveequivalence, resulting in:

Concerning the strict equivalence of identity and materialidentity:

this is simply the necessitation of \ref{ex2.31} and necessitation isa valid S4 rule, though Barcan does not appear to be aware of thevalidity of necessitation in 1947. She first mentions the rule with areference to McKinsey and Tarski (1948) in her 1953 paper, whenshe uses it to extend her results on the deduction theorem for S4. So,her proof of \ref{ex2.33} is more complex and starts similarly to herproof of \ref{ex2.31}. For the hard left-to-right side, we startfrom

from which, given \(\vdash(\beta_1 \uID \beta_1)\), in S4 we canderive

Then given \(\vdash\modalB (\beta_1 \uID \beta_1)\), whose proofrequires \ref{ex2.32}, we can prove

From \ref{ex2.32} and \ref{ex2.33} it also follows that materialidentity is necessarily equivalent to the necessity of identity:

Figures 1 and 2 graphically represent the results holding forS2² and S4² respectively.

Figure 1: Valid implications inS2²

Figure 2: Valid implications inS4²

To sum up, in 1947 Barcan proves that in S4² the materialidentity of two objects necessarily implies not just their strictidentity and the necessity of their material identity, but also thenecessity of their strict identity, because \((\forall \theta)(\theta(\beta_1)\leftrightarrow\theta(\beta_2))\) strictly implies\(\modalB(\forall \theta)\modalB(\theta(\beta_1)\leftrightarrow\theta(\beta_2))\). This meansthat the actual indiscernibility of \(\beta_1\) and \(\beta_2\)implies the impossibility that any property might distinguishthem.

It is unclear which of Barcan’s two main theorems, that materialidentity implies strict identity or that strict identity implies thenecessity of strict identity, best deserves to be called the necessityof identity. The \(\beta_1 \mID \beta_2\) to \(\beta_1 \uID \beta_2\)implication moves from a non-modal notion to a modal one, yet thestarting point, material identity, can hardly be regarded as identity.On the other hand, the \(\beta_1 \uID \beta_2\) to \(\modalB(\beta_1\uID \beta_2)\) implication proves the necessity of a relation thathas a stronger claim to be called identity, but that is already a formof necessity to start with, and hence requires axiom 4 to beestablished.

This however does not detract from the fact that Barcan’s proofsincorporate the key idea that given the indiscernibility of twoobjects, their modal profiles will also go hand in hand, so thatnecessary properties (including the necessary identity to one of them)will also be shared.^[6] Moreover, Barcan immediately understood her result to simply be thenecessity of identity. For example already in her Review of Smullyanshe states and makes use of the following results: “\(N(\alpha =\alpha)\), \((\alpha = \beta)\Rightarrow(N(\alpha = \alpha)\rightarrowN(\alpha = \beta))\), \((\alpha = \beta)\Rightarrow N(\alpha =\beta)\)” (1948: 150).

Burgess (2014) emphasizes the differences between Barcan’s andKripke’s proofs of the necessity of identity and argues thatKripke’s distinct proof may ultimately derive from Quine’s(1953b, 1953c, 1961) search for a simpler proof than Barcan’s.Kripke too attributes the simpler, more standard proof to Quine(2017a: 233, fn. 9).

3. The Dispute with Quine

Marcus’s papers most relevant to this section are: “Reviewof ‘Modality and Description’ by Arthur FrancisSmullyan” (1948), “Modalities and IntensionalLanguages” (1961), “Discussion on the Paper of Ruth B.Marcus” (1962a), “Modal Logic” (1968), “ModalLogic, Modal Semantics and their Applications” (1981b), and“A Backward Look at Quine’s Animadversions onModalities” (1990a).

Starting in the early sixties, Ruth Barcan Marcus’s work becamefocused on the interpretation of modal systems. Much of this work wasin explicit opposition to what Marcus eventually called“Quine’s Animadversions on Modalities” (1990a).Quine (1946, 1947b and 1947c) had originally reviewed her first threepapers, and the friction with Quine was probably triggered by hisinitial review of her 1947 paper on the identity of individuals inmodal systems, of which he said:

Two relations of “identity” between individuals are thendefined. There is a weak one which holds between \(x\) and \(y\)wherever \((F)(Fx \rightarrow Fy)\), and a strong one which holds onlywhere \((F) (Fx \Rightarrow Fy)\). Various theorems concerning the twokinds of identity are derived.As is to be expected, only thestrong kind of identity is subject to a law of substitutivity validfor all modal contexts.

It should be noted that only the strong identity is thereforeinterpretable as identity in the ordinary sense of the word. Thesystem is accordingly best understood by reconstruing the so-calledindividuals as “individual concepts”. (Quine 1947c:95–96, emphasis added)

Marcus was justifiably unhappy with Quine’s failure toacknowledge that she had proved the equivalence of the two kinds ofidentity. The frustration is explicitly voiced in her 1960 paper“Extensionality”:

I am not (as Quine insists in his review of two of my papers onquantified modal logic) proposing that there be more than one kind ofidentity, but only that the distinctions between stronger and weakerequivalences be made explicit before, for one avowed purpose oranother, they are obliterated. (1960: 58)

Marcus voices her annoyance with Quine’s original review as lateas her final, posthumously-published interview with Frauchiger (2015:151) despite Quine’s admittedly rather laconic correction morethan fifty years earlier, of which this is the full text:

Correction to the review XII 95(4). Through some lapse, or possiblythe loss of a second proof sheet, the reviewer missed the last twentylines of the paper. As a result the first two sentences of page 96 inthe review are wrong. They should be supplanted by this: “It isshown that the strong and weak identity are actually coextensive; evenstrictly equivalent, on one choice of axioms”. (Quine 1958:342)

The recanted two sentences are those emphasized in the previousquotation from Quine’s original review.

The rest of this section focuses on Marcus’sphilosophical disputes with Quine, setting aside themisunderstandings and frustrations that at times accompanied thephilosophical exchange. Yet, the existence of some friction with Quineand its apparent initial cause needed to be made explicit before, inMarcus’s own words, being obliterated for “one avowedpurpose or another”—in our case a dispassionateexamination of Marcus’s impressive achievements in philosophy. Areconstruction of the history of this particular initialmisunderstanding on identity, plausibly caused by the loss of a proofsheet, can be found in Burgess (2014); Strassfeld (2022) emphasizesthe sociological and arguably gendered aspects of this impasse.

In her published work Marcus more than once voiced her overalldisheartenment with Quine’s criticisms of the modalities, whichshe felt were like a moving target impossible to pin down. The mirrorfrustration that his most basic points did not come across isexpressed by Quine (1961). Still, Marcus often presents her views inexplicit or implicit opposition to Quine’s and acknowledges thatQuine’s “criticisms and the continuing debate were acatalyst for some of my subsequent work” (1993: x). Thus, someknowledge of Quine’s criticisms of the modalities is required inorder to situate and better understand Marcus’s own thoughtwhich stands in systematic contraposition to Quine’s on acluster of interrelated topics, mainly the fruitfulness of modallogic, the distinction between extensionality and intensionality, thesemantics of proper names and quantifiers, the interpretation of themodalities and essentialism.

Quine first fully voiced his objections to intensional discourse inhis 1943 “Notes on Existence and Necessity” where hepointed out that the law of substitutivity, according to whichcoreferential expressions are substitutable salva veritate, fails inthese contexts. This is problematic as the law of substitutivity isthe linguistic counterpart of the indisputable logico-metaphysicalprinciple of the indiscernibility of identicals, according to which ifa is the same asb anda isF thenb isF. Indeed Quine identifies the two principles(1943: 113). Clear problematic contexts are quotations, where“‘Tully’ has 6 letters” does not follow from“Cicero = Tully” and “‘Cicero’ has 6letters”; and epistemic contexts like “knows that”and “believes that”, where for example “Philip isunaware that Tully denounced Catiline” may be true even if“Philip is unaware that Cicero denounced Catiline” isfalse. To these contexts Quine adds modal contexts when the modalitiesare interpreted as analytic or logical. From the true statements“The number of planets = 9” and “9 is necessarilygreater than 7”, understood as “‘9 is greater than7’ is analytic”, the truth of “The number of planetsis necessarily greater than 7” does not follow given that“The number of planets is greater than 7” is not ananalytic statement.

Additionally, Quine regards quantification across intensionaloperators as meaningless. For example, assuming that the existentialquantifier expresses existence—a given for Quine (1943:116)—“\(\exists x\) (Philip is unaware that \(x\)denounced Catiline)” cannot be properly interpreted, for“What is this object, that denounced Catiline without Philip yethaving become aware of the fact? Tully, i.e., Cicero?” (1943:118). Quine claims that for quotations “this paradox resolvesitself immediately. The fact is that [“‘Cicero’contains six letters”] is not a statement about the personCicero, but simply about the word ‘Cicero’” (1943:114). Quotations induce a shift of reference, from the object to itsname, thus substitutivity between expressions that refer to the samename, as well as quantification over names, can be reinstated. Quinehowever does not extend this kind of solution to the other problematiccontexts, of which he says:

The effect of these considerations is rather to raise questions thanto answer them. The one important result is the recognition that anyintensional mode of statement composition … must be carefullyexamined in relation to its susceptibility to quantification. (1943:124–125)

For more details on Quine’s criticisms of modal logic, Marcus(1990a) offers her own historical reconstruction. See also Kaplan1986, Fine 1990, Burgess 1997, Neale 2000, and Ballarin 2004,2012, and 2021. On the Quine-Marcus debate see Janssen-Lauret2016 and 2022.

Alonzo Church, in his 1943 review of Quine’s “Notes onExistence and Necessity”, pointed out the affinity ofQuine’s opaque contexts to Frege’s oblique ones in“Sense and Reference” (1892 [1948]) and suggested aFregean solution to Quine’s concerns, namely, a shift ofreference: variables within an intensional context can be bound toquantifiers external to the intensional operator if they range overintensional entities, e.g., attributes rather than classes (1943: 46).Quine, though himself skeptical of intensions, came to accept theFregean solution as adequate to reconcile the logico-analyticmodalities with quantification, before eventually rejecting it asinadequate to the task. This explains Quine’s suggestion in hisinitial review of Barcan’s identity paper that her “systemis … best understood by reconstruing the so-called individualsas individual ‘concepts’”.

Yet, Marcus never endorsed indirect, Fregean interpretations of themodalities, of which she said:

The swelling of ontology was for Quine aprima facie groundfor rejection. For me the ground for rejection was the systematicambiguity. (1990a: 233)

And

A forced Fregean shift relative to context would itself be a criticismand a sufficient deterrent. I took reference as univocal in and out ofmodal contexts. (1990a: 233)

Her work is embedded in the Russellian tradition and she stronglyresists the claim that intensional entities are required to interpretmodal discourse. In fact, Marcus immediately subscribed toSmullyan’s (1947 and 1948) claim that Quine’s problems ofsubstitutivity in intensional contexts are spurious. When the singularterms are genuine proper names they can be substituted withinintensional contexts too. When they are descriptions, the sentences inwhich they occur should be analyzed Russell’s way and there willbe scope ambiguities. For example, “Necessarily 9 is greaterthan 7” is true and any other name of 9 can be replacedsalva veritate. Yet, from it we cannot derive“Necessarily the number of planets is greater than 7” bysubstitution as “the number of planets” is not a name.Moreover, the analysis of this last statement uncovers two distinctreadings: the true “There is a unique thing that numbers theplanets and it is necessarily greater than 7” and the false“Necessarily there is a unique thing that numbers the planetsand it is greater than 7”. This Russellian solution wasanticipated, though not endorsed, by Church (1942) and will be laterendorsed by Fitch (1949) too. Marcus claims:

In the reviewer’s opinion, Smullyan is justified in hiscontention that the solution of Quine’s dilemma does not requireany radical departure from a system such as that ofPrincipiaMathematica. Indeed, since such a solution is available, it wouldseem to be an argument in favor of Russell’s method ofintroducing abstracts and descriptions. (1948: 150)

Prompted by Marcus herself, Quine eventually came to recognize thisand finally stated:

The system presented in Miss Barcan’s pioneer papers onquantified modal logic differed from the systems of Carnap and Churchin imposing no special limitations on the values of variables. (1953b:156)

However, he immediately added:

That she was prepared, moreover, to accept the essentialistpresuppositions seems rather hinted in her theorem:

\[(x)(y) ((x=y)\rightarrow (\textit{necessarily} (x=y))),\]

for this is as if to say that some at least (and in fact at most…) of the traits that determine an object do so necessarily.(1953b: 156)

The real problem for Quine is not substitutivity, of names ordescriptions, but the interpretation of quantification acrossintensional operators. In the case of the modalities, the problem, heclaims, is ontological and the result is Aristotelian essentialism.Section 4 of this entry analyzes Marcus’s views of intensionality, names,and quantifiers;section 5 discusses her interpretation of Aristotelian essentialism. We willsee that on all these topics Marcus explicitly dissents from Quine.But before we do that, let us be clear on the very fundamental natureof their disagreement.

One of the few things on which Quine and Marcus agree is the value offormal logic, and they both oppose philosophers like Strawson who areskeptical of it. Yet, Marcus sharply criticizes Quine’sstrictures against the development of formal systems beyondfirst-order logic, which he regards as philosophically unhelpful(Quine 1990). These strictures weaken the position of the formalphilosophers and are detrimental to philosophical progress. Of her ownstand on logic, she says: “I for one have no aversion for anykind of logic” (1963b: 327).

In the opening section of her seminal 1961 paper “Modalities andIntensional Languages”—which anticipates many of hercentral insights on the modalities further developed in subsequentwork—in open opposition to Quine’s defeatist attitudetowards the new quantified modal systems, Marcus states:

I do claim that modal logic is worthy of defense, for it is useful inconnection with many interesting and important questions such as theanalysis of causation, entailment, obligation and belief statements,to name only a few.

If we insist on equating formal logic with strongly extensionalfunctional calculi then Strawson is correct in saying that “theanalytical equipment (of the formal logician) is inadequate for thedissection of most ordinary types of empirical statement”.(1961: 303)

This theme permeates also Marcus’s 1962 paper“Interpreting Quantification”.

Of Quine’s attitude towards opaque contexts, Marcus says:

All such contexts are dumped indiscriminately onto a shelf labelled“referential opacity” or more precisely “contextswhich confer referential opacity”, and are disposed of. But thecontents of that shelf are of enormous interest to some of us and wewould like to examine them in a systematic and formal manner. (1961:306)

In “Modal Logic” (1968) and “Modal Logic, ModalSemantics and their Applications” (1981b), Marcus offers her ownreconstruction of the development of modal logic from C.I. Lewis on.She also mentions the controversies that accompanied the earlydevelopment of quantified modal logic (QML)—failure ofsubstitutivity, problems with quantification, commitment toessentialism, an intensional ontology etc.—and sketches somereplies. But most importantly, she always stresses her persuasion thatthe development of different systems of modal logic, and of formalsemantics, is essential to philosophical progress on a cluster oftopics. In her view, one of the primary motivations for the syntacticconstruction of modal systems “was to give a more systematicaccount of some intuitive conceptions of logical or more generally,metaphysical necessity and possibility” (1981b: 281); similarlyfor alternative interpretations of the operators: causal, temporal,epistemic, deontic, etc. Moreover, the formal semantics of thesesystems is essential to philosophical progress on these topics:

The adequacy of such systems was generally tested against theirintuitive acceptability when translated into ordinary language. Howwell for example did they fit “moral facts” or“epistemic facts”? The development of model theoreticsemantics for modal logic provided a new perspicuous approach to thevariant interpretations of the modalities. (1981b: 290)

Additionally, Marcus emphasizes that not just ordinary but alsoscientific languages employ natural-kind terms and thus seem torequire “languages within which essentialist truths can beframed” (1981b: 285). In her mind, Quine is not only wrong aboutlogic, he is wrong about (the alleged extensionality of) sciencetoo.

4. Intensionality, Ontology, Names and Quantifiers

4.1 Intensionality and Extensionality

Marcus’s papers most relevant to this subsection are:“Extensionality” (1960), “Modalities and IntensionalLanguages” (1961) and “Does the Principle ofSubstitutivity Rest on a Mistake?” (1975). Of marginal interestis also the short 1950 paper “The Elimination of ContextuallyDefined Predicates in a Modal System” where Marcus replies toBergmann’s (1948: 141) claim that contextually definedpredicates are not eliminable in non-extensional languages. In reply,Marcus shows that contextually defined predicates can be eliminatedfrom modal languages if (i) we abandon the principle of extensionalitythat takes materially equivalent predicates to be identical, (ii)replace it with the intensional principle that the identity ofpredicates requires their necessary equivalence, and (iii) takedefinitions to give rise to necessary equivalences. She proves theresult for the modal functional calculus of fourth orderS4⁴.

According to Marcus, there is no absolute principle of extensionality,rather there are degrees of extensionality, and correspondingly ofintensionality. A language or theory is extensional insofar as itreduces a stronger equivalence relation to a weaker one. For objects,this means reducing identity to some form of indiscernibility:

Our notion of intensionality does not divide languages into mutuallyexclusive classes but rather orders them loosely as strongly or weaklyintensional. A language is explicitly intensional to the degree towhich it does not equate the identity relation with some weaker formof equivalence. (1961: 304)

Marcus holds that identity applies only to objects/things/individuals.However, “the identity relation does notconferthinghood” (1986b: 118). Things must exists before they canenter into any relation, including identity. Interestingly, in the1960s Marcus uses the standard identity sign “=” forequality, and reserves “I” for identity. Classesand attributes instead may be equal (to a certain degree) but notidentical:

The concept of identity inPrincipia is systematicallyambiguous not only as prescribed by the theory of types, but on thesame type level. In the second order predicate calculus,“identity” means something different for classes than forattributes, and has still another import for individuals. Mypreference is for the alternative procedure of giving uniform meaningto “identity” and to talk of attributes and classes asbeing equal, but not identical. (1960: 58)

She additionally claims that a language confers“thinghood” to attributes, classes or propositions if itallows identity to hold between them (1961: 304).

Concerning identity, a theory is extensional to the degree to which itreduces it to some form of indiscernibility, either material orstrict. A theory that reduces identity to material indiscernibility ismore extensional than a theory that reduces identity to strictindiscernibility. Further reductions are possible too: a language witha limited stock of predicates may be unable to distinguish congruentobjects or objects that weigh the same, etc. Additionally, thereduction of identity to a particular form of equivalence can be moreor less strong. For example, the claim that ifx andy are strictly indiscernible then they are identical is moreor less strong according to the strength of the conditional, which canbe interpreted as material, strict or even as metalinguistic. So, herown modal languages S2² and S4² were to acertain degree extensional insofar as they defined identity as strictindiscernibility. They were also more extensional than languages withepistemic operators, insofar as strictly equivalent expressions areintersubstitutable in modal but not epistemic contexts:

[E]ven on the level of propositions, we cannot talk of the thesis ofextensionality but only of stronger and weaker extensionalityprinciples. I will call a principle extensional if it …directly or indirectly imposes restrictions on the possible values ofthe functional variables such that some intensional functions areprohibited … (1960: 56–57)

A language that explicitly excludes certain operators, e.g.,epistemic, is directly extensional. Indirectly, languages areimplicitly extensional according to the substitutivity theorems theyendorse (1961: 306). For example, a language where truth-functionallyequivalent sentences are intersubstitutable is more extensional than alanguage with contexts where truth-functional equivalence doesnot warrant substitutivity. The less strict substitutivity principleof the first language implies an exclusion of modal predicates. And inturn a language where strict equivalence warrants substitutivity ismore extensional than a language with contexts where strictlyequivalent expressions are not interchangeable, as it implicitlyexcludes epistemic predicates.

Of particular interest is not only Marcus’s endorsement ofdegrees of extensionality, but also her tendency to treat, so tospeak, intensionality as the default position, to which principles ofextensionality are added with their concomitant criteria: thereduction of identity to weaker (and weaker) forms of equivalence andthe elimination of some predicates (epistemic or modal). The startingpoint after all is natural language in all its richness, and Marcus(1975) ties precise formulations of the principle of substitutivity tothe search for the logical form of fragments of ordinary language. Onthis role for logic see also the opening paragraphs of“Quantification and Ontology” (1972).

4.2 Ontology: Individuals, Classes and Attributes

Marcus’s papers most relevant to this subsection are:“Classes and Attributes in Extended Modal Systems”(1963a), “Classes, Collections, and Individuals” (1974)and “Nominalism and the Substitutional Quantifier”(1978a).

According to Marcus, “that any language must countenance someentities as things would appear to be a precondition forlanguage” (1961: 309). Though Marcus cannot be classified as anominalist, given her endorsement of both classes and attributes, whenit comes to individual things she has nominalistic leanings. Shecharacterizes nominalism not just as insisting on only one category of“individuatable objects” but also as having an“empirical thrust”:

The nominalist’s individuals are of a kind which can beconfronted or in the least, make up such confrontable or encounterableindividuals. They can, so to speak, put in an appearance.Encounterability by the mind’s eye is not generally counted inthe spirit of nominalism. (1974: 352)

Insofar as she appears to be rejecting non-empirically-encounterable(basic) individuals, though accepting type theory, Marcus satisfiesone of her criteria for nominalism. In “Nominalism and theSubstitutional Quantifier” (1978a: 353–354) options for anominalistic account of predicates are considered, but it is not clearthat Marcus subscribes to them.

In “Classes and Attributes in Extended Modal Systems”Marcus develops a modal calculus for abstracts, where the abstractscan be indifferently taken to stand for classes or for attributes.This is not to be understood as a Fregean move, i.e., as the claimthat in extensional non-modal contexts the abstracts may be taken torefer to classes (their extensions) while in modal contexts they mustrefer to attributes (their intensions). In fact in her earlier paper“Extensionality” we find the quite surprisingstatement:

I am not disturbed by the possibility of equal, non-identical classesor attributes, e.g. man and featherless biped. To me it seemsreasonable that there are many empty classes of the same type, e.g.mermaids and Greek gods, equal but not identical. (1960:58–9)

Marcus distinguishes different meanings of the term“class”. In the first intuitive, “atavistic”sense classes are aggregates or collections of objects. This suggeststhe idea of finitely many objects physically gathered together andobservable. The second, more abstract, mathematical notion of classdoes not presuppose finitude or physical proximity, and is tied to theidea that classes are determined by properties:

Attendant to this way of looking at classes, is the assumption thatevery property or condition delimits a class; every class may bedelimited by a property or condition; and if no object satisfies aproperty or condition, then it delimits the null class. (1963a:129)

This second notion, claims Marcus, is closer to the notion ofattribute, in contrast to the first extensional but quite limitedinterpretation. For Marcus the classical functional calculus(first-order logic) focuses on attributes, not on the too limitednotion of classes as aggregates, and “the thesis ofextensionality must be superimposed” (1963a: 130). Clearly, sheis not considering a set-theoretic, non-limited, abstract, butnon-predicative notion of class. Later, she will deem this last,logical conception of classes, to be useful in mathematics, but guiltyof obliterating “the distinction between an itemization ofelements and a statement of conditions for membership” (1974:229). Clearly, this last set-theoretic conception—favored byQuine—is required to regard first-order logic as fullyextensional. On the “extensionalization” of first-orderlogic see also 1986b: 116.

Marcus’s distinction between the itemized and predicativenotions focuses on epistemic and linguistic rather than metaphysicalfeatures. She ties the notion of class, versus attribute, to thepossibility of observing and listing its members by proper names. Suchclasses can be the referents of abstracts in modal contexts, and theabstracts will be intersubstitutable in such contexts too despite theextensional nature of their referents, similarly to the way in whichproper names are so intersubstitutable while maintaining theirordinary referents. Indeed, the substitutibility of abstracts of theform “\(\hat\alpha((\alpha I \mu_1)\vee (\alpha I \mu_2) \vee\ldots (\alpha I \mu_n))\) where \(I\) names the identity relation,and \(\mu_1\), \(\mu_2\) … \(\mu_n\) are individualconstants” (1963: 131) follows from the intersubstitutivity ofnames in modal contexts. Attributes like \(\hat\alpha(\alpha I\mu_1)\) (being identical to \(\mu_1\)) are not regarded as genuinepredicative attributes.

In the later “Classes, Collections, andIndividuals”—published in 1974 but completed in1965—Marcus returns to the same topic. She now uses the term“assortment” for classes in the intuitive sense, reserving“class” for the attributive notion, and claims: “anequivalence relation between assortments is never contingent but anequivalence relation between classes may be” (1974: 230).Attributes, likeplanet named after the goddess of beauty andplanet between Mercury and Earth may be accidentallycoextensive. Butplanet identical to Venus andplanetidentical to Evening Star are necessarily coextensive. Thenecessity of the equivalence of assortments with the same membersfollows from the necessity of identity for objects; and theintersubstitutability in modal contexts of abstracts that list theirmembers by name, rather than describing them via properties, followsfrom the intersubstitutivity of names.

4.3 Names

Marcus’s papers most relevant to this subsection are:“Modalities and Intensional Languages” (1961),“Discussion on the Paper of Ruth B. Marcus” (1962a), and“Review ofNames and Descriptions by LeonardLinsky” (1978b).

One key theme of Marcus’s philosophy anticipated in“Modalities and Intensional Languages” is her famousclassification of proper names as tags:

This tag, a proper name, has no meaning. It simply tags. (1961:310)

The contrast once again is with Quine (1948) who endorses, andactually radicalizes (insofar as he envisions non-descriptivedescriptions like “the pegaziser”) Russell’s ideathat the proper names of the natural languages—in contrast tologically proper names—abbreviate descriptions. We have seen howRussellian logically proper names were employed by Smullyan in replyto Quine’s problems of substitutivity. But Russellian logicallyproper names are not the ordinary names of natural languages.

One interesting, debated question is whether back in 1961 Marcus wasalready proposing, though not fully developing, the referential theoryofordinary proper names which will dominate analyticphilosophy in the seventies, thanks to the work of Donnellan (1970),Kripke (1972), and Kaplan on direct reference (1989, delivered 1977).The answer to this question seems to be neither an unqualified yes nora simple no.

On the one hand, Marcus’s mention of ideal names and of makingrecourse to a dictionary seems to indicate that she is still, likeSmullyan, thinking not of ordinary names, which are not defined inordinary dictionaries, but of Russell’s logical ones. The use ofRussellian names presupposes a special form of acquaintance with theirreferents that preserves thea priori status of necessarilytrue statements of the form “\(a=b\)”, in line with thelogical and analytic interpretation of the modalities on which Quine,Smullyan and Marcus were focused at the time. If \(a\) and \(b\) areideal Russellian names, then “\(a=b\)” is necessary buta priori too. Marcus is also thinking of logical constants,which belong to formal languages and do not have an ordinaryinterpretation in a natural language. Here are some expressions of theRussellian vein of Marcus’s view:

We are here talking of proper names in the ideal sense, as tags andnot descriptions. Presumably, if a single object had more than onetag, there would be a way of finding out such as having recourse to adictionary or some analogous inquiry, which would resolve the questionas to whether the two tags denote the same thing. (1962a: 142)

And to discover that we have alternative proper names for the sameobject we turn to a lexicon, or, in the case of a formal language, tothe meaning postulates. (1963a: 132)

A lexicon which does for names what meaning postulates do forconstants can hardly be claimed to be the sort of biographicaldictionary or encyclopedia of which Marcus speaks in later work (e.g.,in 1980a: 503).

On the other hand, Marcus displays from the very beginning a very keenear for ordinary languages and the changes to which they aresubject:

In fact it often happens, in a growing, changing language, that adescriptive phrase comes to be used as a proper name - an identifyingtag - and the descriptive meaning is lost or ignored. Sometimes we usecertain devices such as capitalization and dropping the definitearticle, to indicate the change in use. “The evening star”becomes “Evening Star”, “the morning star”becomes “Morning Star”, and they may come to be used asnames for the same thing. (1962a: 139)

In fact, Marcus attributes to Russell himself a tendency to treatordinary proper names as referential, despite his official doctrine,see for example “On Some Post-1920s Views of Russell”(1986a).

Given the bitter controversy that took place on these questions in thenineties (see Humphreys & Fetzer 1998, Holt 1996, and Neale 2001),it is worth quoting in full the balanced assessment of this issueoffered by Marcus herself in 1978:

I argued that unlike descriptions, ordinary proper names function like“tags;” that proper names are indifferent to scope in somecontexts of indirect discourse where singular descriptions are not;that unlike different but coreferential descriptions, two proper namesof the same object were intersubstitutable in modal contexts; thatsingular descriptions might sometimes be used as if they were propernames which can be measured by our use of the description to refer tothe object whether or not the object had the defining properties; thatsuch a shift, if institutionalized, could be marked syntactically bycapitalization,vide “The Evening Star is not astar”. …

What was lacking in 1961 was a theory within which such claims couldbe given a coherent account. How can an ordinary proper name used overtime by a wide community of speakers, in the absence of opportunitiesfor direct ostension, have a semantically noncircuitous route to itsreferent. How is it possible to properly name an object in itsabsence. How do we account for those “proper” names whichhave a common use and which do not refer, such as “SantaClaus”; …

Kripke provided us with a “picture” which is far morecoherent than what had been available. It preserves the crucialdifferences between names and descriptions implicit in the theory ofdescriptions. By distinguishing between fixing the meaning and fixingthe reference, between rigid and nonrigid designators, many naggingpuzzles find a solution. The causal or chain of communications theoryof names (imperfect and rudimentary as it is) provides a plausiblegenetic account of how ordinary proper names can acquire unmediatedreferential use. (1978b: 502–503)

4.4 Quantifiers

Marcus’s papers most relevant to this subsection are:“Interpreting Quantification” (1962b), “Reply to Dr.Lambert” (1963b), “Quantification and Ontology”(1972) and “Nominalism and the Substitutional Quantifier”(1978a).

One of the major topics of Marcus’s philosophy is theinterpretation of the quantifiers, and on this too she stands in starkopposition to Quine. The one thing on which they agree is that theinterpretation of the quantifiers must be atemporal: “theoperation of quantification is more fruitfully interpreted asindependent of tense considerations” (1962b: 256). Quine hadmade the same point in 1953a. In 1962b Marcus appears to be joiningQuine against Strawson (1952) while arguing that her interpretation ofthe quantifiers is best equipped to dismiss Strawson’schallenges. Similarly, in response to objections moved by Martin(1962) against the suitability of logic to formalize ordinaryphilosophical discourse, based on the difficulty of clearly specifyingthe domain of quantification, she replies that in her substitutionalinterpretation of the quantifiers no such specification is needed(1963b: 326; 1972: 244–245).

According to the substitutional interpretation of the quantifiers,\((\exists x)Fx\) is true just in case a substitution instance of\(Fx\) is true. Substitution instances of \(Fx\) are formulas like\(Fa\), \(Fb\), etc. where \(a\) and \(b\), etc. are individualconstants of the language. Similarly, \((\forall x)Fx\) is true justin case all substitution instances of \(Fx\) are true. In the standardobjectual or referential interpretation instead, \((\exists x)Fx\) istrue just in case at least an element of the domain satisfies \(Fx\)and \((\forall x)Fx\) is true just in case all elements of the domainsatisfy \(Fx\).

The substitutional account, which is found already in Russell andWhitehead’sPrincipia Mathematica (Marcus 1962b: 254),is preferred by Marcus chiefly because it separates questions ofgenerality from questions of ontology, and in so doing it betterrepresents ordinary uses of expressions of quantification in naturallanguage. Moreover, being free of ontological commitments, it permits,so to speak, the existential generalization of empty names: from“A statue of Venus is in the Louvre” we can derive“\((\exists x)\) (a statue of \(x\) is in the Louvre)”(1972: 245); a statue of Venus (the goddess) is after all a statue ofsomething. The substitutional interpretation has also additionalbenefits: it bypasses Quine’s ontological concerns aboutquantification in and out of modal contexts, and it accommodatesnominalistic inclinations thus allowing quantification to be extendedto other syntactical categories (higher-order and propositionalquantification) free of ontological commitments to properties orpropositions—another qualm of Quine. In “Quantificationand Ontology” Marcus contrasts substitutional interpretations ofthe quantifiers in modal logic not only to Fregean interpretationsthat require the domain of quantification to include intensions, butalso to Kripke’s and Hintikka’s (1963) possible worldsemantics that associate alternative domains of quantification tomerely possible worlds, thus encompassing merely possible entities(1972: 243).

Marcus dismisses the objection that if there are unnamed objects thenthe substitutional account of the quantifiers may verify a universalsentence like \((\forall x)Fx\) even if not all objects are \(F\), aslong all named objects are. This is inevitable for non-denumerabledomains, given that the stock of names is denumerable. In her reply,she points out that this criticism has no bite against nominalists whoare skeptical of non-denumerable collections to start with. She isspeaking on behalf of the nominalist, so it remains unclear whethershe shares the skepticism. More interestingly, referring to thedownward Löwenhein-Skolem theorem, Marcus also claims that

the fact that everyreferential first order language whichhas a nondenumerable model must have a denumerable one gives littleadvantage to the referential view. (1978a: 360)

Marcus’s point does not apply to second-order logic where thetheorem fails, but her main referentialist opponent is Quine whorecognizes only first-order logic as genuine. So, against him, thepoint seems well taken.

While Quine denied reference to proper names and made the (quantifiersand) variables play the role of referring to (a domain of)individuals, Marcus reverses the picture. It is the names that arereferential, not the quantifiers:

On a substitutional semantics of the same first order language, adomain of objects is not specified. Variables do not range overobjects. They are place markers for substituends. Satisfactionrelative to objects is not defined. Atomic sentences are assignedtruth values. (1978b: 357)

The substitutional interpretation is for Marcus the default, generalone. It is just in the specific case when the names in thesubstitution class for the quantifiers are genuinely referential thatthe quantifiers can be read ontologically or existentially, but thedirect referential link is always played by the genuine, non-emptynames (1978b: 358). On substitutional quantification see Dunn andBelnap 1968, Linsky 1972, and Kripke 1976.

5. Essentialism

Marcus’s papers most relevant to this section are:“Essentialism in Modal Logic” (1967) and “EssentialAttribution” (1971).

5.1 Quantified Modal Logic and Essentialism

Quine’s ultimate criticism of quantified modal logic was its(alleged) commitment to Aristotelian essentialism, a world view thathe rejected on philosophical grounds. Against Quine, Marcus arguesthat Quine’s characterization of Aristotelian essentialism iswrong, that modal logic is not committed to Aristotelian essentialismcorrectly understood, and that in any case Aristotelian essentialismis not to be rejected.

For Quine it seems that even the necessity of identity is anessentialist thesis insofar as it presupposes the meaningfulness ofthe distinction between necessary and non-necessary attributes (asopposed to truths). However, Marcus points out that Aristotelianessentialism is not simply the predication ofde renecessities:

What has gone wrong in recent discussions of essentialism is theassumption of surface synonymy between ‘is essentially’andde re occurrences of ‘is necessarily’. (1971:193)

This means that regardless of theirde dicto (in front of aclosed sentence) orde re (in front of a predicate or an opensentence) employment, different interpretations of the modal operatorsare possible. In her work, Marcus focuses on two such interpretations:logical necessity and natural (causal, nomological, physical)necessity.

Marcus argues that Quine’s characterization of Aristotelianessentialism is wrong because thede re predication ofnecessary attributes derived from logical or analytical necessitiesdoes not suffice for essentialism. Yet, somewhat incongruously, Marcusseems to be conceding something to Quine’s understanding ofessentialism when, perhaps inadvertently, she will later state:“identity is an essential feature of things” (1986b: 118).In any case, Marcus defines a weak and a strong form of (alleged)essentialism in line with, and even stricter than, Quine’sunderstanding of essentialism.

According to weak essentialism (WE) there is some non-universal,necessary attribute \(\hat{y}Ay\) that only some objects bear.According to strong essentialism (SE) some attribute applies to someobjects necessarily and to others only contingently (1967: 93):

Both weak and strong essentialism can be proved in a system of QMLlike S5² with identity and abstracts, under the assumptionthat there are at least two individuals. Given that \(a\) and \(b\)are distinct objects, the property of being necessarily identical to\(a\) applies to \(a\) but not to \(b\), i.e., the following holds:\(\modalB (a\in \hat{y}(aIy))\) and \(\neg\modalB (b\in\hat{y}(aIy))\) (1967: 94). This satisfies weak essentialism.

Strong essentialism is also provable under the assumption that thereare two objects \(a\) and \(b\) such that \(Fa\) and \(\neg Fb\) hold(where \(F\) is an atomic contingent predicate). In this case, thequite unnatural attribute ofbeing F or being such that b is notF, namely, \(\hat{y}(Fy\vee\neg Fb)\), this complex attributeholds necessarily of \(b\) but only contingently of \(a\), given that\((Fb\vee\neg Fb)\) is a logical truth, but \((Fa\vee\neg Fb)\) isjust empirically true (1967: 95).

These however are benign forms of ‘essentialism’ which canbe explained away as ultimately reducible to the necessity ofuniversal attributes like \(\hat{y}(yIy)\) and \(\hat{y}(Fy\vee\negFy)\), which Marcus labels “vacuous” (1967: 94–95;1971: 196), whose necessity is ultimately derived from the logicalnecessity or truth of closed sentences like \((\forall x)(xIx)\) and\((\forall x)(Fx\vee\neg Fx)\).^[7] Genuinely essentialist claims instead, like that Socrates isnecessarily human, can surely be symbolized in modal systems, thustheir logical relations to other claims can be more perspicuouslyrepresented, but are not theorems of any standard modal system.Parsons (1967 and 1969) further develops these arguments; Kaplan(1986) defends a similar position; see also Fine 1990 and Kripke 2017aand 2017b.

5.2 Genuine Aristotelian Essentialism

Genuine Aristotelian essentialism, claims Marcus, is sortal andgeneral. Neither universal, tautological attributes (likeself-identity) nor fully individuative predicates (like a fulldescription down to uniqueness) are essential. Essential sortalattributes are properties likeman ormammal whichno object can haveper accidens. Moreover, not all propertiesof an object are essential to it. Marcus proposes the following as adefinition of Aristotelian essentialism (1971: 198): \[\tag{AE} (\forall x)(Fx\rightarrow\modalB Fx)\land (\exists x)(\modalB Fx \land Gx \land \neg\modalB Gx)\land (\exists x)\neg\modalB Fx\]Marcus claims that Aristotelian essentialism is concerned with a formof natural necessity. Rather than being an obscure old metaphysicaltheory, as Quine thought, Aristotelian essentialism is presupposed byscientific discourse. Essential properties are dispositionalproperties that an object cannot cease to have without ceasing toexist. As an example she considers the case

1. of a sample \(s\) of gold (\(Gs\)) which when immersed in aquaregia (\(Rs\)) will necessarily dissolve (\(Ds\)).

Reading the necessity as causal necessity, it follows that

2. being (a sample of) gold disposes \(s\) to dissolve (ifimmersed) in aqua regia and that
3. being immersed in aqua regia causes (sample \(s\) of) gold todissolve.

Formally:

However, from (\ref{ex5_2}) it also follows that being immersed inaqua regia causes \(s\), which is a piece of gold, to dissolve:

but from (\ref{ex5_3}) it does not follow that being a sample of goldcauses \(s\) to dissolve:

How so? The reason is that being gold is an essential property of\(s\), \(\modalB \textit{Gs}\), and from this and (\ref{ex5_2}) thenecessity of the consequent, i.e., (\ref{ex5_4}), follows; but beingimmersed in aqua regia is not essential to \(s\), \(\neg\modalB\textit{Rs}\), hence the necessity of the consequent of (\ref{ex5_3})cannot be proved, and (\ref{ex5_5}) holds. Thus, dissolving ifput in aqua regia \(\hat{y}(Ry\rightarrow Dy)\) is an essentialproperty of gold; but dissolving if made of gold\(\hat{y}(Gy\rightarrow Dy)\) is not an essential property of thingsimmersed in aqua regia. There is no natural kindthings put inaqua regia that might ground such a bizarre disposition (1971:200–202). On Aristotelian essentialism see also Marcus 1975/76:44–45.

6. Actualism and the Barcan Formula

Marcus’s papers most relevant to this subsection are:“Dispensing with Possibilia” (1975/76),“Possibilia and Possible Worlds” (1986b), “BarcanFormula” (1991) and “Are Possible, Non Actual ObjectsReal?” (1997).

In Barcan’s S2¹ and S4¹ 1946 systems thequantifiers and the modal operators interact in the moststraightforward way (Deutsch 1994; Linsky & Zalta 1994). The rulesof the propositional modal systems and of predicate logic are justcombined with no modification. For example, the proof of the converseBarcan formula:

starts from the first-order-logic theorem \(\vdash A \Rightarrow(\exists\alpha)A\), to which it applies first a modal rule ofpropositional S2 (if \(\vdash A \Rightarrow B\) then \(\vdash \modalDA \Rightarrow \modalD B\)) to derive \(\vdash \modalD A \Rightarrow\modalD (\exists\alpha)A\), and then a standard first-order-logic ruleto get the final result.

These systems are not strong enough to prove the Barcan formula:

which is thus assumed as an axiom.

In a variable domain semantics, like in Kripke 1963, where each worldis assigned its own domain of individuals—the individuals whichare assumed to exist in that world—CBF is valid in models wherethe domains of the worlds possible relative to a given worldw (accessible fromw) do not diminish, that is, theycontain all the individuals in the domain ofw, and possiblymore. Symmetrically, BF is valid in models where the domains of theworlds which are possible relative to a given worldw do notgrow, that is, they are subsets ofw’s domain. Hence,the combination of the two formulas is valid when the world domainsare constant. And clearly, both CBF and BF are valid in simplersemantics where one unique non-world-relative domain is associated toa model, as in Kripke 1959 and in the semantic construction used byBarcan Marcus to argue for BF (1961: 319–320).

The addition of BF as an axiom in her 1946 systems seems to indicatethat Barcan found it a natural assumption.^[8] This might have been due to Barcan’s semantic preference for aunique domain and the philosophical predilection for actualism sheexplicitly expresses in her later work. Yet, if Barcan had semanticconsiderations in mind at this early stage in her work, they remainedunvoiced. In the early papers, at least CBF appears to be asyntactically-driven result. Moreover, Barcan’s explicitinterpretative considerations at the time have to do with strictimplication interpreted as deducibility. Indeed, one may regard BF andCBF in Barcan’s early papers as BF and CBF for strictimplication as deducibility. Only later, when the main philosophicaldebates around the interpretation of the modal systems moved away fromimplication and logical consistency towards necessity, first logicaland then metaphysical, talk of possible worlds became widespread andthe use of the \(\Rightarrow\) operator became somewhat obsolete.

In her later work, Marcus strongly supports the Barcan formula basedon philosophical considerations, and often states that her commitmentto actualism is driven by a Russellian strong sense of reality whichalso “guided [her] original formalizations of quantified modallogic” to start with (1975/76: 42). In her view, the“modalities in their primary use concern counterfactuals aboutactual objects” (1986b: 114). Marcus interprets BF as expressinga commitment to actualism insofar as it seems to be saying that if no(actual) thing can beF then it is impossible that there beanF. Of BF and CBF she says:

Interpreted semantically, that came to assigning the same domain ofobjects to every world in the structure. Since this world is one amongthem, the domain of each world was coextensive with this one. Nothingnon-actual has been admitted. (1975/76: 42)

The rejection of merely possible entities (possibilia) is one of thefew theses Marcus shares with Quine. However, she is very critical ofQuine’s (1948) arguments against possibilia. Her maindissatisfaction is with Quine’s claim that merely possibleobjects lack clear criteria of individuation. She interprets thisclaim as fundamentally epistemological, rather than metaphysical, andin any case indecisive given that actual objects too may lack identity(identification) criteria (1986b: 118). For her instead the fact issimply that these putative objects do not exist: “It is not theabsence of criteria that makes us dubious. It is rather that what isabsent is the individual” (1986b: 127). At times her argumentsagainst possibilia are mixed with linguistic considerations,suggesting that both the existence of a material object and itsnameability require that it be reachable by ostension, namely,empirically encounterable.

Marcus concedes that there are two reasons to favor possibilia. Thefirst is the intuitive plausibility of the claim that there might havebeen more, or different, objects than there actually are (1975/76:43); the second is that there are some plausible candidates. These arethose possibilia that are embedded in the history of the actual world,like a half-built house or an alternative chess move that was nottaken (a particular event). Even them however are eventuallyrejected:

These are on the threshold of being candidates for ostension since wecan trace a relevant partial history. But finally, they have nolocation in the actual order. (1997: 255)

See also 1975/76: 46.

Marcus is somewhat critical of Kripke’s variable domainsemantics:

Although in setting up his quantificational structures, Kripke singledout the actual world as worthy of special designation amongalternatives, his syntax and semantics are as I will suggest tooimpoverished to make any use of that special role. (1986b: 113)

This is quite a bold claim that is hard to support, especiallyconsidering how Kripke (1965) gives a special role to the actual worldin the semantics of non-normal systems. Her more specific concernseems to be that variable domains open the door to possibilia,non-ostensible entities that are nonetheless assigned to variables.Moreover, these formal assignments fall short of the actual way inwhich natural-language names are given to actual objects. Her ownsubstitutional account of the quantifiers mitigates these concerns,and affords us the possibility of combining a variable-domainsemantics with a rejection of possibilia, since in the substitutionalinterpretation the quantifiers are associated to world-relative stocksof names available for substitution, not to domains of individuals.Nonetheless, for the actual world the quantifiers can be given anobjectual reading:

Indeed we can reintroduce full fledged reference by associating adomain of objects with the actual world and view our quantifiers asmixed; referential for this world and substitutional otherwise. We canthus dispense with the artifice of domains of possibilia. (1975/76:47)

On the BF see Parsons 1995; on BF and the possible worlds model theorysee Williamson 2013b: Chapters 2 and 3. In contrast to Marcus, Linskyand Zalta 1996, and Williamson 1995 and 1998 interpret BF as committedto the existence of possibilia. Simchen 2013 supports Marcus’sactualist reading; Williamson 2013b rejects both interpretations.

7. Belief and Rationality

Marcus’s papers most relevant to this subsection are: “AProposed Solution to a Puzzle about Belief” (1981a),“Rationality and Believing the Impossible” (1983b),“Some Revisionary Proposals about Belief and Believing”(1990c) and “The Anti-Naturalism of Some Language CenteredAccounts of Belief” (1995). The theme of the empiricalcomplexity of doxastic states is anticipated in“Hilpinen’s Interpretations of Modal Logic” (1980a),a commentary on Hilpinen 1980.

In “A Proposed Solution to a Puzzle about Belief”, Marcusputs forward a naturalistic account of belief in contrast to thelinguistic or quasi-linguistic accounts predominant in analyticphilosophy. We discuss the main points of this short but extremelyrich paper. “A Proposed Solution” centers onKripke’s extremely influential “A Puzzle aboutBelief” (1979), where Kripke proposes a disquotational principlelinking linguistic assent to belief:

(DQ)

If a normal, reflective speaker of English sincerely assents to anEnglish sentence “p”, then he believes thatp.^[9]

Assuming the direct reference theory of proper names, Kripke presentshis famous puzzle. If a speaker, let us say Kripke’s ownbilingual Pierre, is ignorant of some facts—like that Cicero isTully, that “Londres” is the French name of London, orthat Paderewski was both a pianist and a politician—he maysincerely assent both to “Cicero was bald” and“Tully was not bald”, “Londres est jolie”^[10] and “London is not pretty”, “Paderewski has musicaltalent” and “Paderewski does not have musicaltalent”, and even to their conjunctions like “Cicero wasbald and Tully was not bald”. The propositions expressed by thetwo members of each pair are contradictory: in the“Londres”-“London” case we have the singularproposition containing London itself and prettiness, and then itsnegation. Yet Pierre, in the case presented by Kripke, is notirrational, just ignorant of the fact that the two names co-refer. Butthen how can it possibly be right to attribute to him contradictorybeliefs? And, Kripke asks, “Does Pierre, or does he not, believethat London is pretty?” (Kripke 1979: 259). This is thepuzzle.

Kripke’s paper focuses on belief reports, our practices ofascribing beliefs. In her proposed solution to Kripke’s puzzle,Marcus’s focus switches to the metaphysics of belief. Hersolution is very radical insofar as it is not just the proposal ofsome modifications to Kripke’s theory, or the advancement of adistinct but similarly language-centered theory. Instead, Marcusrejects the entire framework of theories of belief within which suchpuzzles emerge. In a Russellian spirit, she points out thatpropositions—the objects of belief and other epistemicattitudes—are not linguistic entities, namely interpretedsentences, nor quasi-linguistic ones, like Fregean thoughts. They areinstead states of affairs, actual, possible, or even impossible. Thus,her first thesis is that: “knowing and believing are attitudestowards states of affairs” (1981a: 504).

Her second main thesis is that, as knowledge presupposes truth, beliefpresupposes possibility: “Ifx believes that p, thenpossible p” (1981a: 505). Clearly, this is an externalconstraint, one of whose obtaining the believer need not be aware.Pierre, for example, doesn’t know that “Londres is prettyand London is not pretty” (importing “Londres” intoEnglish) expresses a contradiction. But if only the possible can bebelieved, it is then the case that, his sincere assent to thissentence notwithstanding, Pierre does not believe it. So,Kripke’s DQ fails, and Marcus puts forward a modifiedversion:

(MDQ)

If a normal, reflective speaker of English sincerely assents to anEnglish sentence “p”, andp is possible,then he believes thatp.^[11]

Marcus’s argument for the thesis that only the possible can bebelieved is simply that this seems intuitively right to her, thoughshe is aware that many do not find this plausible. For example, sheclaims that if she were in Pierre’s situation, and then came toknow that London is Londres, her reaction would not be to say that shehas now changed her beliefs, having relinquished her past belief thatLondres is pretty and London is not pretty; but ratherthat—despite her past assent—she never really believedthat Londres is pretty and London is not pretty, as she never believedthat one thing was both pretty and not pretty. Something else in thevicinity may have been what she believed, maybe that“Londres”, but not “London”, is the name of apretty city. Marcus also points out that if Kripke’s andPutnam’s (1973) referential theory of natural kind terms iscorrect, and so “water is H₂O” is necessarilytrue, then it is impossible to believe that water is notH₂O, and similarly for mathematical necessities (1981a:509). In “Some Revisionary Proposals about Belief andBelieving”, Marcus qualifies her controversial thesis that it isimpossible to believe the impossible by granting that though speakerscannot relinquish their alleged beliefs in impossible states ofaffairs, as such beliefs were not there to start with, there issomething that they were mistaken about and can relinquish, that istheir (past) claims to have such beliefs (1990c: 150).

One consequence of Marcus’s second thesis is that Pierrebelieves that Londres is pretty and he believes that London is notpretty, but he does not believe their conjunction. This however,claims Marcus, is not too unusual a conclusion. It is similar tothe lottery paradox where we believe to a very high degree that thefirst ticket will not win, and so on for each ticket. Yet, we do notbelieve the conjunction of these beliefs. Quite the contrary, we maybe certain that one of the tickets will win. (However, the fact thatin Pierre’s case the beliefs are absolute undermines the analogywith the lottery case). Marcus also points out that though beliefcomes in degrees, assent is absolute. Thus, even if one believes thatthe first ticket will not win, they may still be reluctant to assentto this. This undermines the connection between assent and belief.

One of the most interesting consequences of Marcus’s account isthe following:

If we take seriously that the objects of beliefs are states ofaffairs, then for a speaker to believe thatp he must be in acertain psychological and behavioral state relative to that state ofaffairs. He thinks, behaves,has dispositions to respond as if hebelieved that that state of affairs obtained. (1981a: 508,emphasis added)

It is unclear why Marcus doesn’t simply state that the speakerhas dispositions to respond as if that state of affairsobtained, and her original formulation seems to generate aregress. In later papers, she rephrases it as an attribution ofdispositions to respond as if that belief state obtained (1983b: 330)or to act as if the believed state of affairs obtained (1990c: 140).Some of these dispositions will be linguistic, like being disposed toassent to sentences that (the speaker takes to) express theproposition that they believe. But many dispositions will not belinguistic. For example, someone who believes that London is prettywill be disposed to take a trip there, if they desire to visit prettycities, do not mind the expense, are not afraid of flying, etc. Thisbasic dispositional account of belief is also further tightened, forexample to require that the sentence assented to is fully interpreted,thus excluding sentences with empty names (1990c: 152).

Additionally, linguistic assent turns out not to be required forbelief, and Marcus rejects the strengthened principle of disquotationwhich she attributes to Kripke, which assumes also the converse of DQ,or of MDQ, i.e., that if a normal, reflective, sincere speaker ofEnglish believes thatp (andp is possible) then heassents to the English sentence “p”. Marcus points outthat we must reject the requirement of assent given that:

Higher animals and infants seem clearly to have beliefs, howeverrudimentary. To deny higher animals beliefs is as absurd asDescartes’s denying them pain. (1981a: 509)

However, Kripke’s strengthened disquotation principle is weakerthan what Marcus attributes to him; it requires not assent butdisposition to assent:

A normal English speaker who is not reticent willbe disposedto sincere reflective assent to “p” if and onlyif he believes thatp. (Kripke 1979: 429, emphasisadded)

Later Marcus will claim that even the disposition to assent is notrequired (1983b: 333, fn. 17). Non-speaking animals are not justunable to assent to linguistic sentences, they are also unable to havedispositions to assent. But if the disposition to assent is notrequired for animals to have beliefs, then it is also not required for“normal language users”. Even for them

there is no reason to suppose that for every belief they have there isa sentence that “captures” the belief and to which theywould assent. (1981a: 509)

In the later papers, Marcus develops some of the key points of herdispositional theory of belief. She also considers in detail the viewsof other philosophers (especially in Marcus 1990c and 1995). Thesepapers also criticize the very limited view of rationality, as tied tological reasoning abilities, that underpins linguistic accounts ofbelief:

But this language-centered account is an impoverished view ofrationality. It lacks explanatory force. Why should we dissent fromknown contradictions or inconsistent sets of sentences? A computerwould pay no price for that, nor presumably would a brain in a vat.(1990c: 142)

In contrast, according to her object-centered (i.e., directed tostates of affairs) dispositional account of mental states, rationalitydoes not just consist in eschewing logical contradictions and drawinglogical conclusions, but in overall coherent behavior, where what oneassents to matches their choices and actions: “Rationality is afeature of behavior writ large” (1995: 129). No matter howcoherent our avowals are, dissonant behavior, where our actions do notmatch our avowals, is a form of irrationality. Once assent to“p” (a speech act) is seen as just one of themany actions an agent is disposed to perform if he believes thatp, then the door is open to reject not only the necessity ofassent for belief, but also its sufficiency. Hence, the overallbehavioral dispositions of an agent to act as ifp didnot obtain may indicate that they do not believe thatp,despite their assent top (1995: 113).

8. Moral Dilemmas

Marcus’s papers most relevant to this subsection are:“Iterated Deontic Modalities” (1966), “MoralDilemmas and Consistency” (1980b) and “More about MoralDilemmas” (1996).

In “Moral Dilemmas and Consistency”, Marcus puts forward atheory of moral dilemmas that eschews idealizations and takes intoaccount that our actions are embedded in a world that we onlypartially control. Marcus criticizes the dominant view of moraldilemmas which is based on an excessively demanding notion ofconsistency. She attributes this view in some form or other to W.D.Ross, John Lemmon, Hare, Rawls and Davidson. According to the standardview, a moral code, a set of moral rules or principles, isinconsistent if there are situations, actual or possible, where notall the moral demands generated by the principles can be met. Forexample, a moral code that comprises both the duty to keep one’spromises and the duty of preventing harm requires from us incompatiblecourses of action if we have promised to return weapons to a partywhose intentions are to hurt innocents. This basic moral code is thusdeemed inconsistent. Nonetheless, theprima facieinconsistency is supposed to be resolvable by, so to speak,theoretical means. The principles and rules need to be qualified, orranked, or otherwise modified to iron out all dilemmas, for example bygiving more weight to the demands of benevolence than to the duty ofkeeping promises. Alternatively, on a particularist view, theinconsistency can be solved by a moral intuition that will indicatethe right course of action in a particular case. One consequence ofthis standard view is that the agent who chooses rightlyaccording to the complete code (or by her moral intuition), e.g., doesnot keep her promise of returning weapons to a malevolent party, iscleared of all guilt.

According to Marcus:

What is incredible in such solutions is the supposition … thatwhere, on any occasion, doingx conflicts with doingy, the rules with qualifications or priorities will yieldbetter clear reasons for doing one than for doing the other. (1980b:124)

This is incredible because the underneath assumption that an idealizedagent, with complete knowledge and a perfect will, won’t besubject to moral dilemmas forgets that agents act in the real worldand that:

The circumstances of the world conspire against us. However perfectour will, the contingencies are such that situations arise where, ifwe are to follow one course of action, we will be unable to followanother. (1980b: 127, fn. 6)

Moral dilemmas are thus, to a certain extent, inescapable; and notbecause of our moral and cognitive limits, nor due to a fault in themoral code, but just because we cannot escape our condition of agentsset in a world that we do not control. But then, claims Marcus, thedemand that a consistent moral theory make all moral dilemmasimpossible is too strong and impossible to be met—in fact noteven a theory with just one principle can avoid dilemmas, as we mayfind ourselves in a symmetrical situation where we owe the same to twoparties but can satisfy only one demand.

This calls for a revision of the notion of consistency for moraltheories. The notion of consistency used by Marcus in her moral papersis a “semantic” notion akin to satisfiability. She claimsthat like a set of sentences (a theory) is logically consistent ifthere are possible circumstances in which all the sentences are true,the consistency of a moral code requires only that there be possiblecircumstances in which all its demands can be met (1980b: 128).Moreover, when we face a moral conflict between doingx ordoingy, the unmet demand stays in place. When we refuse toreturn weapons to a malevolent party, we have still broken a promise:our duty to keep our word stays in place because we could indeed havekept our word. If we ought to have kept our promise to start with, andcould have done so, then we ought to have done so, even if we couldnot have done so while also preventing harm. That we cannot doy because we have chosen to dox does not suffice toremove the duty to doy. Guilt is thus the appropriate moralresponse, even when the intractability of the circumstances is not ourfault.

The inevitability of guilt is not for Marcus a tragic conclusion, asguilt and the associated unpleasant feelings play the important roleof motivating us to satisfy the second-order demand “to arrangeour lives and institutions so as to minimize or avoid dilemmas”(1980b: 131). And this is what we ought to do. Even if thissecond-order ought cannot be fully realized, as the world won’tfully cooperate, it stays in place as a regulative principle. Thus,rather than attempt to fix a code that isn’t broken, as if itwere a defective theory, Marcus calls us to improve the world we actin. “Moral Dilemmas and Consistency” ends with theintriguing suggestion that the choice we make, dox or doy, when both choices are morally acceptable, may belegitimately driven by appraisals that are not of a moral nature buthave to do instead with the kind of person we want to be and the kindof life we want to lead (1980b: 135–136). Williams (1973) is aprecursor of the view that dilemmas arise from contingentcircumstances. Foot (1983) is critical of Marcus on guilt.

In the later paper “More about Moral Dilemmas” Marcusrecognizes that the second-order regulative principle is burdensomeand supererogatory. It generates its own practical dilemmas as thereis some tension between the “pursuit of a rich and fulfillinglife” and the “pursuit of a life without moralconflicts” (1996: 29). For Marcus not all practical demands aremoral demands and not “all determinations of values are open tomoral scrutiny” (1996: 35).

Additionally, in this later paper Marcus criticizes a basic axiom anda rule of standard deontic systems (see Chellas 1980: Chapter 6). Shefinds such systems unsurprisingly defective “devised as theywere for a kingdom of ends” (1996: 32). In “IteratedDeontic Modalities” (1966) she had already pointed out someambiguities of interpretation of the deontic operators and urged thatthe operator “\(O\)” (ought) be interpreted as expressingan obligation. She now criticizes the axiom \(\neg (OA \land O\negA)\) as false to the facts of moral dilemmas. The closurerule—from \((A_1\land A_2 \land \ldots \land A_n\rightarrow B\))to \((OA_1\land OA_2 \land \ldots \land OA_n \rightarrowOB)\)—is also invalid given the intensionality of deonticoperators. Indeed starting from the trivial \(((A\land\negA)\rightarrow (A\land\neg A))\) it gives us the false \(((OA\landO\neg A)\rightarrow O(A\land\neg A))\). Additionally, deonticoperators, like epistemic ones, are more intensional than operatorsfor causal and logical necessity. Even when \(B\) is a logical orcausal consequence of \(A\), it is not necessarily the case that\(OA\) implies \(OB\), as deontic operators are sensitive to the wayan action is described. Deontic operators like epistemic ones are notclosed under logical consequence (1996: 29–30).

Like her metaphysical views and her extended view of rationality,Marcus’s take on moral dilemmas and her down-to-earth definitionof consistency for a moral theory—which calls for a practicalrather than theoretical solution to dilemmas—appear to be drivenby Russell’s admonition that a logician must not abandon herstrong sense of reality. No moral code can cover all possiblecircumstances and no moral agent can escape the moral choices andpractical responsibilities inherent to the human condition. One lastremark of Marcus, on guilty feelings and the impulse to organizeone’s life so as to avoid moral dilemmas, is a vivid reminder ofthe attunement to real life underpinning her philosophical work:

Such considerations are particularly appropriate to the question ofthe inevitability of dirty hands in public life. We want in publiclife those who are moved by such feelings and who would therefore tryto avoid such conflicts, yet who are willing to take the moral risk ofentering into public life. It is in such cases that we see the tensionbetween life choices and moral risk. (1996: 33)

Bibliography

Barcan Marcus’s Corpus

Published as Ruth C. Barcan

• 1946a, “A Functional Calculus of First OrderBased on Strict Implication”,Journal of SymbolicLogic, 11(1): 1–16. doi:10.2307/2269159
• 1946b, “The Deduction Theorem in a FunctionalCalculus of First Order Based on Strict Implication”,Journal of Symbolic Logic, 11(4): 115–118.doi:10.2307/2268309
• 1947, “The Identity of Individuals in a StrictFunctional Calculus of Second Order”,Journal of SymbolicLogic, 12(1): 12–15. doi:10.2307/2267171
• 1948, “Review of ‘Modality and Description’, byArthur Francis Smullyan [Smullyan 1948]”,Journal of Symbolic Logic, 13(3): 149–150. Reprintedwith revisions inMarcus 1993: 36–38. doi:10.2307/2267830

Published as Ruth Barcan Marcus

• 1950, “The Elimination of Contextually Defined Predicates ina Modal System”,Journal of Symbolic Logic, 15(2): 92.doi:10.2307/2266968
• 1953, “Strict Implication, Deducibility and the DeductionTheorem”,Journal of Symbolic Logic, 18(3):234–236. Reprinted with revisions inMarcus 1993: 71–73. doi:10.2307/2267407
• 1960, “Extensionality”,Mind, 69(273):55–62. doi:10.1093/mind/LXIX.273.55
• 1961, “Modalities and Intensional Languages”,Synthese, 13(4): 303–322. Reprinted with revisions inMarcus 1993: 3–23. doi:10.1007/BF00486629
• 1962a, “Discussion on the Paper of Ruth B. Marcus”,with W. V. Quine, Saul A. Kripke, J. McCarty, and DagfinnFøllesdal,Synthese, 14(2–3): 132–143.Reprinted with revisions inMarcus 1993: 24–35. doi:10.1007/BF00881990
• 1962b, “Interpreting Quantification”,Inquiry, 5(1–4): 252–259.doi:10.1080/00201746208601353
• 1963a, “Classes and Attributes in Extended ModalSystems”,Proceedings of a Colloquium on Modal andMany-Valued Logics, Helsinki, 23–26 August, 1962, inActa Philosophica Fennica, 16: 123–136.
• 1963b, “Reply to Dr. Lambert”,Inquiry,6(1–4): 325–327. doi:10.1080/00201746308601386
• 1965, “Review ofAristotle’s ModalSyllogisms, by Storrs McCall”,The PhilosophicalReview, 74(4): 539–541. doi:10.2307/2183133
• 1966, “Iterated Deontic Modalities”,Mind,75(300): 580–582. Reprinted with revisions inMarcus 1993: 39–43. doi:10.1093/mind/LXXV.300.580
• 1967, “Essentialism in Modal Logic”,Noûs, 1(1): 91–96. Reprinted with revisions inMarcus 1993: 45–51. doi:10.2307/2214714
• 1968, “Modal Logic”, inContemporary Philosophy:Logic and Foundations of Mathematics, Vol 1, Raymond Klibansky(ed.), Firenze: La Nuova Italia, pp. 87–101.
• 1971, “Essential Attribution”,The Journal ofPhilosophy, 68(7): 187–202. Reprinted with revisions inMarcus 1993: 53–70. doi:10.2307/2024901
• 1972, “Quantification and Ontology”,Noûs, 6(3): 240–250. doi:10.2307/2214772
• 1974, “Classes, Collections, and Individuals”,American Philosophical Quarterly, 11(3): 227–232.Reprinted with revisions as “Classes, Collections, Assortments,and Individuals”, inMarcus 1993: 89–100.
• 1975, “Does the Principle of Substitutivity Rest on aMistake?”, inAnderson, Marcus, and Martin 1975: 31–38. Reprinted with revisions inMarcus 1993: 101–109.
• 1975/76, “Dispensing withPossibilia”,Proceedings and Addresses of the American PhilosophicalAssociation, 49: 39–51. Reprinted in Richard H. Hull (ed.),The American Philosophical Association Centennial Series,2013: 401–412. doi:10.2307/3129990 doi:10.5840/apapa2013260
• 1976, “Wiggins on Identity, Necessity, andPhysicalism”, inPhilosophy of Logic: Papers andDiscussions, Stephan Körner (ed.), Berkeley, CA: Universityof California Press, pp. 132–146.
• 1978a, “Nominalism and the Substitutional Quantifier”,Monist, 61(3): 351–362. Reprinted with revisions inMarcus 1993: 111–124. doi:10.5840/monist197861331
• 1978b, “Review ofNames and Descriptions by LeonardLinsky”,The Philosophical Review, 87(3):497–504.
• 1980a, “Hilpinen’s Interpretations of ModalLogic”, in Georg H. von Wright (ed.),Logic and Philosophy /Logique et Philosophie, Dordrecht: Springer, pp. 31–36.doi:10.1007/978-94-009-8820-0_4
• 1980b, “Moral Dilemmas and Consistency”,TheJournal of Philosophy, 77(3): 121–136. Reprinted withrevisions inMarcus 1993: 125–141. doi:10.2307/2025665
• 1981a, “A Proposed Solution to a Puzzle about Belief”,inThe Foundations of Analytic Philosophy (Midwest Studies inPhilosophy, 6), Peter A. French, Theodore E. Uehling, and Howard K.Wettstein (eds), Minneapolis, MN: University of Minnesota Press, pp.501–510.
• 1981b, “Modal Logic, Modal Semantics and TheirApplications”, inTome 1 Philosophie du Langage, LogiquePhilosophique / Volume 1 Philosophy of Language, PhilosophicalLogic, Guttorm Fløistad and G. H. Von Wright (eds),Dordrecht: Springer Netherlands, 279–298.doi:10.1007/978-94-009-8356-4_11
• 1983a, “Bar-On on Spinoza’s Ontological Proof”,inSpinoza: His Thought and Work, Nathan Rotenstreich andNorma Schneider (eds), Jerusalem: The Israel Academy of Sciences andHumanities, pp. 110–119.
• 1983b, “Rationality and Believing the Impossible”,The Journal of Philosophy, 80(6): 321–338. Reprintedwith revisions inMarcus 1993 143–161. doi:10.2307/2026334
• 1985, “Is There Irrationality in the Existence of aPlurality of Philosophical Theories”,Dialectica,39(4): 321–328. doi:10.1111/j.1746-8361.1985.tb01600.x
• 1986a, “On Some Post-1920s Views of Russell onParticularity, Identity, and Individuation”, In Jules Vuillemin(ed.),Mérites et Limites des Méthodes Logiques enPhilosophie, Paris: J. Vrin. Reprinted with revisions inMarcus 1993: 177–188.
• 1986b, “Possibilia and Possible Worlds”,GrazerPhilosophische Studien, 25/26: 107–133. Reprinted withrevisions inMarcus 1993: 189–213. doi:10.5840/gps1985/8625/265
• 1986c, “Spinoza and the Ontological Proof”, inHuman Nature and Natural Knowledge (Boston Studies in thePhilosophy of Science 89), Alan Donagan, Anthony N. Perovich, andMichael V. Wedin (eds), Dordrecht: Springer Netherlands,153–166. Reprinted with revisions inMarcus 1993: 163–176. doi:10.1007/978-94-009-5349-9_8
• 1988a, “F.B. Fitch 1908–1987”,Proceedingsand Addresses of the American Philosophical Association, 61(3):551–553.
• 1988b, “Letter to the Editor”,Proceedings andAddresses of the American Philosophical Association, 61(5):867–868.
• 1989, “Introduction”, inThemes from Kaplan,Joseph Almog, John Perry, and Howard K. Wettstein (eds), Oxford:Oxford University Press: pp. 3–4.
• 1990a, “A Backward Look at Quine’s Animadversions onModalities”, inPerspectives on Quine, Robert B.Barrett and Roger F. Gibson (eds), Oxford/Cambridge, MA: Blackwell,pp. 230–243. Reprinted with revisions inMarcus 1993: 215–232.
• 1990b, “Max Black (1909–1988)”,Dialectica, 44(1–2): 5–8.doi:10.1111/j.1746-8361.1990.tb01647.x
• 1990c, “Some Revisionary Proposals about Belief andBelieving”,Philosophy and Phenomenological Research,50(supplement): 133–153. Reprinted with revisions inMarcus 1993: 233–255. doi:10.2307/2108036
• 1991, “Barcan Formula”, inHandbook of Metaphysicsand Ontology, Hans Burkhardt and Barry Smith (eds), Munich:Philosophia Verlag, pp. 76–77.
• 1993,Modalities: Philosophical Essays, NewYork: Oxford University Press. doi:10.1093/0195096576.001.0001
• 1995, “The Anti-Naturalism of Some Language CenteredAccounts of Belief”,Dialectica, 49(2–4):113–130. doi:10.1111/j.1746-8361.1995.tb00157.x
• 1996, “More about Moral Dilemmas”, inMoralDilemmas and Moral Theory, Homer E. Mason (ed.), Oxford: OxfordUniversity Press, pp. 23–35.doi:10.1093/oso/9780195096811.003.0003
• 1997, “Are Possible, Non Actual Objects Real?”,Revue Internationale de Philosophie, 51(200/2):251–257.
• 2005, “Ruth Barcan Marcus”, inFormalPhilosophy, Vincent F. Hendricks and John Symons (eds), USA:Automatic Press, 131–140. A short interview with Marcus.
• 2010, “A Philosopher’s Calling” (Dewey lecture,Eastern 2009),Proceedings and Addresses of the AmericanPhilosophical Association, 84(2): 75–92. Reprinted inFrauchiger 2015: 17–37.
• 2011, “C. I. Lewis on Intensional Predicate Logic: A LetterDated May 11, 1960”,History and Philosophy of Logic,32(2): 103–106. doi:10.1080/01445340.2010.522368

Coauthored Work

• Anderson, Alan Ross, Ruth Barcan Marcus, and Richard M.Martin (eds), 1975,The Logical Enterprise, New Haven, CT:Yale University Press.
• Marcus, Ruth B., Bruce Kuklick, and Sacvan Bercovitch, 1979,“Letter on Uninformed Consent”,Science,205(4407, 17 August): 644. doi:10.1126/science.205.4407.644.b
• Marcus, Ruth Barcan, Georg Dorn, and Paul Weingartner (eds), 1986,Logic, Methodology, and Philosophy of Science, VII: Proceedings ofthe Seventh International Congress of Logic, Methodology, andPhilosophy of Science, Salzburg, 1983, (Studies in Logic and theFoundations of Mathematics 114), Amsterdam/New York:North-Holland.

Festschriften

• Sinnott-Armstrong, Walter, Diana Raffman, and NicholasAsher (eds), 1995,Modality, Morality, and Belief: Essays in Honorof Ruth Barcan Marcus, Cambridge/New York: Cambridge UniversityPress.
• Lauener, Henri (ed.), 1999,Festschrift zu Ehren von RuthBarcan Marcus, special issue ofDialectica,53(3/4).
• Marti, Genoveva (ed.), 2013, “Monographic Section on RuthBarcan Marcus (1921–2012)”,Theoria: A Revista deTeoría y Fundamentos de la Ciencia, 28/3(78):353–436.
• Frauchiger, Michael (ed.), 2015,Modalities,Identity, Belief, and Moral Dilemmas: Themes from Barcan Marcus(Lauener Library of Analytical Philosophy 3), Berlin: De Gruyter.doi:10.1515/9783110429558

Secondary Literature

• Ballarin, Roberta, 2004, “The Interpretation of Necessityand the Necessity of Interpretation”,Journal ofPhilosophy, 101(12): 609–638.doi:10.5840/jphil20041011210
• –––, 2012, “Quine on Intensional Entities:Modality and Quantification, Truth and Satisfaction”,Journal of Applied Logic, 10(3): 238–249.doi:10.1016/j.jal.2012.04.001
• –––, 2021, “Quine on Modality”, inThe Routledge Handbook of Modality, Otávio Bueno andScott A. Shalkowski (eds), London: Routledge, pp. 390–399.
• Bergmann, Gustav, 1948, “Contextual Definitions inNonextensional Languages”,Journal of Symbolic Logic,13(3): 140. doi:10.2307/2267815
• Burgess, John P., 1997, “Quinus Ab Omni NævoVindicatus”, inMeaning and Reference, Ali A. Kazmi(ed.),Canadian Journal of Philosophy Supplementary Volume23, 25–65. doi:10.1080/00455091.1997.10715961
• –––, 2014, “On a Derivation of theNecessity of Identity”,Synthese, 191(7):1567–1585. doi:10.1007/s11229-013-0351-8
• Carnap, Rudolf, 1946, “Modalities and Quantification”,Journal of Symbolic Logic, 11(2): 33–64.doi:10.2307/2268610
• Chellas, Brian Farrell, 1980,Modal Logic: AnIntroduction, Cambridge/New York: Cambridge University Press.doi:10.1017/CBO9780511621192
• Church, Alonzo, 1942, “Review of ‘Whitehead and theRise of Modern Logic’, by Willard V. Quine“,Journalof Symbolic Logic, 7(2): 100–101. doi:10.2307/2266316
• –––, 1943, “Review of ‘Notes onExistence and Necessity’, by Willard V. Quine [Quine 1943]”,Journal of Symbolic Logic, 8(2): 45–47.doi:10.2307/2267994
• Cresswell, Max J., 2001, “Ruth Barcan Marcus(1921–)”, inA Companion to Analytic Philosophy(Blackwell Companions to Philosophy 20), A. P. Martinich and DavidSosa (eds), Oxford/Malden, MA: Blackwell, 357–360.doi:10.1002/9780470998656.ch29
• Deutsch, Harry, 1994, “Logic for Contigent Beings”,Journal of Philosophical Research, 19: 273–329.doi:10.5840/jpr_1994_6
• Donnellan, Keith S., 1970, “Proper Names and IdentifyingDescriptions”,Synthese, 21(3–4): 335–358.doi:10.1007/BF00484804
• Dunn, J. Michael and Nuel D. Belnap, 1968, “The SubstitutionInterpretation of the Quantifiers”, Noûs,2(2): 177–185. doi:10.2307/2214704
• Feys, Robert, 1965,Modal Logics (Collection de LogiqueMathématique, Sér. B, 4), Louvain: E. Nauwelaerts.
• Fine, Kit, 1990, “Quine on Quantifying In”, inPropositional Attitudes. The Role of Content in Logic, Language,and Mind (CSLI Lecture Notes 20), C. Anthony Anderson and JosephOwens (eds), Stanford, CA: CSLI Publications, pp. 1–25.
• Fitch, Frederic B., 1949, “The Problem of the Morning Starand the Evening Star”,Philosophy of Science, 16(2):137–141. doi:10.1086/287026
• –––, 1952,Symbolic Logic. AnIntroduction, New York: The Ronald Press Company.
• Fitting, Melvin, 2007, “Modal Proof Theory”, inHandbook of Modal Logic (Studies in Logic and PracticalReasoning 3), Patrick Blackburn, Johan van Benthem, and Frank Wolter(eds), Amsterdam/Boston: Elsevier, 85–138.doi:10.1016/S1570-2464(07)80005-X
• Føllesdal, Dagfinn, 2004,Referential Opacity and ModalLogic (Studies in Philosophy), New York: Routledge. His 1961 PhDthesis as modified in 1963 with an extensive introduction added.doi:10.4324/9780203337295
• Foot, Philippa, 1983, “Moral Realism and MoralDilemma”,The Journal of Philosophy, 80(7):379–398. doi:10.2307/2026455
• Franks, Curtis, 2021, “The Deduction Theorem (Before andAfter Herbrand)”,History and Philosophy of Logic,42(2): 129–159. doi:10.1080/01445340.2021.1889117
• Frege, Gottlob, 1892 [1948], “Über Sinn undBedeutung”,Zeitschrift für Philosophie undphilosophische Kritik, 100: 25–50. English translation,1948, “Sense and Reference”, Max Black (trans.),ThePhilosophical Review, 57(3): 209–230.doi:10.2307/2181485
• Hakli, Raul and Sara Negri, 2012, “Does the DeductionTheorem Fail for Modal Logic?”,Synthese, 187(3):849–867. doi:10.1007/s11229-011-9905-9
• Hilpinen, Risto, 1980, “Some Epistemological Interpretationsof Modal Logic”, inLogic and Philosophy / Logique etPhilosophie, G. H. Von Wright (ed.), Dordrecht: SpringerNetherlands, 19–29. doi:10.1007/978-94-009-8820-0_3
• Hintikka, Jaakko, 1963, “The Modes of Modality”,Acta Philosophica Fennica, 16: 65–81.
• Holt, Jim, 1996, “Whose Idea Is It, Anyway? APhilosophers’ Feud”,Lingua Franca, February1996: 28–39.
• Hull, Richard, 2013, “Biography: Ruth Charlotte BarcanMarcus”, inThe American Philosophical AssociationCentennial Series, Richard H. Hull (ed.), 2013:397–400.
• Humphreys, Paul W. and James H. Fetzer (eds), 1998,The New Theory of Reference: Kripke, Marcus, and Its Origins(Synthese Library 270), Dordrecht/Boston: Kluwer Academic Publishers.doi:10.1007/978-94-011-5250-1
• Janssen-Lauret, Frederique, 2016, “Meta-Ontology,Naturalism, and the Quine-Barcan Marcus Debate”, inQuineand His Place in History (History of Analytic Philosophy),Frederique Janssen-Lauret and Gary Kemp (eds), London: PalgraveMacmillan UK, 146–167. doi:10.1057/9781137472519_12
• –––, 2022, “Ruth Barcan Marcus andQuantified Modal Logic”,British Journal for the History ofPhilosophy, 30(2): 353–383. doi:10.1080/09608788.2021.1984872
• Kaplan, David, 1986, “Opacity”, inThe Philosophyof W.V. Quine (Library of Living Philosophers 18), Lewis EdwinHahn and Paul Arthur Schilpp (eds), La Salle, IL: Open Court,229–289.
• –––, 1989, “Demonstratives. An Essay onthe Semantics, Logic, Metaphysics, and Epistemology of Demonstrativesand Other Indexicals”, inThemes from Kaplan, JosephAlmog, John Perry, and Howard Wettstein (eds.), New York: OxfordUniversity Press, 481–563.
• Kripke, Saul A., 1959, “A Completeness Theorem in ModalLogic”,Journal of Symbolic Logic, 24(1): 1–14.doi:10.2307/2964568
• –––, 1963, “Semantical Considerations onModal Logic”,Acta Philosophica Fennica, 16:83–94.
• –––, 1965, “Semantical Analysis of ModalLogic II. Non-Normal Modal Propositional Calculi”, inTheTheory of Models: Proceedings of the 1963 International Symposium atBerkeley (Studies in Logic and the Foundations of Mathematics),John W. Addison, Leon Henkin, and Alfred Tarski (eds), Amsterdam/NewYork: North-Holland, 206–220.doi:10.1016/B978-0-7204-2233-7.50026-5
• –––, 1971, “Identity and Necessity”,inIdentity and Individuation (Studies in ContemporaryPhilosophy), Milton Karl Munitz (ed.), New York: New York UniversityPress, 135–164.
• –––, 1972 [1980], “Naming andNecessity”, inSemantics of Natural Language, DonaldDavidson and Gilbert Harman (eds.), (Synthese Library), Dordrecht:Reidel. Originally lectures given at Princeton University in 1970.Reprinted and enlarged as a book in 1980,Naming andNecessity, Cambridge, MA: Harvard University Press.
• –––, 1976, “Is There a Problem AboutSubstitutional Quantification?”, inTruth and Meaning:Essays in Semantics, Gareth Evans and John McDowell (eds),Oxford: Clarendon Press, 324–419.
• –––, 1979, “A Puzzle about Belief”,inMeaning and Use: Papers Presented at the Second JerusalemPhilosophical Encounter (Studies in Linguistics and Philosophy3), Avishai Margalit (ed.), Dordrecht/Boston: D. Reidel,239–283. doi:10.1007/978-1-4020-4104-4_20
• –––, 2017a, “Quantified Modality andEssentialism”,Noûs, 51(2): 221–234.doi:10.1111/nous.12126
• –––, 2017b, “Quantified Modal Logic andQuine’s Critique: Some Further Observations”,Noûs, 51(2): 235–237. doi:10.1111/nous.12127
• Lemmon, Edward John, 1957, “New Foundations for Lewis ModalSystems”,Journal of Symbolic Logic, 22(2):176–186. doi:10.2307/2964179
• Lewis, Clarence Irving, 1918,A Survey of Symbolic Logic,Berkeley, CA: University of California Press.
• Lewis, Clarence Irving and Cooper Harold Langford, 1932,Symbolic Logic, London: Century. Second edition 1959, NewYork: Dover.
• Linsky, Bernard and Edward N. Zalta, 1994, “In Defense ofthe Simplest Quantified Modal Logic”,PhilosophicalPerspectives, 8: 431–458. doi:10.2307/2214181
• –––, 1996, “In Defense of the ContingentlyNonconcrete”,Philosophical Studies, 84(2–3):283–294. doi:10.1007/BF00354491
• Linsky, Leonard (ed.), 1971,Reference and Modality(Oxford Readings in Philosophy), London: Oxford University Press.
• –––, 1972, “Two Concepts ofQuantification”,Noûs, 6(3): 224.doi:10.2307/2214771
• Martin, Richard M., 1962, “Existential Quantification andthe ‘Regimentation’ of Ordinary Language”,Mind, 71(284): 525–529.doi:10.1093/mind/LXXI.284.525
• McKinsey, John C.C. and Alfred Tarski, 1948, “SomeTheorems About the Sentential Calculi of Lewis andHeyting”, Journal of Symbolic Logic, 13(1):1–15.
• Neale, Stephen, 2000, “On a Milestone of Empiricism”,inKnowledge, Language and Logic: Questions for Quine (BostonStudies in the Philosophy and History of Science 210), Alex Orensteinand Petr Kotatko (eds), Boston: Kluwer Academic, 237–346.doi:10.1007/978-94-011-3933-5_18
• –––, 2001, “No Plagiarism Here. TheOriginality of Saul Kripke. Review of ‘The New Theory ofReference’ by P.W. Humphreys and J.H. Fetzer (eds.) [Humphreys & Fetzer 1998]”,Times Literary Supplement, issue 5106 (9 February 2001):12–13.
• Parry, William Tuthill, 1934, “The Postulates for‘Strict Implication’”,Mind, 43(169):78–80. doi:10.1093/mind/XLIII.169.78
• Parsons, Terence, 1967, “Grades of Essentialism inQuantified Modal Logic”,Noûs, 1(2):181–191. doi:10.2307/2214584
• –––, 1969, “Essentialism and QuantifiedModal Logic”,The Philosophical Review, 78(1):35–52.
• –––, 1995, “Ruth Barcan Marcus and theBarcan Formula”, inSinnott-Armstrong, Raffman, and Asher 1995: 3–11.
• Prior, Arthur N., 1956, “Modality and Quantification inS5”,Journal of Symbolic Logic, 21(1): 60–62.doi:10.2307/2268488
• Putnam, Hilary, 1973, “Meaning and Reference”,TheJournal of Philosophy, 70(19): 699–711.doi:10.2307/2025079
• Quine, Willard V., 1943, “Notes on Existenceand Necessity”,The Journal of Philosophy, 40(5):113–127. doi:10.2307/2017458
• –––, 1946, “Review of ‘A FunctionalCalculus of First Order Based on Strict Implication’, by Ruth C.Barcan [Barcan 1946a]”,Journal of Symbolic Logic, 11(3): 96–97.doi:10.2307/2266766
• –––, 1947a, “The Problem ofInterpreting Modal Logic”,Journal of Symbolic Logic,12(2): 43–48. doi:10.2307/2267247
• –––, 1947b, “Review of ‘TheDeduction Theorem in a Functional Calculus of First Order Based onStrict Implication’, by Ruth C. Barcan [Barcan 1946b]”,Journal of Symbolic Logic, 12(3): 95–95.doi:10.2307/2267231
• –––, 1947c, “Review of ‘The Identityof Individuals in a Strict Functional Calculus of Second Order’,by Ruth C. Barcan [Barcan 1947]”,Journal of Symbolic Logic, 12(3): 95–96.doi:10.2307/2267230
• –––, 1948, “On What There Is”,The Review of Metaphysics, 2(5): 21–38.
• –––, 1953a, “Mr. Strawson on LogicalTheory”,Mind, 62(248): 433–451.doi:10.1093/mind/LXII.248.433
• –––, 1953b, “Reference andModality”, inFrom a Logical Point of View: 9Logico-Philosophical Essays, Cambridge, MA: Harvard UniversityPress, pp. 139–159.
• –––, 1953c, “Three Grades of ModalInvolvement”, inProceedings of the 11th InternationalCongress of Philosophy, Volume 14, Amsterdam: North-Holland, pp.65–81. doi:10.5840/wcp11195314450
• –––, 1958, “Corrections to the Review of‘The Identity of Individuals in a Strict Functional Calculus ofSecond Order’, by Ruth C. Barcan [Barcan 1947]”,Journal of Symbolic Logic, 23(3): 342.doi:10.2307/2964293
• –––, 1961, “Reply to ProfessorMarcus”,Synthese, 13(4): 323–330.doi:10.1007/BF00486630
• –––, 1990, “Comment on Marcus”, inPerspectives on Quine, Robert B. Barrett and Roger F. Gibson(eds), Oxford/Cambridge, MA: Blackwell, p. 244.
• Russell, Bertrand and Alfred N. Whitehead, 1910, 1912, 1913,Principia Mathematica, 3 volumes, Cambridge: CambridgeUniversity Press.
• Simchen, Ori, 2013, “The Barcan Formula inMetaphysics”,THEORIA. An International Journal for Theory,History and Foundations of Science, 28(3): 375–392.doi:10.1387/theoria.6918
• Smullyan, Arthur Francis, 1947, “Review of ‘TheProblem of Interpreting Modal Logic’, by W. V. Quine [Quine 1947a]”,The Journal of Symbolic Logic, 12(4): 139–141.doi:10.2307/2266498
• –––, 1948, “Modality andDescription”,Journal of Symbolic Logic, 13(1):31–37. doi:10.2307/2268137
• Strassfeld, Jonathan, 2022, “‘I Am Aware That ThisLetter May Be Offensive’: The Unapologetic Achievements of RuthBarcan Marcus and Marjorie Glicksman Grene”,Journal of theHistory of Ideas, 83(4): 579–600.doi:10.1353/jhi.2022.0038
• Strawson, Peter F., 1952,Introduction to Logical Theory,London: Methuen.
• Wiggins, David, 1976a, “Identity, Necessity andPhysicalism”, inPhilosophy of Logic: Papers andDiscussions, Stephan Körner (ed.), Berkeley, CA: Universityof California Press, pp. 96–132.
• –––, 1976b, “Reply to Comments”, inPhilosophy of Logic: Papers and Discussions, StephanKörner (ed.), Berkeley, CA: University of California Press,159–179.
• Williams, Bernard, 1973,Problems of the Self, Cambridge:Cambridge University Press. doi:10.1017/CBO9780511621253
• Williamson, Timothy, 1995, “Review ofModalities.Philosophical Essays, by Ruth Barcan Marcus [Marcus 1993]”,Philosophical Books, 36(2): 120–122.doi:10.1111/j.1468-0149.1995.tb02919.x
• –––, 1998, “Bare Possibilia”,Erkenntnis, 48(2/3): 257–273.doi:10.1023/A:1005331819843
• –––, 2013a, “In Memoriam: Ruth BarcanMarcus 1921–2012”,The Bulletin of SymbolicLogic, 19(1): 123–126. doi:10.2178/bsl.1901070
• –––, 2013b,Modal Logic as Metaphysics,Oxford: Oxford University Press.doi:10.1093/acprof:oso/9780199552078.001.0001
• Zeman, Joseph Jay, 1973,Modal Logic: The Lewis-ModalSystems, London: Clarendon Press.

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Acknowledgments

I corresponded with Ruth Barcan Marcus in 1999 and then 2006. Duringthe 1998–99 academic year, Marcus attended some meetings of theUCLA weekly workshop in philosophy of language run by David Kaplan,Joseph Almog and Tony Martin. She was kind enough to read some of mywork and in March 1999 she sent me a generous and supportivehand-written letter of comments where she also expounded some of herviews. In 2006 we corresponded by email about the Barcan formula andon that occasion she sent me copies of some of her correspondence withQuine,inter alia. Her last email to me ended with theself-standing sentence “Perhaps you might want to dothat”. This I took to be an invitation to write about some ofher work.

I thank Graham Moore who has assisted me in the early stages ofpreparation of this entry.