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Jhap Handout: Ruth Barcan Marcus and Quantified Modal Logic

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Jhap Handout: Ruth Barcan Marcus and Quantified Modal Logic JHAP HANDOUT: RUTH BARCAN MARCUS AND QUANTIFIED MODAL LOGIC FREDERIQUE JANSSEN-LAURET 1. Ruth Barcan's Early Work and Its Significance Was Barcan the originator of quantified modal logic [1, 2], and of direct reference theory [8]? Or was it Carnap (1947) and Kripke (1970) respectively? Or just Kripke (1963, 1970)? I'll argue that Barcan was not only the first to publish a quantified modal logic, but that hers, deeply entwined with her direct reference theory of names, was more influential especially in overturning the extensionalist consensus in early analytic philosophy, and in changing Quine's mind. Quine had long been vigorously anti-modal; when he found that Carnap had embraced intensional languages, he shot off a letter saying, `your principle of tolerance may finally lead you even to tolerate Hitler' (Quine 1990, p. 241). But his debate with Barcan Marcus led him to abandon several arguments which he had to concede were bad or not effective against her { in part because while they had different views there was common ground between them on metaphysics and ontology. 2. W.V. Quine and Ruth Barcan Marcus on Ontology { Russellian legacy of ontological questions: logical atomism and the world being built up out of unanalysable, directly knowable constituents. { Russell argued that only `this', `that', and `I' are real proper names: they must stand for something we know directly. He also offered a theory of definite descriptions: they ascribe some predicate(s) to exactly one thing; possibly but not necessarily something directly perceived. |Two different developments of Russellian approach to ontology. W.V. Quine and Ruth Barcan Marcus were each inspired by Russell's approach to ontology. Each borrowed one element of his view (ontology by acquaintance or ontology by description) and ditched the other element. Quine, who believed only in knowledge by description, believed that ontology could get by using only descriptions and no proper names. Ruth Barcan Marcus, who believed in knowledge by acquaintance in a broader sense than Russell, held that proper names can be used to refer to and give us reason to believe in objects we know directly. [3, 4] 1 2 FREDERIQUE JANSSEN-LAURET Global Holism (Quine) Extreme foundationalism: (Barcan- Marcus) • Contact with objects always medi- • Objects are encounterable directly ated by best theory [18] by acquaintance [11] • Variables as categoremata • Names as categoremata [4] • Logical form: p9x'(x)q, objectual • Logical form: px = tq for directly quantifiers referential t • Dispenses with names, paraphrasing • Dispenses with quantified categore- them as definite descriptions mata: substitutional reading 3. Quine Against Modal Logic: On the Back Foot in Debate with Ruth Barcan Marcus Three phases/styles of argument to Quine's opposition to quantified modal logic. 3.1. Use/Mention Argument. Early '40s Quine: `the result of applying \necessarily" to a statement is true if, and only if, the original statement is analytic.' [13, p. 121] Though not yet categorically opposed to analyticity, he thinks to quantify into modal contexts is a use-mention confusion: they're quotational [6]; rebutted implicitly by Barcan Marcus [2]. Crucially, Barcan's system is an uninterpreted proof theory. It's all metamathematics. The question of use vs. mention doesn't apply if words aren't used to stand for things. 3.2. Abstract Objects Argument. Quine concedes her point [15]. He revises his anti- modal arguments to incompatibility with materialism: quantification into modal con- texts is coherent but quantified over abstract intensional concepts: `quantified modal logic is committed to an ontology which repudiates material objects' [14, p. 47a]. This is Quine's argument against Carnap, because Carnap needed individual concepts to explain contin- gent identity. E.g. `the morning star is not necessarily the evening star' is true because the evening star concept and the morning star concept are distinct. Quine had had this argument since 1938 and neither he nor Carnap changed their minds. Rebutted by Barcan Marcus: She was a nominalist and did not believe in concepts [9, pp. 307-311];[11], and she believed that identity was necessary. `You may describe Venus as the evening star and I may describe Venus as the morning star, and we may both be surprised that as an empirical fact, the same thing is being described. But it is not an empirical fact that (17) Venus I Venus and if `a' is another proper name for Venus (18) Venus l a.' (Barcan Marcus 1961: 310). `Consider the claim that (13) alb is a true identity. Now if (13) is such a true identity, then a and b are the same thing. It doesn't say that a and b are two things which happen, through some accident, to be one. True, we are using two different names for that same thing, but we must be careful about use and mention. If, JHAP HANDOUT: RUTH BARCAN MARCUS AND QUANTIFIED MODAL LOGIC 3 then, (13) is true, it must say the same thing as (14) ala. But (14) is surely a tautology, and so (13) must surely be a tautology as well.' (Barcan Marcus 1961: 308). 3.3. Essentialism Argument. Modal logic requires essentialism, and essentialism is incomprehensible. Statements of the form `x is essentially F ' have an underlying form which attributes analyticity to sentences ascribing F -ness to x. Even if `rationality is involved in the meaning of the word \man" while two-leggedness is not; but two-leggedness may at the same time be viewed as involved in the meaning of \biped" while rationality is not, it makes no sense to say of the actual individual, who is at once a man and a biped, that his rationality is essential' [17, p. 22]. But Barcan Marcus proved that her quantified modal logic did not entail essentialism [9, pp. 317-318]. For details see [3]. 3.4. Modal Inconstancy Argument. Quine softens his mathematical cyclist argument to modal inconstancy. The term is from Lewis but the idea is Quine's: Essentialism is comprehensible only relative to a background of assumptions. Note: while Quine's arguments above are bad ones, modal inconstancy is still defensible [5, 7] `Certain properties of a thing or substance are under investigation, against a background of others that are not being questioned. The utility of this contrast, dependent again on the project of the moment, has doubtless nurtured the age-old belief in an eternal distinction between essence and accident. I part company with the essentialists and the modal logicians only when they accord these modes a place in the austere and enduring description of reality' [20, p. 94]. `the respectable vestige of essentialism [which] consists in picking out those minimum distinctive traits of a chemical, or a species, or whatever, that link it most directly to the central laws of the science' is `of a piece rather with the chemical or biological theory itself' [19, p. 52]. (Barcan Marcus was only moderately essentialist so they are no longer poles apart [12].) Quine remained opposed to possible worlds and mere possibilia, i.e. modal ontology. He had long argued they're incompatible with his theory of ontological commitment as they don't have clear criteria of identity [16, p. 23]. Barcan Marcus rejected mere possibilia, so although she thought some of Quine's arguments were not very good, they were not far apart on that topic [10]. References [1] Ruth C. Barcan. A functional calculus of first order based on strict implication. Journal of Symbolic Logic, 11(1):1{16, 1946. [2] Ruth C. Barcan. The identity of individuals in a strict functional calculus of second order. Journal of Symbolic Logic, 12(1):12{15, 1947. [3] Frederique Janssen-Lauret. Meta-ontology, naturalism, and the Quine-Barcan Marcus debate. In Fred- erique Janssen-Lauret and Gary Kemp, editors, Quine and His Place in History, pages 146{167. Pal- grave Macmillan, Basingstoke, 2015. 4 FREDERIQUE JANSSEN-LAURET [4] Frederique Janssen-Lauret. Committing to an individual: Ontological commitment, reference and epis- temology. Synthese, 193(2):583{604, 2016. [5] Frederique Janssen-Lauret. The Quinean roots of Lewis's Humeanism. The Monist, 100(2):249{265, 2017. [6] Frederique Janssen-Lauret. Willard van orman quine's philosophical development in the 1930s and 1940s. In The Significance of the New Logic. Cambridge University Press, Cambridge, 2018. [7] Fraser MacBride and Frederique Janssen-Lauret. Meta-ontology, epistemology and essence: On the empirical deduction of the categories. The Monist, 98(3):290{302, 2015. [8] Ruth Barcan Marcus. Modalities and intensional languages. Synthese, 13(4):302{322, 1961. [9] Ruth Barcan Marcus. Modalities and intensional languages. Synthese, 13(4):302{322, 1961. [10] Ruth Barcan Marcus. Dispensing with possibilia. Proceedings and Addresses of the American Philo- sophical Association, 49:39{51, 1975-76. [11] Ruth Barcan Marcus. Nominalism and the substitutional quantifier. The Monist, 61(3):351{362, 1978. [12] Ruth Barcan Marcus. A backward look at Quine's animadversions on modalities. In R. Barrett and R. Gibson, editors, Perspectives on Quine, pages 230{243. Blackwell, Oxford and Cambridge, Mass., 1990. Reprinted in her Modalities. [13] W.V. Quine. Notes on existence and necessity. Journal of Philosophy, 40(5):113{127, 1943. [14] W.V. Quine. The problem of interpreting modal logic. Journal of Symbolic Logic, 12(2):43{48, 1947. [15] W.V. Quine. Review of the identity of individuals in a strict functional calculus of second order by Ruth C. Barcan. Journal of Symbolic Logic, 12(3):95{96, 1947. [16] W.V. Quine. On what there is. Review of Metaphysics, 2:21{38, 1948. [17] W.V. Quine. Two dogmas of empiricism. Philosophical Review, 60:20{43, 1951. [18] W.V. Quine. Existence and quantification.
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