Abstract
Quine’s ‘Two Dogmas of Empiricism’ is generally seen as overturning Carnap’s epistemological picture of mathematics and the sciences. However, I wish to stress how this paper grew out of arguments not having anything to do with large-scale epistemological concerns, but ones originally presented against quantified modal logic. Quine thought he could demonstrate the impossibility of adding anything like ordinary quantification to modal logic, but Barcan Marcus did exactly this. In fact, as I will argue, ‘Two Dogmas ...’ can be seen as growing out of a 1947 paper of Quine’s where Barcan Marcus is the explicit target. Later, in certain exchanges with Quine, Barcan Marcus puts forward and defends a consistent and interesting position on matters of ontology and the philosophy of language. This chapter will examine Barcan Marcus’s role in both the debate over analyticity and the debate on (meta-)ontology.
I would like to thank the audiences to which I presented these ideas for their useful feedback. I would also like to thank my class on the history of modality for many useful discussions. In particular, I would like to thank two M.A. students from this class, Estefanía Cubaque and Robert Charles Dillon, for reading an early draft of this chapter and providing useful comments. I would also like to thank the editors of the present volume for many useful comments and suggestions.
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Notes
- 1.
See Barcan Marcus, R. (2010). A Philosopher’s Calling. Proceedings and Addresses of the American Philosophical Association, 84(2), 75–92. Other information for this biography was taken from Williamson, T. (2013). In Memoriam: Ruth Barcan Marcus 1921–2012. Bulletin of Symbolic Logic 19(1), 123–126; and from the entry of the Jewish Women’s Archive: https://jwa.org/encyclopedia/article/marcus-ruth-barcan.
- 2.
Janssen-Lauret (2015) is a recent exception.
- 3.
I will refer to her as Barcan Marcus throughout this chapter as this is the name she published under for most of her life. Her early papers were published under the name Ruth C. Barcan, but as Williamson notes (Williamson, 2013), Alonzo Church made her publish under her ‘legal name’ when he found she was married. Much of the biographical information in this introduction can be found in Martí (2012) and Williamson (2013).
- 4.
I discuss these various pressures in Sect. 3 of my Lavers (2016). Below I discuss only the influence of Gödel’s results on Carnap’s philosophy of mathematics.
- 5.
Quine came to realize that definability in arithmetic did not render a concept unimpeachable.
- 6.
Carnap, however, can no longer reject questions about the meaning of terms (for example numerical expressions) as misguided.
- 7.
It was, however, a topic of conversation for their in person meeting in 1949.
- 8.
The Barcan formula is the claim that \(\Diamond \exists x Px \supset \exists x \Diamond Px\). Barcan Marcus viewed talk of possibility not as talk of other worlds, but as talk of different ways actual things could be. The Barcan formula follows from such a view of possibility. If it is possible for something to have the attribute F, then there is some existing (actual) thing that could have the attribute. She did not believe in mere possibilia—see ‘Dispensing with Possibilia’ in (Barcan Marcus, 1993).
- 9.
In the three way correspondence, it is clear that one of his main goals in terms of addressing the question of analyticity is still to define analyticity in non-modal terms. “Problems of meaning, analysis, analytic truth, necessity, etc. are, in the literature, intimately bound up with two kinds of things which I deplore: Platonism and intensional logic. My purpose (in what concerns synonymy) has been to separate the above-named problems from Platonism and intensional logic; to isolate them so that they may be talked about nominalistically and extensionally. Thus isolated, the problems take the form essentially of a single problem: behavioristic definition of intensional synonymy. I don’t say this problem can be solved; what I say is that this is the way the problems under consideration should be conceived, if at all. And that I can’t understand such things as the philosopher’s (e.g. Carnap’s) concept of “analytic truth” unless this problem be solved” (White, 1999, 344–345).
- 10.
The relevant part of the paragraph is in footnote 8.
- 11.
True, the box is out front and so could be eliminated as Quine proposes in the 1947 article. This would have the definition of synonymy being given in terms of analyticity, which Quine wanted to avoid.
- 12.
This phrase is taken from (Quine, 1943, 124).
- 13.
That they are often talking past each other is clear. Each rejects basic assumptions of the other. As we will see, Barcan Marcus does not accept that quantification exposes our ontological commitments. Also, as one can see in Quine (1961), Quine does not accept Barcan Marcus’s view that identity, extensionality and substitutivity come in grades of various strength.
- 14.
Here we are treating ‘The Morning Star’ and ‘The Evening Star’ as names. For Barcan Marcus there is no syntactic test for whether something functions as a name or as a description. If we were to treat it as a description, then we would be in a similar position to that described above.
- 15.
It may have problems of its own but it is not an ad hoc device brought in to solve just one problem.
- 16.
In a later article (Quine, 1977), Quine returns to a version of the number of planets argument. Here, however, Quine is clear about the distinction between de re and de dicto readings of names. He points out that the problems he sees arise only on the de dicto reading. That said, the de re reading of names, which he associates with Kripke’s rigid designators, leads to essentialism on Quine’s view. “A rigid designator differs from others in that it picks out its object by essential traits” (Quine, 1977, 8). Here we see an example of Quine moving from attempting to show the impossibility of adding extensional quantification to modal logic to holding that QML involves a commitment to essentialism. This is the topic to which we now turn.
- 17.
Of course, we ought not accept Quine’s ableist assumptions. Even in Quine’s day there were cyclists without two legs.
- 18.
I am assuming that the definitions of these properties do not contain individual constants. \((Pa \vee \lnot Px)\) is a property a could be shown to have of necessity, even if this does not hold for all objects.
- 19.
Included in Barcan Marcus (1993).
- 20.
He does later at one point accuse Barcan Marcus of a use/mention confusion: “Thus consider her ‘informal argument: (12) If p is a tautology, and p eq q, then q is a tautology’. Her adoption of the letters ‘p’ and ‘q’, rather than say ‘\(S_1\)’ and ‘\(S_2\)’, suggests that she intends them to occupy sentence positions. Also her ‘eq’ is perhaps intended as a sentence connective, despite her saying that it names some equivalence relation; for she says that it could be taken as ‘\(\equiv \)’ . On the other hand her clauses ‘p is a tautology’ and ‘q is a tautology’ do not show ‘p’ and ‘q’ in sentence position. These clauses show ‘p’ and ‘q’ in name positions, as if they were replaceable not by sentences but by names of sentences” (Quine, 1961, 324). Barcan Marcus in jest describes this as her fall from grace on the question of use/mention in Quine’s eyes. See Barcan Marcus (1993, 222).
- 21.
Quine, in the last essay he prepared for publication during his lifetime, (Quine, 2001), reaffirms his commitment to extensionalism, but mentions only clarity and the convenience of intersubstitutability salva veritate of coextensive terms as points in favour of extensionalism.
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Lavers, G. (2022). Ruth Barcan Marcus’s Role in the Mid-Twentieth Century Debates on Analyticity and Ontology. In: Peijnenburg, J., Verhaegh, S. (eds) Women in the History of Analytic Philosophy. Women in the History of Philosophy and Sciences, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-031-08593-2_11
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