Ruth Barcan Marcus and quantified modal logic

ABSTRACT

Analytic philosophy in the mid-twentieth century underwent a major change of direction when a prior consensus in favour of extensionalism and descriptivism made way for approaches using direct reference, the necessity of identity, and modal logic. All three were first defended, in the analytic tradition, by one woman, Ruth Barcan Marcus. But analytic philosophers now tend to credit them to Kripke, or Kripke and Carnap. I argue that seeing Barcan Marcus in her historical context – one dominated by extensionalism and descriptivism – allows us to see how revolutionary she was, in her work and influence on others. I focus on her debate with Quine, who found himself retreating to softened, and more viable, versions of his anti-modal arguments as a result. I make the case that Barcan's formal logic was philosophically well-motivated, connected to her views on reference, and well-matched to her overall views on ontology. Her nominalism led her to reject posits which could not be directly observed and named, such as possibilia. She conceived of modal calculi as facilitating counterfactual discourse about actual existents. I conclude that her contributions ought to be recognized as the first of their kind. Barcan Marcus must be awarded a central place in the canon of analytic philosophy.

KEYWORDS:

• Ruth Barcan Marcus
• modal logic
• modality
• direct reference
• W.V. Quine

Acknowledgments

Thanks to audiences at McMaster University, especially Greg Frost-Arnold, Alexander Klein, Sandra Lapointe, and Audrey Yap, and the University of Durham, especially Nancy Cartwright and Sara Uckelman, and to Sophia Connell, Claire Gilson, Fraser MacBride, Kenneth Westphal, and two anonymous referees for this journal.

Notes

1 In the “List of Officers and Members of the Association for Symbolic Logic”, Barcan is listed as ‘Barcan, Dr Ruth C (Mrs Jules A. Marcus)’, Martha Kneale appears as ‘Kneale, Mrs W.’ (for ‘William’), and multiple female professors' names appear in the form ‘Harris, Prof. Marjorie (Miss)’; ‘Onderdonk, Prof Virginia (Miss)’, ‘Swabey, Prof. Marie C. (Mrs W.C.)’, appending unnecessary titles serving only to indicate their marital status.

2 As whole books could be written on Barcan Marcus' contributions to analytic philosophy and logic, some issues are beyond the scope of this paper; for example, I do not have space to go into detail about Barcan Marcus' reply to Quine's ‘number of the planets’ argument, and I will not attempt to settle the lengthy Smith-Soames debate or contend in detail with Burgess' (also lengthy) papers on Barcan Marcus, Kripke, and Quine.

3 For brief biographies of Barcan Marcus, see Gendler, “Ruth Barcan Marcus”, and Barcan Marcus, “A Philosopher's Calling”.

4 An anonymous referee points out that Carnap's Principle of Tolerance had social and political, as well as logico-philosophical, goals (see Carus, Carnap and Twentieth-Century Thought, 252–61; Creath, “The Gentle Strength of Tolerance”; Yap, “Feminism and Carnap's Principle of Tolerance”). Carnap certainly seems to have found Quine's comparison galling, sounding uncharacteristically annoyed in his reply (Carnap, “Correspondence”, 245; see also Janssen-Lauret, “Quine's Philosophical Development”).

5 Here I use a slightly simplified presentation of Lewis' propositional modal logics based on Lewis and Langford's 1932 Survey of Symbolic Logic, rather than the original versions in C.I. Lewis' 1918 Survey of Symbolic Logic. The 1918 version has as a consequence that if p is false then p is impossible, but the 1932 version lacks this flaw. For ease of exposition I have used brackets in place of Lewis and Langford's Principia dots, and ‘$\text{□}p$’ instead of ‘$\sim \diamond \sim p$’.

6 An anonymous referee asks why I do not consider views on which the possible worlds of Kripke's system are ‘mere technical devices’ not requiring belief in the existence of possible worlds. My answer is twofold: first of all, since this is a historical paper, I am concerned primarily with the position of Barcan Marcus' system and philosophy in the mid-twentieth century debate about modality. This debate was driven in part by the assumption that those who use possible-world models (or other models positing intensional abstracta such as concepts) must believe in the posits of their models, an assumption denied by Carnap for general anti-metaphysical reasons but otherwise widespread, as I show in this paper with respect to Quine's criticisms of Carnap, with respect to the Quine-Barcan debate, and with respect to Quine's objections to Kripke. See also Janssen-Lauret, “The Quinean Roots”, for more on Quine's ontology-focused anti-modal arguments and Lewis' replies. Secondly, I share Quine's view that philosophers should believe in the posits of their best theories, and that if any manner of speaking is considered a mere façon de parler or technical device, any apparent ontological commitments which it appears to have must be clearly explained away.

7 Most advocates of modal systems which presuppose a possible-world semantics and an objectual interpretation of the quantifiers choose systems which validate the Converse Barcan Formula, but not the Barcan Formula. This is because, given these presuppositions, the Barcan Formula is interpreted as saying that if in some possible world, something is Φ, then there is something in the actual world which is possibly Φ. Although Linksy and Zalta and Williamson defend that reading of the Barcan Formula, most advocates of possible worlds believe in mere possibilia, objects which exist in other possible worlds but not in the actual one. As a result, they choose systems which do not validate the Barcan Formula. In her early work, in the 1940s, Barcan did not present an interpretation for her system, nor a preferred reading of the Barcan Formula. By 1961, as we'll see below, her preferred reading appears to be ‘if possibly something is Φ, then there (actually) is something which is possibly Φ’. Objections to the Barcan Formula which presuppose that it quantifies over possible worlds are therefore not effective against Barcan's own view.

8 I am grateful to an anonymous referee for encouraging me to stress this point more.

9 I am grateful to an anonymous referee for the suggestion to say more about Barcan Marcus' relationship to Russell. The referee also contends that views similar to Barcan Marcus' and Russell's are expressed in Smullyan, “Modality and Description” reviewed by Barcan Marcus (“Review of A. Smullyan”) and Fitch, “The Problem”. Fitch's paper, like Fitch's “Attribute and Class” which I discuss below, explicitly acknowledges the influence of Barcan Marcus on Fitch's view. Smullyan's pertains to the response to Quine's number of the planets argument which, as I noted in footnote 2 above, is beyond the scope of the present paper but which I intend to discuss in the future.

10 For more on Russell and Jones, see Janssen-Lauret, “Grandmothers of Analytic Philosophy”.

11 For more on the uses of Barcan Marcus' substitutional account of quantification and its role in her overall system, see Janssen-Lauret, “Meta-Ontology, Naturalism, Quine-Barcan”, and Janssen-Lauret, “Committing to an Individual”, both of which argue that Barcan Marcus' view amounts to an alternative view of ontological commitment with its own canonical language to rival Quine's.

12 An anonymous referee raises the objection that even if Barcan's formal system is plausibly inspired by her views on direct reference, the expressive potential of that system without constants remains weaker than the full theory of the direct reference of proper names which the referee contends “Kripke, Kaplan and others promulgated in the seventies”. This is not quite correct. It is true that a system without constants is weaker in its expressive power than a system with constants, specifically with respect to expressing identity statements, as explained in Barcan Marcus, “Modalities and Intensional Languages”, 310, and Janssen-Lauret, “Committing to An Individual”, 597–9. But Barcan Marcus' “Modalities and Intensional Languages”, published in 1961, nine years before the start of the seventies, does have the full direct reference theory. Although it lacks the causal theory of reference, Barcan Marcus (“A Philosopher's Calling”, 85–6) ascribes the causal theory to Geach's 1969 “The Perils of Pauline”, not to Kripke.

13 Later Barcan Marcus viewed modal discourse about actualia as counterfactual descriptions of actual objects, and modal discourse purporting to be about mere possibilia as consisting in false Russellian descriptions (Barcan Marcus, ‘Quine's Animadversions’), so her view remained ontologically parsimonious.

14 An anonymous referee suggests that Kripke might answer the question by taking the union of all of his domains of discourse. But this answer does not lay to rest the difficulties of inter-world identity. If we do not know whether a and b, the members of two different sets representing possible worlds, are identical or distinct, we do not come to know whether they are identical by taking the union of the two sets. It is the case that a and b are either identical or distinct, and so it is the case that there are either two things, a and b, in the union set or just one thing. But we cannot come to know which one of these alternatives is the case unless we first determine whether a and b are identical, and that is precisely the problem of inter-world identity. Criteria of inter-world identity must be given before it can be determined what is in the union set of the domains of all possible worlds (provided that this collection is not too large to be set-sized).

15 An anonymous referee suggests that this implies that philosophers of disability and opponents of disablism should take an interest in modality. I think that the referee's suggestion is plausible; see, for example, Janssen-Lauret, “Anti-Essentialism, Modal Relativity” §3 for a case against Kripkean origin essentialism which considers first-personal statements by speakers discussing their own genetic illnesses or disabilities.

16 An anonymous referee suggests that Barcan Marcus' reluctance to take biological sex as essential may be connected to her feminist views. Barcan Marcus did profess feminist views in her “Philosopher's Calling”, 80–1, 86–8. For example, she pointed out the absurdity of the objection made to her appointment as chair of philosophy at the University of Illinois that there had never previously been a female chair at that university. Barcan Marcus did not, as far as I am aware, explicitly connect her feminism to her views on essentialism. It does seem plausible to speculate, as the referee does, that a feminist in the 1970s might find it easier to see how biological sex might not be an essential property. I conjecture, for example, that familiarity with the distinction between biological sex and gender as a social and psychological category, popularized by feminists in the 1960s and 1970s, might make it easier for a philosopher to consider it possible that one and the same person in the social-psychological sense might have had a different biological sex.