Russell vs. Meinong: The Legacy of 'On Denoting'

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Russell Vs. Meinong : the Legacy of "On Denoting" Routledge Studies in Twentieth Century Philosophy (Online) ; 29 Griffin, Nicholas.; Jacquette, Dale. Taylor & Francis Routledge 0415963648 9780415963640 9780203888025 English Russell, Bertrand,--1872-1970.--On denoting-Congresses, Meinong, A.--1853-1920--(Alexius),-Congresses. 2009 B1649.R94R88 2009eb 121/.68 Russell, Bertrand,--1872-1970.--On denoting-Congresses, Meinong, A.--1853-1920--(Alexius),-Congresses.

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Page v Russell vs. Meinong The Legacy of “On Denoting” Edited by Nicholas Griffin and Dale Jacquette New York London

7 & x < 5). It is not clear that I can do this unless ‘>’ and ‘}. Let the extension of φ be the set S. Then the antiextension of φ, i.e., the extension of non-φ, S–, could be defined thus: For each ai, if ai S then aj S– just in case either aj = ai+1 and i is odd, or aj = ai-1 and i is even, or aj = ai and either i = 1 or i = n. Double negation will thus return us to S. However, the double negation condition is also met if we define S– as follows: For each ai, if ai S then aj S– just in case either aj = ai+1 and i is even, or aj = a i-1 and i is odd, or aj = ai and i = 1 or i = n. 16. See, e.g., Mally 1904:127. 17. This holds only for what he calls ‘nuclear properties’; see ‘The Status Counter-Examples’. 18. See also Jorgensen 2004 for further problems with Parsons’ definition, which, however, he prefers to Routley’s. 19. I’m grateful for many long discussions with Carolyn Swanson, who convinced me that Meinong’s style of predicate negation had problems that I hadn’t seen. 20. For a charming example of how such a result is necessary for an adequate theory of fiction see Priest (1997). 21. To adopt this solution does not necessarily prevent one from making a distinction between sentential and predicate negation—if one can be made out. But such a distinction, whatever plausibility it has or lacks, will not help with the consistency counter-examples. 22. As Greg Restall pointed out to me, the problem can be generalized further: For any claim P of any kind whatsoever, freedom of assumption delivers ( ιx) P (and of course ( ιx)~P, as well), so (UCP) renders the theory trivial. 23. Meinong incorporated the independence thesis into his theory of objects early on: Meinong 1904a: 82 ( GA 2:489–90). Mally subsequently rejected the principle (cf. Mally 1912). 24. Otherwise, freedom of assumption would be restricted as well: attempts to characterize an object as the existing golden mountain would succeed only in referring to the golden mountain. 25. See also McMichael and Zalta (1979) where the theory is presented with a somewhat different terminology and notation. Rapaport (1978) has a similar theory. In the more restrictive field of fictional objects, Woods makes an analogous distinction between history-constitutive predications and fictionalizations (Woods 1974:42ff), a position criticized in Griffin (2005a). 26. Most modern versions of item theory (e.g., Routley 1980:496; Jacquette 1985) prefer to dispense with both notions and deal with the status counterexamples by adopting (RCP). This certainly results in a simpler, more elegant form of the theory, as Jacquette argues in some detail. 27. This is evidently Meinong’s preferred solution, cf. 1915:283. 28. Findlay’s exposition (1933: Ch. 4) is clearer than Meinong’s (1915: Ch. 37), but neither does a good job of justifying the notion. 29. From an item-theoretic point of view, rejecting the transition from (2) to (3) calls into question Gilles’ status as an object. 30. Routley suggests this parallel (1980:268). 31. One doubts that he took this point very seriously: preserving classical or traditional logic was rarely of much concern to him. 32. Marriage being a symmetrical relation, it is identical to its converse. Similar problems, however, arise with asymmetrical and nonsymmetrical relations.

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Page 230 33. Woods (1974:27) would deny that Anna Karenina’s lesbian lover is even a nonexistent item, since there is (as yet) no work of fiction to bring her into nonexistence, so to speak. Woods makes an important distinction between fictional items and what he calls ‘nonesuches’, which are not items at all (cf. 1974: Ch. 2). 34. I think Parsons introduced the ‘immigrant/native’ terminology (Parsons 1980:51–52). On the whole in dealing with an object that is an immigrant to the context of supposition, I prefer the term ‘imported’, since the supposer does the importing. The object does not move of its own accord. 35. There is no contradiction here, even though Buckingham Palace is the same object in both contexts, since truth-value assignments are always relative to a context and V(qu(φa ),s) = T and V(qu(φa ),a) = F are consistent assignments (‘s’ is here the context of supposition; ‘a’ is the actual world). The situation is similar to that which is familiar from worlds semantics, though contexts are not worlds: they are typically much less complete and much more disorderly. (Cf. Sylvan 1997:176–77, where, however, the talk is about ‘set-ups’ rather than contexts. The model here of course, is Routley and Meyer’s setup semantics for relevant logic. Cf. Routley and Routley 1972, Routley and Meyer 1972a, 1972b, 1973.) Worlds, on the other hand, may be contexts. In particular, the actual world often is the context of supposition, especially for fact-stating (or putatively fact-stating) discourse; for such discourse, the actual world is typically the default context. 36. I’m not suggesting this is an outcome Woods would embrace, but, without it, it seems clear that his fictionalized Gladstone will acquire all manner of inconsistent fictionalized properties and this, in turn, will make it difficult to preserve intuitively valid inferences about him in any particular fictionalization. 37. This last is essential in any case in order to make consistent truth-value ascriptions to sentences containing indexicals or ambiguous proper names, for example. 38. My main reason for wanting to admit nonesuches as nonexistent items is the need to preserve inference rules such as particularization (quantifier introduction). It seems to me that we ought to be able to infer from ‘The present King of France is bald’ to ‘Some item is bald’. Preserving the inferential role of such singular terms is of more than marginal concern. There is no reason that I can see that would distinguish the greatest prime from the round square as a nonesuch. Yet obviously there are mathematically important inferences to be made about the greatest prime—not least the inference to its impossibility. 39. Why then does it seem so natural (and also quite right) to say ‘Sherlock Holmes is a detective’? I think the answer is just cultural familiarity. Conan Doyle’s stories are so well-known (if only by reputation) that it is easy for us to access (or switch to) the context of supposition of the stories with no more prompting than the use of Holmes’ name. A less familiar fictional detective’s name does not elicit the same response, because, without further clues, we are less easily able to access the context of supposition. But obviously, when the context precludes the Conan Doyle stories, as when someone asks for the name of a private detective to consult about their affairs, proffering Holmes’ name would be distinctly unhelpful: when the context is the actual world, ‘Holmes is a detective’ no longer seems obviously right. 40. I’m grateful to Rhonda Anderson, Carolyn Swanson and Charissa Varma for many long discussions of item theory during the initial preparation of this paper. Different versions were read at the Australasian Association of Logic conference at Macquarie University in July 1997 (a conference dedicated to the memory of Richard Sylvan); at the Mistakes of Reason conference in honour of John Woods at the University of Lethbridge in April 2002; at the Russell vs.


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Page 231 Meinong conference to celebrate the centenary of ‘On Denoting’ at McMaster University in May 2005; at the Fourth Principia International Symposium at Florianopolis, Brazil, in August 2005; and to the philosophy department at McMaster University. I am grateful to participants on all these occasions for their comments. Needless to say, my most fundamental debts are to Richard Sylvan, though sadly I was never able to discuss the paper with him. REFERENCES GA : Alexius Meinong, Gesamtausgabe , ed. R. Haller and R. Kindinger, 8 vols., Graz: Akademische Druckund Verlagsanstalt, 1969–78. Chisholm, R., ed. (1960) Realism and the Background of Phenomenology , Glencoe, IL: The Free Press. Copeland, B. J. (1979) ‘On When a Semantics is not a Semantics: Some Reasons for Disliking the Routley-Meyer Semantics for Relevant Logic’, Journal of Philosophical Logic 8: 399–413. Cox, M. (1997) Twelve Victorian Ghost Stories, Oxford: Oxford University Press. Findlay, J. N. (1933) Meinong’s Theory of Objects and Values , 2nd edn, Oxford: Clarendon 1963. Gabbay, D. M. and Wansing, H., eds. (1999) What is Negation?, Dordrecht: Kluwer. Griffin, N. (1996) ‘Denoting Concepts in The Principles of Mathematics’, in R. Monk and A. Palmer (eds), Bertrand Russell and the Origins of Analytical Philosophy , Bristol: Thoemmes: 23–64. ——. (2005a) ‘Through the Woods to Meinong’s Jungle’, in A. Irvine and K. Peacock (eds), Mistakes of Reason: Essays in Honour of John Woods, Toronto: University of Toronto Press. ——. (2005b) ‘Russell’s Early Semantics’, paper presented to the British Society for the History of Philosophy, St. Catherine’s College, Oxford. Jacquette, D. (1985) ‘Meinong’s Doctrine of the Modal Moment’, Grazer Philosophische Studien 25/26: 423–38. Jespersen, O. (1924) The Philosophy of Grammar, London: Allen and Unwin, 1963. Jorgensen, A. K. (2004) ‘Types of Negation in Logical Reconstructions of Meinong’, Grazer Philosophische Studien 67: 21–36. Mally, E. (1904) ‘Zur Gegenstandstheorie des Messens’ in Meinong (1904b): 121–262. ——. (1912) Gegenstandstheoretische Grundlagen der Logik und Logistik , Leipzig: Barth. McMichael, A. and Zalta, E. (1979) ‘An Alternative Theory of Nonexistent Objects’, Journal of Philosophical Logic 9: 297–313. Meinong, A. (1904a) ‘The Theory of Objects’, trans. I. Levi, D. B. Terrell and R. M. Chisholm, in Chisholm (1960): 76–117. ——., ed. (1904b) Untersuchungen zur Gegenstandstheorie und Psychologie , Leipzig: Barth. ——. (1907) Über die Stellung im System der Wissenschaften , Leipzig: Voigtländer. ——. (1910) On Assumptions, 2nd edn (1st edn 1902), trans. J. Heanue, Berkeley: University of California Press, 1983. ——. (1915) Über Möglichkeit und Wahrscheinlichkeit, Leipzig: Barth = GA 6. ——. (1917) On Emotional Presentation, trans. M. Schubert Kalsi, Evanston: Northwestern University Press, 1972. Parsons, T. (1978) ‘Nuclear and Extranuclear Properties, Meinong and Leibniz’, Noûs 12: 137–51.


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Page 232 ——. (1980) Nonexistent Objects, New Haven: Yale University Press. Peacock, K. A. and Irvine, A. D., eds. (2005) Mistakes of Reason. Essays in Honour of John Woods, Toronto: University of Toronto Press. Priest, G. (1997) ‘Sylvan’s Box: A Short Story and Ten Morals’, Notre Dame Journal of Formal Logic 38: 573–82. Rapaport, W. (1978) ‘Meinongian Theories and a Russellian Paradox’, Noûs 12: 153–80. Restall, G. (1999) ‘Negation in Relevant Logics. (How I Stopped Worrying and Learned to Love the Routley Star)’, in Gabbay and Wansing (1999): 53–76. Routley, R. (1980) Exploring Meinong’s Jungle and Beyond , Canberra: Research School of Social Sciences, Australian National University. Routley, R. and Meyer, R. K. (1972a) ‘The Semantics of Entailment, II’, Journal of Philosophical Logic 1: 53–73. ——. (1972b) ‘The Semantics of Entailment, III’, Journal of Philosophical Logic 1: 192–208. ——. (1973) ‘The Semantics of Entailment, I’, in H. Leblanc (ed.), Truth, Syntax and Modality, Amsterdam: North Holland: 199–243. Routley, R. and Routley, V. (1972) ‘Semantics of First-Degree Entailment’, Noûs 6: 335–58. ——. (1973) ‘Rehabilitating Meinong’s Theory of Objects’, Revue internationale de philosophie , 27: 224– 54. Russell, B. (1903) The Principles of Mathematics, 2nd edn, London: Allen and Unwin, 1964. ——. (1905a) ‘On Denoting’ in Russell (1994): 415–27. ——. (1905b) Review of Meinong (1904b), in Russell (1994): 596–604. ——. (1907) Review of Meinong (1907), in Essays in Analysis , ed. D. Lackey, London: Allen and Unwin, 1973: 89–93. ——. (1994) The Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–05 , ed. A. Urquhart, London: Routledge. Sylvan, R. (1995) ‘Re-Exploring Item Theory. Object Theory Liberalized, Pluralized and Simplified but Comprehensivized’, Grazer Philosophische Studien 50: 47–85. ——. (1997) Transcendental Metaphysics. From Radical to Deep Pluralism , Cambridge: The White Horse Press. Woods, J. (1969) ‘Fictionality, and the Logic of Relations’, Southern Journal of Philosophy 7: 51–63. ——. (1974) The Logic of Fiction, The Hague: Mouton. Zalta, E. N. (1983) Abstract Objects. An Introduction to Axiomatic Metaphysics , Dordrecht: Kluwer.


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Page 233 11 Contra Meinong Peter Loptson Some philosophers have historical interests in Alexius Meinong and his theory of objects. Others think that some version or other of his theory is actually true. My focus in this paper is on the latter view. Before turning to the motivations to Meinongianism, however, and whether they justify that theory, it may be useful to situate the fundamental topic of Being and Non-Being within the broad framework in which Meinong, and his great opponent, Russell, were working (and which still operates to a degree now). There are two distinct and incompatible pictures of the Being/Non-Being divide, both of which figure prominently in late nineteenth and early twentieth-century philosophy. According to one, there is an unbridgeable gulf, a chasm or abyss, between Being and Non-Being. Something either is, or it isn’t. A question that is very much secondary, for this conception, is what may turn out to characterize the things that there are, with one party (they may be called the nominalists) drawn to the idea that all of the things that there are are spatio-temporal particulars (and, possibly, complexes—events, states of affairs, facts—involving them), and another party holding that some things that there are are nonspatial (perhaps including mental things and/or abstract things). The second of these parties may choose to use the term ‘existence’ just to stand for spatio-temporal things, and the term ‘subsistence’ to stand for abstract things (and mental things, on some views); but this is merely terminological, or taxonomical, and some prefer simply to identify a single condition, called being, existing, being real or subsisting, and noting that there are some quite basic kinds the things this condition applies to. The second position in the fundamental divide resuscitates a version of the old Platonic doctrine of degrees of being. (And in fact the basic contrast itself can plausibly be seen as anchored in an elemental semantical division between those who think being admits of degrees, and those for whom this idea is unintelligible.) This position has the idea that a fullest degree of being attaches to spatio-temporal items. Then a paler, lesser degree of being—still real being, but (somehow) ‘less’ so—attaches to ideal and abstract things (including mathematical objects, concepts and propositions). Then, for some (not all) on this wing, there is a third, particularly


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Page 234 ‘pale’ category of being, possessed by anything able to be thought of. (For some who take this ‘bolder course’, the specially ‘pale’ items are limited to possibles, for others they include also impossibles.) The historical Meinong, as I read him (I appreciate that others have differing interpretations), actually, inconsistently, vacillated between both these fundamental camps (within his long article ‘The Theory of Objects’ [1904]). Most fundamentally, and in the first instance, he belongs to the first one; and sees as his bold and exciting insight, that the objects his theory affirms (apart from the ones with existence, and subsistence—the two taxa of being) don’t need to have, and don’t have, any sort of being at all. They have properties, but not ( any kind of) being, and—this again is what he thinks is his important breakthrough—we see, through this fact, that having properties just is altogether independent of being. But then Meinong goes on to, in effect, retract this idea, with the doctrine of what he calls Aussersein , the theory of a kind of being that is beyond (the usual sorts of) being. Either Aussersein is an ontic category of some kind, or it is nothing. As an ontic category, it is a ‘third degree’ of being. The Meinong intended in the present paper is chiefly the Meinong who doesn’t affirm Aussersein , though the objections to come will also militate against the one who does. I think that those who are drawn to embrace some version of Meinong’s theory of objects are usually so drawn with one or other of three motivating, or persuading, rationales. One involves an idea that natural language is well-anchored, that is, semantically determinate, clear, and that it enjoys a primacy over philosophical attempts to revise or regiment it, or even establish something linguistic that would be parallel or alternative to it, and that natural language straightforwardly and not finally disputably affirms Meinongian sentences—Sosein-affirming sentences, specifically, property ascriptions to unreal things. We might think of other kinds of cases or contexts where natural language data seems readily to give rise to outcomes of high philosophical theory. We may observe that the tomato on the table is red and that the fire truck that just went by the house is red , and infer that the tomato on the table and the fire truck that just went by the house have something in common , indeed, that there exists—must exist—a certain something or other, which will, in turn, need to be of a certain ontological type or kind, which can qualify as what these objects have in common, namely, the property of being red . The first route to Meinong holds, in a comparable manner, that there are claims we rather straightforwardly and unproblematically make, which will imply that some things have properties, even though, in the cases concerned, these things aren’t real . Although I am—perhaps a bit tendentiously—assigning those moved in this way to adopt Meinongian convictions a set of strong, firm intuitions about certain natural language sentences, namely, that they are clearly and straightforwardly true, and clearly and straightforwardly imply Meinong’s theory (or something close to it), in complete fairness it should be noted—


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Page 235 allowed—that someone might become a Meinongian, under this broad motivating aegis, where they simply held that Meinong was the best bet, or option, among several competing and conflicting ones. This more semantically diffuse or nuanced path might hold that the natural language data is apparently conflicting, hence that the theorist prompted to theory by that data must make choices, and (perhaps) Meinongianism is then seen as the least objectionable of the choices. At any rate, the fundamental idea remains the same: that things we regularly hold true point to the theory of objects. A second motivating path to a Meinongian stance, philosophically, stems from an idea that there is in actual fact no single semantical or logical anchor, that logics and semantical structures are multiple and are devised, or constructed, rather than discovered, and a Meinongian structure or model (perhaps more than one) is doable; nothing falls apart when models with domains that include unreal things are put together, and something interesting and coherent results—as much as one will or can get from any semantical framework or logic. Finally, what I think is the third road to Meinong has important similarities with the first two, explicitly rejecting anchored metaphysicality, as the second one implicitly does (at least for logic ), and affirming that, since no sentences are true in an ontologically substantive— reality-disclosing—sense, Meinongian sentences are among the disparate array of linguistic phenomena, neither better nor worse than others, and able to plant themselves as workably and effectively as might be desired for a well-behaved segment of language. Strictly speaking, this third route will not lead to the historical Meinong, since he affirmed the cogency of metaphysics. The third route, in its most modest version, takes the view that many semantically well-behaved sentences, even whole segments of natural language, simply do not have ontological or metaphysical import, even where they may have grammatically subject-predicate form, and that among these ‘extra-ontological’ sentences are many that assign properties to unreal things. In a full-blown, not modest, version this stance denies that any sentences are genuinely ontological or metaphysical, and takes it as unproblematic, accordingly, that perfectly adequate sentences say, for example, that Sherlock Holmes was a Victorian detective given to wearing deerstalker caps. The second of the three indicated routes to Meinong is a formalist one, chiefly attracting logicians; the first has appeal for friends of ordinary language, some of whom (though certainly not all) are quite antiformalist; the third is more likely to draw neopragmatists, who think that quite a lot of what we say, possibly, in fact, all of it, does not purport to capture reality. All three of these motivating stances can be phrased nonlinguistically—as Meinong himself put his theory, and perhaps might still prefer that his supposed insights be rendered. Each of the three rationales can also be represented by, or paired with, a conception of logic, more precisely, of the logical space within which logic itself is to be found. The first corresponds to the idea that, at least as we would think of it now, classical logic as it


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Page 236 stands, conceived as embodying the whole of the broad structure of truth-assertion and valid inference, is mistaken at least in its claimed comprehensiveness, and inadequate, needing correction and revision, and capable of receiving it (that is, rather than being rejected outright), in Meinongian as well as other directions. The true logic will have a classical proper part, or a proper part that is a modified version of classical logic; and also a Meinongian part, corresponding formally to such ideas as that if Holmes is a detective then some things are detectives and Holmes has some properties (even though, of course, Holmes is unreal, a fictional creation of Conan Doyle). The second framework might be said to correspond to the philosophy of logic of Carnap, where logics are developed, and may be ‘adopted’, for heuristic reasons or reasons of formal interest; some of these logics will be classical, or partly classical, and others Meinongian (and others altogether nonstandard in still other ways). The third framework, or perspective, may share with the first a commitment to there being a—complex—logic that gets things right; but denies the intelligibility (or possibly just the even minimal utility) of classical logic, the ‘true’, or most adequate, logic being a free logic, a logic without existence presuppositions or content. (For the second framework, free logics are just some among the varied, interesting denizens of the house of logic.) Meinong himself, it will be clear, is closest to the first of these frameworks. For him metaphysics is a genuine science, even if its object (that is, its Objekt ) is only a proper part of the still more comprehensive science of objects ( Gegenstanden ). For Meinong also existence has metaphysical content. (In fact, for him, existence requires spatio-temporal content. The more comprehensive genus, of which existence is a species, is Sein, or Being—also sometimes identified as Wirklichkeit, or Reality. Things with Sein, or Wirklichkeit, but lacking Existenz , or Existence, have Bestand , or Subsistence. Meinong is indeed one of those philosophers of whom Quine famously complained, ‘who have united in ruining the good old word “exist ”’(1963:3).) At any rate, Meinong’s interests, and commitments, are not those of a Carnapian formalism; nor, for all his imaginative, for his opponents extravagant, interest in the supposed world beyond Being, and its truths, does Meinong share Wittgensteinian limitations of the intelligibly thinkable and sayable to structures and patterns delineable in ‘our’ forms of life (even if, for some of those Wittgensteinians and neopragmatists, our forms of life include such appropriately assertible items as that Santa Claus is bearded, Superman can fly but isn’t female, and inferences they and their like may warrant). In the present paper, I ignore the second and third of the motivating roads to Meinong, and confine myself to the rationale which is in fact, I think, closest historically to Meinong’s own position, and the theory to which it led him—the Gegenstandstheorie , which Russell, after apparently accepting it in The Principles of Mathematics, in 1903, rejected and sought to refute, in his correspondence with Meinong and in ‘On Denoting’, in 1905.


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Page 237 I want now to state two assumptions, both of which I believe are highly plausible, and which I know that many other philosophers share. Among those philosophers are Bertrand Russell and (I think) Alexius Meinong. The first assumption is that every genuine and unambiguous statement or proposition is equivalent to a statement or proposition which is perspicuous, that is, which represents, or constitutes, a precise or determinate content in (so-called) logical space. This is meant to be an assumption about sentences of natural languages, though it is intended to apply also to sentences of ideal or artificial languages which have been constructed to be languages adequate for science (or for a scientific philosophy). This assumption may be thought to be quite anodyne, hardly worth saying; perhaps on the grounds that it will be analytically true, given that attention has been restricted to unambiguous statements and propositions. On the other hand, it might be regarded as covertly affirming the central tenet of Russell’s logical atomism, according to which all and only true statements/propositions are equivalent to representational symbolic contents which are isomorphic with discrete determinate facts of the world. That thesis is anything but anodyne. In fact, I take the central logical atomist tenet to imply but not be implied by the perspicuity assumption, which is meant to affirm that there is always something definite, and with an in-principle intelligible structure, said, or meant, by unambiguous statements or propositionexpressing sentences of natural and scientific language. The differences between the two might be seen further by noting that logical atomism requires either a correspondence or a deflationary theory of truth, while the perspicuity assumption would also be compatible with a coherence theory. The second assumption I am making is that at least some true perspicuous statements or propositions are ontological or existential or metaphysical in character. They say or imply that something exists or is real. According to this assumption there are existential/ontological facts, independent of ways that observing or representing minds may screen, filter, interpret or regiment linguistic or other data. This assumption is certainly made by both Russell and Meinong, and also, I think, by most other philosophers. It is denied, however, by some pragmatist or neopragmatist philosophers, as well as by logical positivists and some Wittgensteinian and ordinary language philosophers; at least this appears to be the case. Russell—and Quine—make the stronger assumption that all perspicuous discourse is ontological or metaphysical in the sense I mean to identify. They articulate and affirm what Quine called the principle of ontological commitment. Worked through, it is equivalent to Russell’s denial of the Meinongian principle of the independence of Sosein from Sein. Accordingly, it would be question-begging, in a paper meant to argue for the superiority of a Russellian stance to that of Meinong, to assume global or comprehensive ontological commitment, or the principle that Sosein entails Sein (that is, that having properties entails being). However, the principle that at least


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Page 238 some perspicuous discourse is existence-implying, or metaphysical, is common to both Russell and Meinong. The central issue dividing Russell and Meinong is precisely whether there is ever Sosein-ohne-Sein ( Sosein without Sein—property-having without being). The case for Russell, and against Meinong, is multifaceted. There are what we may think of as passive, or negative, arguments, and also active, or positive ones. The former include Occamist—Occam’s razor —arguments that there is simply no need to postulate a Meinongian body of designated propositions which embody the Sosein without Sein idea; that all putative such propositions can be handled, treated, in ways wholly consonant with the Russell Sosein-entails-Sein principle. The active, or positive, arguments include Russell’s own, that the Gegenstandstheorie actually implies formal contradictions, that it will require existent round squares that must, and can’t, exist. Another Russellian argument, its ground more diffuse than the latter, stems from the idea that the really truth-expressing propositions— the ones genuinely, and strictly, corresponding to what is actually so—may well not—in plenty of actual cases don’t—closely resemble sentences of ordinary speech. The latter frequently turn out to be the flotsam and jetsam of vulgar discourse, by no means to be expected to express anything perspicuously, and certainly not to be looked to as affording a foundation, or a body of exemplary cases, of serious theory . So, according to this line of thought, even if some speakers may be found who will affirm sentences appearing to assign properties to Holmes, and so on, this is appearance not reality, that is, these sentences won’t be genuine Soseinsobjektiven. I offer on this occasion a case for Russell, and against Meinong, that is less formal, and less theoretically deep, than either of the latter Russellian arguments. It will embody something of the impulse of the first of the kinds of objections to Meinong just indicated—that there is no good reason to be a Meinongian—with something of the spirit of the second—that there are costs that the theory of objects incurs that make it unpalatable if not formally dismissable. The case I offer is also, unlike Russell’s own, a fundamentally empirical one. The ideas I develop in setting it out may possibly correspond to concepts and distinctions in the huge speech act theory literature, or elsewhere, which I haven’t managed to learn about. If so, I welcome being pointed to places in that literature where these or similar notions appear. I suppose that, in the real world, belief attitudes are not limited to believing-true, believing-false and being undecided about. We also, in many cases, kind of believe something, or believe that there is something right about something, or that it is more or less true, without necessarily straightforwardly believing that it , as it stands, is true. I want to say that we may endorse some propositions (or proposition-like items) in both the kind-of-believe, and the believe-true situations. Against that background: quite often, when we speak (or, for that matter, write), we say one thing, but


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Page 239 there is something else, not obviously or trivially synonymous or equivalent (and in at least some cases definitely neither synonymous or equivalent), that we could have said instead, and which, had we done so, we would have recognized or endorsed as more or less saying what it was that we did say. In some such cases, we wouldn’t have thought of that alternative, on that occasion. If someone else says it, we may well think (and say), that puts it better (more clearly, more eloquently, more succinctly, more appropriately, and so on) than I did—or puts it worse; or puts it about the same—but, in any case, that was an alternative, that would have served, and that I would endorse as more or less conveying the information, or covering the approximate ground, that I did. In others of these cases, the speaker, aware of alternatives, has deliberately chosen one of them as preferred, on the occasion. Sometimes such a process of choice may seem more or less random; it was not that one of these alternatives was judged best; rather, any of them (or some proper subset of them, with more than one member) would have done, and one doesn’t, maybe couldn’t, see a difference, that would matter, for opting for one, but given that one wanted to say a certain something, and this was one of the available options for doing it (apparently as good as any other), this was the one utilized. This is of course compatible with there having been, possibly in all such cases, causes, which might or might not be known (or knowable) to the speaker, and indeed might or might not be explanatorily acceptable to the speaker, of why the actually utilized sentence or expression was the one opted for. I want particularly to focus on cases of the kind I am describing where the members of the option set of expressions that would serve to (more or less) say what the speaker said, and which the speaker does or would endorse as doing so, are not literally synonymous with or, at least straightforwardly, strictly equivalent to each other; and, indeed, members of option sets which may (in actual fact) differ in truthvalue from each other. I want to allow cases where it might be arguable that a given pair of such expressions may be, at some semantical or metaphysical depth level, necessarily co-extensive. But generally, an option set, for present purposes, is to be a set of expressions which seem obviously or overtly different, and nonequivalent, ways of having said (more or less) the same thing, to an adequate or appropriate degree, or with one saying better what was said, on the occasion and in the setting in which something was said, and which the speaker would be prepared to endorse as doing so. So, speaker S says (quotation marks are to be taken as Quinean corner quotation) ‘ e ’; but would recognize not-obviously-equivalent ‘ e 1’, ‘ e 2’, … ‘ en’ as also being able to serve as, do duty for, what S was saying when ‘ e ’ was said. One very straightforward kind of case of the sort of phenomenon intended will be where ‘ e ’ involves a reference to an object S is observing and the referential expression is a proper name or definite description; S’s option set in this case will presumably include an ‘ ei’ where the name/description is replaced with a suitable pronoun, the act of utterance perhaps also involving an appropriate gesture. Here is another


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Page 240 example. A small (imaginary) Ontario city, Middlebury, has an annual athlete of the year award. I am talking with Fred. I remember that Bob is seen out jogging every morning, looks mighty fit, won a Middlebury race, and is a friend of the mayor’s. I say, ‘Bob ought to be a contender for Middlebury athlete of the year.’ Fred reminds me that Bob won the Toronto marathon a few months earlier. I knew this, but had briefly forgotten it. ‘The man who won the Toronto marathon ought to be a contender for Middlebury athlete of the year’ will be in my option set, along with what I had said, and it will be a case of what I will call a trumping member of an option set, for the speaker. Along with other properties to be explained presently, a trumping member of an option set will often be a reason for someone’s viewing it as trumping. As noted as well, some of e 1, … en may, in some circumstances, differ in truthvalue. Some cases of this kind will be posed by the sorts of cases raised by Donnellan, with his notion of referential uses of definite descriptions. Presumably a speaker might, having the appropriate false beliefs, be prepared to endorse each of e 1 through en as saying, or serving to say, more or less, what the speaker actually did say, but one or more of the set actually be false. There will also be cases where a speaker might hesitate, or be unsure, as to whether a given sentence is indeed a member of an option set for the speaker on a particular occasion. It also seems clear, as was suggested above, that a speaker might, in many actual situations, be prepared to assert that some members of what we are calling an option set expresses, more aptly, or accurately, what the speaker said or meant to say. (The speaker need not think a case of a more apt or accurate, and a less apt or accurate, pair of members of an option set, to be one such that the first is true and the second false, though they may think this.) Where members of an option set would be judged by the speaker more apt or accurate than others, we may say that a sentence of the former subset of the option set trumps , or would trump , less apt members. The speaker may of course have actually uttered a sentence such that no other sentence in his or her option set would trump it. Or—and this is the sort of case I particularly wish to focus on—there is a sentence, which someone might draw to the attention of the speaker, which the speaker would acknowledge to be a member of the speaker’s option set on a given occasion, and acknowledge also that it trumps the speaker’s actual utterance. Where this happens, we may say that a trumping sentence is the sentence of fundamental or primary commitment of the speaker who has committed himself or herself to the option set (or who would do so), and the speaker, in this case, withdraws or would withdraw, endorsement of or commitment to any trumped member of the subset. The speaker might say, or think, in such circumstances, Yes, that captures the idea better, or, anyway, is at least a little more accurate, strictly or literally speaking, than (at any rate) these alternatives. It will be clear that these notions of option set, and trumping, are approximate-boundaried ones—a speaker might , in some cases, hesitate, be unsure, or change his or her mind as to whether a


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Page 241 pair of sentences did , for that speaker, say more or less or approximately the same thing, in the intended sense; it will be clear also that it is the speaker who is normally to be taken to be authoritative in the matter. The idea I have been developing for real world contexts of belief attitudes, propositions or statements which may be endorsed as more or less or approximately true, but then surrendered or found less satisfactory than alternatives which will (typically) be nonequivalent and may differ in truth-value (the originally provisionally endorsed proposition or statement false, the ‘better’ successor which ‘trumps’ it true), finds an analogue on the plane of philosophical theory. Interestingly, this analogue plays a central role in the philosophy of Russell. The concept of displacement ‘identity’ (or so-called identity) was developed in 1960s discussions of materialism in the philosophy of mind. The position which came to be called eliminative materialism argued that so-called ‘mental states’ were really in fact brain states. Comparisons were made with other instances in the history of common sense belief, and science, where observed phenomena were conceptualized in ways that were at best approximately true, and in fact, strictly speaking, false and inadequate. (So-called ‘witches’, for example—who, had they really been witches, would have to have had supernatural powers—were actually (identical to) solitary herbgathering women living in the woods and perhaps practising a pre-Christian nature religion.) The eliminative materialists regarded ‘folk psychology’ (the belief that there are beliefs, desires and so on) as a long-standing mistaken body of theory, which does refer, or purport to refer, to real phenomena, though inaccurately. Folk psychology is (for eliminative materialists) ‘kind of’ true, or has genuine parts of reality correctly targeted, but is ‘trumped’ by the more accurate theoretical structures and models of neurophysiology. Historically, the first reasonably clear case of a philosophical eliminativist—philosophical theorist offering ‘analyses’ of phenomena captured not-quite-accurately by previous philosophy, and common sense, is perhaps Hume. Be that as it may, a central and active methodological goal and practice of Russell’s philosophy, at more or less all stages, and for abstract as well as empirical phenomena, is precisely a programmatic eliminativism along just these kinds of lines. Now to Meinong sentences , as alleged to obtain or occur, and to be affirmed and endorsed, in natural language. I note first that sentences—or states of affairs—in which apparent singular referring expressions for, or apparent singular reference to, unreal things, but where the apparent reference is within psychological or other intentional contexts, will not be reckoned as Meinongian sentences here; although a psychological or intentional case that implied (or was argued to imply) a statement asserting that an unreal object had some property would be a case where the statement implied was Meinongian. Thus, Bill is painting a picture of Leda and the swan is not a Meinongian sentence, nor is Mary believes that Artemis is a huntress, or Ponce de Leon sought the fountain of youth. In addition, sentences, or states of affairs that identify unreal things as unreal will not


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Page 242 count as Meinongian sentences. Thus, Hamlet is George’s favourite literary character, and Holmes was Conan Doyle’s best-known fictional creation are not Meinongian sentences. The latter category may seem slightly more problematic than the former in this regard. That is, some Meinongians—though not Meinong himself, on our evidence—might want to construe Holmes as an object , having, in addition to the properties of being a detective, and English, the property of being fictional. The treatment of ascriptions of being—hence, also, of non-being (what Meinong will have called Nichtseinsobjektiven )—is itself a topic of complexity in philosophical semantics, and metaphysics. It will suffice for present purposes to say that it is entirely in the spirit of Meinong, as well as Russell, to differentiate radically Soseinsobjektiven—property-and-relation-ascribing propositions—from Seinsobjektiven (including Nichtseinsobjektiven ). Meinong and Russell agree about the radical differentiation; what they disagree about is what the relations are between the categories of item so differentiated. Standard examples of bona fide Meinong sentences are, then: (1) Holmes is a detective. (2) Superman can fly. (3) The most powerful of the Greek gods fathered Apollo. Meinongians, at least of the first type we identified at the beginning, and likely Meinong himself, would identify each of (1)–(3) as expressing true Soseinsobjektiven—property-ascribing propositions—asserting something of an object , which, as it happens, doesn’t exist. Further, they hold that (1)–(3) are or would be affirmed regularly, widely, and unproblematically, by speakers of natural language, perhaps by all of them with knowledge of the relevant object and innocence of philosophical semanticists’ theories. The latter sentence is of course a factual claim about what appropriate linguistic anthropological investigation would disclose. I now make a comparable factual claim, which I hold empirical investigation would substantiate. The claim is that for each natural language speaker of the theory-innocent sort just referred to, who affirms any of (1)–(3) or any comparable Meinongian sentence, and who realizes that the apparent subject of the sentence is fictional, there will be an option set, that will include a sentence of the type (4) The stories represent that Holmes is a detective. Alternatives might be: (4′) Holmes is supposed to be a detective, as he figures in the Conan Doyle stories. Many other, similar, sentences may be devised; and comparable variants for each of (2) and (3), and for every Meinongian sentence putatively about


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Page 243 Holmes or the king of the Greek gods, will also readily be imaginable, and constructible. The further claim I make is that for every natural language speaker, S, with an option set including (1) and (4)—or suitably comparable variants—(4) will trump (1). Generalizing, and schematizing, the factual claim is that for every Meinongian sentence ‘ p’, in which an unreal object of fiction or other cultural activities is purportedly characterized as having or lacking some property, and which a speaker asserts, there will be an option set sentence ‘it is story-represented that p’ (or a suitable variant) which will, for that speaker, trump ‘ p’. At the same time, the factual claim will assert in addition, no parallel actuality-qualifying assertions are to be met with, posing a comparable trumping phenomenon, with regard to real-world statements. ‘Paris is in France in the actual world’ does not trump ‘Paris is in France’. The latter suffices; it is at something like the end of the perspicuity road (so to speak). There is indeed a ‘prejudice in favour of the actual’ in ordinary (and for that matter, theoretical) thought and speech. The kind of ‘treatment’ defended here in respect of fictional objects is, it will be noted, similar to accounts offered in the literature, by such philosophers as Stuart Brock (2002), Charles Crittenden (1991), Richard Purtill (1973), and Leonard Linsky (1967). What is (very modestly) novel in my account is the set of claims of empirical linguistic anthropology that I have made, and the ‘option set’ and ‘trumping’ ideas. The advantages of the latter are that they will not require (as other treatments do) that Meinongian sentences are actually elliptical for explicitly context-disclosing or context-affirming sentences. Rather, the idea is that the typical speaker, presented with an appropriate context-affirming sentence, will invariably prefer the latter as saying better , at any rate, as saying more literally accurately (in the sense of approximate saying-the-same-thing equivalence identified here), what the Meinongian sentence has said. It may be noted that my empirical claims are about more or less theory-innocent natural language speakers who assert or would be prepared to endorse Meinongian sentences. There may also of course be among the general population natural Russellians, people innocent of theory who, knowing them unreal, would never assert that Holmes is a detective or Hamlet a prince. I actually think that there are lots of natural Russellians. At any rate, whatever their numbers, the option set and trumping ideas will be unnecessary in their cases for adding to the empirical case against Meinongian intuition. So: the natural Meinongians (if there are any) kind-of-believe Meinongian sentences, or in some cases may actually believe them true. The natural Russellians believe Meinongian sentences to be false (or that they fail to be true). For both, the appropriately corresponding story-representational sentence will trump the Meinongian sentence. These claims have of course been made just for Meinongian sentences which are embedded in stories , story fragments or other imaginative activities (including dreams), conscious (or unconscious) devisings of individuals


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Page 244 or cultures. While this is clearly evident for the typical objects with which Meinong begins, and which motivate, for him and his followers to the present day, the Meinongian theory of objects, some Meinongian objects, it is held, are bereft of story or contextual setting. Indeed, for Meinong himself, and most of his followers, a Meinongian object may be constituted by any individualized clustering of properties. The purple eighty-kilogram five-footed elephant presently sitting on G. W. Bush might be such an object. What one notes in advocacies of (what I will call) story-bereft Meinongian objects is that the sole Sosein (property-aggregate) claimed as plausibly assigned them consists in properties alleged to be analytically implied by the defining conception of the object (so-called ‘nuclear’ properties of the object). So, for this Meinongian view, the proposition expressed by ‘The purple eighty-kilogram fivefooted elephant presently sitting on G. W. Bush is an elephant’ will be an allegedly true Soseinsobjektiv generated by the Meinongian object indicated, and all other (allegedly) true Soseinsobjektiven will be comparable. Now, completely independent of Meinongian sentences, of either the story-embedded or the story-bereft kind, we may note a class of sentences of type ‘The F is G’, where there does really exist a unique F object, and where G is analytically contained in F . ‘The present king of Sweden is a king’ will be a good example of this class. Is the just-quoted sentence analytically true? For those who may be disposed to affirm that it is, it may be observed that there will be an option set sentence for someone who may assert the sentence about Sweden’s sovereign, namely, ‘If the present king of Sweden exists, then the present king of Sweden is a king’, which—I claim—will trump the original, for any such speaker. If this is right, then the alleged analyticity of the class of sentences under review will provide no motivating rationale for Meinongianism. Those not disposed to view ‘The present king of Sweden is a king’ as analytic will decline to do so precisely because there might not have been such an individual as King Carl XVI Gustaf, and Sweden might presently have been a republic. Some more empirical claims. I actually think that natural language speakers innocent of Meinong, Russell and their theoretical preoccupations would be quite mystified by story-bereft Meinongian objects. They wouldn’t know what to make of them, and certainly wouldn’t rush forward to register the appropriate Meinongian semantical intuitions. For the story-bereft objects, I claim, the natural theorybereft speaker would welcome Russell’s theory of descriptions, as regimenting, in a helpful way, sentences in which they might figure, including the allegedly analytic Soseinsobjektiven involving them. Companion to such welcoming would be a cheerful acceptance of the Russellian treatment of the Swedish kinds of cases just discussed. Story-embedded Meinongian objects pose more complexity, as the argument of this paper acknowledges. Russell’s theory of descriptions will handle the story-bereft objects directly and


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Page 245 straightforwardly, and the trumping procedure will, less directly, handle the story-embedded objects. It will be clear that, if the foregoing series of arguments is cogent, the alleged natural language ground and support for Meinongianism will be undercut. It will be untrue that the natural mind, or semantical or (wide-sense) ontological intuitions encapsulated in natural language, have a Meinongian component or impulse. For the trumping category of sentences in the relevant option sets do not imply Meinong’s principle of the independence of Sosein from Sein. That it may be represented in a story that something is the case, or that the details of some cultural or symbolic artifact involve supposing, regarding or depicting something as being so no more imply that principle than do facts of our dreams, or works of art, or their contents, imply this. There may still be claimed to be difficulties posed by some of the natural language semantic data, which none of the foregoing account of story-embedded and story-bereft alleged items, and the option set and trumping ideas, will in a satisfactorily clear way address. Perhaps the most difficult cases are posed by (alleged) comparisons between real and unreal objects. Imagine that Sam reads and admires War and Peace , in which the historical Napoleon and the fictional Pierre are characters. Sam, it might be claimed, likes Pierre better than Napoleon, and thinks that the latter is far less morally impressive than the former. What is the would-be Russellian to make of such a fact as that? Sam knows that Napoleon was real, and Pierre not; maybe he has done some historical investigation, and thinks that Tolstoy has represented the real Napoleon fairly accurately, certainly on the moral side of things. Sam’s belief is about the real Napoleon, whom Sam is conceiving of both as the character in Tolstoy and as the real person. And Sam thinks that Pierre was morally superior to that individual. (Pierre, if you’ve read the novel, you will agree is indeed a loveable and admirable character in the story.) If I’m right about my empirical linguistic anthropological claims, then Sam will agree that a member of her option set will be (some factual equivalent of) ‘It is represented in War and Peace that there is an individual Pierre, that there is Napoleon, and that Pierre is more morally impressive than Napoleon.’ And Sam will endorse the latter sentence, agree both that it trumps how she might have expressed her view and that she holds that view. Sam can add that the real historical personage Napoleon appears as a character in the novel, depicted as Tolstoy depicts him. Still another case, discussed in the literature, is posed by ‘Holmes is more famous than any existing detective’ (and comparable cases). Here I will want to make further use of the idea of approximate factual equivalence utilized earlier. The just-quoted sentence is equivalent in at least this sense to ‘People think more about Sherlock Holmes than they do about existing detectives, and they have storyderived conceptions of Holmes that are more extensive than conceptions they have of existing detectives.’

file:///K|/A-DATA%20CH91%20(F)/BU3%20%20Incoming/Meinong/0415963648__gigle.ws/0415963648/files/page_245.html[2/12/2011 12:36:02 πμ]

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Page 246 There are still other difficult cases. Consider someone, say, George, who is extremely fearful. Among the things he fears are spiders and serial killers; but he also fears ghosts and fire-breathing dragons. It may be that his deepest fears include these last two, and what most terrifies him of all is a particular firebreathing dragon about which he has nightmares. Of George it may seem correct to say, Some of the things he most fears don’t exist , and, indeed, The thing he most fears doesn’t exist . Both of these sentences, if true, pose challenges for standard classical logic, since with quantification interpreted objectually, they will turn out to be self-contradictory. In both cases, I argue (though I agree that the results are a bit convoluted), we can produce perspicuous ‘equivalents’, along the lines previously indicated, that won’t have this result. I think that compound treatments along these lines should in general be successful in pre-empting putative cases for Meinongian objects. I would supplement them with the idea that the anti-Meinongian (Russellian or otherwise) can and should make ample use of helpful abstract entities, specifically with properties and relations and concepts (regarded either Platonistically or psychologically, as may suit), and with the abstracta known as ways . There is the way that Robert walks, the way (or ways) that Picasso paints pictures and so on. There are also ways things (processes, events, individual characters) are represented in artistic or other imaginative artifacts. All such ways can be (I think correctly) asserted to be real, without implying the reality of individuals which may figure in the ‘way’ when it is a representational ‘way’. The way that Romeo is represented as longing for the absent Juliet is a really existing thing, which might be (sometimes, surely, is) really exemplified in an existing human being. Some ways are, it seems, self-contradictory or impossible. There is the way a round square would be, if there were one. ( That way would consist in being both round and square.) Ways are, presumably, items that very closely resemble properties. At any rate, they too will be helpful arrows for the antiMeinongian quiver. It will be clear that the foregoing is both an informal and an incomplete treatment of the fundamental Meinongian theme. In addition to having made only modest engagement with the immense secondary literature on ‘objects of thought’, some of that theme’s key topics remain unaddressed here, in particular, the need to give an adequate account of the semantics of (apparent) proper names which never, at any time, denote. The latter need is specially acute if we find persuasive the Kripkean rigid designation and causal transmission treatment of proper names that do denote. The general line defended in this paper is that fictional contexts are parasitic on non-fictional, real-world ones. This would suggest, I think, that fictional names should be treated somewhat as implied by Carnap’s individual concepts, adapted in turn by Quine’s ‘pegasizing’ sorts of predicates. But this does require careful and more detailed exploration.


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Page 247 REFERENCES Brock, S. (2002) ‘Fictionalism about Fictional Characters’, Noûs 36.1: 1–21. Chisholm, R., ed. (1960) Realism and the Background of Phenomenology , Glencoe, IL: The Free Press. Crittenden, C. (1991) Unreality: the Metaphysics of Fictional Objects, Ithaca, NY: Cornell University Press. Linsky, L. (1967) Referring, London: Routledge and Kegan Paul. Meinong, A. (1904) ‘The Theory of Objects’, trans. I. Levi, D. B. Terrell and R. M. Chisholm, in Chisholm (1960): 76–117. Purtill, R. (1973) ‘Meinongian Deontic Logic’, Philosophical Forum 4: 585–92. Quine, W. V. O. (1963) ‘On What There Is’, in From a Logical Point of View , New York: Harper Torchbooks.


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Page 248 12 Who is Afraid of Imaginary Objects? Gabriele Contessa There are more things in the heaven and earth Horatio, than are dreamt of, in your philosophy —William Shakespeare, Hamlet , Act I, Scene V THE PROBLEM WITH IMAGINARY OBJECTS People often use expressions such as ‘Sherlock Holmes’ and ‘Pegasus’, which appear to refer to imaginary objects, and make assertions about them such as: (1) Sherlock Holmes smokes a pipe and (2) Sherlock Holmes was created by Arthur Conan Doyle in the late nineteenth century. In what follows, I call internal those sentences that, like (1), talk of imaginary objects as if they were concrete actual objects and external those sentences that, like (2), talk of imaginary objects as fictional characters, mythological creatures and so on (whatever these entities might be). I call object-fictional those internal sentences that occur in a work of fiction and metafictional those sentences, whether internal or external, that occur outside of a work of fiction and are about that work of fiction. Thus, (1) is an object-fictional sentence if it occurs in one of Arthur Conan Doyle’s stories but it is a metafictional sentence if it occurs in the context of the discussion of Conan Doyle’s works. Prima facie, speakers’ reference to imaginary objects would seem to be incompatible with a widely accepted philosophical principle. One of the first formulations of this principle in western philosophy can be found in Plato’s Sophist (237B–E). In this paper, however, I refer to a much more recent formulation of the principle, which has been put forward by John Searle (1969), who calls it the Axiom of Existence. In Searle’s formulation, the Axiom of Existence states: ‘Whatever is referred to must exist’ (77). The problem is that, if we take ‘existence’ to designate the mode of being that is proper of actual concrete objects such as flesh-and-bone people,


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Page 249 animals and material objects, then imaginary objects, like Sherlock Holmes and Pegasus, do not exist and therefore, according to the Axiom of Existence, it is not possible to refer to them. Those who accept the Axiom of Existence have two options. They can either maintain that reference to imaginary objects is only apparent or that imaginary objects exist after all. In what follows, I call eliminativist any account according to which imaginary objects do not exist and reference to imaginary objects can be explained away as merely apparent. To show that apparent reference to imaginary objects is not genuine philosophers have usually relied on one of three main strategies. In ‘Eliminativist Approaches’, I briefly outline each of them and argue that they all fail to be fully descriptively adequate. In ‘Hospitable Approaches’, I consider the option of admitting that imaginary objects exist and that reference to them is genuine reference. I call any account that maintains that imaginary objects in some sense exist hospitable. Different hospitable accounts however disagree as to the nature of imaginary objects. According to possibilist accounts , imaginary objects are possible concrete objects, while, according to abstractist accounts , they are actual abstract objects. I argue that neither option is fully satisfactory. I then outline a hospitable account, the dualist account , which, as I argue, combines the advantages of the versions of the possibilist account and the abstractist account without sharing their respective disadvantages. According to the dualist account, imaginary objects have an intrinsically dual nature and they cannot be entirely reduced to either abstract objects or imaginary objects. An imaginary object is an abstract object that stands for a possible object. Before starting the examination of the various accounts to imaginary objects, it is important to note that this paper is meant to be a piece of descriptive and not prescriptive metaphysics, to use Peter Strawson’s distinction (1959). That is, its aim is to make philosophical sense of the practice of talking and thinking about imaginary objects and of the intuitions that underlie this practice. It is not meant to modify or censor this practice and intuitions but to uncover their implicit presuppositions. ELIMINATIVIST APPROACHES The Predicate Account The first eliminativist strategy I examine, the predicate account , attempts to paraphrase the sentences in which apparently referential expressions occur into synonymous sentences containing no such expressions. Bertrand Russell (1905) and Willard van Orman Quine (1948) are probably the most prominent advocates of the paraphrase programme. In its most ambitious version, the paraphrase is supposed to show the ‘logical form’


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Page 250 of the sentence (like in Russell 1905). According to a more modest version, the paraphrase simply proves that reference to imaginary objects could be avoided without changing the meaning of the sentence. The paraphrase would show that reference to imaginary objects is ultimately dispensable and does not commit us to the existence of these objects. The general idea that underlies the paraphrase programme is that (1) is synonymous with (3) There exists one and only one x such that x is Sherlock Holmes and x smokes a pipe. In the notation of first order logic, (3) has the form x(( Px) ^ ( y( Py → x = y)) ^ Q x), where ‘ Px’ is interpreted as ‘ x is Sherlock Holmes’ and ‘ Qx ’ as ‘ x smokes a pipe’. Thus, (3) does not contain any referring expression. It only asserts the existence (and the uniqueness) of an entity that has the property of being Sherlock Holmes and states that that entity also has the property of being a pipe smoker . If one concedes that the expression ‘Sherlock Holmes’ as it occurs in (3) is not a name but it is only part of a strange-looking predicate, the first step of the programme seems thus successfully completed: (3) does not contain any expression referring to nonexistent entities. However, one might wonder whether any genuine metaphysical advantage is gained from this move. Advocates of the predicate account propose to interpret sentences containing expressions that apparently refer to objects that do not exist as sentences that contain empty predicates. If, on the one hand, the advocates of the predicate account embrace an intensional view of predicates as expressions referring to properties, then they exclude nonexistent entities from their ontology only at the price of admitting uninstantiated properties in it. This is a price that many would not be willing to accept. First, most philosophers who are realist about properties would not be willing to include noninstantiated properties in their ontology (Loux 2002). Second, an ontology that contains noninstantiated properties is not necessarily more austere than an ontology that contains nonexistent objects. If, on the other hand, they embrace a strictly extensional view of predicates, such that two predicates are the same if they have the same extension, then they have to accept that the predicates ‘ x is Sherlock Holmes’, ‘ x is Dr. Watson’, ‘ x is Pegasus’ and, say, ‘ x is the highest prime number’ are, in fact, the same predicate, for they both have as their extension the empty set. Both options seem unsatisfactory. The second step, however, is probably even more problematic. If (3) is to be a paraphrase of any internal sentence such as (1), then (1) and (3) must be synonymous and synonymous sentences necessarily have the same truth-value. But it is far from obvious that (1) and (3) have the same truthvalue. On Russell’s early account, (3) is plainly false. No actual concrete object satisfies the predicate ‘ x is Sherlock Holmes’. However, knowledgeable speakers


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Page 251 unconcerned by philosophical issues would agree that (1) is ‘ in some sense ’ true and its negation false. For example, if a student writes on a true-or-false literature test that (1) is true, her answer is right, if she writes that (1) is false, her answer is wrong. Any descriptively adequate account of the semantics of fictional sentences should be able to account for the fact that some internal sentences such as (1) are ‘ in some sense ’ true and others, such as (4) Sherlock Holmes is an astronaut, are ‘ in some sense ’ false. I call these two phenomena, respectively, the qualified truth and the qualified falsity of internal sentences . Even if one was ready to deny that internal sentences such as (1) and (4) can be true or false in any sense or even have a truth-value, however, it does not seem possible to deny that external sentences, such as (2), are unqualifiedly true. That is, they are true according to historical facts and not just true relatively to some work of fiction. One day an historian of literature might claim that (2) is actually false: Sherlock Holmes was created by someone other than Conan Doyle and Conan Doyle only stole her idea. To support this claim, she would need factual evidence. I call this phenomenon the unqualified truth of external sentences . The predicate account cannot account for the unqualified truth of external sentences. In fact, according to it, external sentences like (2) would appear to be no less false than internal sentences like (1). The predicate account thus is not descriptively adequate (and, to be fair to its advocates, it is not even intended to be so). Speakers who utter sentences like (1) or (2) do not, thereby, implicate that the entities to which they are referring exist as concrete actual objects. In the attempt to avoid any form of ontological commitment to imaginary objects, advocates of the paraphrase programme systematically misconstrue the meaning of the sentences in which expressions referring to imaginary objects occur, and systematically misinterpret what the speakers mean to say when they utter those sentences. It is worth noting here that similar problems are also faced by those accounts, like Peter Strawson’s (see 1950), according to which statements that contain nonreferring expressions, such as (1) and (4), are neither true nor false or those who, like the late Russell (1957), maintain that statements of these sort are untrue rather than simply false. None of these accounts can account for the intuition that, whereas (1) and (4) may both be literally false, (1) is in some nonliteral sense true. The Pretence Account Consider now a second eliminativist account: the pretence account . The pretence account, which in some version or other has been advocated by the


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Page 252 likes of Kendall Walton (1973, 1990), and Gareth Evans (1982), is based on the idea that reference to imaginary objects is not genuine but only pretended and that, therefore, it is not in breach of the Axiom of Existence.1 According to the pretence account, the sentences that occur in a work of fiction belong to a special mode of discourse: fictional discourse, which is to be carefully distinguished from ordinary factual discourse. In writing or uttering an object-fictional sentence in which expressions that appear to refer to imaginary objects occur, the author of a work of fiction pretends that she is referring to actual objects and that she is providing the audience with true information about the objects. The author also intends the audience to participate in the pretence by pretending that the author is referring to something rather than nothing and that what she says about that something is true (cf. Currie 1991: Chapter 1). Advocates of the pretence account usually note that fictional discourse is a form of make-believe similar to children playing with blobs of mud pretending that they are pies (Walton 1973) or to someone shadowboxing pretending that he is fighting imaginary opponents (Evans 1982). The pretence is, to a certain extent, also carried over in internal metafictional sentences. When a speaker utters an internal sentence such as (1) outside of the context of a work of fiction, both the speaker and its audience pretend that ‘Sherlock Holmes’ refers to a real person. Unlike object-fictional sentences, however, internal metafictional sentences are not necessarily pretended to be true. An internal metafictional sentence is pretended to be true only if it is implied by object-fictional sentences in the relevant work of fiction, so that none would pretend a sentence such as (4) to be true. The pretence account faces various problems. Here, I consider only one, which is that the pretence account does not seem able to account for the unqualified truth of external sentences such as (2). There seems to be a perfectly legitimate sense, although maybe not an entirely literal one, in which Conan Doyle ‘created’ Sherlock Holmes. When uttering (2), a speaker and their audience do not seem to be pretending that ‘Sherlock Holmes’ refers to any concrete actual object nor do they pretend that Arthur Conan Doyle created that object. Rather, the speaker seems to be providing her audience with genuine information about the author of the fictional character that is identified by the name ‘Sherlock Holmes’. Testimony to this is the fact that, even if we are able to pretend that, say, Anna Karenina was created by Conan Doyle, we do not seem able to pretend that Holmes was created by Conan Doyle because we actually believe that Holmes was created by Conan Doyle, for it would seem that one can pretend that p is true only if one does not believe that p is true. The Mention Account This leads us to consider a third strategy to paraphrase away reference to imaginary objects, which I call here the mention account . According


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Page 253 to the mention account, when someone is apparently using an expression that refers to an imaginary object they are actually only mentioning that expression.2 According to this account, (1) would be shorthand for (5) Someone wrote a story containing ‘Sherlock Holmes smokes a pipe’ (or containing sentences implying this).3 If (1) was actually only shorthand for (5), then the use of the expression ‘Sherlock Holmes’ in (1) would be ultimately dispensable. The mention account however cannot account for either external sentences or object-fictional sentences. Consider external sentences first. According to the schema suggested above, (2) would be shorthand for (6) Someone wrote a story containing ‘Sherlock Holmes was created by Arthur Conan Doyle in the late nineteenth century’ (or containing sentences implying this). Clearly, (2) is not shorthand for (6). An advocate of the mention account could probably claim that, even if that particular schema does not work in external contexts, it is still possible to claim that external sentences are shorthand for sentences in which the expression ‘Sherlock Holmes’ is only mentioned. If the advocates of the mention account want their claims to be taken seriously, however, they should propose a set of paraphrase schemas that are meant to deal with all external sentences, including ‘Sherlock Holmes is my favourite character in English literature’ or ‘Sherlock Holmes uses abductive reasoning more frequently than Hercules Poirot’. Until then it is not possible to seriously assess their claim that all external sentences are shorthand for sentences in which expressions which refer to imaginary objects are only mentioned. Moreover, the suggested paraphrase schema does not seem to work with object-fictional sentences either. If (1) occurred in one of Conan Doyle’s stories, it cannot be interpreted as shorthand for (5). In fact, in his stories, Conan Doyle is not reporting the content of someone else’s stories to his readers. Advocates of the mention account could probably concede that, when it occurs in the context of objectfictional sentences, the expression ‘Sherlock Holmes’ is used and not mentioned. Nevertheless, they could claim, the expression is not used referentially or, even if it is used referentially, it does not refer to anything. The problem with such a possible reply would be that, in object-fictional sentences, ‘Sherlock Holmes’ seems to be used referentially and seems to refer to a certain character in the novel and not to others. By writing a sentence like (1) in one of his stories, Conan Doyle meant to tell us that the character to which he refers to as ‘Sherlock Holmes’ and not any other of the characters in the novel smokes a pipe. Thus, not only does ‘Sherlock Holmes’ seem to be used referentially in object-fictional sentences, but also


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Page 254 it seems to be used to refer to a certain object and not others. The practices of writing and reading works of fiction (in which there is more than one character) presupposes that different expressions can be used to refer to different characters. If ‘Sherlock Holmes’ and ‘Professor Moriarty’ failed to refer to different objects, we would not be able to distinguish between ‘Sherlock Holmes smokes a pipe’ and ‘Professor Moriarty smokes a pipe’. HOSPITABLE APPROACHES As they stand, none of the main attempts to show that reference to imaginary objects is not genuine seems to be descriptively adequate and some of the problems that these accounts have encountered could be taken as evidence that reference to imaginary objects is, after all, genuine. Those who adopt a hospitable approach, are willing to grant that whatever is referred to must exist. From this assumption, however, they reach the opposite conclusions: since it seems possible to genuinely refer to imaginary objects, imaginary objects must exist. Since they are not concrete actual objects, they must have a different ontological status. The agreement among advocates of hospitable approaches, however, does not go much further than this. Hospitable accounts can be roughly grouped into two broad families: possibilist and abstractist accounts. Even if both possibilist accounts and abstractist accounts maintain that imaginary objects exist, possibilists and abstractists have rather different ideas as to what they are. Possibilist Accounts The main idea behind possibilist accounts is that imaginary objects, though not actual, exist and, as such, they can be referred to. Among the various possible variations on the possibilist theme, I consider only two here, which I call the combinatorial account and the possible world account . The combinatorial account is inspired by Alexius Meinong’s theory of objects and Terence Parsons’ neo-Meinongian account of nonexistent objects (Parsons 1980).4 To illustrate the combinatorial account, suppose that one could write a list of all actual objects and next to each of them the set of the properties5 the object instantiates. Once we run out of actual objects on the first column, however, we can still continue the list of sets of properties by writing all sets of properties that are not coinstantiated by any actual object. For example, since no actual mountain is made of gold, the properties goldness and mountainhood are not members of the set of properties of any actual object. According to the combinatorial account, to each set of properties that are not coinstantiated by any actual object corresponds one and only one possible object. So, we can continue our list by adding one possible but


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Page 255 not actual object for each set of properties that are not coinstantiated by any actual object. It is among these objects that, according to the combinatorial account, the referent of ‘Sherlock Holmes’ can be found. Since no actual object instantiates the properties of, say, being a detective and living at 221B Baker Street , according to the combinatorial account, there is a possible object that instantiates those properties. So, ‘Sherlock Holmes’ refers to a nonactual object whose set of properties includes the property of being a detective and living in 221B Baker Street . On this account, (1) is true because being a pipe smoker is among the properties of that object and (4) is false because being an astronaut is not. The combinatorial account is riddled with problems. I consider only a few here.6 The first is that of identifying the object to which ‘Sherlock Holmes’ refers within the multitude of merely possible objects. The advocate of the combinational account would probably suggest that it is possible to make a list of all the properties attributed to Sherlock Holmes by his author and then find the object on the list that has those properties. This suggestion however is not satisfactory. Suppose that the set H includes all the properties that Conan Doyle attributes to Holmes in his works. Many objects on our list will have H as a subset of the set of their properties. Some of them have a mole on the left shoulder, while others do not. Some are allergic to dust and others are not. Which one of them is Sherlock Holmes? The description of Sherlock Holmes that can be gathered from Conan Doyle’s works does not single out any one of them as the unique referent of ‘Sherlock Holmes’. The advocate of the combinatorial principle, however, could stipulate that ‘Sherlock Holmes’ refers to the object that has all and only the properties attributed to it by his author.7 So, ‘Sherlock Holmes’ refers to the object on our list that has H as its set of properties. This suggestion, however, generates even more problems. Consider two here. First of all, we would tend to think that, say, Sherlock Holmes has a mother even if Conan Doyle never mentioned that. Second, if we are to explain that Sherlock Holmes is not an astronaut by pointing out that being an astronaut is not included among the properties in H, the fact that having a mole on the left shoulder is not included in H either would seem to force us to conclude that Sherlock Holmes does not have a mole on the left shoulder, which is unwarranted given that it is perfectly compatible with Doyle stories that he has one. Another problem is that possibilist accounts cannot account for the truth of external sentences. (2) does not seem to be true because ‘Sherlock Holmes’ refers to a possible object among whose set of properties, alongside that of being a detective and that of being a pipe smoker , includes that of having been created by Conan Doyle. This last property of Sherlock Holmes just does not seem to be on the same level as the other two. If ‘Sherlock Holmes’ referred to the possible but not-actual object that coinstantiated all and only the properties attributed to Sherlock Holmes by Conan Doyle,


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Page 256 then he would not instantiate the property of being created by Conan Doyle because this property is not a property that was ever attributed to it by Conan Doyle—it is an actual property of Sherlock Holmes. To put it more vividly, if someone fitting Conan Doyle’s description of Sherlock Holmes had existed, he would be a brilliant detective who smokes a pipe and lives in Baker Street, but he would not have been created by Conan Doyle. An even more serious problem is that, as Saul Kripke (1980) has convincingly argued, there is simply no real or counterfactual situation in which some real person or other could have been Sherlock Holmes. It is not sufficient for something to fit the description of Sherlock Holmes in order for it to be Sherlock Holmes (in fact, it is not even necessary). Even if, unbeknownst to Conan Doyle and the rest of us, there was someone who actually had all the properties attributed to Holmes in Conan Doyle’s works, including being called ‘Sherlock Holmes’, ‘Sherlock Holmes’ in (1) would still not refer to that person. Therefore, having all the properties which are attributed to Sherlock Holmes is not sufficient to be the referent of ‘Sherlock Holmes’ in (1). If the combinatorial account is afflicted by many problems, the other version of the possibilist account that I consider here, the possible world account inspired by David Lewis’s account of truth in fiction (1978), does not fare much better—and for similar reasons. According to the possible world account, there is a possible world in which Conan Doyle’s stories are literally true. In fact, since there is more than one way in which Conan Doyle’s stories could be true of a world (as there is much that those stories leave unspecified), Conan Doyle’s stories do not identify one but many possible worlds. Now, in each of these worlds, there is a brilliant detective whom the inhabitants of that world refer to as ‘Sherlock Holmes’, who smokes a pipe and who lives in Baker Street. According to the possible world account, ‘Sherlock Holmes’ in the actual world refers to the person who is referred to as ‘Sherlock Holmes’ in one of these fictional worlds. The possible world account is afflicted by problems that are very similar to those that characterized the combinatorial account. The first is that there are a number of different worlds that are compatible with Conan Doyle’s stories and in each of those worlds there is a brilliant detective whose name is ‘Sherlock Holmes’. In some of these worlds, Sherlock Holmes has a mole on his left shoulder, in others not. In some of those worlds, unbeknownst to Dr. Watson, he is an astronaut, in others, not. If we were to take seriously the claim that ‘Sherlock Holmes’ actually refers to one of the Sherlock Holmes that inhabit these possible worlds, the advocate of the modal account should be able to determine which one. However, since the description of Sherlock Holmes in Conan Doyle’s stories is incomplete, none of these identifications seems to be more warranted than any other. Moreover, unless one manages to rule out worlds in which Sherlock Holmes, unbeknownst to the narrator of


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Page 257 the stories, Dr. Watson, participates to a secret space programme, the modal account cannot rule out that (4) is after all true. Another problem is that the possible world accounts cannot account for the truth of external sentences. It does not seem possible to maintain that (2) is true because ‘Sherlock Holmes’ refers to a possible object among whose properties is that of having been created by Conan Doyle. In fact, on most accounts of the nature of possible worlds, it would seem that, if ‘Sherlock Holmes’ in (2) refers to the inhabitant of a possible world, he has not been created by Conan Doyle but exists independently of him. An even more serious problem is the one raised by Kripke. It is not sufficient to have all the properties which are attributed to Sherlock Holmes in order to be the referent of ‘Sherlock Holmes’ in (1). Abstractist Accounts According to abstractist accounts, insofar as the expression ‘Sherlock Holmes’ refers at all, it refers to an abstract entity: a character in a series of works of fiction. Thus, even if Sherlock Holmes is not an actual person and does not actually smoke a pipe, he (or it?) exists. It is one of the best-known characters of detective fiction, who was created by Arthur Conan Doyle and appeared for the first time in the 1887 novel A Study in Scarlet. Accordingly, we should distinguish two uses of the expression ‘Sherlock Holmes’. The first is the objectfictional use. This is the use that Conan Doyle makes of the name within the context of a work of fiction. In this use, the name, which appears to refer to an extraordinary detective in Victorian London, simply fails to refer to anything. The second use is the metafictional use. This is the use that Conan Doyle and his readers make when talking about the leading character in many of Conan Doyle’s works. In this use, the name ‘Sherlock Holmes’ refers to an abstract object (a fictional character) that is part of another abstract artefact (a novel or a short story). The abstract account succeeds where all of the other accounts I have examined so far fail: it manages to explain reference to imaginary objects in external contexts such as (2). In that sentence, the expression ‘Sherlock Holmes’ refers to an actual abstract entity and attributes to that entity a genuine (abstract) property, that of having been created by Arthur Conan Doyle. However, the standard abstract account does not seem equally successful in dealing with those cases in which expressions appear to be referring to imaginary objects that occur in an internal context outside of a work of fiction such as (1) and (4). In fact, the expression ‘Sherlock Holmes’ fails to refer to anything and the whole sentence is either false or fails to have any truth-value. Whereas Conan Doyle could not possibly misdescribe Holmes within the context of the stories he wrote, however, there seems to a sense in which someone would be misdescribing Holmes if she uttered (4). Note that she would not be misdescribing him because he is actually an abstract entity


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Page 258 and abstract entities cannot be astronauts, but because, as I have already noted, there seems to be a sense in which it seems to be true that Sherlock Holmes is a detective. To avoid this problem, various strategies have been proposed. I consider two here. The first, which has been proposed by van Inwagen (1977), claims that sentences such as (1) should be paraphrased as: (7) There exists a place in a work of fiction where the property being a pipe smoker is ascribed to Sherlock Holmes. In other words, when an expression referring to an imaginary object appears in an internal context, the sentence can be paraphrased as saying that a ternary relation, ascription, holds between an abstract object, a property and a passage in a work of fiction. Van Inwagen’s account faces two main problems. The first is that there seem to be properties that are not attributed to imaginary objects in any passage of a work of fiction but that nonetheless seem to be, in some sense, true of the object. Suppose that somewhere in Conan Doyle’s stories one can find the sentence: (8) Sherlock Holmes lives in 221b Baker Street. Suppose also that the following sentence is nowhere to be found in those stories: (9) Sherlock Holmes lives closer to Regent’s Park than to Hyde Park. Given the topography of Victorian London, (8) implies (9). However, whereas the schema underlying (7) can be used to account for our intuition that (8) is in some sense true, it cannot be used to account for our intuition that (9) is in some sense true as well. In fact, we have assumed that nowhere in Conan Doyle’s stories Holmes is ascribed the property of living closer to Regent’s Park than to Hyde Park. In general, fictional characters seem to have more properties than the ones which are attributed to them in the fictional works of which they are part. Literary critics and readers sometimes engage in passionate discussions about whether Hamlet is clinically depressed or whether or not Holmes is a misogynist, even if these properties are not attributed to them by their authors. These opinions are only partly based on the properties which these characters are explicitly ascribed in the works of fiction of which they are part. They are also based on the readers’ background assumptions about what other properties these characters would have, if they actually had the properties they are ascribed. To the extent to which inferences such as the one from (8) to (9) are legitimate (and I think that, to some extent, they are), the qualified truth of (9) is to be explained as much as that of (8).


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Page 259 A second problem is that, according to van Inwagen’s account, the expression ‘Sherlock Holmes’ does not refer to anything when it occurs within a work of fiction. As Nathan Salmon (1998) noted, strictly speaking, nothing can be attributed the property of being a pipe smoker by the occurrence of (1) in the context of Conan Doyle’s stories. Since in the sentences that occur in those stories, the expression ‘Sherlock Holmes’ fails to refer to anything and, a fortiori, it does not refer to the abstract entity Sherlock Holmes. The second version of the abstractist account that I consider here is the one outlined by Salmon (1998). On Salmon’s account, ‘Sherlock Holmes’ refers to the same object, an abstract entity, in both objectfictional and metafictional sentences. Since obviously abstract entities do not smoke, (1) is false. Nevertheless, Conan Doyle and his readers pretend that it is true by pretending that the abstract object to which we refer as ‘Sherlock Holmes’ smokes a pipe. It is important to note that this version of the abstract account differs from the pretence account in one crucial detail. According to the former, the speaker is genuinely referring to something (an abstract object), while according to the latter the speaker is only pretending to refer to something while referring to nothing. Salmon’s account has the advantage of avoiding some of the problems of the other abstractist accounts by eliminating the asymmetry in the analysis of object-fictional and metafictional sentences that characterizes other abstractist accounts. According to this version, the expression ‘Sherlock Holmes’ refers to the same abstract object in both its object-fictional and metafictional uses. But, whenever the expression occurs in external sentences, the speaker pretends that that object is a person. Against Salmon’s account, Sarah Sawyer (2002) has argued that it is not clear what the pretence involved in it amounts to. Sawyer claims that if this pretence amounts to pretending that ‘Sherlock Holmes’ refers to a real man rather than an abstract object, then the abstract object to which the expression actually refers becomes explanatorily redundant and the account incurs in (some of) the problems that afflicted the pretence account. If, on the other hand, the pretence amounts to pretending that an abstract entity is a real person, according to Sawyer, it is not clear how or even whether we can do so. Whereas it is clear how one can pretend to be on a sunny beach when one is not, claims Sawyer, it is not clear how one can pretend that the number two is a man who plays croquet (at least, if we consider the number two to be an abstract entity). And, since Sherlock Holmes is an abstract object, the kind of pretence involved in Salmon’s account seems more similar to the second case of pretence than to the first case. Sawyer’s dilemma does not seem particularly serious. If the first interpretation of Salmon’s account was correct, the abstract object would definitely not be explanatorily redundant. In fact, it would be the object to which ‘Sherlock Holmes’ actually refers both in external and internal sentences (even if, when it occurs in internal sentences, we pretend it refers to something else). If the second interpretation was correct (as I tend to


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Page 260 believe), it is not clear where the difficulty of pretending that the number two is a man who plays croquet exactly lies. The difficulty noted by Sawyer may arise from the fact that the entity referred to as ‘Sherlock Holmes’ cannot be a person in any possible world. Sawyer would be suggesting that it is at least doubtful whether one can pretend that something that is metaphysically impossible is the case. Since pretending that p seems to require pretending that ‘ p’ is true, the difficulty noted by Sawyer would probably stem from the fact that it is not clear whether one can pretend that p, if p is metaphysically impossible. In fact, in the case of a logical impossibility, it seems outright impossible to pretend that, say, a hula-hoop is both round and not round. However, the same does not seem to apply to the case of metaphysical impossibility. People seem to be able to pretend that what is metaphysically impossible is the case. For example, even if no dog could have been a horse in any metaphysically possible world, children sometimes pretend that their dog is a horse. However, Salmon’s account is not immune from problems. For example, the account seems to imply that any referring expression that occurs in an object-fictional sentence and does not refer to any concrete actual object refers to an abstract object. Thus, whereas ‘London’ and ‘Scotland Yard’ in Conan Doyle’s stories refer, respectively, to the city of London and to its police headquarters, ‘Sherlock Holmes’ brother’ and ‘Sherlock Holmes’ violin’ refer to two abstract objects. Of the first one, we pretend that it is the brother of the abstract object to whom ‘Sherlock Holmes’ refers (even if abstract objects do not have brothers); of the second, we pretend that it is the violin which belongs to the abstract object to whom ‘Sherlock Holmes’ refers (even if abstract objects do not own violins). Now, suppose that the following sentence occurs in one of Conan Doyle’s stories: (10) Sherlock Holmes shook his head. If ‘his’ in (10) means ‘Sherlock Holmes’s’ as it would seem, then, according to Salmon’s account, ‘his head’ in (10) must refer to an abstract object, for Sherlock Holmes is an abstract entity and, as such, has no head.8 More precisely, ‘his head’ must refer to an abstract object that we pretend to be the head of the abstract object ‘Sherlock Holmes’ refers to. If this was the case, however, Salmon’s account would have some bizarre consequences. For one thing, Salmon would have to admit that Sherlock Holmes and Sherlock Holmes’ head are two distinct abstract objects and that, in writing his stories, Conan Doyle created two distinct abstract artifacts: Sherlock Holmes and Sherlock Holmes’ head. An advocate of Salmon’s account might reply that this analysis misrepresents their view. According to Salmon’s account, we pretend that Sherlock Holmes is a person and, in so doing, we pretend it has a head. Thus, in (10), ‘his head’ refers to the head that we pretend Sherlock Holmes has. In other


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Page 261 words, we refer to his ‘pretended’ head. However, either Sherlock Holmes’ ‘pretended’ head exists or does not. If it does not exist, then the advocate of Salmon’s account could not refer to it without being in breach of the Axiom of Existence. If it is a real object, it is either an abstract object like Sherlock Holmes or it is a different kind of object. If it is an abstract object, then the view gives rise to the bizarre consequences I have mentioned above. If it is some other kind of real object, the advocates of Salmon’s account still owe us an account of what kind of object the head of a fictional character is. The Dualist Account Both the view that imaginary objects are possible concrete objects and the view that they are actual abstract objects seem to capture some of our intuitions about imaginary objects. However, neither of them seems to be entirely satisfactory. It is interesting to note that the two views seem to some extent complementary—one view seems to be successful where the other fails and vice versa. The view that imaginary objects are actual abstract objects seems to be successful in accounting for our intuitions that (some) external sentences are literally true and that (all) internal sentences are literally false. However, it does not seem to be able to accommodate the intuitions that (some) internal sentences are nevertheless ‘ in some sense ’ true. The view that imaginary objects are possible concrete objects, on the other hand, seems to be partially successful in accounting for the fact that some internal sentences are ‘in some sense’ true. However, it seems to take those sentences too seriously for, on that view, those internal sentences that are true are literally true not just true ‘ in some sense ’. Moreover, on that view, it is not clear how to vindicate the intuition that (some) external sentences are literally true. This complementarity, I suspect, stems from the fact that both accounts fail to recognize the ‘dual’ nature of imaginary objects and attempt to fully reduce them to either abstract or possible objects. In this section, I argue that it is possible to defend an account that explicitly acknowledges the peculiar dual nature of imaginary objects and, therefore, combines the main advantages of possibilist and abstractist accounts without sharing their respective problems. I call this account the dualist account . According to the dualist account, an imaginary object is an abstract object that stands for a possible object. ‘Sherlock Holmes’ refers to an abstract object: a fictional character that has real properties such as that of having been created by Arthur Conan Doyle in the late nineteenth century. This actual abstract object, however, stands for one of the many merely possible objects that are compatible with the description of Sherlock Holmes in Conan Doyle’s novels: an exceptionally brilliant detective who, among other things, lives at 221b Baker Street and smokes a pipe. Sherlock Holmes, thus, is not one of the possible objects that have all the properties that are attributed to him in Conan Doyle’s stories but only stands for one of them. According to the dualist account, external


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Page 262 sentences such as (2) are literally true because ‘Sherlock Holmes’ refers to an abstract object that was actually created by Conan Doyle at the end of the nineteenth century. Internal sentences like (1), on the other hand, are all literally false because ‘Sherlock Holmes’ refers to an abstract object and abstract objects do not smoke pipes nor do they have any other concrete property. Nevertheless, the abstract object Sherlock Holmes acts as a stand-in for one of the possible objects who, among other things, are detectives, smoke a pipe, and live at 221B Baker Street. So, even if (1) is literally false, we usually consider it to be in some sense true—true ‘by proxy’ so to speak. (This is not unlike when we talk of an actor as if he was the character he plays in a movie. Although our assertions are literally false of the actor they are in some sense true because they are true for the character the actor plays in the movie.) Analogously, we consider some of them false ‘by proxy’ as well (not only literally false) if they are false of all the possible objects that the fictional character Sherlock Holmes stands for. Finally, we consider them neither true nor false (in the nonliteral sense) if they are true of some of the objects Sherlock Holmes stands for and false of the others. Three remarks are in order here. The first two remarks concern ontological economy. Admittedly, the dualist account is ontologically inflationary for it requires that we include both abstract objects and possible objects in our ontology. However, this, in and of itself, is not a reason to reject the dualist account. We are not supposed to accept the dualist account because it is more ontologically parsimonious than the other accounts. We are supposed to accept it because, unlike the other accounts, it is descriptively adequate—it vindicates a large number of intuitions that seem to underlie the way we talk and think of imaginary objects. Ockam’s razor urges us not to postulate entities unless they are indispensable. So, if there was an account of imaginary objects that was as descriptively adequate as the dualist account but more austere ontologically, I think we should prefer it to the dualist account. In lack of such an account, however, we have to accept the dualist account with all its ontological baggage. The question of ontological economy should be raised only when two equally descriptively adequate accounts are available. The second remark is that the ontological baggage that comes with the dualist account may be less heavy than it could seem at first. In fact, the dualist account does not commit us to any specific view about abstract and possible objects and most philosophers agree that, since our language seems to be committed to both categories of objects, we need to have some account of talk of abstract and concrete objects. I think that, insofar as one has some descriptively adequate way of accounting for the ordinary talk of abstract and possible objects, they will be able to adopt the dualist account. The third remark concerns the standing-for relation. Here, I only want to note that the relation that holds between the abstract object that is the


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Page 263 character and the possible object for which it stands is not some mysterious relation. Most philosophers accept that some objects stand for other objects. For example, the name ‘Julius Caesar’ stands for Julius Caesar, and that this blue area on this map stands for Lake Ontario, and, that when we count five objects on our fingers, each finger stands for one of those objects. The relation that holds between the abstract and the possible object is just another instance of this familiar stand-for relation. If we had a satisfactory philosophical account of it in all these other cases, we would have an account that applies to our case. As I have mentioned, I take it that the best argument in favour of the dualist account is that it combines the respective advantages of possibilist and abstractist accounts without sharing their respective disadvantages. Consider the problems of the possibilist account first. According to the dualist account, ‘Sherlock Holmes’ refers to an abstract object that actually exists. It is therefore metaphysically impossible for it to be an actual person in some other possible world. This is not to deny that there are to be possible worlds in which there is a brilliant detective who lives in Baker Street, and so on, and whom the inhabitants of that world refer to as ‘Sherlock Holmes.’ It is only to deny that that possible person is Sherlock Holmes (where ‘Sherlock Holmes’ is used as a rigid designator and refers to the same object in all possible worlds). In that possible world, Sherlock Holmes (where ‘Sherlock Holmes’ is used as a rigid designator and refers to the same object in all possible worlds) simply does not exist—it is a possible abstract object. The dualist account is not even affected by the various problems arising from the identification of a specific imaginary object among the possible ones. In fact, Sherlock Holmes is not a possible object—it is an abstract object that stands for one of the many possible objects that fit Conan Doyle’s description of Sherlock Holmes. Thus, in order to determine what the referent of ‘Sherlock Holmes’ is, we do not need to exactly identify the possible object for which ‘Sherlock Holmes’ stands insofar as it stands for one or other of the possible objects that have all the properties that Holmes is attributed in Conan Doyle’s stories. Since the description of this object that can be gathered from Conan Doyle’s story is necessarily incomplete, it will be always to a certain extent underdetermined exactly for which possible object Sherlock Holmes stands. But the fact that we cannot determine exactly which possible object Sherlock Holmes stands for does not seem to be a problem insofar as we can identify the abstract object denoted by ‘Sherlock Holmes’ (that is, one of the fictional characters introduced by Conan Doyle in A Study in Scarlet in 1887). Consider now the objections against the two versions of the abstractist account, which I discussed in ‘Abstractist Accounts’. The first problem with van Inwagen’s account is that it cannot account for the fact that imaginary objects seem to have properties that are not ascribed to them in the works of fiction of which they are part. The dualist account, however, does not


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Page 264 seem to have troubles in accounting for this. In fact, if the topography of Victorian London is assumed to be true of the possible world that the fiction describes, then anyone who lives in Baker Street in that world lives closer to Regent’s Park than to Hyde Park. The dualist account also avoids the second problem faced by van Inwagen’s account. The expression ‘Sherlock Holmes’ refers to the same object in both metafictional and object-fictional sentences and in both internal and external contexts, namely, an abstract object. However, in internal contexts, this object acts as a stand-in for a possible object. Those sentences in a work of fiction which ascribe concrete properties to a fictional character are thus to be interpreted, within that context, as descriptions of the possible object for which the fictional character stands and not as directly ascribing those properties to an abstract object. In other words, sentences like (1) and (8) are false if interpreted as sentences about the abstract object but are true of the possible object for which the abstract object stands. The dualist account is also immune to the difficulty that faced Salmon’s account. In fact, according to the dualist account, ‘his head’ in (10) does not refer to Sherlock Holmes’s head but to the head of (one of) the possible object(s) for which Sherlock Holmes stands. The dualist account which I have sketched in this paper still needs to be developed as there are some phenomena (such as the possibility of incoherent fictions) that need to be accounted for. However, the dualist account has already an advantage over its rivals—it succeeds in accounting for a set of phenomena that are not jointly accounted for by any of them—and as such is a very plausible candidate for an account of imaginary objects. NOTES 1. An additional footnote in the reprint of (Strawson 1950) seems to suggest that also Strawson subscribed to such a view of imaginary objects. 2. A similar view has been proposed by Gilbert Ryle (1933). 3. Such a formulation of the paraphrase schema is due to Charles Crittenden (1991). Even if Crittenden is a critic of the mention account, his formulation of the paraphrase schema underlying the mention account seems to be the best available one. 4. Neither Meinong nor Parsons however seem to accept the combinatorial account as outlined here (or any other of the accounts I consider here for that matter). Both Meinong and Parsons seem to believe that nonexistent objects have no reality whatsoever and yet they can be referred to. If this interpretation is correct, they both reject the Axiom of Existence altogether and their position cannot be identified with any of the positions I consider here. 5. In presenting the combinatorial account, I roughly follow Terence Parsons’ presentation of his own account. Parsons specifies that the properties must be nuclear where, intuitively, being red or being 6 meters tall are examples of nuclear properties and being existent and being possible are examples of nonnuclear ones. This distinction is of paramount importance for the combinatorial account, but we will not need to clarify it further in this context.


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Page 265 6. Similar objections to the combinatorial account have been put forward by Daniel Hunter (1981). A different set of problems for the combinatorial account has been presented by Barry Smith (1980). 7. This seems to be the position actually held by Parsons. 8. A similar problem about creationism in fiction in general has been inspired by Takashi Yagisawa (2001). As I argue, I think that creationism in fiction does not necessarily fall prey of this problem. REFERENCES Crittenden, C. (1991) Unreality: The Metaphysics of Fictional Objects, Ithaca, NY: Cornell University Press. Currie, Gregory (1990). The Nature of Fiction, Cambridge: Cambridge University Press. Evans, G. (1982) The Varieties of Reference, Oxford: Clarendon Press. Hunter, D. (1981) ‘Reference and Meinongian Objects’, Grazer Philosophischen Studien 14: 23–36. Kripke, S. (1980) Naming and Necessity , Cambridge, MA: Harvard University Press. Lewis, David (1978). ‘Truth in Fiction’, American Philosophical Quarterly , 15: 37–46. Loux, M. J. (2002) Metaphysics: A Contemporary Introduction , 2nd edn, London: Routledge. Parsons, T. (1980) Nonexistent Objects, New Haven: Yale University Press. Quine, W. V. O. (1948) ‘On What There Is’, Review of Metaphysics , reprinted in W. V. O. Quine, From a Logical Point of View , New York: Harper and Row, 1953. Russell, B. (1905) ‘On Denoting’, Mind, n.s. 14: 479–93. ——. (1957) ‘Mr Strawson on Referring’, Mind, n.s. 66: 385–89. Ryle, G. (1933) ‘Imaginary Objects’, Proceedings of the Aristotelian Society , Suppl. vol. 12: 18–43. Salmon, N. (1998) ‘Nonexistence’, Noûs 32: 277–319. Sawyer, Sarah (2002). ‘Abstract Artifacts in Pretence’, Philosophical Papers , 31: 283–98. Searle, J. R. (1969) Speech Acts: An Essay in the Philosophy of Language, Cambridge: Cambridge University Press. Smith, B. (1980) ‘Ingarden vs. Meinong on the Logic of Fiction’, Philosophy and Phenomenological Research 41: 93–105. Strawson, P. F. (1950) ‘On Referring’, Mind, n.s. 59: 320–44. ——. (1959) Individuals: An Essay in Descriptive Metaphysics , London: Methuen. van Inwagen, P. (1977) ‘Creatures of Fiction’, American Philosophical Quarterly 14: 299–308. Walton, K. L. (1973) ‘Pictures and Make Believe’, Philosophical Review 82: 283–319. ——. (1990) Mimesis as Make-Believe: On the Foundations of the Representational Arts, Cambridge, MA: Harvard University Press. Yagisawa, T. (2001) ‘Against Creationism in Fiction’, Philosophical Perspectives 15: 153–72.


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Page 266 13 Russell’s Definite Descriptions de re Gregory C. Landini DEFINITE DESCRIPTIONS IN PRINCIPIA MATHEMATICA The pure (unapplied) formal language of modern classical predicate logic contains denumerably many predicate letters Fij (where i indexes the number of places of arguments and j the number of the predicate letter) together with denumerably many variables, and denumerably many individual constants t1, … , tn . Where the term t is free for x in A (a well-formed formula of the language of the theory), classical logic counts every instance of ( x) Ax → A( t/ x) as an axiom. In classical logic, a free variable must be given an interpretation in the semantics for the theory and hence the domain of any model for the theory must be nonempty. This makes the inclusion of individual constants innocuous. There is always at least one entity in the domain to provide an interpretation of the individual constants of the language—though we may have to assign all the constants to this entity. Principia Mathematica (1910) has a quantification theory which is classical. It counts as an axiom every instance of the schema where y is a variable free for x in A.1 More carefully, for philosophical reasons it adopted a system in section *9 from which the quantificational system of section *10 was to be derived. The analog of *10.1 in the system of section *9 is this: where y is free for x in A. Principia cites the presence of a free variable in *10.1 (and *9.1) as the source of its existential commitment to at least one individual. We find: The assumption that there is something is involved in the use of the real variable, which would otherwise be meaningless. This is made explicit


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Page 267 in *9.1, and in the proof of *9.2 which is the same proposition as *10.1. (Whitehead and Russell 1964:225) In 1919, Russell had a change of heart. In his Introduction to Mathematical Philosophy he thought it a ‘defect of logical purity’ that Principia ’s quantification theory has existential theorems concerning individuals (1953:201). A purist will want to countenance the empty domain since he thinks that a proper calculus for logic must be free of existential commitment to individuals. In the 1925 secondedition of Principia , Russell took some steps in that direction. He offered a new quantification theory without free variables called ‘section *8’. Central to Russell’s system are definitions of subordinate occurrences of quantifiers in terms of formulas where all quantifiers are initially placed. Quine’s Mathematical Logic (1940) offered a deductive system without free variables fifteen years later. In Quine’s system, the axiom schema where y is a variable free for x in A, is replaced by its universal closure

where z 1, … , zn are all the variables free in A. Quine’s system exploits vacuous quantifiers that cannot be eliminated. The vacuous universal closure of an existential formula is a thesis of the system, even when the formula is contradictory. Russell’s system of *8 does better. It works without vacuous quantifiers (226). But Russell fell short of generating a quantification theory inclusive of the empty domain. Quine succeeded. Adjusting his system of quantification theory without free variables, Quine was able to accommodate the empty domain (see Quine 1995:220–23). Ineliminable vacuous quantifiers again play a central role. Quine countenances as a theorem, since he regards it as tautologous in form. Russell would not, since he counts it as an abbreviation for the existential formula: Russell’s approach is very appealing. Russell’s system of *8 can be adjusted to accommodate the empty domain without appeal to vacuous quantifiers (Russell 1953:203 fn; see Landini 2005). When logical purity is our focus, it seems quite inappropriate to allow the language of logic to include individual constants. Of course, it is quite natural to accept individual constants into the language of an applied


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Page 268 theory couched within predicate logic, adjusting the axioms accordingly. For instance, if the applied theory is elementary astronomy, and we want to have ‘all planets revolve around the sun’ as a proper axiom, then we assign ‘ Pv’ for ‘ v is a planet of our Solar System’, and ‘ R( v, u)’ for ‘ v revolves around u’, and add the axiom ( x)( Px → R( x, t 1)). In the intended interpretation, t 1 will be assigned to the Sun. In ‘On Denoting’, Russell admonishes us not to do this. We are not to form applied theories by adding proper axioms containing individual constants. Returning to our example of astronomy, Russell would have us add the proper axiom: The intended interpretation then assigns ‘ S’ to a property that singles out the sun uniquely. Karel Lambert has helped pioneer systems of ‘free logic’ which embrace both the purity of quantification theory and yet allow individual constants. In such systems, individual constants are ‘free’ of ontological import. For example, if t is a variable or individual constant free for x in A, Lambert’s free logic allows neither ( x) Ax → A( t / x), nor A( t / x) → ( x) Ax . Rather, with E as a primitive, Lambert’s system accepts every instance of the following: Moreover, where t and tn are individual constants, the system has the usual axioms of identity theory even when these constants do not denote. The following are axiom schemata Astronomers—Lambert is fond of supposing—used the name ‘Vulcan’ with impunity, discovering only later that there is no such planet to account for the perturbations in the orbit of Mercury (2003a: 14). Russell’s approach to forming an applied theory will have nothing of this. If astronomers used a name, there is something they named! Though Principia maintains there are no terms besides variables in logic, the work does endeavour steadfastly to make it appear as though ‘ ι xφ x’ is a term. Principia has: Whitehead and Russell write: ‘Whenever we have E!( ιxφ x), ιxφ x behaves, formally, like an ordinary argument to any function in which it may occur’


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Page 269 (174). It is important, however, not to be misled by appearances. Principia ’s ‘ ιxφ x’ is not a genuine term. Unfortunately, the status of ‘ ιxφ x’ is obscured by views concerning the general nature of definitions in Principia . There are two approaches to formal definition. On one approach, definitions are simply notationally convenient stipulations. The definiendum of a definition is simply a convenient notation for the definiens . On the other approach, definitions are axioms extending the notation of the language (in a noncreative and eliminable way). Lambert assumes that the definitions of Principia are axioms introducing new signs which are, however, noncreative and eliminable in the sense that any formula in which they occur is equivalent to a formula of the language in which they do not occur (11). On this later approach, the definiendum counts among the well-formed expressions of the formal objectlanguage.3 Assuming that definitions in Principia are axioms, Lambert holds that Russell has two distinct theories of definite descriptions: one in ‘On Denoting’, where definite (and indefinite) descriptive phrases of ordinary language are eliminated by paraphrase when transcribed into a quasiformal language; and another in Principia , where incomplete symbols are added by means of axioms to form a definitional extension of the formal object-language (11). As a result, Lambert finds that the theory of definite descriptions in Principia is ‘weaker’ than that of ‘On Denoting’ because it is open to ‘technical complaints’. Lambert’s technical complaints derive from his assumption that in Principia , ‘definite descriptions occur in positions in statements often occupied by (logically proper) names or variables, and that E! occurs in positions in statements occupied by predicates’ (3). On this basis, Lambert holds that the statements ψ a and ψ(ιxφ x) have the same syntactic form in Principia but have different logical forms since the definiens of the latter is a quantification via the definitional axiom: Lambert concludes that Principia ‘violates the condition that formal languages not be misleading in their syntax with respect to logical form’ (10). This is mistaken. The definiendum of *14.01 is ‘[ ιxφ x][ψ(ιxφ x)]’ not ‘ψ ( ιxφ x)’. In fact, one may exploit the scope operator as a variable binding operator, writing the definition thus: The sole reason Principia uses [ ιxφ x][ψ(ιxφ x)] rather than [ ιxφ x][ψx] is to allow the convenience of omitting scope markers when smallest scope is intended. Principia ’s omission of scope markers makes it appear as though definite descriptions are genuine terms. But the convenience is not part of the formal symbolism. In Principia ’s formal language ιxφ x is never in the


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Page 270 subject position of a predication without its scope marker. This dispenses with Lambert’s ‘technical complaints’. Realizing that ‘ ιxφ x’ is not a term and ‘ψ(ιxφ x)’ is not a well-formed formula helps immensely to clear up misunderstandings. Consider Principia ’s Lambert objects that the syntax of ‘E!(ιxφ x)’ puts ‘E!’ in the predicate position of ‘ψ’ in the formula ‘ψ(ιxφ x)’. But we have just seen that there is no formula ‘ψιxφ x’ in Principia and so no position of ‘ψ’ for ‘E!’ to occupy. Consider This is not akin to a universal instantiation involving a term ‘ ιxφ x’. Recall that universal instantiation in Principia is this: where y is a variable free for x in A. Removing abbreviations from *14.18 we have: There is no instantiation involving a definite description in Principia . There is no term ‘( ιxφ x)’. Admittedly, there are passages of Principia which seem to conflict with this. Lambert calls attention to Principia ’s At first blush, this definition seems illicit unless definite descriptions are genuine terms. But Whitehead and Russell explain that the complete form of the definition is: The existence of *30.01 does no harm to Russell’s thesis that definite descriptions are not terms of the language of logic. It is widely thought that Principia ’s definitions do not determine an order of application when ‘ ιxφ x’ is involved. For example Principia has: What in Principia determines the order of application of definitions? Are we to get


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Page 271

or is it to be

Only one can be correct, since a given definiendum cannot have multiple definiens . This is yet another misunderstanding produced by thinking that ‘ ιxφ x’ can occupy a subject position in a formula. The solution is simple. There is no formula ιxAx = y of Principia , so it cannot be an instance of the definiendum of definition *13.01. Definitions formed with free variables apply only to genuine terms (free variables) of the language of Principia . One of the great benefits of Principia ’s treatment of definite descriptions is that it provides an apparatus for clarifying ambiguous uses of definite descriptions in ordinary language—uses that Russell warns are apt to generate (among philosophers) speculative metaphysics. Russell’s example from ‘On Denoting’ is ‘The present King of France is not bald’. Russell wryly points out that what is needed is not a Hegelian synthesis here (1905). It is rather that there are two scopes:

The primary scope is false, for there is no present King of France. The secondary is true. The distinction is also handy when it comes to evaluating sentences such as: Russell’s technique admonishes us to replace the ordinary name ‘Holmes’ with an ordinary definite description involving the uniqueness property H. We can then distinguish the following: The first is the primary scope and clearly false. The second is true. There is always exactly one primary scope, but there can be several secondary scopes. Where C is a truth-functional context, every instance of the following is a theorem of Principia governing the scope of a definite description:


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Page 272 When we have E!( ιxAx ), and a truth-functional context C(…), primary and secondary scopes are equivalent. For instance we have:

If C is not a truth-functional context, then scopes will not always be equivalent, even when the antecedent condition E!( ιxAx ) is met. A celebrated example occurs when C(…) is (necessity). We know that, if we count Pluto and no others from the Kuiper Belt, the number of planets (of our solar system) is 9. We have E!( ιxPx ), where ‘ Px’ stands for ‘ x numbers the planets’. Thus, it seems true that There is an x that numbers the planets and necessarily it is greater than 7. But it is false that It is false that necessarily there is an x that numbers the planets which is greater than 7. The number of planets in the solar system is contingent. There could well have been some other number of them. As we see, the theory of definite descriptions has many applications both in philosophy and outside of it. The apparatus can be wonderfully clarifying. Consider its use in explaining the logarithmic expression ‘Loga ( x)’. The conceptual clarity of replacing occurrences of ‘Loga ( x)’ by ‘( ιv)( av = x)’ speaks volumes. Another application, of course, is in the notation of functions and limits. We have: With the help of Weierstrass and the clarity of Russell the calculus can be free from the metaphysics of infinitesimals. DEFINITE DESCRIPTIONS AND PRINCIPIA’S ‘NO-CLASSES’ THEORY The conceptual clarity brought about by the theory of definite descriptions does not automatically bring with it ontological parsimony. Russell’s theory of definite descriptions has a straightforward application to the development of a theory of sets. But using the theory of definite descriptions to single out sets obviously does not avoid the ontological assumption of sets. The theory of definite descriptions can be employed by a typed theory of classes. But it is also perfectly compatible with Zermelo-Frankel set theory which adopts


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Page 273 type-free axioms for set existence that are not logical truths. The use of definite descriptions simply enables one to avoid class abstract terms of the form {z : Az}. In a naïve ontology of classes, we have a comprehension principle for classes which takes the membership sign ‘ ’ as a primitive of the language:

where x is not free in A. The principle of extensionality is this:

To see how to avoid class abstract terms of the form {y : Ay}, we have only to notice that we can apply Russell’s theory of definite descriptions and use contextual definitions of for the class of all and only those y satisfying the formula A. We arrive at the following: Since the extensionality axiom schema assures the uniqueness of the class, we need not trouble over the uniqueness clause in the contextual definition of the definite description. Thus, for primary scope, we have: For example, we arrive at: Of course, definite descriptions introduce scope distinctions and these are tedious. Quine offered contextual definitions for class abstract terms that parallel the results of the theory of descriptions but avoid the attending scope distinctions (see 1980:259). He has: In any event, we see that the mere employment of a definite description instead of a class abstract term does not do away with an ontology of classes.


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Page 274 So how does this square with Russell’s autobiographical comment that the theory of descriptions ‘was the first step toward solving the difficulties which had baffled me for so long’ (1967:79)? The baffling difficulties, of course, pertained to paradoxes such as that of the class of all and only those classes that are not members of themselves. The solution was Russell’s ‘no-classes’ theory according to which ‘classes, are in fact, like descriptions, logical fictions or (as we say) “incomplete symbols”’ (1953:182). How then is Russell’s theory of definite descriptions related to Principia ’s ‘no-classes’ theory? We must first come to appreciate that Principia is indeed a no-classes theory! Unfortunately, reductiveidentity interpretations of Principia abound. For instance, Linsky writes that ‘Russell is indeed ontologically committed to some logical constructions, despite their expression by “incomplete symbols”’ (1999:117). On Linsky’s view, there are classes in Principia —they are just identified with attributes (propositional functions in intension). Linsky writes: Seeing that classes are not objects is enough to resolve the paradox of sets. But this is not to say that classes simply do not exist. To see that they aren’t objects is rather to see that they really play the same role as higher-order entities, propositional functions, to which type distinctions do apply…. The technique used is contextual definition, rather than explicit definition, but the effect is not any more of a wholesale ontological elimination than is the theory of definite descriptions. (130, 131) It is important to see that this is quite mistaken. Principia is genuinely a ‘no-classes’ theory. Classes are not identified with any entities of the ontology of Principia . If classes were to be assumed, they would be extensional entities. Classes of classes (of individuals) are identical if and only if they have exactly the same classes (of individuals) as members. In contrast, attributes of attributes that are coextensive may fail to be identical. To solve this problem, a reductionist identification of classes with attributes relies on the existence of an extensional attribute correlated with each attribute. Let φ be an attribute of φ. Suppose χ is such that ψ x ↔x φ x fails to assure that χφ ↔ χψ. This happens, for example, when the context χ(φ) is φ = F . Now observe that corresponding to χ there is the attribute Σ, namely, We now have that for any attributes (of individuals) φ and ψ,


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Page 275 It is tempting to imagine that Principia recovers extensionality by finding an attribute Σ to stand in for a class. This is a reductive-identity interpretation; a class is an attribute such as Σ. This is not what is found in Principia . Quite literally Principia maintains that there are no classes. It is not a reductive identity. Rather, it offers a reconstruction of the structure of a type-theoretical ontology of classes without the ontology. Principia replaces statements in the type-theoretical language of classes with statements in the language of predicate variables. It begins from the following type-stratified comprehension principle: where φ( t 1 … tn ) is not free in A. No new comprehension assumptions are needed to emulate a typetheory of classes. Instead, we find the following definition: This is a stipulative definition. The left-hand side is a convenient way of abbreviating the right. Thus it immediately meets the criteria of eliminability and noncreativity central to proper definitions. To emulate the presence of a relation of membership central to the type-theoretical ontology of classes, Principia introduces the definition: Again, this stipulative definition introduces a notational convenience. To see how the two definitions work, observe that by employing the definitions one immediately gets an analog of the type-theoretical class abstraction: Principia emulates this with the following theorem schema: This theorem schema is forthcoming because the definitions yield But observe that Abstraction applies only to entities of type t . It does not apply to classes of classes of entities of type t . In order to emulate classes of classes, Principia offers a new definition. Suppressing type indices, we find:


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To understand the definitions, we must examine Principia ’s use of bound lower-case Greek. Observe that definitions involving lower-case Greek must be applied before any contextual definitions of classes or definite descriptions. We have already seen that definitions framed with genuine variables do not apply to incomplete symbols. Thus, definitions framed with incomplete symbols must be applied before definitions framed with genuine variables. For instance, we find In this definition, α and β are schematic and stand in for ŷAy and ŷBy, respectively. One must apply *22.03 before applying *20.01. Observe as well that scope markers are not part of the definitions of bound lower-case Greek because Whitehead and Russell intend that the scope of the class symbol be interpreted in its narrowest possible occurrence in the instances of these definitions. To see this, let us illustrate the recovery of Abstraction for classes of classes of individuals. Principia has: Restoring the scope marker, we have: To see how the type-theoretical analog of Abstraction is a theorem, remove the lower-case Greek by *20.07 to arrive at:

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Page 277 Putting all this together, we have: This is how Principia emulates a type-regimented analog of Abstraction for classes of classes of entities of type t . The nature of Principia ’s emulation of a type-theory of classes should now be clear. Principia is not advocating a reductive identity theory which identifies classes with attributes in intention. We observed that by typical ambiguity, *20.01 emulates classes of entities of all types. But since Principia classes are not entities *20.01 does not emulate classes of classes of entities. Indeed, a similar result applies to *20.08. Although *20.08 emulates classes of classes (of entities of all types), it does not provide for classes of classes of classes of entities. The pattern is nonetheless clear. It is quite straightforward to see that what is needed is a recursive definition with respect to emulating classes. This would be done as follows:

Where t < o, we have:

Observe, however, that general recursive definition does not show how to emulate classes of relationsin-extension (relations e of individuals), nor does it emulate relationse of classes (of individuals) and the like. Principia discusses the emulation of relationse in its section *21. There is clearly an analogy between the introduction of the membership sign for classes and its definition for membership with relatione symbols. We find: A better notation would have preserved the membership sign thus: No special problems arise for relatione symbols. Interestingly, the emulation of heterogeneous relationse (that is, relationse between individuals and

file:///K|/A-DATA%20CH91%20%28F%29/BU3%20%20Incoming/Meinong/0415963648__gigle.ws/0415963648/files/page_277.html[2/12/2011 12:04:19 πμ]

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Page 278 classes, or between classes of different types, and so on) is a central feature of Principia . The importance of understanding Principia as a ‘no-class’ (and no-relationse ) theory cannot be over emphasized. A recent objection to Principia ’s treatment of class symbols illustrates the point. Linsky reports that in conversation, Martin observed that some classes in Principia are coextensive over classes and fail to be coextensive over attributes (2004:4401). For instance, let F and G be coextensive attributes of individuals that are not identical. By Principia ’s definitions we arrive at the following: This appears to Linsky and Martin to be a difficulty. There is no genuine difficulty, however. A typetheory of classes (as entities) naturally makes no distinctions between entities of type t that are classes and those that aren’t. This is because it takes membership xt y( t ) as a primitive relation involving entities of type t . Martin is concerned that Principia should distinguish classes of entities that are classes of type t and classes of entities of type t that are not classes. In failing to do this, he thinks that Principia has ‘too many’ classes. In truth, Principia has no classes at all. We cannot import into Principia the primitive notion of membership from the typetheoretical ontology of classes. In particular, Principia ’s does not say that the class ŷt (φ( t ) yt ) is a member of the class ŷ( t )( y( t ) = F ( t )), where membership is the unanalysable or primitive notion of a type-theory of entities that are classes.9 Martin would be justified in regarding Principia ’s emulation of the type-theory of classes as problematic if one could find formulas B and C that are such that: But there are no such formulas in Principia .10 There are no classes in Principia’s ontology. Principia ’s discussion of classes is an eliminativistic theory, not a reductive-identity theory. The eliminativistic technique of Principia ’s ‘no-classes’ theory originated with a theory that preceded Principia —a theory Russell called the ‘substitutional theory’ of propositional structure. Interpreting Principia as a theory of types of attributes in intension has as a consequence that the structure of types has no direct connection to the theory of definite descriptions. But the historical relationship between Russell’s ‘no-classes’ theory and the theory of defi** nite descriptions is that the original ‘no-classes’ theory was a technique


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Page 279 for emulating a type theory of attributes (and thereby classes) from within a type-free theory of propositions. Logic in this theory is designed to get along without comprehension principles for attributes. Prior to Principia , Russell held that logic is the science of the structure of the logical objects he called ‘propositions’. Propositions are akin to states of affairs; some obtain, others do not obtain. The language is one-sorted. There are no special styles of variables; all the variables are individual (entity) variables— including the letters ‘ p’, ‘ q’, ‘ r’, and so on. Russell held that there is a logical relation of ‘implication’ holding between propositions, and he used the sign ‘ ’ for the relation. The sign is to be flanked by terms to form a formula. Thus, ‘ x y’ expresses a relation between objects x and y no less so than ‘ xRy’. In order to facilitate this, nominalizing brackets are needed to transform a formula into a term— we must have terms {A} that are not variables. Hence, we put ‘ x {y x}’ or more conveniently, ‘ x . . y x’. We have:

The language permits quantification such as ‘( x)( x . . y x)’. This is quite unlike the modern predicate calculus, which takes the sign ‘→’ as a connective between formulas A and B to form a formula A → B . As Quine pointed out long ago, to write ‘( P)( P . → . y → P)’ is a use-mention confusion. (In this paper, we have taken care to use different symbols to mark the difference, reserving the symbols , ~ for the early Russellian use.) Propositions are intensional objects with finely grained identity conditions. Even logical equivalence is not sufficient for their identity. For instance, we can have {x . . y x} ≡ {x x} and not {x . . y x} = {x x}. There is an easy transformation of the type-theoretical language of predicate variables into the type-free language of substitution. To see this, let us compare the comprehension principle of a type theory of attributes with the comprehension principle for substitution.11 We have:

The parallel is quite close. The type symbol on a given predicate variable in Principia is related to the number of variables needed in the language of substitution. A few examples clarify this:


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Page 280 The substitutional analog of type is the number of substitutions. For the type ( o) of an attribute of individuals, substitution employs two variables p and a . The expression p/ a ; x abbreviates the definite description ( ιq )( p/ a ; x! q), that is, the q differing structurally from p at most in that x occurs in it at just those places in which a occurs in p. Removing the definite description in ( S)1 in accordance with *14.01, we have: For the next type, we illustrate with ( S)2. Here we find the type (( o)) involves the use of three variables and the definite description ( ιq )( s / t , w; p, a ! q) of the entity q differing structurally from s at most in that p and a occur in it in exactly those places in which t and w occur in s (respectively). Removing the definite description in ( S)2 we arrive at: The use of definite descriptions of propositions resulting from substitutions builds type into formal grammar. That is, there are no types of entities in the substitutional theory. Types of attributes are emulated by means of its constructions. In this way, types become part of logical grammar. The typefree substitutional logical reconstruction that emulates a typetheory of attributes in intension embodies a type structure. The substitutional theory of classes develops in a way that parallels that of Principia . More accurately put, Principia develops in a way that parallels the constructions of substitution. Indeed, we can translate anything in Principia’s primitive notation into substitution without much ado.12 On an objectual reading that makes the predicate variables of Principia range over a type-regimented ontology of attributes in intension, Russell loses his motivation for the ‘no-classes’ theory. One may as well embrace a typetheoretical ontology of classes. A type theory of attributes in intension seems every bit as ad hoc as a solution of the paradox as a typed theory of classes. Russell knew this, and it is prominently on his mind when, in 1907, during the era of his substitutional theory, he wrote: ‘Types won’t work without noclasses. Don’t forget this’ (1907). By ‘no-classes’ he meant that some construction must be found that builds the structure of type distinctions into logical grammar.13 A naïve formal system which embraces Russellian propositions together with bindable predicate variables (even restricting them to predicate positions alone) is contradictory. The contradiction is simple. Consider the property φ such that:


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Page 281 We get the contradiction: φ({φ x xx}) ≡ ~φ({φ x xx}). Russell knew of this contradiction in 1903. A paradox very similar to it appears in Appendix B of Principles and is discussed in letters to Frege (Landini 1992). At first, Russell wondered if the lesson of this sort of paradox is that there are logical paradoxes that type theory cannot address. But the paradox did not dissuade him in 1905 from embracing a type- and order-free theory of propositions, for he had then rejected bindable predicate variables in favour of his substitutional theory. Interestingly, in that same year Russell did consider an Epimenides paradox of propositions (1994). The paradox did not detain him. It involves essential appeal to contingent psychological notions of ‘assertion’ or ‘belief’ which he then viewed as outside the purview of pure logic. Matters were not so sanguine in 1906, when Russell discovered a paradox unique to his substitutional theory of propositional structure.14 Comprehension of propositions in substitution yields the following: This yields: Investigating Liar paradoxes of propositions to facilitate ideas towards solution, Russell reluctantly came to conclude that an ontological commitment to propositions requires that they be ramified into a hierarchy of orders.15 That is, the language of the substitutional theory would have to be regimented with order indices on its variables. The language now requires the restriction that fixes the order m of a term of the form {A}m . The restriction is this: if n is the highest order subscript of any variable v (bound or free) in A, then m = n if v is free and m = n + 1 if v is bound. Of course, in an identity statement the orders must be the same, and universal instantiation must respect order. If we demand: The paradox cannot go through. Similarly, consider the following version of the Liar:

Regimenting the language by orders, we have


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Page 282 Ramification thus avoids the contingent propositional liar. But ramification is the devil—as Russell came to realize. Without mitigation, it destroys the impredicative quantifiers that are essential to mathematics. In the end, he abandoned his ontology of propositions and with it his substitutional solution of the paradoxes plaguing logicism. DEFINITE DESCRIPTIONS AND INTENTIONALITY Outside of the eliminativistic aims of the constructions of the substitutional theory, Russell’s theory of descriptions is perfectly compatible with Zermelo-Frankel sets. Indeed, it is every bit as compatible with Homeric gods, nonexistent objects and even a ‘Meinongian jungle’16 of incomplete and impossible objects. The theory does, however, undermine a central impetus in natural language for postulating entities of such a jungle. It untangles the old conundrum that we seem to refer to (or think about) nonexistent entities, if only to affirm their nonexistence. On Russell’s view, we cannot refer to or think about what is not. Rather we refer to and think about everything. We do this (admittedly by an as yet unresolved mystery) by employing quantification. We do not refer to Pegasus in affirming his nonexistence; rather, we think that everything fails to be uniquely winged and a horse. Ontological commitment, Quine was fond of saying, comes only through the bound variables of quantification. The doctrine is shared by Russell.17 What then is a Meinongian? If one’s motivations for postulation of nonexistent objects lie in metaphysical postulations grounding causal possibilities of nature law, logic, logical modalities and the like, one is not, ipso facto, a Meinongian. Quite distinct motivations underly the adoption of Meinongian ontologies. The differences lie in the motivations, not the objects. I propose that we define a Meinongian as one whose motivations for postulating nonexistent particulars stem from the quest to form a theory of intentionality. With a resolve and bravery that is exemplary, Meinong confronted the phenomenological datum that a thought can point towards an object other than itself. Focus on intentional contexts led him to the following lesson: If a thought points to an object so and so, there is an object so and so to which the thought points. To state what object a referential mental act is directed towards seems to require that there is an object —if only one that is intentionally inexistent. Consider, the following:


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Page 282 Ramification thus avoids the contingent propositional liar. But ramification is the devil—as Russell came to realize. Without mitigation, it destroys the impredicative quantifiers that are essential to mathematics. In the end, he abandoned his ontology of propositions and with it his substitutional solution of the paradoxes plaguing logicism. DEFINITE DESCRIPTIONS AND INTENTIONALITY Outside of the eliminativistic aims of the constructions of the substitutional theory, Russell’s theory of descriptions is perfectly compatible with Zermelo-Frankel sets. Indeed, it is every bit as compatible with Homeric gods, nonexistent objects and even a ‘Meinongian jungle’16 of incomplete and impossible objects. The theory does, however, undermine a central impetus in natural language for postulating entities of such a jungle. It untangles the old conundrum that we seem to refer to (or think about) nonexistent entities, if only to affirm their nonexistence. On Russell’s view, we cannot refer to or think about what is not. Rather we refer to and think about everything. We do this (admittedly by an as yet unresolved mystery) by employing quantification. We do not refer to Pegasus in affirming his nonexistence; rather, we think that everything fails to be uniquely winged and a horse. Ontological commitment, Quine was fond of saying, comes only through the bound variables of quantification. The doctrine is shared by Russell.17 What then is a Meinongian? If one’s motivations for postulation of nonexistent objects lie in metaphysical postulations grounding causal possibilities of nature law, logic, logical modalities and the like, one is not, ipso facto, a Meinongian. Quite distinct motivations underly the adoption of Meinongian ontologies. The differences lie in the motivations, not the objects. I propose that we define a Meinongian as one whose motivations for postulating nonexistent particulars stem from the quest to form a theory of intentionality. With a resolve and bravery that is exemplary, Meinong confronted the phenomenological datum that a thought can point towards an object other than itself. Focus on intentional contexts led him to the following lesson: If a thought points to an object so and so, there is an object so and so to which the thought points. To state what object a referential mental act is directed towards seems to require that there is an object —if only one that is intentionally inexistent. Consider, the following:


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Page 283 Ponce de Leon searches for the fountain of youth. Thus, there is something for which Ponce de Leon searches. The conclusion seems to be reached by existential generalization alone. But, in fact, there is no fountain of youth; there is nothing for which Ponce (in his present act) is searching. A Meinongian concludes that existential generalization should yield that there is something for which Ponce’s intentional act is aimed —that is, a fountain of youth, albeit only as an ‘intentionally inexistent’ fountain of youth. But there is no genuine term ‘the fountain of youth’ in Russell’s logic. The inference from premise to conclusion cannot be an instance of A( t / x) → ( x) Ax . How can a Russellian even represent the premise? Obviously, it will not be possible to construe the premise as: From this, the conclusion that there is a fountain of youth would follow. The Russellian must resort to paraphrase to capture the intentional import of ‘searches’. But it is far from obvious how paraphrase together with the Russellian account of definite descriptions untangles the conundrum. What sort of ‘objects’ are Meinongian objects of intentionality? One might imagine grades of ontological status, ‘existence’, ‘being’ and so on to explain intentional inexistence. But this was not Meinong’s view. Maintaining an independence of sosein (being so) from sein (existence), Meinong held that there are objects of which it is true to say they are not. By this he meant that phenomenology should be ontologically free and he thought that logic must follow suit. Russell was sympathetic with the epistemic realism embodied in Brentano and Meinong’s thesis of intentionality, but he bridled at Meinong’s thesis that logic must be formed in such a way that the variables of quantification involved in ‘there is’ do not make an ontological commitment. A proper characterization of Meinongianism must be sensitive to the foundational motivations for Meinongian object theory. Russell’s motivations in ontology were not to provide an account of intentionality or reference. The difference is nicely illustrated by examining an argument by Lambert that Russell’s rejection of Meinong’s theory of objects was unprincipled and arbitrary.18 The argument runs as follows. In ‘On Denoting’, Russell criticized Meinong for ‘infringing the law of contradiction’ by holding that ‘every grammatically correct denoting phrase stands for an object ’ (107). Lambert observes that with ιxAx as a genuine referring expression for which the axiom holds, one can derive A( ιxA ) from the very plausible principle MD:


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Page 284 Taking the class abstract notation {z : Bz} to abbreviate the definite description ( ιx)( y x ↔yBy ), we see that schema A( ιxAx ) readily yields naïve class abstraction: y ( ιx)( y x ↔yBy ) ≡yBy . (Simply let Aξ be y ξ ↔yBy .) Lambert concludes that Russell is arbitrary in having a negative attitude towards Meinongian object theory and yet a positive attitude towards a logical conception of a class (2003b). Lambert maintains that Russell’s paradox of the naïve theory classes and Russell’s paradox for naïve Meinongian theory of objects both stem from a common source—the naïve assumption that A( ιxAx ). Lambert’s argument assumes that Russell’s theory of definite descriptions is part of a theory of reference. But no theory of reference provides a ‘common source’ underlying both naïve class abstraction and Meinong’s account of intentionality. In fact, it is far from clear that a viable theory of intentionality requires a Meinongian theory of objects of thought. Russell’s logicism, on the contrary, requires a reconstruction and rehabilitation of the logical notion of a class. Russell’s theory of definite descriptions was not intended as part of a theory of reference or intentionality. In this respect, it is unfortunate that Russell’s theory of definite descriptions is often regarded as a part of the ‘linguistic turn’ in philosophy focusing on language, communication and reference. What motivates Meinongians is the problem of understanding intentionality. Caution is in order, however. There is significant disagreement as to what field the investigation of intentionality belongs. Does the analysis of intentionality belong to empirical psychology, cognitive science, theory of causation, biochemistry, philosophy of mind? Is the theory of intentionality a part of the philosophy of logic itself? With an ontology of propositions construed as necessary entities of logic, Russell found it hard to resist pressing them into service of his revolt against Idealism. Russellian propositions, as states of affairs containing physical objects themselves, are directly apprehended as objects of propositional attitudes. This is a comforting ally of Realism. But we must not be misled. The notion of a Russellian proposition, as a state of affairs, is not the notion of a ‘proposition’ as a meaning—an entity posited to explain what is preserved in translation of one language into another or what is conveyed in acts of communication and reference. Russellian propositions are intensional entities, not intentional entities. This explains Russell’s insistence that in spite of its snowfields, Mt. Blanc is a constituent of the proposition ‘Mt. Blanc is white’ (see Frege 1980:163, 169). What is incredible is the thesis that a ‘meaning’ (intentional entity) contains a mountain with all its snowfields. That is surely absurd, but Russell never held it. In Principles , Russell advanced a theory according to which there are denoting concepts which are ‘about’ (other) entities. It will therefore be surprising to be told that the problem of intentionality was not driving


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Page 285 Russell’s early ontology of denoting concepts and propositions. Aboutness seems to concern intentionality. According to Principles , the denoting concept ‘ Every man’ is about every man. Indeed, it is in virtue of denoting concepts that Russell is able to assure that thinking about the infinite is possible. To think that every even natural number greater than two is the sum of two primes does not require the impossible mental act of entertaining infinitely many thoughts—one about each natural number. Instead, we entertain the proposition: Every even natural number greater than two being the sum of two primes which contains the denoting concept ‘ every even natural number ’. Russell explains that denoting concepts provide ‘the inmost secret of our power to deal with infinity’ (1964:73). Comments like these make it appear as though denoting concepts and propositions are advanced by Russell to provide a theory of meaning. In truth, denoting in Principles is a purely logical relation; it is part of the ontology of pure logic. As such, denoting concepts and propositions are postulated by Russell quite independently of his epistemic theory or his conception of mind. Russell’s early logic was a theory of propositional structure. He required an account of the constituents of those propositions indicated by nominalized formulas which are formal implications—formulas containing bound variables of the new quantification theory of Peano (and Frege). The theory of denoting concepts was Russell’s attempt to form a bridge between the Medieval/Aristotelian logic of categoricals and the bound variables occurring in the formal implications of quantification theory. Russellian propositions are intensional objects, not intentional objects. Principles spoke of those propositions containing denoting concepts (‘as concept’) as being about (in a logical and nonpsychological sense) objects. It is far from clear that this is the ‘aboutness’ of an intentional act. Russell came to abandon denoting concepts in 1905. The theory of denoting concepts of Principles faced ‘an inextricable tangle’. Russell could not solve the problem of what is to be the structure of propositions involving denoting concepts. Socrates (the person) can only occur in a proposition in one way. He occurs in the proposition Socrates’s being human as logical subject of the proposition. The property humanity, on the other hand, is capable of what Russell calls a ‘two-fold occurrence’ in a proposition. It occurs predicatively (or ‘as concept’) in the proposition Socrates’s being human and occurs as term in Humanity’s belonging to Socrates . Like properties, denoting concepts have a two-fold capacity. In the proposition: The centre of mass of the Solar System’s being a point the denoting concept ‘ The centre of mass of the Solar System ’ occurs in away akin to a predicative occurrence. It occurs as logical subject in the proposition:


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Page 286 ‘ The centre of mass of the Solar System ’ being a denoting concept. To display the difference, as we have above, one needs to use inverted commas to act as a genuine proper name (of a denoting concept). If there are no such genuine names, then we cannot display the ontological difference. But the difference remains. The problem is not about how to display it. The problem is that Russell could not devise a theory of propositional structure adequate to the two-fold occurrences of denoting concepts.19 Consequently, he abandoned the theory of denoting concepts in his article ‘On Denoting’. Russell still maintained, however, that Logic is the science of propositional structure. He had to concede that the constituents of propositions named by nominalization of formulas (formal implications) containing the bound variables of the new quantification theory could not be explained by means of the theory of denoting concepts. The bridge offered in Principles had its foundations in clay. When it collapsed, Russell was left with no solution of the problem of the ontological constituents of general propositions. By 1906 the problem was moot. Only those formulas that are quantifierfree can be nominalized to form singular terms for propositions. There are no general propositions—though there are plenty of general sentences that are meaningful. Propositional attitudes such as belief will have to be reconstructed—at least where belief of a ‘general proposition’ is concerned. By modern lights, ontological commitments in logic are questionable. Modern logic has been jaded by the discovery of paradoxes involved with the assumption of purely logical objects. But one should not fear that contradictions concerning ‘meanings’ will arise within formal theory for logic which embraces an ontology of Russellian propositions. There is no reason to be concerned over paradoxes such as that of a person S who believes that every proposition he now believes is false (and all of whose other beliefs are indeed false). Such a paradox is not part of pure logic. To be sure, on Russell’s account of logic as the science of propositions, every well-formed formula of the formal theory of logic can be nominalized to form a term. But this certainly does not assure that expressions such as ‘believes’, ‘asserts’ and such expressions of propositional attitudes are part of the formal language of the calculus for pure logic. Quite clearly they are not. They are part of an applied theory of psychology or philosophy of mind and reference. An ontology of Russellian propositions certainly does not require that belief be regarded as a ‘propositional attitude’ in a literal sense, that is, a relation of a mind to a Russellian proposition. Modern conceptions of logic will have nothing of Russellian propositions as logical objects. Indeed, it will not accept any intensional entities as a part of the ontology of logic. On the modern conception, pure logic should be ontologically free. Modern predicate calculi allow only individual variables as bindable. This means that the seemingly logical assertion that every x has some attribute will become a thesis of a nonlogical theory—a theory


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Page 287 of properties. Is logic captured by the modern predicate calculus? Some say that it is not. Indeed, some (Platonists, let us say) offer a calculus for logic that embraces logical objects—intensional entities such as properties and relations (that is, attributes). Attributes are intensional in the sense that coexemplification is not sufficient for their identity. (Renate and cordate are typical examples, for while they are coexemplifying—one has a kidney if and only if one has a heart—the attributes are not identical.) As objects, attributes can be exemplified by others—for example, goodness exemplifies the property of abstractness. Not everyone among us is a Platonist—not the least of which is because unbridled Platonism is inconsistent. Russell demonstrated this conclusively with the contradiction of the attribute that an attribute φ has if and only if φ does not have itself. Platonism is on the skids. But this does not force the position that logic is captured completely by the predicate calculus. There are those, shall we say Fregeans, who reject Platonism in favour of a conception according to which attributes are logical entities but not logical objects . (This may be paired with the thesis that there are no logical objects—logical objects being apt to produce contradictions.) Predicate variables must remain in predicate positions in the grammar of the calculus. Only object expressions can occupy subject positions. In this Fregean conception, quantification such as ( φ)φx is sui generis . No paradoxes arise in such a theory. On the Fregean theory, attributes live in the configurations of objects, and are not themselves objects for which identity or nonidentity relations hold. The expression ‘φ = ψ’ is illicit for this puts a predicate variable in a subject position. The Fregean will have to be content with φ y ↔y ψ y. How then is one to express what the Platonist so easily writes as ‘the attribute φ exemplifies the property of being exemplified by something’. The Fregean will have to be content with ‘( x)φ x’. But the Fregean can capture a version of the Platonist’s ‘φ exemplifies some property’ in a way that keeps the predicate expression ‘φ’ in a predicate position. He can write ‘( M ) Mxφ x’. The subscripted ‘ x’ in ‘ Mxφ x’ is to remind us that we are dealing with a form such as ‘( x)φ x’ where a bound individual variable is involved. Similarly, the Fregean can recover a version of the Platonist locution ‘the property of being exemplified by some object has the property of being such that every property exemplifies it’. The Fregean writes, ‘(φ)( x)φ x’. A Platonist will write that the property of being exemplified by some object has some property. The Fregean can write ‘( Σ)(Σφ( x)φ x)’. The theory of intentionality is not part of the philosophy of logic. Meinongian objects transcend the logical objects postulated as part of a philosophy of logic—including objects such as logically (or causally) possible worlds and their inhabitants. We may legitimately call upon intensional objects in an account of intentionality. But the challenge for Russellians (and anti-Meinongians) with a ‘robust sense of reality’ is to do justice to the data of intentionality without Meinongian objects. The challenge is daunting because the problem is little smaller in scope than the problem of


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Page 288 giving an adequate account of the mind itself. But this makes the research programme even more interesting. PUZZLES ABOUT PROPOSITIONAL ATTITUDES In ‘On Denoting’ Russell illustrated how his new account of descriptions can solve puzzles concerning propositional attitudes. One of his examples concerned the following argument. The conclusion seems to follow from the premises by application of logical principles. Yet the conclusion is false and the premises are true. We have: To assess the logical form of the argument, and thereby determine whether its conclusion follows validly from the premises, we must first transcribe the argument into the formal canonical language of logic. To transcribe the ordinary language argument, Russell has: Russell’s diagnosis of the puzzle is that there is a ‘logical mirage’ produced by the ordinary language use of the expression ‘the author of Waverley ’. This is not a genuine term of formal logic. Transcription of the argument into the language of logic reveals that the law of identity does not apply. The inference to the conclusion assumes that the following is an instance of the law of identity,

According to Russell, the above is not an instance of the law of identity. The law is this:

where A* is just like A except that y replaces one or more free occurrence of x in A and y is free for x in A. We cannot instantiate the quantifiers of the law of identity to ‘the author of Waverley ’ and ‘Scott’ since there are no


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Page 289 such terms in the formal language of Principia . Quantifiers always instantiate to variables—variables are the only terms. The sentence ‘George IV wished to know whether the author of Waverley is Scott’ does not lend itself naturally to an ambiguity of scope of the definite description ‘the author of Waverley ’ because it is clear in Russell’s example that George IV has the concept of authoring Waverley in mind.20 But certainly primary scopes concerning definite descriptions in the context of propositional attitudes are possible. Moreover, primary and secondary occurrences will not always be equivalent, even when the description is satisfied. For example, it may well be true that there is exactly one morning star and a person S who believes it to be bright, that is,

It is false that S believes there is exactly one morning star and that it is bright. The first scope is a de re ascription of belief to S. The de re reading does not attribute to S the concept ‘morning star’. S may well have a quite different concept in mind in his belief about Venus. It is the person making the ascription that has this concept ‘morning star’ in mind, not the person S to whom the belief is ascribed. In a de re ascription, we may well not know what concept is used by the person to whom the belief is ascribed. Such de re ascriptions of propositional attitudes are certainly captured by Russell’s theory of definite descriptions. There is a problem, however, with pairing de re ascriptions with Russell’s early thesis that propositions are objects of propositional attitudes. At the time of publishing ‘On Denoting’, Russell held that propositions are the direct objects of the attitudes. Using our nominalizing brackets to mark terms for Russellian propositions, one may ask, what proposition is the object of S’s belief in the de re reading

Since only Venus (the planet) satisfies the description, the proposition ascribed to S here is {Bv }, that is, {Venus is bright}. But this is certainly not intended by our de re ascription. The de re ascription intends to leave open how S refers to Venus—it certainly should not determine that S has the state of affairs {Venus is bright}, containing Venus itself, before his


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Page 290 mind. Rather, we want to say that S refers under some description or other and, though we don’t know which, we do know that that description picks out the morning star. We can, of course, avoid the difficulty if we rid ourselves of the early Russellian position that belief is a relation to a proposition. We can drop our nominalizing brackets and hold that the de re ascription does not represent the structure of the cognition of the person S. This approach to quantification de re into propositional attitude contexts relies on a semantic distinction between ‘belief of … ’ and ‘belief that … ’. The distinction is not captured in the syntax of the ascription. Moreover, such a distinction must rely on pragmatic matters sensitive to the context in which the ascription is made. Either way, the distinction is out of sorts with Russell’s ‘logical mirage’ solution in ‘On Denoting’. Russell was surely after a syntactic solution, not a semantic/pragmatic distinction between ‘belief of … ’ and ‘belief that … ’ (and like distinctions for other propositional attitudes). A new application of Russell’s theory to de re ascriptions of propositional attitudes is needed if we are to preserve Russell’s assumption that propositions are objects of the ‘propositional attitudes’. A solution to the problem readily suggests itself. Quantification de re into propositional attitudes must make perspicuous the conceptual cognitive structures employed by the person having the propositional attitude. We can do this if we permit the language to include bindable predicate variables. We have: Expanding the scope marker this is: Our de re belief ascription asserts is that S employs some (unknown) concept φ in referring descriptively to the morning star. In this way, the Russellian can embrace quantification de re without relying on a semantic/ pragmatic distinction between ‘belief of’ and ‘belief that’. It is therefore attractive as a way of preserving the ‘logical mirage’ (or syntactic) solution that Russell was after. The fundamental maxim is this: In de re quantification into propositional attitude contexts, one must display the relevant structure of the cognition of the person having the attitude. On this approach, we have the following chart of forms for belief expressions:


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Page 291 No individual variable may occur free inside the context of a propositional attitude. Only predicate variables may occur free in such contexts. The maxim wrought from our examination of Russellian scope distinctions of definite descriptions is that quantification de re into propositional attitudes must display, to an appropriate degree, the structure of the cognitive state of the person engaged in the attitude. If we pair this with the thesis that the structure of cognition is quantificational, we arrive quite naturally at the thesis that the structures that must be represented in de re quantification into propositional attitudes are akin the Frege’s hierarchy of levels of concepts. The account merges Frege’s notation of levels of functions with Russell’s theory of definite descriptions. Frege’s hierarchy of levels must not be conflated with a hierarchy of types of attributes in intension. In a type of the form ψ( t )(φ t ) the attribute ψ( t ) is understood as unstructured. (An example might be redness exemplifying the property of being abstract.) Fregean hierarchy of levels is a quite natural feature of structure of conceptual processes—assuming that quantification structures of government and binding are essential to the cognitive processes underlying reference and predication. The Fregean hierarchy of types of quantifier concepts is founded upon the notion that concepts must fit together so that concept expressions always occur in predicate positions. As Frege puts it, level n and level n + 1 concepts ‘mutually saturate’. Let us adopt the following notation for the levels of concepts. We have Mxfx the mutual saturation of a first-level concept fx , with a second-level concept Mxφ x which can involve quantifier binding an individual variable. Similarly, Σφ[ Mxφ x] represents the mutual saturation of a second-level concept Mxφ x with a third-level concept Σφ[ξ xφ x] which may involve a bound firstlevel concept variable. This notation keeps concept expressions in predicate positions, and thus the hierarchy of levels of concepts is made perspicuous in the notation. By means of the Fregean expression of levels, we now have the following new expressions of our language of propositional attitudes: The letters φ, M , Σ are variables and so may be bound de re by quantifiers. We can go further in this way, generating new variables for higher levels of concepts. This account of de re quantification into propositional attitude contexts suggests a straightforward solution of contingent liar paradoxes and like paradoxes of propositional attitudes. Frege’s hierarchy of levels is a natural component of our demand that de re quantification into propositional attitude


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Page 292 contexts give a syntactic representation of the structures employed in the process of cognition. Once such structures are in place, all attempts to formulate a liar paradox (of propositional attitudes) fail. In short, the hierarchy of levels (akin though it is to simple type theory) blocks paradoxes without ramification. Of course, the first step is to abandon Russellian propositions as entities to which propositional attitudes such as belief are related. The form ‘ s bel p’ with ‘ p’ as a variable is illicit. This variable does not display the cognitive structure of the belief. The general solution is that all contingent paradoxes of propositional attitudes involve such illicit de re quantification. Consider the following attempt to recover a contingent propositional liar with the modern connectives (without assuming a theory of Russellian propositions). We have:

One arrives at the contradiction: θy ↔y ¬θy. At first blush it may seem that our strictures on quantification de re into propositional attitudes do not block this contingent paradox. But the source of paradox (B) lies in a misconception about the mind’s ability to control the objects of its referential acts. Assumption #b is based on the reasonable intuition that we can determine our minds to refer to a particular object (insofar as that object satisfies a concept employed in a referential act of cognition). But upon reflection that is not what #b asserts, for ψ is not an object of S’s belief. The property ψ is used in the intentionality of the belief, in directing the belief to a specific object. Consider:

Suppose that we also have:

Both beliefs are then cases of S having a belief about the entity a , via a definite description. But the concepts P and Q are not coextensive. For this reason, assumption #b should be rejected as impossible. On the basis of these successes, we have strong reason for thinking that paradoxes of propositional attitudes can be solved by a form of simple type-stratification—our stratification of Fregean levels together with our strictures governing quantification de re into propositional attitudes. Meinongians take intentionality as the raison d’etre for postulating inexistent objects of thought. Their mistake, as a Russellian would see it,


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Page 293 is in their failure to imagine quantificational logical forms for intentional attitudes. They are misled by the surface grammar of natural language. Consider again the puzzle: Ponce de Leon searches for the fountain of youth. Thus, there is something for which Ponce de Leon searches. Searching is an intentional act. It is quite distinct from non-intentionally finding (happening across) something. The logical form of the surface grammar makes it appear to be the same as that of the following argument. Ponce de Leon finds the fountain of youth. Thus, there is a something that Ponce de Leon finds. The logical form here is this: If Ponce finds the fountain of youth, then there is an object that he finds. In contrast, intentionally finding (searching and finding what one searched for) and searching (which leaves open whether one finds what one is searching for) concern the intentionality of cognition. Thus, cognitive structures are now involved in ascriptions of such intentional acts. How shall the Russellian capture this? There is a scope ambiguity in the statement ‘Ponce de Leon searches for the fountain of youth’. The person ascribing the intentional state may be the one who uses the description ‘the fountain of youth’ and who aims only to ascribe to Ponce the use of some descriptive concept co-referential with it. On the other hand, the ascription may be read as saying that the descriptive property fountain of youth is employed by Ponce in his acts of searching in question. There are degrees of de re ascription in this case. Consider this: Explanation of this unusual formula is in order. We have seen that in quantification de re into propositional attitudes we must represent (to an appropriate extent) the structure of the cognition of the person to whom the propositional attitude is ascribed. The idea is naturally allied to a theory according to which Ponce’s mind is (among other things) a system of interconnected quantificational structures. These quantificational structures are abstract entities which are exemplified by or implemented by physical processes of a sort that remains mysterious.22 We saw that the quantificational structures that constitute cognition can be modeled by means of the


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Page 294 Fregean language of levels of concepts. The Fregean language exploits the subscripted variables to indicate the presence of bound variables involved in those quantificational structures. That is why delta occurs as subscript to ‘Ponce’. The expression says that Σ is a searching routine occurring among the quantification structures of Ponce’s mind. The clause, Σφ[ Mz φ z ], says that M is a quantificational structure involved in Σ. Thus the clause, says that the quantificational concept ‘the fountain of youth’ is involved in Ponce’s searching routine Σ. This interpretation of the ascription does not assure that Ponce himself employs the concept Y (fountain of youth) in his cognitive act of searching. Nor is it committed to their being a fountain of youth. A de re ascription that does commit the person making the ascription to the existence of the fountain of youth is this: From here, of course, we can existentially generalize to arrive that the conclusion that there is some object for which Ponce was searching, that is, To make our ascription to Ponce de dicto, we have: This says that Ponce himself uses the concept Y (fountain of youth) in his cognitive acts of searching in question. I have no doubt that this is yet too simplistic. What makes intentional ascriptions and quantification into propositional attitudes so difficult is that they require an adequate philosophy of mind. There is little consensus on what such a philosophy should look like. But the point should be made. Russell hoped that his theory of descriptions shows how to dissolve the ‘logical mirages’ found in puzzles and contingent paradoxes of quantifying into propositional attitudes. His hope was to find a syntactic (structural) representation of the logical forms involved. By uniting Fregean levels of quantifier concepts with Russell’s quantificational approach to definite descriptions, we can imagine some of the needed logical forms. Contingent Liar paradoxes of propositional attitudes are solved in this theory without ramification.


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Page 295 NOTES 1. More exactly, it adopted a ramified type-stratified analog. 2. The symbols for the logical connectives here differ from those in Principia for reasons that will be explained later. 3. Lambert’s account of definitions in Principia cannot be correct where the definitions of Principia ’s section *9 are concerned. The usual derivations underlying the validity of the replacement of logical equivalents in extensional contexts, essential to the axiomatic approach to definition, have to be proven using the definitions of *9 itself. 4. This device is used in Hughes and Cresswell, Introduction to Modal Logic , New York: Routledge, 1996:325. 5. We are omitting issues concerning predicativity. Thus we have removed the sign ! from Principia ’s definition of the identity sign. 6. We have added the scope marker ( Principia to *56 , p. 80) and neglected the issue of predicativity for convenience. Moreover, circumflex notation is removed to avoid controversies surrounding the interpretation of predicate variables in Principia . 7. I have added the scope marker. As with *20.01 the scope marker must be part of the definition *20.08. Its omission is an oversight. 8. Whitehead and Russell explicitly draw the analogy. See Principia to *56 , p. 81. 9. It says: . 10. Linsky’s reply to Martin’s problem focuses on *20.081 and the problematic use of circumflex Greek in Principia . On the present account, circumflex Greek (as with all occurrences of circumflex in Principia ) should be dropped from the work as it plays no role but to mark subject position occurrences of predicate variables. 11. Actually ( S) is a theorem schema derivable from the axiom schema for Russell’s substitutional theory. See Landini 1998a. 12. Russell clearly had this in mind. See Russell 1908. 13. In my view, Principia does not embrace a type-regimented or a ramified and type-regimented ontology of attributes. Instead it embraces a nominalistic semantics for its predicate variables and the notion that these variables are internally limited by their significance conditions. See Landini 1998a. 14. This is the po/ ao paradox. See Landini 1998a. 15. In my view, this was a mistake. Liar paradoxes of propositions are irrelevant to the substitutional theory. See Landini 2004. 16. This phrase is part of the wonderfully rich and interesting book by Richard Routley (Sylvan), Exploring Meinong’s Jungle and Beyond (Australian National University Monograph, 1980). 17. Russell, like Quine, demands an objectual account of the bound individual variables of quantification. 18. Lambert reports that he is developing an idea due to David Kaplan. 19. This is the Gray’s Elegy problem set out in ‘On Denoting’. See Landini 1998b. 20. In conversation with Nathan Salmon at the conference, it became clear that a de re reading of (1) is not indicated in Russell’s example. 21. This paradox is a version of a paradox discussed by Francesco Orilia (1996). 22. This account of mind may be attractive to the computational theory of mind because quantification structures seem amenable to emulation by recursive processes. But this may be too optimistic. The impredicative higher-level


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Page 296 quantifiers essential to Frege’s hierarchy of levels of concepts transcend first-order recursive functions. REFERENCES Frege, G. (1980) Philosophical and Mathematical Correspondence, G. Gabriel, H. Hermes, F. Kambartel, C. Thies, A. Veraart (eds.) and trans. H. Kaal, Chicago: University of Chicago Press. Lambert, K. (2003a) ‘Russell’s Version of the Theory of Descriptions’, in Free Logic: Selected Essays, Cambridge: Cambridge University Press: 1–15. ——. (2003b) ‘The Reduction of Two Paradoxes and the Significance Thereof’, in Free Logic: Selected Essays, Cambridge: Cambridge University Press: 33–43. Landini, G. (1992) ‘Russell to Frege 23 May 1903: I Believe I have Discovered that Classes are Entirely Superfluous ’, Russell, 12: 160–85. ——. (1998a) Russell’s Hidden Substitutional Theory , New York: Oxford University Press. ——. (1998b) ’ On Denoting Against Denoting’, Russell 18: 43–80. ——. (2004) ‘On Insolubilia and Their Solution by Russell’s Substitutional Theory’, in G. Link (ed.), One Hundred Years of Russell’s Paradox, Berlin: Walter de Gruyter: 373–99. ——. (2005) ‘Quantification in Principia ’s *8 and the Empty Domain’, History and Philosophy of Logic 26: 47–59. Linsky, B. (1999) Russell’s Metaphysical Logic , Stanford, CA: CSLI Publications. ——. (2004) ‘Classes of Classes and Classes of Functions in Principia Mathematica ’, in G. Link (ed.), One Hundred Years of Russell’s Paradox, Berlin: Walter de Gruyter: 435–47. Orilia, F. (1996) ‘A Contingent Russellian Paradox’, Notre Dame Journal of Formal Logic 37: 105–11. Quine, W. V. O. (1940) Mathematical Logic , Cambridge, MA: Harvard University Press. ——. (1980) Set Theory and Its Logic , Cambridge, MA: Harvard University Press. ——. (1995) ‘Quantification and the Empty Domain’, in Selected Logic Papers, Cambridge, MA: Harvard University Press. Russell, B. (1905) ‘On Denoting’, Mind 14: 479–93. ——. (1907) ‘On Types’, manuscript in Bertrand Russell Research Center, McMaster University. ——. (1908) ‘Mathematical Logic as Based on the Theory of Types’, American Journal of Mathematics 30: 222–62. ——. (1953) Introduction to Mathematical Philosophy, London: Allen and Unwin. ——. (1964) The Principles of Mathematics, New York: W.W. Norton. ——. (1967) Autobiography 1872–1914, vol. 1., Boston: Little Brown and Co. ——. (1994) ‘On Fundamentals’ in A. Urquhart (ed.), The Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–1905, London: Routledge: 359–413. Whitehead, A. N. and Russell, B. (1964) Principia Mathematica to *56, Cambridge: Cambridge University Press.


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Page 297 14 Quantifying in and Anti-Essentialism Michael Nelson Bertrand Russell’s theory of descriptions, doctrine of acquaintance, and distinction between knowledge by description and knowledge by acquaintance are truly brilliant, profound, and (even if not in the exact form proposed by Russell) correct.1,2 But these Russellian doctrines are sometimes misapplied. This is nowhere more the case than in their application to W.V.O. Quine’s famous attack on quantified modal logic (QML).3 Quine argued that QML is problematic and should be rejected. QML is the combination of standard firstorder quantification theory with sentential modal logic.4 The distinctive formulae of QML, and the ones that Quine found particularly problematic, are ones in which a quantifier is outside the scope of a modal operator and binds a variable within that operator’s scope. The following is an example. (1) x Gx. (1) is a natural formalization of the sentence ‘Something is necessarily a gorilla’, for example. Many have thought that Quine’s arguments are answered by carefully applying Russell’s theory of definite descriptions and his doctrine of logically proper names.5 I think it fair to say that this is the standard response to Quine. Yet it is this application of Russellian theory that I shall here bemoan. Once Quine’s argument is properly understood, it becomes clear that the Russellian response, as I shall call it, fails. These are the topics of the first four sections. This is not to say that Quine’s arguments are successful. Indeed, I think that there are several ways to undermine them. In the fifth section, ‘Quantifying in for the Anti-Essentialist’, I develop two responses. Both are independent of theses about the semantics of definite descriptions or proper names—theses essential to the Russellian response. THE PSEUDO-QUINEAN ARGUMENT AGAINST QML Before I can present the Russellian response, I need to present an argument. But the response in question is only a response to an argument that is not


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Page 298 Quine’s. So, in this section I shall present what I call the pseudo-Quine argument against QML. This argument captures a common understanding of Quine’s argument. In the second section I shall present the Russellian response. In the third and fourth sections, ‘The Real Quine’ and ‘The Failure of the Russellian Response’, I present what I think is Quine’s real argument and show how that argument is immune to the Russellian response. Pseudo-Quine’s argument turns on a(n attempted) derivation of a contradiction. Recall Frege’s famous case of Hesperus and Phosophorus. Pseudo-Quine uses a version of this case to show that ‘modal logic violates Leibniz’s principle’ (Smullyan 1948:31), or the Indiscernibility of Identicals (II), which is the principle that, for all x and y, if x = y, then, for all properties F , x is F iff y is F .6 From this pseudo-Quine concludes that quantifying into modal environments is nonsensical. Pseudo-Quine’s argument turns on two claims. The first is that modal logic violates II and the second is that such violations render quantified modal sentences unintelligible. In support of the first, consider the following trio of sentences. (2) Necessarily, Hesperus is a heavenly body seen first in the evening sky. (3) Hesperus is Lucifer. (4) Necessarily, Lucifer is a heavenly body seen first in the evening sky. We are supposed to agree that (2) and (3) are true and (4) is false.7 But (2), (3), and II entail (4). II is a metaphysical principle. What pseudo-Quine really needs is a semantic principle: A substitution principle. The following is a start. SUB: For any pair of singular terms a and b, if the identity statement a = b is true, then, for any pair of sentences s and s′ , where s′ differs from s only in the replacement of an occurrence of a in s with b, s is true iff s ′ is true.8 (4) differs from (2) only in the replacement of an occurrence of ‘Hesperus’ with the codesignating ‘Lucifer’. So, (2) and (4) seem to be the right form to satisfy the antecedent of SUB. So, SUB seems to require that (2) is true iff (4) is true. But the data seems to indicate that (2) is true and (4) is false. Above I identified two claims driving pseudo-Quine’s argument. The first was that modal logic violates II and the second was that such a violation renders quantified modal sentences unintelligible or otherwise problematic. I’ve discussed the first. Let me now turn to the second. Is (*) below true or false of the single object Hesperus/Lucifer/Venus? (*) Necessarily, x is a heavenly body seen first in the evening sky. Given that (2) is true, it would seem that we should say that (*) is true of that object; given the falsity of (4), it would seem that we should say that (*)


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Page 299 is false of that object. The same condition cannot both be true of and false of a single object (at a single time and in a single world). Assuming there is no equivocation or shift of context in the condition, this would require that a single object both have and not have some property, which violates the principle of noncontradiction. So, we cannot make coherent sense of (*)’s being true or false of an object like Venus. But then we cannot make sense of a quantified modal sentence like (5) below. (5) There is something x such that, necessarily, x is a heavenly body seen first in the evening sky. If we read the quantifier ‘there is’ objectually and we accept a standard semantics for such quantifiers, then the truth or falsity of (5) is defined in terms of the truth or falsity of (*) under an assignment of some object to the variable x. In general, the truth of a quantified sentence is defined in terms of the truth under an assignment of the relevant open sentence. We define (QF)’s truth in terms of the truth under an assignment (of objectual value(s) to the free variable(s)) of the open sentence that results from dropping the initial quantifier; in our case, (OF) below. So, because modal logic violates SUB, we cannot make sense of the distinctive formulae of QML. That is pseudo-Quine’s argument. The claim that the Russellian response targets is that (i) (2) and (4) differ in truth-value and yet, (ii) given SUB and the truth of (3), (2) and (4) should not differ in truthvalue. For ease of future reference, let’s call this the pseudo-claim. THE RUSSELLIAN RESPONSE Depending on how one understands the terms ‘Hesperus’ and ‘Lucifer’ in (2)–(4), the Russellian argues that either (i) or (ii) of the pseudo-claim is false. According to the Russellian, Quine’s argument turns on equivocating between these different ways of understanding those terms. To see why, we must first articulate some Russellian doctrines. I shall thus present a detour through Russell’s doctrine of acquaintance and Russell’s theory of definite descriptions—key doctrines employed in the Russellian response—before returning to the Russellian response itself.


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Page 300 Russell’s Doctrine of Acquaintance and Theory of Descriptions A full, or even adequate, account of Russell’s important notion of acquaintance is out of the question. But a brief description is both necessary and sufficient for present purposes. Russell maintained that every constituent of a thought that an agent is in a position to entertain is something with which she is acquainted.9 Being acquainted with x enables one to entertain thoughts that contain x as a direct, selfrepresenting constituent and one is in a position to entertain such a thought only when one is acquainted with x.10 Call this the Acquaintance Principle . Russell thought that we are acquainted only with our sense data and universals.11 So, Russell thought that we can only think directly about our own sense data and universals. Why did Russell maintain that we are not acquainted—and hence not capable of thinking directly about —material objects? A primary, although not exclusive, reason is broadly Fregean. One is acquainted only with that for which misidentification is rationally impossible. If one is presented with o and it is possible to be presented again with o and rationally not realize it is the same object as before, then one is not acquainted with o;12 one’s thoughts about o are, in that case, indirect. This line of reasoning relies on the Fregean claim that identity confusions are to be explained in terms of differences in thoughtconstituents. The thought that Hesperus is Hesperus is distinct from the thought that Hesperus is Lucifer precisely because of the possibility of misidentification. From this it follows that if one can be presented with an object and rationally not realize that it is the same object that one has been presented with before or in another way, then one’s thought is not directly about that object. For if the thought were directly about the object, there would be no difference in thought grasped, violating the above Fregean claim about cases of misidentification. If there were no difference in thought-constituents in cases of misidentification, then agents would be in a position to believe contradictions while having no internally accessible way of correcting them. And this Russell, like Frege, seems to have found unacceptable. This aspect of Fregeanism forced Russell to deny that we are acquainted with material objects and hence deny that our thought about such objects is direct.13 In claiming that Russell had Fregean motivations for a restrictive view of the objects of acquaintance I am not denying that there are important differences between Russell and Frege. There are significant differences, the most important being that acquaintance played no role in Frege’s view of how thoughts are about the world. Frege maintained that all thought is indirect; we do not think directly about anything, on Frege’s view. Russell, on the other hand, maintained that we think directly about certain entities and that this provides the foundation for all thought whatsoever, whether direct or indirect, about external reality, as we shall see below.14 The Acquaintance Principle is closely related to Russell’s notion of a logically proper name. A logically proper name has as its sole semantic


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Page 301 function that of contributing to the proposition expressed by a sentence in which it occurs its referent. Given the Acquaintance Principle, it follows that, if one understands a logically proper name, then one is acquainted with the object that name names. This is because understanding an expression involves, at least, grasping thoughts with the content of that expression as a constituent. We have seen above that the Acquaintance Principle, combined with Russell’s adoption of a Fregean attitude towards misidentification, led Russell to deny that we can think directly about material particulars. Russell admitted that there is a material reality filled with material particulars that we can and do think about. But all such thought, Russell insisted, is indirect in the sense that the items thought about are not direct constituents of the proposition grasped and that there are no logical proper names of such entities that any of us understand. Thought about material particulars, Russell claimed, is thought by description. By (1910), the canonical form that thought about a concrete particular existing in space and time took is something like the following: The thing that caused THIS [demonstratively referring to one’s occurrent sense datum] is such-and-such . An example is in order. Suppose I am sitting before a green apple and say to myself, ‘That apple is green’. I am acquainted with the universals APPLE and GREEN. But I am not acquainted with the individual apple itself, as misidentification with respect to it is possible. My thought about the apple is descriptive. In virtue of my visual experience of the apple, I am acquainted with a sense datum caused by the apple. Call this sense datum BILL . The content of my thought, according to Russell, is then something like the following. Such propositions are general and thus indirect with respect to the external object (in this case, the apple) itself, but singular and thus direct with respect to the sense datum (in this case, BILL) being demonstratively referred to. Because this is the canonical form thought about material reality takes, such thought is ultimately grounded in acquaintance, albeit acquaintance with sense data as opposed to material reality itself. This is in stark contrast to the canonical form such thought takes in Frege’s system, in which there is no direct reference to sense data or any individuals at all.16 So far the discussion has focused on Russell’s views of acquaintance. This has led us to another famous doctrine of Russell’s—the theory of descriptions. Before spelling that view out in more detail, however, I would first like to discuss Peter Strawson’s (1990) critique of Russell’s view of thought about material reality.17 A key claim Strawson makes is that physical bodies are basic particulars , by which he means that we can identify material bodies without identifying other kinds of particulars (like mental particulars or events) but not vice versa. Strawson’s notion of identification


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Page 302 is related to the possibility of speaking (and presumably thinking) about an object and ascribing properties to it. For both Strawson and Russell, our ability to speak and think about objects in the world is based on demonstrative reference (what Russell called acquaintance). In this, both Strawson and Russell are opposed to Frege. But, whereas Strawson claimed that the objects demonstratively referred to are physical bodies in one’s immediate perceptual environment, Russell, as we have seen, maintained that such reference is to one’s occurrent sense data. In an apparent attempt to establish his view over Russell’s, Strawson writes: On other criteria than the present, private experiences have often been the most favoured candidates for the status of ‘basic’ particulars; on the present criteria, they are the most obviously inadmissible. The principles of individuation of such experiences essentially turns on the identities of the persons to whose histories they belong. A twinge of toothache or a private impression of red cannot in general be identified in our common language except as the twinge which such-and-such an identified person suffered or is suffering, the impression which suchand-such an identified person had or is having. Identifying references to ‘private particulars’ depend on identifying references to particulars of another type altogether, namely persons. (41) Russell should agree that private particulars (sense data) are dependent on persons in the sense that for any private particular m , there is some person p such that, necessarily, if m exists, then m is had by p. But from this it does not follow that in order to identify a private particular one must first identify the person to whom that private particular belongs. If it is my private particular and it is immediately before me, then, says Russell, I can think of it directly without first identifying the owner of the private particular; after all, the sense data is immediately present to me in my experience. Strawson conflates the metaphysical dependence of private particulars on persons and the semantic or psychological dependence of having to independently identify the bearer of a given private particular in order to identify, and hence think about, it. These two kinds of dependences come apart precisely in the firstperson case: Although all private particulars (mine included) are metaphysically dependent on their bearers, I can directly refer to my own occurrent private particulars without first independently identifying myself. Russell’s view is consistent with the ontological dependence of sense data. Strawson developed an influential ‘massive reduplication’ argument (20). One of the conclusions Strawson drew from this argument is that identifying, and hence talking and thinking about, objects outside one’s immediate perceptual environment ultimately rests on relating those objects spatiotemporally to objects in one’s immediate perceptual environment and their spatio-temporal location, where the latter are demonstratively identified. That is, Strawson takes the argument to support the broadly Kantian claim that


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Page 303 demonstrative identification of one’s spatio-temporal location in a system of particulars bearing spatiotemporal relations to one another ultimately grounds our ability to identify objects outside our immediate perceptual contact. This conclusion runs contrary to Russell’s view, according to which (to use Strawson’s terminology), it is mental particulars that are the (identificationally) basic individuals. But, I shall argue, Russell’s view can actually accommodate the insight behind Strawson’s reduplication argument. I was just sitting in my chair in my office and I am now standing outside in the hall thinking about that chair. But suppose that we live in a universe with massive reduplication in which there is a qualitatively indiscernible chair in a qualitatively identical office adjacent to a qualitatively identical hall on the other side of the universe. It is intuitive that I am nonetheless thinking about the chair in my office and not its qualitative twin. But then my thought is not purely qualitative, as otherwise it would not be determinately about one of the chairs rather than the other. Strawson concludes that I must relate the chair in the room I just left to my spatio-temporal location, which I think about demonstratively and hence nonqualitatively, in order to have a description that uniquely picks it out as opposed to its qualitatively twin. The first chair, and not its qualitative twin, bears the appropriate spatio-temporal relations to my present spatio-temporal relation, which I identify demonstratively. Hence, I am able to think determinately about objects outside my present perceptual environment by relating them spatiotemporally to my present spatio-temporal location, where I pick the latter out demonstratively. I think that the reduplication argument provides powerful support for the claim that our thought about material reality is not all purely qualitative.18 It thus succeeds in refuting a purely Fregean view. But it does not refute Russell’s view. Russell does not, remember, maintain that our thought about material particulars is all purely qualitative. He can deliver the intuitive results concerning reduplication cases. This is because demonstrative identification of our own sense data provides just as good an anchor as one’s spatio-temporal location; indeed, demonstrative identification of any individual that other individuals bear unique, discernible relations to will work. For Strawson, my thought is about the chair in the room next to me rather than the chair in the other region of the universe in virtue of its spatiotemporal relation to me now and my ability to think about my current spatio-temporal location directly. Russell gets the same result by relating the chair to my sense data. Just as the locations of the two chairs in the reduplication universe are different, so too are the sense data they cause. Only the chair in my office is the cause of the sense datum that, on Russell’s view, I demonstratively identify; the other chair causes a numerically distinct sense datum. So, if I can demonstratively identify my own sense data and then identify other objects in relation to those sense data, I have met the theoretical challenges the possibility of reduplication present. I have located, as it were, my thoughts in such a way as to make them about the proper objects, even in the reduplication universe.


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Page 304 Strawson’s reduplication argument, whatever its exact intended effect, does not offer reason to abandon Russell’s view. Let’s move now to Russell’s theory of description. We have seen that Russell’s notion of thought by description is supposed to enable one to think about items with which one is not acquainted consistent with the Acquaintance Principle. In order for descriptive thought to play this role, one must have a theory of descriptive thought according to which the individual the thought is (indirectly) about is not a constituent of that thought. Russell had just such a theory, first presented in his classic (1905) and more rigorously in Alfred North Whitehead and Russell (1925). Whitehead and Russell introduced into their formal language an operator—the iota-operator—to translate sentences with definite descriptions in subject position—sentences of the form The F is G . This addition did not constitute an extension of their formal language; iota-phrases are mere ‘abbreviations of convenience’, always eliminable in terms of other pieces of vocabulary of the language. So, for example, the ‘iota-sentence’ is definitionally equivalent, by *14.01, to the following ‘iota-less sentence’. Definite descriptions are thus, in their logical form, quantificational phrases. The sentence ‘The heavenly body seen first in the evening sky is a heavenly body seen first in the evening sky’, for example, is logically equivalent to and analysed in terms of the sentence ‘There is exactly one heavenly body seen first in the evening sky and that object is a heavenly body seen first in the evening sky’. The combination of definite descriptions and sentential operators create scope ambiguities. To use Russell’s favourite example, (6) below is ambiguous. (6) The present King of France is not bald. This sentence as a whole can be taken either to be primarily a quantificational sentence or primarily a negated sentence. If the first, we are ‘giving the definite description wide scope’; if the second, we are ‘giving the definite description narrow scope’. We can represent these options as follows: As iota-formulae are definitional shorthands for iota-less-formulae, (6w) and (6n) are equivalent to the following iota-less-formulae.


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Page 305 (6wexpanded) and (6nexpanded) are not truth-functionally equivalent.20 In truth-functional environments, scope differences affect truth-value—that is, there is a difference in truth-value between the wide and narrow scope readings—only when the unique existence assumption is not satisfied, as *14.3 claims. But Russell was clear that, outside truth-functional environments, scope ambiguities do lead to differences in truth-value even when the existence assumption is satisfied, as his case of George IV puzzlement over who authored the Waverley series in (Russell 1905) makes clear. Although George IV wonders whether or not Scott is the author of Waverley , he does not wonder whether or not the author of Waverley is the author of Waverley . There is a scope difference that leads to a difference in truth-value here, even though the existence assumptions are satisfied, because of the nontruthfunctional environment created by the attitude verb. Russelling Quine We now have the needed machinery to present the Russellian response to Quine’s argument against QML. Recall (2) and (4). (2) Necessarily, Hesperus is a heavenly body seen first in the evening sky. (4) Necessarily, Lucifer is a heavenly body seen first in the evening sky. According to the pseudo-claim , (i) (2) and (4) differ in truth-value and yet, (ii) given SUB and the truth of the identity claim (3), (2) and (4) should not differ in truth-value. Appealing to Russell’s distinction between logically proper names and definite descriptions, we can distinguish two ways of understanding (2) and (4). First, ‘Hesperus’ and ‘Lucifer’ might both be logically proper names; second, ‘Hesperus’ and ‘Lucifer’ might be disguised definite descriptions.21 And, given the interaction between definite descriptions and modal operators, the second comes in two varieties: One in which the definite description takes wide scope with respect to the modal operator and another in which it takes narrow scope. Because the modality creates a nontruth-functional environment, this scope ambiguity might affect truth-value even when existence assumptions are satisfied. The Russellian claims that, in the first case, (2) and (4) have equivalent truth-values and, in the second, they either have equivalent truthvalues or else (4) does not follow from (2) and (3) by SUB. But in neither case does both (i) and (ii) obtain. So, either way, the pseudo-claim is false. Let me fill this out in more detail. Suppose first that both terms are logical proper names. Call this option (A). Then (2) is true just in case (4) is. This is because under option (A) (2) and (4) express exactly the same proposition, as both singular terms ‘Hesperus’ and ‘Lucifer’ are, given the truth of the identity statement (3),


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Page 306 logical proper names of the same individual and hence contribute the same object to the proposition they express.22 So, in this case, (i) of the pseudo-claim is false. Suppose, then, that both ‘Hesperus’ and ‘Lucifer’ in (2) and (4) are disguised definite descriptions. For simplicity, let’s suppose that the first is equivalent to ‘the heavenly body seen first in the evening sky’ and the second to ‘the heavenly body seen last in the morning sky’. Then (2) and (4) should be read as (2d) and (4d) below, respectively. (2d) Necessarily, the heavenly body seen first in the evening sky is a heavenly body seen first in the evening sky. (4d) Necessarily, the heavenly body seen last in the morning sky is a heavenly body seen first in the evening sky. Let us further suppose Russell’s theory of definite descriptions, a theory Quine accepted.23 Then we face a choice. Given that ‘necessarily’ functions as a sentential operator, (2d) and (4d) are ambiguous in terms of scope. That is, there is both a wide and narrow scope reading of each (2d) and (4d), as follows. (Let Ex abbreviate ‘ x is a heavenly body seen first in the evening sky’ and Mx abbreviate ‘ x is a heavenly body seen last in the morning sky’.)

We shall show that, in the first case, (i) of the pseudo-claim is false and, in the second case, (ii) of the pseudo-claim is false and hence that, either way, the pseudo-claim is false. Suppose first that we give both descriptions wide scope. Call this option (B). Then we understand (2) and (4) as having the logical forms given by (2dw) and (4dw). But (2dw) and (4dw) do not differ in truth-value, as the object that uniquely satisfies the condition Ex also satisfies the condition Mx . If we assume that Venus is only accidentally seen first in the evening sky, then both are false; if we assume otherwise, then both are true. So, under option (B) there is no variance of truth-values between (2) and (4) and hence (i) of the pseudo-claim is false. Suppose then that we give both descriptions narrow scope. Call this option (C). Then there is indeed a difference in truth-value between (2) and (4), as (2dn) is true and (4dn) is false (assuming, as seems evident, that it is possible for a heavenly body to be seen first in the evening sky without being seen last in the morning sky). So, we secure (i) of the pseudo-claim only with option (C). But in that case, we jeopardize (ii) of the pseudo-claim, for the variance in truth-value does not, in that case, violate ‘Leibniz’s principle’, or, more precisely, SUB. It is a misapplication of SUB to use it to derive (4dn)


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Page 307 from (2), taken in any way, and (3) or (4), taken in any way, from (2dn) and (3). a and b in SUB range over only genuine singular terms, which, given Russell’s theory of descriptions, definite descriptions are not. We have considered three options for understanding (2) and (4). No understanding has led to a variance in truth-values that violates Leibniz’s principle. It is only by equivocating between these options that we secure both (i) and (ii) of the pseudo-claim. Quine has not shown that QML violates Leibniz’s principle and has failed to derive a contradiction. THE REAL QUINE24 Smullyan first applied Russell’s doctrines to Quine’s argument against QML in the way detailed above.25 Although the application is brilliant, it also rests on a misunderstanding of Quine’s argument. In all fairness to Smullyan, he was responding to Quine’s (1947),26 which was, even by Quine’s own lights, confused in important ways27 and failed to bring out the heart of Quine’s objection. But, by 1953, when Quine significantly rewrote and combined (1943) and (1947) to create the first version of ‘Reference and Modality’, the best statement of Quine’s objection to QML, it became clear that Quine’s argument does not turn on deriving a contradiction, as Smullyan and his followers conceived it. Instead, Quine’s argument turns on attempting to show that interpreting the characteristic formulae of QML requires Aristotelian essentialism. The Russellian response is simply silent about any alleged connections between QML and Aristotelian essentialism and thus fails to truly address Quine’s argument. Quine thought that modality requires a reduction to the notion of analyticity and ultimately logical truth. But this reduction is at odds, Quine argued, with the combination of modal logic and standard first-order quantification logic. For the combination requires Aristotelian essentialism, which is contrary to the original reductionist project of grounding modality in analyticity and ultimately logical truth and the notion of synonymy. So much the worse, concluded Quine, for QML.28 The intelligibility of QML requires that we make sense of an object, independently of how and even if it is designated, satisfying the condition Gx. (Equivalently, we need to make sense of the open sentence Gx being true of an object, independently of how and even if it is designated.) This is because QML is intelligible only if formulae like (1)—( x) Gx—are intelligible and the intelligibility of such formulae require the intelligibility of the notion of an object satisfying the condition Gx. Quine’s challenge is then to make coherent sense of this notion without resort to Aristotelian essentialism. He claimed the challenge could not be met. We need two things to spell this line of argument out in more detail: First, we must characterize Aristotelian essentialism; second, we must be more precise about the condition Gx.


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Page 308 One might think that it is straightforward to characterize the thesis of Aristotelian essentialism. One would expect Quine to have given a clear and careful characterization of the thesis and then proceed to operate only with that characterization, given the crucial role the thesis plays in his argument. But things are not, I fear, as one would expect. Fully working this out exposes a serious set of equivocations in Quine’s argument, as I argue in the fifth section, ‘Quantifying in for the Anti-Essentialist’. But we need at least a working conception to get going. For this, we turn to Quine’s own words. Reversion to Aristotelian essentialism is required if quantification into modal contexts is to be insisted on. An object, of itself and by whatever name or none, must be seen as having some of its traits necessarily and others contingently, despite the fact that the latter traits follow just as analytically from other ways of specifying it. (Quine 1980:155) This means adopting an invidious attitude toward certain ways of uniquely specifying x, for example [as ‘Hesperus’, say], and favouring other ways, for example [as ‘Lucifer’, say], as somehow better revealing the ‘essence’ of the object. (155) We can glean the following characterizations of the thesis of Aristotelian essentialism from these sampled passages. The thesis of Aristotelian essentialism is the thesis that there is a privileged proper class of designators of an object that best reveal that object’s necessary properties:29 the ‘essence revealing’ designators. And this despite the fact that those properties do not analytically follow from some nonprivileged designators of the object and other, contingent properties do analytically follow from some nonprivileged designators. Later I shall distinguish other characterizations of the thesis of Aristotelian essentialism present in the passages. Let’s turn to explicating the condition Gx. There are at least three ways of construing . We might first construe it in terms of logical truth. Then, in making sense of an object satisfying the condition Gx, we need to say what it is for an object to logically satisfy a condition Gx.30 Second, we might construe it in terms of analytic truth. Then, in making sense of an object satisfying the condition Gx, we need to say what it is for an object to analytically satisfy a condition Gx. Finally, we might construe it in terms of metaphysical necessity. Then, in making sense of an object satisfying the condition Gx, we need to say what it is for an object to ( metaphysically ) necessarily satisfy a condition Gx. Quine is clear that his concern is with strict necessity analysed in terms of logical and analytical truth.31 Although it is an interesting and important question whether or not a Quinean argument works when is construed in terms of metaphysical necessity—and in particular whether or not understanding the notion of an object, independently of how and even whether


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Page 309 it is designated, satisfying a condition as a matter of metaphysical necessity requires some philosophically controversial thesis of essentialism—it is a question I shall not here pursue. Following Quine, I shall be concerned with a construal of necessity in terms of analytical and logical truth. Quine claims that (2) is true, which is likely to sound strange to contemporary ears. First, most of us naturally read an unadorned ‘it is necessary that’ in terms of metaphysical necessity and it is indeed hard to think that as a matter of metaphysical necessity Venus is seen first in the evening (unless one is a metaphysical necessitatarian). But Quine had in mind strict necessity. Second, like Russell, Quine typically thought of ordinary proper names as disguised definite descriptions and so naturally read ‘Hesperus is a heavenly body seen first in the evening sky’ as equivalent to something like ‘The heavenly body seen first in the evening sky is a heavenly body seen first in the evening sky’. So, putting these two points together, the claim that (2) is true comes to, according to Quine, the claim that the sentence ‘The heavenly body seen first in the evening sky is a heavenly body seen first in the evening sky’ is analytically true. This does not sound strange, even if it is strange to think that that is what (2)’s truth involves. We now have all the pieces to spell out Quine’s argument in detail. Quine claims that making sense of the distinctive formulae of QML requires making sense of an object, independent of how it is designated, analytically and ultimately logically32 satisfying a condition. And he thinks that the fact that (2) is true and (4) is false proves an insurmountable problem to this task, provided we are to avoid commitment to Aristotelian essentialism.33 Avoiding Aristotelian essentialism involves not privileging one way of designating an object over others when determining whether or not that object necessarily has some given property. But without such a privileging, we are at a loss when asked whether or not Venus, for example, necessarily has the property of being a heavenly body seen first in the morning sky. Because (2) is true, we should say that it does; because (4) is false, we should say it does not. We get a consistent answer concerning whether or not Venus analytically satisfies the condition ‘ x is a heavenly body seen first in the evening sky’ only if we privilege one of these ways of designating Venus, letting, say, what analytically follows from the designator ‘the heavenly body seen last in the morning sky’ be determinative of what conditions Venus analytically satisfies and ignoring the fact that some of those conditions do not analytically follow from other ways of designating Venus. Hence, QML is committed to Aristotelian essentialism. But Aristotelian essentialism is contrary to properly grounding modality in analyticity. Thus, QML should be rejected. Quine’s argument against QML turns on what we can call Quine’s Challenge: The challenge of explicating the notion of an object logically or analytically satisfying a condition in terms of the more familiar notion of a (closed) sentence being logically or analytically true without committing


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Page 310 oneself to Aristotelian essentialism and while recognizing the fact that, for some objects, different ways of designating it are analytically tied to different predicates. Now it might seem tempting to simply insist that the truth of (2) and falsity of (4) are irrelevant to whether or not Venus analytically satisfies the condition Ex. But that is a hard pill to swallow. The notions of (syntactic) logical and analytic truth primarily apply to closed sentences. So if we are going to make sense of an open sentence being (syntactically) logically or analytically true of an object, it must be in terms of the logical or analytic truth of a closed sentence. And to make sense of an object analytically satisfying the condition Gx just is to make sense of the open sentence Gx being analytically true of that object. But then the fact that (2) is true and (4) false, given the identity statement (3), is very relevant to whether or not Venus analytically satisfies Ex. The notions of logical and analytic satisfaction are dependent on the notions of logical and analytic truth. A strong case can be made, supported by standard model theory for first-order predicate logic, that the order of dependence is reversed for the notion of truth (conceived of as a property of sentences) and the notions of satisfaction and true of. The truth of a simple sentence Fa is explicated in terms of an object (the object assigned to a ) satisfying the condition Fx . But the notions of logical and analytic satisfaction simply cry out for analysis in terms of logical truth and the analyticity of closed sentence. Quine’s problem is a problem only if one adopts an objectual theory of quantification. If we adopt a substitutional theory, then we would explicate the truth of a quantified sentence like (1) in terms of the truth of some closed sentence and so would not have to avail ourselves of (and hence make sense of) the notion of an object satisfying the condition Gx.34 Similarly, if we treated the quantifier in (1) as a conceptual quantifier, then, again, we would not have to make sense of the notion of an object satisfying the condition Gx. This is because conceptual quantifiers range not over objects but rather over individual-concepts (that is, concepts that uniquely determine a single object). Although this point is correct as far as it goes, it is irrelevant to Quine’s Challenge. If it is standard, firstorder quantification theory that we are adding to sentential modal logic, then we must make sense of an object satisfying the condition Gx. Quine’s argument against QML assumes that the Q is standard, objectual quantification theory. As Quine says: ‘What I’ve been talking about is quantifying, in the quantificational sense of quantification, into modal contexts in a modal sense of modality’ (Marcus et al. 1963:116). (By ‘quantificational sense’ he clearly means objectual; by ‘modal sense’ he means strict modality.) So we cannot simply reject the demand to explicate the notion of analytic satisfaction. We can change the subject, if we like, and we might even be able to justify changing the subject by showing that the alternative substitutional and conceptual conceptions of quantification


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Page 311 are superior to the standard objectual conception. But that is not to answer Quine’s argument, as that argument is targeted against objectual quantification into modal environments. I think that the foregoing discussion captures the essence of the strongest version of Quine’s argument against QML, although I certainly have not followed Quine’s own presentation. Indeed, in presenting Quine’s argument I have not explicitly employed the notions of purely referential and nonpurely referential occurrences of singular terms (or what in (1943) Quine called purely designative occurrences ) and opaque environments. And I have not relied on Quine’s Thesis—the thesis that quantifying in to an opaque environment is incoherent—which is essential to some understandings of Quine’s argument. David Kaplan (1986:230) distinguished two kinds of arguments Quine raised against quantifying in: Logical arguments, which aimed to establish the incoherence of quantifying into opaque environments in general, and nonlogical, metaphysical or epistemological arguments, which aimed to show that there were suspect metaphysical or epistemological theses underlying the attempt to quantifying in to a particular opaque environment. I have here focused on Quine’s nonlogical, metaphysical argument against QML.35 This, I think, is where Quine’s insights are to be found. Quine’s worry was that QML required the suspect metaphysics of Aristotelian essentialism. He thought this because he saw that different designators of a single object are analytically connected to different predicates and so, he concluded, in saying what is analytically true of an object we must privilege certain such singular terms as ‘better revealing’ that object’s essence, which is just to embrace Aristotelian essentialism. Answering Quine’s worry thus requires showing that QML is free of essentialist commitments and thus answering Quine’s Challenge. THE FAILURE OF THE RUSSELLIAN RESPONSE In the previous section I described what I take to be Quine’s argument against QML. The key difference, for present purposes, between that argument and pseudo-Quine’s argument, described in the first section, is that, whereas pseudo-Quine attempts to derive a contradiction from the fact that (2) and (3) are true and (4) false, relying on SUB, Quine did no such thing. I claim that, although successful against pseudo-Quine’s argument, the Russellian response is unsuccessful against Quine’s argument. The Russellian response turns, remember, on showing that either (i) that (2) and (4) do not differ in truthvalue; or (ii) (2) and (3) do not entail, via SUB, (4). The response is successful, I claim, in this. But it is simply irrelevant to Quine’s argument. To respond to Quine one needs to show either that interpreting the characteristic formulae of QML does not require commitment to Aristotelian essentialism and more particularly that we can make sense of the notion of an object, independently of how and even


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Page 312 whether it is designated, logically satisfying a given condition without privileging a proper class of designators of the object, or that Aristotelian essentialism is not as problematic as Quine made it out to be. That is, one needs to either meet head-on what I called Quine’s Challenge or develop a defensible essentialist metaphysics. Nothing the Russellian says helps on either of these fronts. The Russellian response does not help answer Quine’s Challenge as it either assumes the sense of the notions of logical or analytic satisfaction that we have been asked to explicate (when we consider the terms to be descriptions with wide scope, or something just as problematic when we consider the terms to be logically proper names) or simply confirms one of the points that pushes Quine’s argument (when we consider the terms to be descriptions with narrow scope). And, of course, the Russellian does not help with an essentialist metaphysics either. Let me spell this in more detail. Earlier I distinguished three ways of understanding (2) and (4) the Russellian offers—options (A)–(C). The Russellian rightly points out that none of those options allow us to say both that (2) and (4) differ in truth-value and that (4) should follow from (2) and the true (3) by SUB. Quine can and should admit this;36 it is simply irrelevant to Quine’s Challenge. Option (A) is the most delicate, so I shall postpone its discussion. Option (B) offers no help in answering Quine’s Challenge. Under this option, we understand (2) and (4) as (2dw) and (4dw) respectively, reproduced below. Both (2dw) and (4dw) involve occurrences of applying to an open sentence. But then in claiming that (2dw) and (4dw) have the same truth-value—or indeed any truth-value at all—we have simply helped ourselves to the very notion we have been asked to analyse. Answering Quine’s Challenge, remember, requires explicating the truth or falsity of quantified modal sentences in terms of modal sentences with applying only to a closed sentence. Option (C) is more promising on this front. On this option, recall, we understand (2) and (4) as (2dn) and (4dn), respectively, reproduced below. Both (2dn) and (4dn) only have closed sentences within the scope of . But the problem with (2dn) and (4dn) is that, if we are to avoid Aristotelian essentialism and so treat all ways of designating an object as equally telling of what conditions it logically satisfies, then we seem forced into the contradiction of saying that one and the same object—Venus—both does and does not logically satisfy the condition Ex. This contradiction does not


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Page 313 involve any application, questionable or otherwise, of SUB. So the Russellian’s complaint with option (C) is irrelevant. What drives Quine’s argument at this point is the desire to treat all designators of Venus on a par when it comes to determining Venus’s necessary properties. And this does not rest on attempting to substitute one definite description for another within the scope of . Rather, it rests on a desire to eschew commitment to Aristotelian essentialism. I said above that option (A) raises delicate issues. Let me now take them up. Under option (A), we understand (2) and (4) as (2lpn) and (4lpn), respectively. (Let h and l be logically proper names both assigned Venus as values.) It might be thought that (2lpn) and (4lpn) avoid the problems I raised for options (B) and (C). Unlike (2dw) and (4dw), neither contain an open sentence governed by ; unlike (2dn) and (4dn), (2lpn) and (4lpn) seem to have the same truth-value. Quine wants us to explicate what it is for an open sentence to be analytically true of an object in terms of the analytic truth (or lack thereof) of a closed sentence. We now see that the reduction should be carried out in terms of closed sentences containing logically proper names of the object in question. Venus analytically satisfies the condition Ex, we might say, because the closed sentences Eh and El are analytically true (or, alternatively, Venus does not analytically satisfy the condition Ex because the closed sentences Eh and El are not analytically true). Just what we wanted, right? No. First, notice that if we go this route we must still exclude from the class of ‘essence revealing’ designators of Venus either ‘the heavenly body seen first in the evening sky’ (if we count both (2lpn) and (4lpn) as true) or ‘the heavenly body seen last in the morning sky’ (if we count both (2lpn) and (4lpn) as false). (Even if definite descriptions are neither genuine names nor singular terms, surely they are designators.) But this is just the kind of privileging that a denier of Aristotelian essentialism seeks to avoid. Ruth Barcan Marcus famously distinguished a tag for an individual from a singular description of that individual (1963:85). The distinction is consciously reminiscent of Russell’s distinction between logically proper names and definite descriptions. ‘This tag’, Marcus writes, ‘a proper name, has no meaning. It simply tags’ (84). By saying that a tag ‘has no meaning’, Marcus means that it does not contribute a descriptive condition to the proposition expressed by a sentence in which it occurs. By claiming that ‘it simply tags’, Marcus means that is simply introduces an individual directly for the rest of the sentence to then go and attribute a property to. If we help ourselves to the traditional notion of a proposition (something Marcus seems not terribly comfortable with), we then get that sentences with tags


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Page 314 express singular propositions—exactly what Russell thought of sentences with logically proper names. Marcus claimed, in effect, that if there are two tags a and b of the same individual, then a = b is a tautology and indeed analytic. She suggests ‘there would be a way of finding out, such as having recourse to a dictionary or some analogous [nonempirical] inquiry, which would resolve the question as to whether the two tags denote the same thing’ (Marcus et al. 1963:115).37 Marcus is here pursuing option (A). Saul Kripke responded to Marcus’s proposal by claiming that it requires acceptance of Aristotelian essentialism. That seems to me like a perfectly valid point of view. It seems to me the only thing Professor Quine would be able to say and therefore what he must say, I hope, is that the assumption of a distinction between tags and empirical descriptions, such that the truth-values of identity statements between tags (but not between descriptions) are ascertainable merely by recourse to a dictionary, amounts to essentialism itself. The tags are the ‘essential’ denoting phrases for individuals, but empirical descriptions are not, and thus we look to statements containing ‘tags’, not descriptions, to ascertain the essential properties of individuals. Thus the assumption of a distinction between ‘names’ and ‘descriptions’ is equivalent to essentialism. (Marcus et al. 1963:115) Kripke is right that option (A) leads to Aristotelian essentialism and hence does not constitute a solution to Quine’s Challenge.38 When Kripke went on to develop his distinction between rigid and nonrigid designators—a distinction related to, although importantly different from, as there are rigid definite descriptions, Marcus’s distinction between tags and descriptions—and argue that identity sentences with rigid designators are, if true, necessarily true and that modal sentences containing rigid designators reveal the necessary properties of individuals, in (1971) and (1980), he was clear that he was simply embracing essentialism, not eschewing it. There are further reasons to be suspicious of the doctrine of logical proper names and the appeal to (2lpn) and (4lpn) in answering Quine’s Challenge. We should remind ourselves of the peculiar nature of l and h. As logically proper names, their sole semantic function is to introduce an object into the proposition expressed by sentences in which they occur. Thus, the sentences Eh and El closely resemble the open sentence Ex under an assignment of Venus for x. The most plausible way of assigning propositions to these sentences has them all expressing the same singular proposition containing Venus and the property being a heavenly body seen last in the evening sky . Their only differences reside in the fact that the valuation of variables, as opposed to the interpretation of the individual constants, supply Venus as value in the latter case. Given this similarity, it seems strange to say that the alleged analyticity of the one is any less problematic than the alleged analyticity of the other, even if the other is a closed sentence.


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Page 315 If one were puzzled with the attribution of analyticity to a valuated open sentence Ex, as Quine evidently was, this puzzlement is not dispelled by appealing to an attribution of analyticity to sentences like Eh and El. We have little more understanding of what is involved in their logical or analytic truth than we have understanding of the notion of analytic satisfaction. We have a more or less good understanding of why a sentence like ‘The heavenly body seen first in the evening sky is a heavenly body seen first in the evening sky’ is a (syntactic) logical truth and a sentence like ‘The heavenly body seen last in the morning sky is a heavenly body seen first in the evening sky’ is not. This is made all the more apparent if we assume something like Russell’s theory of descriptions, whereby the first is analysed as [ ιxEx ] Ex and the second as [ ιxMx] Ex. We can then point out that anything that satisfies the condition Ex is thereby guaranteed to satisfy the condition Ex, but not so for satisfying the condition Mx . It is for this reason that the first is guaranteed to be true in virtue of its form alone whereas the second is not. And if we help ourselves to the notion of synonymy, then, again, we can explain the analytic status of a sentence like ‘Everything that is a vixen is a female fox’ by pointing out that ‘vixen’ and ‘female fox’ are synonymous and so, by replacing synonym with synonym, we get the logically true syntactic form ‘Everything that is a vixen is a vixen’. But we lack a similar grip on why we should count a sentence like Eh as logically (in the syntactic sense) or analytically true. Indeed, once we see that Quine intended to mean either ‘is a logical truth that’ or ‘is analytic that’, where analyticity is explicated in terms of synonymy and logical truth, it seems to me that we should not be so willing to take as unproblematic the truth of sentences like (2lpn) and (4lpn). If anything, we should be explicating what it is for such a sentence to be logically (in the syntactic sense) or analytically true in terms of the less problematic sentences that do not contain logically proper names. Indeed, it is very hard to see how anything beside identity claims (like l = l) could be thought to be logically or analytically true. (If we focus on a syntactic (as opposed to propositional) conception of logical truth, it is hard to see how we could count h = l as logically true. But if it is not logically true, we have to once again be discerning about what designators we consult in determining whether or not Venus satisfies the condition x = l.) Option (A), although initially attractive, is a dead-end. I conclude that the Russellian response is ineffective against Quine. An effective anti-essentialist response must answer Quine’s Challenge and doing that requires very different resources from those employed by the Russellian response. QUANTIFYING IN FOR THE ANTI-ESSENTIALIST There are three broad attitudes one may take towards the argument ascribed to Quine in ‘The Real Quine’, given the failure of the Russellian response.


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Page 316 The first two are alike in that they do not attempt to pry apart QML and Aristotelian essentialism and thus do not take up answering Quine’s Challenge, while the third does just that. My primary focus here shall be on articulating a version of the third. The first broad attitude one might take is that of Quine himself: Accept Quine’s conclusion and reject QML as ‘conceived in sin’ and unfit for use (and perhaps even mention).39 Although some—some even distinct from Quine40—have gone down this dark road, I think it too drastic this early in the game. The second reaction is to accept that QML requires or at least is best articulated in light of Aristotelian essentialism and embrace Aristotelian essentialism. I think this is the typical reaction to Quine, even if its proponents do not always appreciate that that is what they are doing. I have argued that that is where options (A) and (B) of the Russellian response lead and we have already seen that Kripke is consciously a proponent of this response. Although I am most sympathetic with this line of response,41 in this paper I wish to explore a third reaction to Quine’s argument, which is to seek to sever Aristotelian essentialism and QML. There are, broadly, two ways to develop an anti-essentialist version of QML. Both turn on offering nonstandard semantics for de re modal claims. Crudely, the first makes their truth ‘all too easy’ and the second makes their truth ‘all too difficult’. Although my focus here shall be on a version of the latter, I shall begin by briefly presenting a version of the former. David Kaplan, in (1968), showed us how to make de re modal claims cheap and consistent with antiessentialist commitments.42 Kaplan proposed that we posit extra quantificational structure when analysing modal operators. Let c range over individual-concepts, φ be the determining relation that obtains between an individual-concept and the individual that falls under it,43 G be the concept associated with Gx, and A be short for ‘is analytically connected to’;44 so, for example, A(G, c) should be read as ‘G is analytically connected to c’. Then we can say that the open sentence Gx is analysed as c(cΔx & A(G, c)) (read ‘there is an individual-concept that determines the value of x and that individual-concept is analytically connected to the concept G’). It is important to note that the freevariable x takes individuals as value and so is set to be bound by an ordinary, objectual quantifier. Kaplan’s proposal is within the framework of a theory of objectual quantification. Positing this extra quantificational structure proves useful in defusing Quine’s argument because it allows us to distinguish two ways in which an object might ‘fail to satisfy’ the condition Gx. (Kaplan works the account out more fully for the case of propositional attitudes, articulating the notion of suspended judgement, which he distinguishes from not believing. I am here making the analogous distinction for the case of modality.) The Kaplanesque analysis of that condition allows for a choice regarding the scope of any negation operators, much as Russell’s theory of definite description predicts scope interactions between definite descriptions and negation. So, we should distinguish (7) and (8).


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Page 317 (7) is true of an object o just in case there is no individual-concept determining o that is analytically connected to G, whereas (8) is true of o just in case there is an individual-concept determining o that is not analytically connected to G. (8) is consistent with there being other individual-concepts determining o that are not analytically connected to G, given that a single object can fall under multiple individualconcepts. With the distinction between (7) and (8) in hand, one can be nondiscriminating about the designator one consults in determining which conditions an object analytically satisfies, thus avoiding Aristotelian essentialism, without producing contradiction and while admitting that (2) is true and (4) is false. (2) is true, we are supposing. So we should infer, given the existence of Venus, that Venus satisfies the condition Ex. (4) is false, we are supposing. So we should infer that Venus—the very same object!— satisfies the condition ~ Ex. This does not lead to a contradiction because Venus satisfies that last condition when it is construed as c(cΔx & ~A(E, c)) and, remember, one and the same object can consistently satisfy both the conditions c(cΔx & A(E, c)) and c(cΔx & ~A(E, c)), provided different individual-concepts provide the grounds of their truth.45 In general, it is not contradictory to say that one and the same object satisfies the conditions Gx and ~ Gx, as long as the negation in the second condition is construed as taking narrow scope with respect to the posited extra quantificational structure. So, we have avoided both contradiction and Aristotelian essentialism. The Kaplanesque response is brilliant. But it has several odd consequences.46 I discuss these consequences, as well as different versions of the basic strategy (some of them not requiring that extra quantificational structure be posited in the logical form of modal sentences to achieve the desired result), in Nelson (unpublished a). I mention the strategy here not to recommend it but rather to highlight the fact that there are a number of anti-essentialist strategies for making sense of QML available. My focus in the remainder of this paper, however, shall be on a very different anti-essentialist strategy that does not have these odd consequences. The strategy is based on a response to Quine first presented, to my knowledge, by Ruth Barcan Marcus in (1967) and later developed by Terence Parsons in (1967) and (1969). Marcus distinguished what we can call trivial and philosophically problematic necessary properties.47 She then argued that interpreting the characteristic formulae of QML only requires ascribing trivial necessary properties to objects and that an object’s having trivial necessary properties is consistent with the motivating spirit of anti-essentialism. So, QML is free of any philosophically problematic essentialist theses; Quine’s Challenge is met. I shall call this the Marcus/Parsons response . The strategy allows us to recognize a distinction between necessary and contingent properties and see these as genuine properties of objects (as


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Page 318 opposed to the Kaplanesque strategy considered above, which leads to a collapse of that distinction and the Quinean view, which entails that no objects have any properties as a matter of necessity). So, for example, it is Venus itself, independently of how or even whether it is designated, that is necessarily such-and-such and contingently so-and-so. But this is a long way from embracing anything that runs contrary to the analysis of necessity in terms of analyticity. The proponent of the Marcus/Parsons strategy maintains that there is a middle ground between a form of essentialism that sees objects, independently of how or even whether they are designated, having certain properties necessarily and a form of essentialism that runs contrary to the linguistic conception of necessity, according to which all necessity is ultimately linguistic or conceptual necessity. Occupying this middle ground provides for a powerful response to Quine’s Challenge. We need three things to spell this out more fully. First, we need a characterization of the distinction between trivial and philosophically problematic necessary properties. Second, we need support for the claim that QML only requires that objects have trivial necessary properties. And third, we need support for the claim that anti-essentialism is compatible with objects having trivial necessary properties. A necessary property of o is a trivial necessary property just in case necessarily every object necessarily has it. A philosophically problematic necessary property of o, on the other hand, is a necessary property that o necessarily has but other objects do not. We can then say, again following Marcus, that philosophically problematic forms of essentialism48 are ones that not only distinguish the necessary properties an object has from its contingent properties, but that go on to deny that every necessary property is had by every object.49 That is, philosophically problematic essentialist theses ascribe not only trivial necessary properties but philosophically problematic necessary properties to objects. Take the property being either exactly 5′9″ or not exactly 5′9″. It is a logical truth that everything is either exactly 5′9″ or not exactly 5′9″. So it is unobjectionable to say of me in particular that I am necessarily either exactly 5′9″ or not exactly 5′9″. That does not make me special and does not require that I possess some metaphysically mysterious objective nature contrary to the linguistic doctrine of necessity. The necessity resides in the aforementioned linguistic necessity. We can go further. It is unobjectionable to say that I analytically or logically satisfy the condition ‘ x is either exactly 5′9″ or not exactly 5′9″’. We can acknowledge that analyticity and logical truth are fundamentally features of closed sentences and explicate the notions of analytic and logical satisfaction in terms of these more fundamental notions. The explication does not require Aristotelian essentialism, in any philosophically problematic form, and does not lead to contradiction. We can see this by noting that, for any designator t such that t designates me, the closed sentence t is either exactly 5′9″ or not exactly 5′9″ is analytically true. There is no need


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Page 319 to privilege any proper class of designators as being more ‘essence revealing’ than other designators, given that every sentence of the above form is analytically true and so substituting any designator of me is guaranteed to deliver the same results. The reduction of the notions of analytic and logical satisfaction to the notions of analytic and logical truth does not require Aristotelian essentialism. An ‘invidious’ form of essentialism is one that would see certain necessary properties attaching to certain privileged entities and not to other entities. Such a form of essentialism may well require the world, independently of how we talk about it, to be the ultimate grounds of such necessary properties and thus may run contrary to the linguistic and conceptual conceptions of necessity. But this is not true of trivial necessary properties. If QML only requires that objects have trivial necessary properties, it is free of any philosophically problematic essentialist theses. I said above that the Marcus/Parsons response required three ingredients. We have presented the first and the third and now it is time for the second: Supporting the claim that interpreting the characteristic formulae of QML requires only attributing to object trivial necessary properties. Quine challenges the proponent of QML to explicate the notions of analytic and logical satisfaction in terms of the more familiar notions of analytic and logical truth (conceived as properties of closed sentences). The explication must avoid Aristotelian essentialism and yet be consistent with the fact that different predicates are analytically and logically connected to different ways of designating a given object. We propose to do this by setting up our system so that objects only have trivial necessary properties. The following principle does the job. REDUC: For any object o and condition Fx , o analytically/logically satisfies Fx just in case the universal closure of that condition xFx is analytically/logically true (that is, ).50 REDUC entails that objects only analytically or logically have properties that are trivial properties. We can see this by noting that (9) below is a consequence of REDUC, where is taken to be ‘it is analytic that’. (9) (9) says that if something is analytically such-and-such, then everything is analytically such-and-such. If REDUC is true, then a given object analytically satisfies a given condition just in case the universal closure of that condition is analytic. So, if something analytically satisfies a given condition, everything analytically satisfies that condition. But then nothing about the particular object in question determines whether or not it analytically satisfies a given condition; that is completely a matter of the logical status of the condition itself.


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Page 320 We should distinguish three characterizations of the thesis of Aristotelian essentialism. (1) The thesis of Aristotelian essentialism0 (TAE0) is the thesis that an object, independently of how or whether it is designated, necessarily has some properties. (2) The thesis of Aristotelian essentialism1 (TAE1) is the thesis that an object, independently of how or whether it is designated, necessarily has some properties and contingently has other properties, despite the fact that some of those contingent properties analytically follow from some ways of specifying the object in question. (3) The thesis of Aristotelian essentialism2 (TAE2) is the thesis that there is a privileged class of designators of an object that best reveal that object’s necessary properties, despite the fact that those properties do not analytically follow from other, nonprivileged designators of the object and other, contingent properties do analytically follow from some other, nonprivileged designators. Quine’s argument that QML runs contrary to the linguistic doctrine of necessity because it requires the thesis of Aristotelian essentialism turn on conflating these theses. There really is no simple distinction between ‘essentialism’ and ‘anti-essentialism’, as Quine and his followers seem to think. While we can grant that Quine is right that TAE2 is incompatible with anti-essentialist motivations in general and the linguistic doctrine of necessity in particular, he fails to establish that interpreting the characteristic formulae of QML entails TAE2. And while TAE0 is indeed a consequence of any interpretation of QML and, given a plausible assumption to be spelled out below, TAE1 is too, neither of these principles are incompatible with either the linguistic doctrine of necessity or anti-essentialist motivations. Quine needs a single thesis of essentialism that is both required by QML and incompatible with the linguistic doctrine of necessity. But there is no single thesis with both features.51 Let me substantiate these claims. Interpreting the formulae of QML requires TAE0, given that we have adopted a standard objectual semantics for quantified sentences. Let’s take ‘ x is self-identical’ as our example, which I shall take to be equivalent to x = x. I aim to show that, insofar as there are any objects, something analytically satisfies that condition (provided QML is sensible). x( x = x) is a classical logical truth and so x( x = x) is true. Not even Quine would balk at this, given his acceptance of the notion of logical truth. What I want to show now is that this is incompatible with claiming that x x = x is false, assuming the latter claim is deemed sensible. This would be straightforward if we were operating with a metaphysical notion of necessity, explicable in terms of truth at all possible worlds. x( x = x) is true just in case every world w is such that, for every individual o Dw, o = o at w. But if x x = x is false, then there is some object


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Page 321 o such that there is some world w at which there is a representer of o—say o′, which may just be o itself—such that o′ Dw and o′ ≠ o′ at w, which contradicts the conditions under which x( x = x) is true. Things are not so simple for us, however, as we are operating with a notion of strict necessity. Part of the problem here is that the very notion of logical satisfaction is up for grabs. So we need to take more care in arguing for the incompatibility of the truth of x( x = x) and falsity of x x = x. Suppose x x = x is false. We should then ask why. Not because there is some instance of t = t that is not logically true. x( x = x) is logically true and so every instance of t = t is logically true. But then surely every object is such that it satisfies x = x, assuming we are to make sense of an object analytically or logically satisfying a condition at all. There is no way of admitting that the characteristic formulae of QML are meaningful but simply insisting that we ‘count them all as false’ in order to avoid all commitments to any essentialist theses. Let’s grant that TAE0 is a consequence of claiming that the characteristic formulae of QML are meaningful. Should this be cause for fear? Not if we explicate the notion of logical satisfaction in terms of REDUC. There is nothing foreign to the spirit of anti-essentialism in TAE0, providing we are willing to saying that the only necessary properties any object has are necessary properties every object has, which is just what REDUC tells us. Let’s move, then, to TAE1. Whereas TAE0 is the thesis that objects have necessary properties, TAE1 is the thesis that an object has some properties necessarily and others contingently. TAE0 is weaker than TAE1, as TAE0 is compatible with there being only one way an object has a property: namely, necessarily. To see why this distinction is significant, recall the Kaplanesque view. This view falsifies TAE1. It is easiest to see this if we conceive the posited extra quantificational material introduced into de re modal claims as quantifying over designators rather than individual-concepts. (The argument works without this simplification.) So conceived, the Kaplanesque view says that o analytically satisfies the condition Fx just in case there is some designator t such that t designates o and Ft is analytically true. Suppose that o satisfies the condition Fx ; that is, suppose that o just plain old possesses the property associated with the condition Fx . Then there is guaranteed to be a designator that both designates o and is analytically connected to the condition Fx , assuming that there are any designators of o. The argument for this employs a trick Quine used to answer Church, discussed in note 27. Suppose that n is an individual constant with o as value and that the G designates o. Then both the object identical to n that is F and the G that is F designate o as well. Both descriptions are unique, as we have already supposed that n names only one object o and so only one object o satisfies x is an object identical to n and we have already supposed that the G designates o and so (assuming Russell’s theory of definite descriptions) there is only one object o that satisfies Gx and


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Page 322 we have already assumed that o also satisfies the condition Fx . So, putting it all together, we are guaranteed that o uniquely satisfies the condition x = n & Fx and the condition Gx & Fx . In both cases, the extra that is F in the two designators simply goes along for the ride, if you like. But notice that the sentences the object identical to n that is F is F and the G that is F is F are analytically true (assuming the descriptions designate). So, insofar as an object satisfies a condition, then, given the understanding of the notion of logical satisfaction provided by the Kaplanesque view, it analytically and logically satisfies that condition. Here’s the basic idea behind this argument. Insofar as we have a designator of an object, we can build a definite description of that object that contains any predicate that it satisfies. But then we are guaranteed to have a designator of that object that is analytically connected to any predicate it satisfies. So, given the Kaplanesque view, every object analytically satisfies any condition that it satisfies, which entails that no object contingently possess any property. So the Kaplanesque view leads to an obliteration of the distinction between necessary and contingent possession of a property and hence entails that TAE1 is false. Of course the Kaplanesque view requires TAE0, given that the view requires that objects necessarily satisfy conditions. (This follows, indeed, from the fact that the Kaplanesque view treats the quantifiers in the characteristic formulae of QML as standard objectual quantifiers.) REDUC and the claim that some closed sentences are analytically true and others, although true, are not analytically true, however, entails TAE1. For example, although I satisfy the condition ‘ x is writing’, I do not, given the understanding of the notions of analytic and logical satisfaction provided by REDUC, analytically or logically satisfy that condition, as the universal closure of that condition (that is, ‘Everything is writing’) is neither analytically nor logically true. So, I am mere contingently writing, although I am (for example) necessarily self-identical, given REDUC. Unlike the Kaplanesque view, the Marcus/Parsons view entails TAE1. But like TAE0, TAE1 is consistent with the reduction of all necessity to analyticity and logical truth, construed as properties of closed sentences, as I have argued, and thus deserves the title ‘anti-essentialist’. Let’s move to TAE2. We can admit that this thesis is indeed at odds with the reductionist ambitions of the linguistic doctrine of necessity. So, Quine must have TAE2 in mind when he writes: ‘Essentialism is abruptly at variance with the idea, favoured by Carnap, Lewis, and others, of explaining necessity by analyticity’ (Quine 1980:155). Privileging a proper class of designators is indeed at odds with seeing all necessity as fundamentally flowing from verbal necessity and not having an ontological basis in a mindindependent reality. For one owes some explanation for why that class of designators is being privileged and it seems hard to see how one could appeal to anything other than extra-linguistic facts in offering such an explanation.


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Page 323 The quote continues: ‘For the appeal to analyticity can pretend to distinguish essential and accidental traits of an object only relative to how the object is specified, not absolutely. Yet the champion of quantified modal logic must settle for essentialism’ (155). This claim is true only if Quine has in mind TAE0 and, given the assumption of a genuine distinction between contingently and necessarily having a property, TAE1. But it is decidedly false for TAE2. The champion of QML can avoid TAE2 by accepting either REDUC or the Kaplanesque view, both of which imply that TAE2 is false, as we have seen. To summarize, insofar as we assume standard objectual quantification theory, then the proponent of QML is committed to TAE0. And insofar as the system of QML allows for false instances of the schema , then TAE1 is also true. But both TAE0 and TAE1 are consistent with the linguistic doctrine of necessity. TAE2, on the other hand, is indeed inconsistent with this form of anti-essentialism. But interpreting the characteristic formulae of QML simply does not require TAE2. So Quine is wrong in thinking that the project of interpreting the characteristic formulae of QML—where quantifiers are objectual and necessity is strict—requires a philosophically problematic form of essentialism. The form of essentialism QML requires is philosophically unproblematic; the form of essentialism that is philosophically problematic is not required by QML. John Burgess, in (1997), is one of the few proponents of Quine’s argument against QML to address the possibility of analysing the truth-values of the characteristic formulae of QML in terms of the analytic status of closed sentence via REDUC.52 It is instructive to look at Burgess’s treatment of the matter. Burgess claims that Quine’s critique is limited to what Burgess calls ‘non-trivial de re modality’, by which he intends to exclude interpreting the characteristic formulae of QML in terms of REDUC (27). Burgess is not explicit about what he means by ‘ de re modality’ and there are at least three very different conceptions of the de re/de dicto distinction: One characterizing the distinction syntactically, in terms of whether or not open sentences are governed by a given operator; the other semantically, in terms of whether or not substitution of codesignating expressions within a given operator preserves truth-value; and the third metaphysically, in terms of whether or not given predicates correspond to genuine properties of objects.53 It is reasonable to interpret Burgess as being primarily concerned with a syntactic characterization of that distinction, as that is most directly related to QML. The characteristic formulae of QML are syntactically de re precisely because they involve open formulae governed by modal operators whose free variables are then bound by a quantifier outside the scope of that modal operator. In saying what he means by the ‘non-trivial’ in ‘non-trivial de re modality’, Burgess offers the example of explicating in terms of the trivialization axiom TA.


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Page 324 TA eliminates any doubt that the modal operator is intelligible, but only at ‘the cost of making the introduction of the modal notion pointless’ (28). And there is a very clear sense in which the modal notion we have interpreted has been rendered pointless by our efforts: TA (together with its converse, evidently valid of any alethic necessity operator) obliterates the distinction between material truth and necessary truth as it renders every truth necessarily true. Introducing is worth the trouble only if there are true claims that are not necessarily true and so only if TA is invalid. We have in TA a model of a problematic trivialization. With this example in mind, Burgess moves to trivializations of de re modality. A modal trivializing axiom is one that leads to a collapse of necessary truth to material truth. By analogy with the case of TA, a de re modal trivializing axiom is one that leads to a collapse of de re modality to de dicto. Burgess offers the following as an example of what he has in mind. (10) is an immediate consequence of REDUC. So, if Burgess is right, then any interpretation of QML that entails REDUC—like the Marcus/Parsons view—simply fails to address Quine’s argument as, according to Burgess, Quine’s argument is targeted at nontrivializing interpretations of QML that invalidate (10).54,55 TA is our model of a problematic reduction. But is (10) similarly problematic? Burgess writes: (10) corresponds to the trivializing definition to which F holds necessarily of a thing just in case it is necessary that F holds of everything—a definition that could silence any critic who claimed the notion of de re modality to be more obscure than that of de dicto modality [that is, a critic just like Quine—see in particular (1943)], but would do so only at the cost of making the introduction of de re notation pointless. (28, bold added) Burgess is too quick in assimilating the problematic character of TA to (10) and REDUC. TA is troubling because it leads to a collapse of material and necessary truth. The worth of modal logic rests precisely on drawing this distinction. But what is the similarly crucial distinction that a proponent of REDUC fails to preserve? Burgess never spells it out. There still is a difference between de re and de dicto formulae, if one cashes that distinction out syntactically. Now granted, the truth-value of any de re formulae is defined in terms of the truth-value of de dicto formulae. But a proponent of Quine’s argument can hardly complain about that; Quine’s Challenge requires that we explicate the de re formulae in terms of de dicto formulae! If we were


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Page 325 allowed to explicate the de re formulae entirely independently of any de dicto formulae, Quine’s argument would never get off the ground. Burgess’s ban on trivializing axioms is tantamount to a demand that one’s QML be problematically essentialist. But then Burgess’s ban reduces Quine’s complaint that QML requires a philosophically problematic essentialism to the banality that, provided proponents of QML are to interpret the characteristic formulae of QML in such a way as to be problematically essentialist, then they are committed to problematic essentialism. We should all agree with that. But, it would leave unsettled the interesting question whether or not proponents of QML need to interpret the characteristic formulae in a problematically essentialist (that is, nontrivializing) manner. I claimed that the ban on trivializing axioms is equivalent to the requirement that the system be essentialist in a philosophically problematic way. Here’s why. Suppose all trivializing axioms are false. In particular, suppose that the trivializing axioms that both REDUC—(10) reproduced below—and the Kaplanesque view—(11) reproduced below—entail are false. Let us grant Quine’s point that there are pairs of designators t and t ′ that both designate the same object but that are analytically connected to different predicates. (Only the most extreme necessitarians —a conceptual necessitarian, according to whom every truth is analytically true—would claim otherwise. And such a view entails (11), assuming there is room in such a view for de re modality, and so has already been excluded by our assumption above.) Then one can consistently ascribe necessary properties to objects only if one privileges a certain subclass of designators in determining which conditions an object necessarily satisfies. But this is our TAE2, which we know to be philosophically problematic. Burgess does not justify the claim that the trivializing axioms (10) and (11) make ‘the introduction of de re notation pointless’ in the way in which accepting TA makes ‘the introduction of the modal notion pointless’. The trivializing axioms (10) and (11) do make necessary properties less interesting. It is only the substantive, philosophically problematic necessary properties that are interesting and their interest brings with it their problematic character. But this essentialism is not intrinsic to the characteristic formulae of QML. The interesting necessary properties are philosophically problematic necessary properties like necessarily being greater than 7 and necessarily being human; properties that a proper subset of the objects there are necessarily have. I am not arguing that we should refuse to ascribe philosophically problematic necessary properties to objects. Rather, I am arguing that such ascriptions are independent of thinking that QML is coherent. If one has no qualms about ascribing such properties to objects


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Page 326 and looks to QML to formalize such attributions, there is no question that in interpreting the characteristic formulae of QML one will deny the trivializing axioms. But that is only because one has brought philosophically problematic essentialist theses to QML; it is not forced on one merely in virtue of sitting at QML’s table. Quine’s argument is worth worrying about only if he can show that those who are not antecedently inclined to think that objects have problematic essences are forced to ascribe such essences in interpreting QML. And that requires rejecting Burgess’s ban on trivializing axioms. But once the ban is lifted, as I have argued, Quine’s argument is unconvincing, as it turns on an equivocation between distinct essentialist theses. My claim that Quine’s argument turns on equivocating between distinct theses of essentialism parallels Parsons’s (1967) and (1969) response to Quine, who in turn was following points implicit in Marcus (1967). Parsons too accused Quine of equivocating on his use of ‘Aristotelian essentialism’, or, when the argument did not employ that term, of equating claims like ‘Everything is necessarily self-identical’ with claims like ‘Something is necessarily greater than 7’ or ‘Something is necessarily human’. There is, I hope, something to be said in favour of resurrecting this response, as these points have either been completely ignored—as they are, for example, in Neale (2000)—or misappreciated—as they are, for example, in Burgess (1997). But I do not think that Marcus and Parsons were completely successful in developing an interpretation of QML free of all problematic essentialist theses. This is because Marcus’s and Parsons’s systems validate the necessity of identity, which is contrary to the spirit of antiessentialism and incompatible with the linguistic doctrine necessity. I show this by arguing that the necessity of identity leads to TAE2. After supporting this contention I shall show how to free the Marcus/Parsons view from these remaining essentialist commitments. In claiming that identity properties are problematic as necessary properties, one must distinguish selfidentity properties from being-identicalto-x properties. It is only the latter kind of identity properties that are problematic as necessary properties. Let’s take a particular example of the second kind of property: the property being identical to George W. Bush . GW instantiates both the properties being identical to GWB and being self-identical . But GW, and GW alone, instantiates the former whereas every object instantiates the latter. So the two properties are distinct, as there are objects (everything other than GW) that instantiates the one but not the other. The first property is referential with respect to GW or individual-involving . Indeed, on my view this property is constructed from GW and the two-place relation is identical to by abstraction. The second property, on the other hand, is individual-independent. Whereas the first property presupposes the existence of a particular object—GW—the second property does not. Indeed, the notation of attribute abstraction well encodes this


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Page 327 difference. With that notation, the property being identical to GWB is represented as whereas the property being self-identical is represented as

This is all to follow quite closely (Marcus 1967:94). So, in claiming that identity properties are problematic as necessary properties, I mean individualinvolving identity properties; the individual-independent identity property is a paradigm of a trivial necessary property. The necessity of identity is the following thesis. Why does NI commit one to a problematic form of essentialism? There are several reasons. First, it is philosophically problematic precisely because so many have been keen to reject it, as it witnessed by the work of Allan Gibbard (1975) and David Lewis (1986), to name just two opponents of the thesis. And the rejection of this thesis is, in some minds, tied to an adequate resolution of certain philosophical puzzles, like the puzzle of material constitution, the problem of qualitative change across time, and the problem of accidental intrinsics. Marcus and Parsons are correct in thinking that commitment to just the necessity of identity is less problematic than commitment to other essentialist claims, like the claim that some things are necessarily human. There are grades of problematic essentialist attributes and necessary identity attributes are surely the lowest grade. One might think that I am necessarily MN, for example, without thinking that I thereby have an Aristotelian essence or a substantive nature. One might say that the only general necessary properties objects have are trivial necessary properties and the only discriminating necessary properties objects have are necessary identity attributes. This is surely a weaker form of essentialism than claiming that objects also have general necessary properties like being human as well; that is, necessary properties that are both discriminating, in the sense that they are not possessed by all objects, and general. But there is a clear sense in which any theory that entails that I am necessarily MN, for example, is stronger than a theory that denies that any object has any philosophically problematic property. But there is a more robust reason for an anti-essentialist proponent of QML to reject NI. Proponents of NI widely recognize that NI is true only if


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Page 328 a and b are what Saul Kripke calls rigid designators (1971, 1980). ‘George Bush is the current president of the US’ is true even though, on the intuitive view, ‘Necessarily, George Bush is the current president of the US’ is false. The common explanation is that ‘the current president of the US’ nonrigidly designates GW in virtue of contingent properties he instantiates, whereas ‘George Bush’ does not. But, as we have seen in ‘The Failure of the Russellian Response’, this distinction between rigid and nonrigid designators requires embracing the very ‘invidious’ distinction between ways of designating objects Quine challenged proponents of QML to avoid; it leads directly to TAE2. So, a proponent of NI is either left with no explanation of the intuition that, although ‘George Bush is the current president of the US’ is true, its necessitation is false, or else embracing TAE2. We can go a step further. Employing once again Quine’s trick of building richer descriptions from others, we can see that accepting both NI and the ‘equal-treatment to all ways of designating an object’ attitude Quine’s anti-essentialism forces on us requires the claim that an object necessarily possesses every property it possesses, which is bad news indeed to the Marcus/Parsons view. Suppose o in fact satisfies the condition Fx , whether uniquely or not. Then we can construct a definite description that designates o and includes the predicate Fx by using the Quinean trick—say, the description the G that is F , where we assume o to uniquely satisfy the condition Gx. Let n be any designator of o. Then the G that is F = n is true. But, given NI, so too is its necessitation. But then o necessarily satisfies the condition Fx . For if it did not, the necessitation of the above identity would not be true. The idea behind the argument is easiest to see if we wax metaphysical and speak in terms of possible worlds. Suppose the G that is F = n , where n is any arbitrary designator of o, is true just in case its necessitation is true. Then the G that is F designates o with respect to every world w (at which it designates anything at all). But the G that is F designates an object with respect to a world w only if that object satisfies both Gx and Fx at w. But then o satisfies Fx in every world w (in which o exists). So o necessarily satisfies Fx if it satisfies Fx at all. This result is highly problematic for the proponent of the Marcus/Parsons view. Because objects evidently satisfy different conditions—that is, there evidently are pairs of objects o and o′ and condition Fx such that o satisfies Fx and o′ does not satisfy Fx —the elimination of the distinction between necessarily having a property and merely contingently having a property is incompatible with the claim that objects only have trivial necessary properties, in the sense that the only necessary properties any object has are necessary properties every object has. So, the very strategy employed by the Marcus/Parsons response is incompatible with both NI and the indiscriminating attitude towards ways of designating objects Quine’s anti-essentialism requires.56 The Marcus/Parsons response itself thus requires that NI be false.


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Page 329 Grant me that the necessity of identity (NI) is problematic in a way that the necessity of self-identity (NSI) is not. NI: If a = b, then, necessarily, a = b. NSI: Everything is necessarily self-identical. Then our problem becomes: How do we devise our modal logic so that it allows necessitation on the instantiation of self-identity, thus allowing us to infer from the fact that something is self-identical that it is necessarily self-identical, but not the instantiation of an individual-involving identity properties? That is, how can we validate NSI and invalidate NI? It turns out that we have already done it. We should simply accept an unmodified form of REDUC. REDUC: For any object o and condition Fx , o analytically/logically satisfies Fx just in case the universal closure of that condition xFx is analytically/logically true. GW analytically and logically satisfies ‘ x is self-identical’ (or x = x) because the universal closure of that open sentence (that is, x( x = x)) is analytically and logically true. But the universal closure of the condition x = GW (that is, x( x = GW )) is neither logically nor analytically true. Indeed, it is false under every interpretation with a domain with more than two objects or in which GW does not exist. So GW does not analytically or logically satisfy ‘ x is GW’. Everything is logically (and hence analytically) selfidentical, but nothing, including Bush himself, is logically (or analytically) identical to GW. So, NSI is valid but NI is not. We have banished the last remnants of the philosophically problematic essentialist consequences left in Marcus’s and Parsons’s views. CONCLUSION The Russellian response to Quine’s argument against QML was presented and evaluated. It was found to rest on a misunderstanding. Rather than turning on deriving of a contradiction from the failure of intersubstitutivity of codesignating singular terms within modal sentences, as the Russellian reads Quine, Quine’s argument turns on the allegation that QML requires a problematic form of Aristotelian essentialism. Once Quine’s argument is properly understood, we find that the Russellian response simply fails to adequately address its main contention. But Quine’s argument fails to convince. The argument conflates different conceptions of the thesis of Aristotelian essentialism. QML does indeed


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Page 330 require one form of that thesis: The thesis that an object, independently of how or whether it is designated, necessarily has some properties. But that thesis is consistent with the linguistic doctrine of necessity. Another form of the thesis is indeed inconsistent with the linguistic doctrine of necessity: The thesis that there is a privileged class of designators of an object that best reveal that object’s necessary properties, despite the fact that those properties do not analytically follow from other, nonprivileged designators of the object and other, contingent properties do analytically follow from some other, nonprivileged designators. But QML does not require that thesis. I developed two ways of interpreting the characteristic formulae of QML, both of which entail the first thesis and the negation of the second. These interpretations silence any Quinean worries that QML is at odds with a robustly anti-essentialist metaphysics. Philosophically suspect essentialist metaphysics are not built into the fabric of QML but rather brought to QML from some external source. NOTES 1. Thanks to the members of my fall 2004 opacity class at Yale University—Christopher Holownia, Samuel Newlands, Gaurav Varirani, and Leslie Wolf—where this material was first worked out. Thanks also to numerous discussions with Troy Cross, Michael Della Rocca, and Robin Jeshion. I presented this material at the ‘Russell vs. Meinong’ conference at McMaster University in May 2005. Thanks to those present for discussion and especially the organizers, Nicholas Griffin and Dale Jacquette, for the opportunity to participate in such a unique event. I have also presented versions of these ideas at Arizona State University, University of Toronto, University of Massachusetts-Amherst, University of California-Riverside, and at a lunch philosophy discussion at Yale University. ‘The real Quine’ and ‘Quantifying in for the Anti-Essentialist’ of the present paper overlap with Nelson (‘Anti-Essentialism and the de re ’), which in turn is the first of a trio of papers exploring the relationships between essentialism and modal metaphysics (the other members being Nelson (‘On the Contingency of Existence’) and (‘Necessary Essence’)). 2. Both the theory of descriptions and the views of acquaintance were present in Russell (1905), but the former was more fully developed in Whitehead and Russell (1925) and the latter in Russell (1903) and (1905). 3. Quine developed his attack on QML in a number of papers, especially (1943), (1947), (1953a,b), and (1961). 4. There are perplexing issues concerning how this combination is to be pulled off, even after Quinean worries with the bare possibility of such a combination are settled. Most of these issues revolve around whether to employ fixed or varying domains. I discuss this issue in Nelson (forthcoming). Also, it is contentious whether or not the characteristic S4 and S5 axioms constitute part of a system of our ordinary modal thinking. (See Salmon (1989) for compelling arguments that they do not.) For the present paper, however, we can set these concerns to the side. 5. Smullyan, in (1947) and (1948), was the first to present this response, followed by Fitch (1949) and Marcus (1948) and (1963). Russell himself never, to my knowledge, discussed this use of his doctrines.


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Page 331 6. The evidently true II is distinct from its evidently, at least after due reflection, false converse— the Principle of the Identity of Indiscernibles (PII), that, for all x and y, if, for all qualities F , x is F iff y is F , then x = y. Qualities are object-independent properties. So, for example, the property being identical to Adam is not a quality of Adam (although it is a property of Adam), precisely because it is dependent on Adam. If object-dependent properties were included in the scope of the second-order quantifier in PII, then we would have a principle even more evident than II. (Both Adam and Bill having the property being identical with Adam is obviously sufficient for Bill’s being identical with Adam.) PII is philosophically interesting only when the indiscernibility is qualitative indiscernibility. Historical proponents of the principle, and in particular Leibniz, clearly intended the principle in this way. For an excellent discussion of this matter, see Adams’s classic (1979). 7. I shall discuss why Quine thought that (2) is true in ‘The Real Quine’. For now, we shall simply grant it. 8. SUB is obviously invalid. The truth of ‘“Hesperus” starts with the letter “h”’ and ‘Hesperus is Lucifer’ hardly suffices for the truth of ‘“Lucifer” starts with the letter “h”’. We at least need to exclude substitution within quotation. We also need to exclude substitution that affects the semantic values of other elements of the sentence. Quine’s example of ‘so-called’ most plausibly fit this bill. Because an occurrence of ‘so-called’ refers to the name that occurs before it, the truth of ‘Giorgione was so-called because of his name’ and ‘Giorgione is Barbarelli’ does not guarantee the truth of ‘Barbarelli was socalled because of his name’, as the substitution affects the semantic value of ‘so-called’. (This is not Quine’s description of why substitution fails, but it comes to more or less the same thing. For Quine’s account, see 1980:140–41, where Quine proposes to analyse ‘so-called’ sentences explicitly in terms of quotation-sentences. Quine appreciated that we do not need to analyse all opaque environments in terms of quotation (1980:144), even if Quine clearly preferred such reductions, analysing ‘believes that’ in terms of ‘believes true’ and ‘it is necessary that’ in terms of ‘is analytically true’, the latter of each pair taking sentence-names as objects.) Some would say that substitution within the scope of propositional attitude verbs like ‘believes’ are not truthpreserving. But this is controversial and I think false. Propositional attitude verbs do not create counterexamples to the simplistic form of SUB given in the text. For a defence of this claim, see Salmon (1986). I argue for the claim in Nelson (2005). Present purposes do not require a precise formulation of SUB. The formulation presented in the text suffices. 9. I am attributing to Russell a structured proposition view, which he seems to have held early in his career (for example, in (1903) and (1905)), where a proposition is the bearer of truth-value, what a sentence says, and the object of propositional attitudes and so what an agent grasps, entertains, believes, and asserts. Such entities are structured in the sense that they are built from prior materials and have constituents as parts. (Frege too held a structured proposition view, although Frege differed sharply with Russell about their constituents.) Russell was not easy with this ontological commitment, even when he was espousing it. Part of what Russell found worrisome was the classic problem of the unity of the proposition: The problem of accounting for what ‘glues’ the disparate constituents of a proposition together into a single entity capable of bearing a truth-value. By (1906) Russell began developing his multiple relation theory of judgement, which received its fullest development in (1913), which allowed him to eschew commitment to propositions, at least as the objects of the attitudes. For simplicity, I shall ignore


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Page 332 these developments and present Russell as an unequivocal proponent of the structured proposition view. 10. The Acquaintance Principle makes an appearance in Russell (1905). But it is not until (1910) and (1912) that the views being described here are fully developed. 11. Russell sometimes claimed that we are also acquainted with ourselves. But he typically seems to have been convinced by Humean doubts about the self’s self-presentation and hence he seems to have been dubious of one’s acquaintance with one’s self qua substance as opposed to acquaintance with one’s mental states. 12. In an ingenious case, Austin, in (1990), shows that Frege-cases do not require temporally separated presentations of the same object. He describes a case—what he calls ‘the two tubes case’—in which an agent looks through two tubes, one for each eye, at a single object but is unsure whether the object seen with her right eye is the same as the object seen with her left eye, as she knows that the tubes can be directed in independent directions. (The object perceived, we can suppose, is a simple object—a paper clip, say—that the agent knows has many indistinguishable, as far as the agent is concerned, twins about it.) For simplicity, however, I shall deal in the text solely with temporally separated presentations of a single object. No significant issues turn on this. 13. Contemporary neo-Russellians who follow Russell in thinking that we can think directly about certain items have a more permissive view of the objects of acquaintance, including material particulars in this class. (Kaplan’s pioneering work (1989) is typically the starting point for such work, although Russell himself started out with such a position, maintaining, for example, that Mount Blanc itself is a constituent of the thought that Mount Blanc has snowfields .) They must thus deny the Fregean claim that whenever misidentification is possible, there is a difference in thought constituents. Neo-Russellians might still agree with Fregean intuitions about the truth and falsity of belief and other propositional attitude ascribing sentences, but insist that those truth deliverances do not require a difference at the level of thought constituents (following, for example, Crimmins and Perry 1989 or Richard 1990), or they may go on and deny as well the Fregean intuitions about the truth and falsity of propositional attitude ascribing sentences (following, for example, Salmon (1986)). But, given that misidentification of material particulars is obviously possible, a permissive theory of acquaintance requires denying what I called in the text the Fregean attitude towards misidentification, according to which all cases of misidentification are to be explained in terms of a difference in thought constituent. I am conceiving of the acquaintance relation as whatever enables direct thought. Jeshion (2002) presents a view according to which there is acquaintanceless direct thought about concrete objects. What I have been saying here is, however, consistent with her view, as her main aim is to show that the capacity to directly think about an object does not require causal contact with that object and can be achieved by descriptive thought, provided the thought plays a certain cognitive role; it is the cognitive role, not some other factors, that is determinative of whether an act of thinking is directly about its object or indirectly about it. I have not committed myself to any particular view on the perplexing matter of the conditions under which acquaintance is secured or direct thought is possible. 14. Kaplan’s (1975) is a very insightful discussion of the differences between Frege’s and Russell’s philosophies of language and thought. 15. I shall be more precise regarding the ultimate form of this thought on Russell’s view below, when discussing Russell’s theory of descriptions.


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Page 333 16. Thanks to Nicholas Griffin for correcting my misunderstanding of Russell’s views on sense data as mental entities. 17. Strawson does not, in all of Part 1, mention Russell by name. But it seems that he had Russell in mind as his target, as the opening sentence of the passage quoted in the text strongly suggests. 18. This intuition is even stronger with thoughts about oneself. When I think to myself, ‘I am hungry’, my thought is about me, not the guy who looks just like me and is having the same form of thought. I do not think about myself, as opposed to someone else, in virtue of having a purely qualitative description that determines me, for otherwise, in the reduplication universe, I could not succeed in thinking about myself. 19. This notation for marking scope distinction does not correspond to the notation used by Whitehead and Russell, although it achieves the same effect. I get it from Neale (2000). 20. As things actually are, (6nexpanded) is true because nothing uniquely satisfies ‘ x is present King of France’. (6wexpanded) is false because its first conjunct is false for the same reason (6nexpanded) is true. 21. It is also possible, of course, that one of the terms is a logically proper name and the other a disguised definite description. I only consider the unmixed possibilities as the mixed possibilities do not change the situation. 22. In claiming that in this case (2) and (4) express the same proposition, I am assuming a simple view of the semantics of ‘necessarily’. In particular, I am assuming that modals like ‘necessarily’ are only sensitive to the content of the expressions they govern. This can be denied, as I show in my ‘AntiEssentialist and the de re ’. I there show that one can claim that both ‘Hesperus’ and ‘Lucifer’ are genuine proper names and hence that both subsentences of (2) and (4) express the same proposition, but insist that nonetheless (2) and (4) themselves differ in truth-value because ‘necessarily’ is sensitive to more than just the content of the expressions it governs. For simplicity I shall stick with a simplistic understanding of how ‘necessarily’ functions. It should be noted that the more complex understanding is no help to Quine as his argument fails if we accept it. 23. Here is a sampling of passages in which Quine endorses Russell’s theory of descriptions: Quine 1937:85; 1948:5–7; 1951:30; 1953a: 173. 24. My understanding of Quine’s argument owes much to Fine’s excellent (1989) and (1990). 25. Burgess (1997:44–45, including n25), accuses Marcus of not giving Smullyan priority credit in developing the Russellian response. He notes that in Marcus (1963), Marcus does not cite Smullyan but instead calls the scope response ‘familiar’ and notes that in an earlier paper Marcus cites Fitch but not Smullyan. However, Marcus reviewed Smullyan’s paper (Marcus 1948), where, of course, she credits Smullyan, and she writes in the republished version of ‘Modalities in intensional languages’ included in her (Marcus 1993): ‘It is worth noting that in saying, in the text that follows, that “I have never appreciated the force of the original argument” about failures of substitutivity in modal contexts, I had assumed that Smullyan’s paper “Modality and Description” . . . was fully appreciated. Smullyan had shown that Russell’s theory of descriptions, properly employed with attention to scope, dispelled the puzzles’ (3). 26. Quine’s earlier (1943), however, did not suffer from these problems. 27. The flaws Quine recognized are independent of the Russellian response. Quine (1947) purports to show that there are intractable problems in providing modality a solid foundation ‘if one cares to avoid a curiously idealistic ontology which repudiates material objects’ (43). More precisely, Quine there


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Page 334 argued that QML ‘is committed to an ontology which repudiates material objects (such as the Evening Star properly so-called [i.e., the planet Venus itself]) and leaves only multiplicities of distinct objects (perhaps the EveningStar-concept, the Morning-Star-concept, etc.) in their place’ (47). By (1953b), Quine saw that not even the banishment of material objects and the replacement of the ‘curiously idealistic’ entities in their place suffices to avoid the problem. The argument for this, found in Quine (1980:152–53), is ingenious. In essence, Quine notes that the same intensional object is picked out by both A and ( ιx)[ p & ( x = A)], insofar as p is a true sentence. But if p is contingently true, then the replacement of A with its codesignating ( ιx)[ p & ( x = A)] within the scope of a modal can affect truthvalue. The move to intensional entities was supposed to solve Quine’s problem by delivering entities such that all of the different ways of designating them are analytically equivalent. But, as the above argument shows, not even intensional entities satisfy this condition; indeed, no object satisfies that condition, as long as we have descriptions and any contingency. 28. Quine (1980:156) turns this argument back against modal logic itself in an ingenious way. Given that the modal operator is to be explicated in terms of analyticity, if we only allow modal operators to attach to closed sentences, which is what we must do if we are to stop just short of QML, then we have robbed ourselves of any reason for introducing them. This is because every modal formula p will be equivalent to a nonmodal sentence like ‘The sentence “ p” is analytically true’. Assuming is to be explicated in terms of analyticity, it is only from the promise of quantifying in that modal logic proves its worth. 29. Quine tends to speak of essential and accidental properties when it is clear what he means is merely necessary and contingent properties. An essence, properly called, rather than a mere necessary property, is a property that answers the What is it? question. The distinction is present in Aristotle, but it is Fine (1994) and (1995) who is responsible for bringing this important distinction back into focus. As Quine’s argument targets the notion of a necessary property (as opposed to an essential property properly called), I shall replace his talk of the former for the latter. 30. There are at least two ways of construing the notion of logical truth. The first is syntactic, as truth in virtue of syntactic logical form, and the second is propositional, as truth in virtue of propositional logical form. We can see how these two conceptions come apart by considering the possibility of two distinct, nonlogical expression types, e and é , with the same content. Both is and is e xpress the same proposition. But because e and é are not part of the logical vocabulary, it is highly plausible to insist that the first is a logical form that is true in any interpretation of the nonlogical vocabulary whereas the second is not, in which case the first is true in virtue of syntactic logical form alone whereas the second is not. If, however, we are operating with a propositional conception of logical truth, then, as both sentences express the same proposition, it is implausible to think that the one is a propositional logical truth and the other is not and indeed it is highly plausible that both are logically (under the propositional conception) true. This divergence is most clear for the neo-Russellian, who insists that ordinary proper names like ‘Hesperus’ and ‘Lucifer’ are directly referential expressions. Because such expressions are pieces of the nonlogical vocabulary, there is a clear difference in the syntactic logical form of ‘Hesperus is Hesperus’ and ‘Hesperus is Lucifer’. At the level of syntactic logical form, the first is of the form is whereas the second is of the form is . There is a clear sense in which the first is guaranteed to be true by its logical form


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Page 335 alone whereas the second is not. But at the propositional level, because both sentences express the very same proposition (again, assuming neo-Russellianism), it is hard to see how we are going to find any way to similarly distinguish the logical form of what they express. On standard neo-Russellian views, both sentences express the singular proposition represented as . It is extremely plausible to say that the form of this proposition is guaranteed to be true and so both identity sentences are logically true under the propositional conception. In the text I shall focus exclusively on syntactic logical form, which was clearly Quine’s focus. The propositional conception raises important and fascinating issues, but they are beyond the scope of the present paper. Thanks to Nathan Salmon for very helpful discussion of this topic. 31. ‘The notion [of analyticity, although, as Quine says, itself lacking a satisfactory foundation] is clearer to many of us, and obscurer surely to none, than the notions of modal logic; so we are still well advised to explain the latter notions in terms of it’ (1947:45). ‘The general idea of strict modalities is based on the putative notion of analyticity’ (1980:143). 32. Why ultimately logical truth? Because Quine explains analyticity in terms of logical truth and synonymy. A statement is analytic ‘if by putting synonyms for synonyms (e.g., “man not married” for “bachelor”) it can be turned into a logical truth’ (1947:44), where two expressions are synonyms just in case they mean the same thing (see paragraph 5 of the same paper) and a truth is a logical truth just in case it is deducible by the logic of truth-functions and quantification from true statements containing only logical signs (see paragraphs 2 and 3 of the same paper). 33. As we have the Russellian response fresh in mind, I should stress that Quine can stipulate that (2) is to be taken as (2dn) and (4) as (4dn). The Russellian agrees that, so understood, (2) is true and (4) is false. That is all Quine needs. In particular, he does not further need to maintain that that variation in truth-value itself violates Leibniz’s principle or SUB. We will see that that plays no role in the argument, as I present it. 34. Marcus makes this point in (1963). It was also discussed in the famous general discussion that followed her presentation, an edited transcript of which is published as (Marcus et al . 1963). I think it unfortunate that this point was not sufficiently separated from the other objections Marcus raised to Quine’s argument, as it really stands on its own. If one insists on treating quantifiers substitutionally, then Quine’s arguments against QML, in the form he presents them, do not get off the ground. There are, however, two points to be made. First, as I say in the text, this fact should not really bother Quine, as his intended target is the combination of standard, objectual quantification theory and modal logic. Second, it is not clear that the move to substitutional quantification avoids all Quinean worries. The Hesperus case is supposed to establish that all of the following sentences being true: t = t′ , Gt , and ~ Gt′ . If the quantifiers are substitutional, there will be no problem in accounting for the consistency of and , even when we have just a single object in our domain, provided we can account for the consistency of Gt and ~ Gt′ when we have just a single object in our domain (and where all individual constants have values). This is because the first only requires there be some singular term s such that the relevant substitution instance is true and the second only requires there be some singular term s′ such that the relevant substitution instance is true. But there is still a problem. We need to either block the derivation of x(φ Gx & ~φGx) or, if the derivation is allowed, explain why it is not contradictory. The simplest form the derivation will take will involve substituting t for t′ in ~φGt ′, conjoining


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Page 336 the result with Gt , and then applying EG. One might deny the validity of the substitution, of course, but nothing about operating with a substitutional conception of quantification is going to help here. Also, there may well be more devious ways of deriving the result. On the other hand, one might allow the derivation and show that the derived result is (strangely!) consistent by claiming that different occurrences of x governed by the same substitutional quantifier can take different terms as substitutional instances. I’m not sure how to make this idea precise in the model theory, but I do not doubt that it can be done. 35. In (1956), Quine presented a similar argument against quantifying in to propositional attitude verbs like ‘believes’ and ‘knows’. Quine took a very different attitude towards the results, however. Whereas he was inclined to dismiss as completely misguided any notion of quantifying in to modal operators, he found quantifying in to propositional attitude verbs—or something that looks very much like that— indispensable and so posited a semantic ambiguity in ‘believes’, positing (or is it uncovering?) a relational, three-place verb and a distinct nonrelational, two-place verb. The former permitted quantification (although not into an opaque position) and the latter did not. Although the arguments are similar—indeed, both of Kaplan’s two critiques of Quine are simultaneously run as critiques of both Quine’s arguments concerning modality and propositional attitudes—I think that fundamentally different considerations are raised, given that Quine’s most powerful arguments against quantifying in, in my opinion, are his nonlogical arguments, which turn on very different metaphysical and epistemological assumptions: The argument against QML turns, as we have seen, on antiessentialist assumptions and ultimately reductionism of all forms of necessity to linguistic necessity, whereas the arguments against quantifying in to propositional attitude verbs turn on Fregean assumptions about cases of misidentification. 36. Quine’s ‘Reference and Modality’ went through three versions, with the three printings of From a Logical Point of View . Although Quine did finally come around to seeing what is right about the Russellian response in the third version—he writes: ‘Then, taking a leaf from Russell [namely (1905)], he [Smullyan] explains the failure of substitutivity by differences in the structure of the contexts, in respect of what Russell called the scopes of the descriptions’ (Quine 1980:154)—Quine’s initial response to Smullyan was confused. In the first version of ‘Reference and Modality’, Quine responded to Smullyan by claiming that his ‘argument depends on positing a fundamental division of names into proper names and (overt or covert) descriptions, such that proper names which name the same object are always synonymous … He observes, quite rightly on these assumptions, that any examples which … show failure of substitutivity of identity in modal contexts, must exploit some descriptions rather than just proper names. Then he undertakes to adjust matters by propounding, in connection with modal contexts, an alteration of Russell’s familiar logic of descriptions. [Footnote:] Russell’s theory of descriptions, in its original formulation, involved distinctions of so-called “scope”. Change in the scope of a description was indifferent to the truth-value of any statement, however, unless the description failed to name. This indifference was important to the fulfillment, by Russell’s theory, of its purpose as an analysis or surrogate of the practical idiom of singular description. On the other hand, Smullyan allows difference of scope to affect truth-value even where the description concerned succeeds in naming’ (Quine 1953:155). (The same passage survives the first revisions of 1963; see Quine 1961:154.) Quine is simply wrong that Smullyan is revising Russell’s


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Page 337 theory of descriptions by finding scope ambiguities that affect truth-value without failures of existence. Whitehead and Russell are clear that scope ambiguities between operators and descriptions do not result in differences of truth-value unless the description does not designate holds only for extensional environments. Indeed, as mentioned above, Russell’s own solution to King George’s wonderment requires as much. (Marcus notes these changes in Quine’s argument and the mistakes of his earlier attitudes (1990:236).) Quine is extremely nonchalant about this radical revision from the first to second set of revisions; see Quine 1980: vii. 37. Neale writes: ‘It would seem that if the common-sense mode of inference [of substituting salva veritate codesignating singular terms] is to be maintained in modal logic, co-referential names will have to be synonymous. No-one has rushed to embrace this view yet. Perhaps they will’ (2000:297). Neale seems unaware that Smullyan, Fitch, and Marcus all clearly endorse the view he cites as something someone might embrace. I have already cited Marcus’s endorsement of the view. Smullyan writes: ‘However, we observe that if “Evening Star” and “Morning Star” proper-name the same individual they are synonymous and therefore B [the sentence “Evening Star is congruent with Evening Star & ~(Evening Star is congruent with Morning Star”] is false’ (Smullyan 1947:140). Fitch references Smullyan on this point with approval (Fitch 1949:138). Furthermore, critics of the Smullyan/Fitch/Marcus view have noticed it too. Church’s review of Fitch (Church 1950) focuses primarily on this point, which he finds objectionable. Church writes: ‘It would seem to the reviewer that, as ordinarily used, “the Morning Star” and “the Evening Star” cannot be taken to be proper names in this sense [i.e., synonymous]; for it is possible to understand the meaning of both phrases without knowing that the Morning Star and the Evening Star are the same planet. Indeed, for like reasons, it is hard to find any clear example of a proper name in this sense’ (63). (It should be noted that Church’s argument against Fitch’s view can just as easily be used to show that any contentious philosophical analysis—even Frege’s own analysis of number —is not sense preserving and hence the explicans and explicandum of a successful philosophical analysis are not synonymous. I think that this should cast doubt over this form of argument.) 38. Quine seems to not have appreciated Kripke’s comments. In the published version of the discussion, Quine follows Kripke’s remarks by more or less changing the subject, talking about substitutional quantification and complaining that Marcus does not properly understand the nature of quantification. Kripke brings him back to the point of appealing to tags as the essence-revealing designators by saying: ‘Now then granted this, why not read “there exists an x such that necessarily p of x” as (put in an ontological way if you like) “there exists an object x with a name [i.e., tag] a such that p of a is analytic”. Once we have this notion of name, it seems unexceptionable’ (116). Quine then comes around to Kripke’s earlier point that, although not contradictory and in no way involving the rejection of objectual quantification, contrary to his previous complaint, the suggestion requires accepting the Aristotelian essentialist privileging of a proper class of designators as revealing the essence of an object. It doesn’t appear, however, that he appreciates that that was exactly what Kripke had originally said. 39. It was Marcus who first characterized Quine’s attitudes towards QML as that of being conceived in the sin of confusing use and mention (Marcus 1963:77). Quine embraced the characterization (Quine 1963:97). 40. Recently both Burgess (1997) and Neale (2000)—the later reversing his assessment of Quine’s arguments in his earlier (Neale 1990), where he defended the Russellian response—have taken this attitude.


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Page 338 41. I take up the task of attempting to articulate such a view, developing a broadly Aristotelian conception of substance and essence, in Nelson (unpublished b). 42. Kaplan developed a very different response to Quine in (1986). I think this later response suffers from some of the difficulties I argued afflict option (A). A detailed discussion of Kaplan’s rich and difficult paper is, however, not possible here. 43. I follow Kaplan in using Church’s ∆-notation, although this is, strictly speaking, a relation between expressions and individuals. Kaplan knowingly vacillates between having the extra quantifier range over individual-concepts (his preferred conception) and expressions (following Quine’s preference of avoiding intensional entities). As Church famously pointed out—in, for example (Church 1943:45)—construing propositional attitude verbs as relating agents to sentences seems to require that the agent in question understands the language used in the report, which is very much at odds with our practice of reporting beliefs using embedded sentences that the alleged believers would not use to express their beliefs and might not even understand. I do not think that Quine ever met this worry. He famously wrote: ‘We may treat a mouse’s fear of a cat as his fearing true a certain English sentence. This is unnatural without being therefore wrong. It is a little like describing a prehistoric ocean current as clockwise’ (Quine 1956:186). Although an excellent turn of the pen, it seems clear that Quine fails to explain how we can truly say that a mouse fears-true an English sentence. Ascribing a clockwise current to a prehistoric ocean does not require the existence of clocks in prehistoric time, any more than our using actual resources to describe a counterfactual circumstance in which, say, there are no words, requires that there are words in that counterfactual circumstance being described. But this is a false comparison to the case of treating a mouse’s fear of a cat as fearing-true an English sentence when one is fairly certain the mouse does not understand English. Here we are not describing one situation from the perspective of another. Even if avoiding intensional entities were desirable, I do not think Quine has succeeded in showing how it is possible. 44. The notion of analytic connection can simply be taken as a primitive. Alternatively, if we assume a realist attitude of structured concepts, we can explicate the notion in Kantian terms, as follows. One concept is analytically connected to another just in case the one is a literal constituent of the other. For example, the concept being a two-legged animal is connected to the concept being an animal as the former literally contains the latter as a constituent part, in much the way the expression ‘animal’ is contained in the complex expression ‘a two-legged animal’. 45. It would indeed lead to contradiction if we concluded from the falsity of (4) that Venus satisfies the condition ~ c ( c∆x & A(E, c )). But we should not be tempted by this inference (and all the more so in light of the truth of (2)). Such an inference would be like concluding that there is no way I went to work from the fact that I did not run to work naked, given the Kaplanesque analysis of the structure of modal sentences. 46. One of its more striking consequences is that every object necessarily has every property it has; that is, there is only one way for an object to have a property and that is to necessarily have it. The account also entails, given the most straightforward extension to ◊, that every object possibly has every consistent property. (I set aside identity properties, which I shall discuss below.) Kaplan saw these consequences. He writes: Although our analysis of Nec avoids essentialism, it also avoids rejecting: (42) Nec (‘ x = the number of planets’, nine), which comes out true on the understanding


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Page 339 (43) α(∆(α, nine) & N = the number of planets ) in view of the facts that N the number of planets = the number of planets ) and ∆(‘the number of planets’, nine). (1968:221–22) That is, because there is a designator of nine analytically tied to the condition ‘ x = the number of planets’—to wit, ‘the number of planets’—it turns out, given Kaplan’s analysis, that nine analytically satisfies that condition. (I present a more rigorous argument for this in the text.) Kaplan continues: ‘In a sense, we have not avoided essentialism but only inessentialism, since so many of nine’s properties become essential. Small consolation to know of our essential rationality if each blunder and error is equally ingrained’ (222). Kaplan similarly complains that his analogous account of de re belief puts ‘Ralph en rapport with an excess of individuals’ (222). In §§8–9, he adds conditions that make de re modal properties and de re belief much more difficult by restricting the class of designators one looks to in determining whether or not an object necessarily satisfies a condition to the names ‘necessarily denote’ their objects, in the case of modality, and to designators that are vivid representations of their objects (for the believer) in determining what believer believes of, in the case of propositional attitudes. These restrictions demonstrate, early on, the seeds of Kaplan’s rejection of his anti-essentialist (antiessentialists should not want to carve off a special class of designators as revealing objects’ real, mindindependent and substantive nature) and his Fregeanism (Fregeans should deny that there is any substantive notion of rapport). 47. Like Quine, both Marcus and Parsons speak of essences. But, again like Quine, it is clear that what they meant by ‘essence’ is just a necessary property. (See n29.) Trivial necessary properties are not essences, properly called, as they hardly make a start at answering Aristotle’s What is it? question. Indeed, they make absolutely no distinction among the class of individuals there are, as every individual has every trivial necessary property and no individual has any nontrivial necessary property, as we shall see. This is what makes them so anti-essentialist friendly and so radically unfit to be genuine essences. So, I read Marcus and Parsons as intending to speak of necessary properties in general as opposed to essences in particular. 48. In calling such theses ‘philosophically problematic’, we are not calling them false. (Indeed, as I already said, I am a proponent of such a philosophically problematic thesis.) Even the most avid essentialists should admit that the necessary properties they acknowledge are more problematic— although they may wish to say richer and more useful for it—than the trivial necessary properties discussed below. 49. Marcus also distinguishes weakly essentialist theses from strongly essentialist theses. A thesis is weakly essentialist just in case nothing is such that it could contingently possess a problematically necessary property; that is, just in case everything is such that, necessarily, if it possesses a problematic necessary property at all, then it does not possess it contingently. A thesis is strongly essentialist , on the other hand, just in case it is possible for an object to contingently possess a problematically necessary property. To see the distinction, compare the property being human with the property being statueshaped. A standard essentialist about humanity will claim that, although not every object is necessarily human and so we have ourselves a problematic necessary property, every object that is human is necessarily human. (So, nothing is contingently human.) And this fact is itself nonaccidental, being constitutive of the property being human. A standard essentialist about being statue-shaped who denies that composite entities are identical to the matter out of which they are composed


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Page 340 will claim that the bronze statue is necessarily statue-shaped while the piece of bronze out of which the bronze statue is composed, albeit statue-shaped, is not necessarily statue-shaped, as it could have survived being squashed. (See, for example, Wiggins (2001).) If every problematic necessary property were like being human (according to the standard essentialist about humanity), then only weak essentialism would obtain. But if there are necessary properties like being statue-shaped (according to the standard constitution theorist), then strong essentialism is true. This distinction, although both insightful and important, is inessential to the present discussion. 50. Note that it would not do to say that o analytically or logically satisfies Fx just in case xFx is true, given that xFx might be nonanalytically true. 51. This line of argument draws on Parsons (1967) and (1969). 52. This possibility is not even mentioned, for example, in Neale’s defence of Quine in (Neale 2000). Neither Burgess nor Neale address (or even cite) Kaplan’s view. 53. I discuss these three conceptions of the de re / de dicto distinction and explore their inter-relations in more depth in Nelson (unpublished a). 54. Burgess says that Quine’s critique is limited to nontrivial de re modality. However, he offers no textual evidence that Quine appreciated the difference between trivial and nontrivial de re modality. Indeed, the ease with which Quine slides between claiming that proponents of QML must count as true statements like ‘Everything is necessarily self-identical’ to claiming that proponents of QML must count as true statements like ‘Something is necessarily greater than 7’ strongly suggests that he did not appreciate the difference. 55. I take it that Burgess would similarly object to the Kaplanesque view sketched above precisely because it has a ‘trivializing’ effect, albeit of a different sort from the trivializing effect of the Marcus/Parsons strategy. (This is but a guess, as Burgess does not discuss Kaplan (1968).) Although (10) is invalid on the Kaplanesque view, something perhaps just as bothersome is valid: Namely, (11). x( Fx Fx ). (11) can be seen to be ‘trivializing’ because it obliterates the distinction between necessarily having a property and contingently having a property. I believe my discussion of (10), which follows, can be applied to (11) as well. 56. Now no doubt Marcus herself would respond to this by rejecting the indiscriminate attitude. If one wants to get at the essence of an object, one should look at tags and not descriptions of the object. But, as I have already argued in ‘The Real Quine’, the very distinction between tags and definite descriptions is already essentialist, in Quine’s sense of the notion; that is, appealing to such a distinction will lead one to TAE2. REFERENCES Adams, R. (1979) ‘Primitive Thisness and Primitive Identity’, Journal of Philosophy 76: 5–26. Austin, D. (1990) What’s the Meaning of ‘This’?, Ithaca/London: Cornell University Press. Burgess, J. (1997) ‘Quinus ab omni naevo vindicatus’, in A. Kazmi (ed.), Meaning and Reference. Canadian Journal of Philosophy , Suppl. vol. 23: 25–65. Church, A. (1943) Review of Quine ‘Notes on Existence and Necessity’, Journal of Symbolic Logic 8: 45– 47. ——. (1950) Review of Fitch’s ‘The Problem of the Morning Star and the Evening Star’, Journal of Symbolic Logic 15: 63.


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Page 341 Crimmins, M. and Perry, J. (1989) ‘The Prince and the Phone Booth: Reporting Puzzling Beliefs’, Journal of Philosophy 86: 685–711. Fine, K. (1989) ‘The Problem of de re Modality’, in J. Almog, J. Perry and H. Wettstein (eds), Themes from Kaplan, New York: Oxford University Press: 197–272. ——. (1990) ‘Quine on Quantifying In’, in C. Anderson and J. Owens (eds), Propositional Attitudes, Stanford, CA: CSLI Publications: 1–25. ——. (1994) ‘Essence and Modality’, Philosophical Perspectives 8: 1–16. ——. (1995) ‘The Logic of Essence’, Journal of Philosophical Logic 24: 241–73. Fitch, F. (1949) ‘The Problem of the Morning Star and the Evening Star’, Philosophy of Science 16: 137– 41. Gibbard, A. (1975) ‘Contingent Identity’, Journal of Philosophical Logic 4: 187–221. Jeshion, R. (2002) ‘Acquaintanceless de re Belief’, in J. Campbell, M. O’Rourke and D. Shier (eds), Meaning and Truth: Investigations in Philosophical Semantics, New York, NY: Seven Bridges Press: 53– 78. Kaplan, D. (1968) ‘Quantifying In’, in D. Davidson and H. Hintikka (eds), Words and Objections: Essays on the Work of W. V. Quine , Dordrecht: Reidel: 206–42. Originally published in Synthese 19: 178–214. ——. (1975) ‘How to Russell a Frege-Church’, Journal of Philosophy 72: 716–29. ——. (1986) ‘Opacity’, in E. Hahn and P. Schilpp (eds), The Philosophy of W. V. Quine , La Salle, IL: Open Court: 229–89. ——. (1989) ‘Demonstratives’, in J. Almog, J. Perry and H. Wettstein (eds), Themes From Kaplan, Oxford: Oxford University Press: 487–504. Kripke, S. (1971) ‘Identity and Necessity’, in M. Munitz (ed.), Identity and Individuation, New York: New York University Press: 135–64. ——. (1980) Naming and Necessity , Cambridge, MA: Harvard University Press. Based on lectures delivered at Princeton University in 1970. Lewis, D. (1986) On the Plurality of Worlds , Oxford: Blackwell. Marcus, R. B. (1948) Review of Smullyan’s ‘Modality and Description’, Journal of Symbolic Logic 13: 149–50. ——. (1963) ‘Modal Logics I: Modalities in Intensional Languages’, in M. W. Wartofsky (ed.), Proceedings of the Boston Colloquium for the Philosophy of Science , Dordrecht: Reidel: 77–96. ——. (1967) ‘Essentialism in Modal Logic’, Noûs 1: 90–96. ——. (1990) ‘A Backward Look at Quine’s Animadversion on Modalities’, in R. Barrett and R. Gibson (eds), Perspectives on Quine , Oxford: Blackwell: 230–43. ——. (1993) Modalities: Philosophical Essays, New York: Oxford University Press. ——. et al. (1963) ‘Discussion’, in M. W. Wartofsky (ed.), Proceedings of the Boston Colloquium for the Philosophy of Science , Dordrecht: Reidel: 105–16. Neale, S. (1990) Descriptions, Cambridge, MA: MIT Press. ——. (2000) ‘On a Milestone of Empiricism’, in A. Orenstein and P. Kotatko (eds), Knowledge, Language and Logic, Dordrecht: Kluwer: 237–346. Nelson, M. (2005) ‘The Problem of Puzzling Pairs’, Linguistics and Philosophy 28: 319–50. ——. (forthcoming) ‘On the Contingency of Existence’, in L. Jorgensen and S. Newlands (eds), Essays in Honor of R. M. Adams , Oxford: Oxford University Press. ——. (unpublished a) ‘Anti-Essentialism and the de re ’. ——. (unpublished b) ‘Necessary Essence’. Parsons, T. (1967) ‘Grades of Essentialism in Quantified Modal Logic’, Noûs 1: 181–200.


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Page 342 ——. (1969) ‘Essentialism and Quantified Modal Logic’, Philosophical Review 78: 35–52. Quine, W. V. O. (1937) ‘New Foundations for Mathematical Logic’, American Mathematical Monthly 44: 70–80. Reprinted in his From a Logical Point of View , 80–102. Citations to reprinting. ——. (1943) ‘Notes on Existence and Necessity’, Journal of Philosophy 40: 113–17. ——. (1947) ‘On the Problem of Interpreting Modal Logic’, Journal of Symbolic Logic 12: 43–48. ——. (1948) ‘On What There Is’, Review of Metaphysics 2: 21–38. Reprinted in his From a Logical Point of View , 1–20. Citations to reprinting. ——. (1951) ‘Two Dogmas of Empiricism’, Philosophical Review 60: 20–43. Reprinted in his From a Logical Point of View , 20–47. Citations to reprinting. ——. (1953a) ‘Three Grades of Modal Involvement’, Proceedings of the XIth International Congress of Philosophy 14: 65–81. Reprinted in his 1976 The Ways of Paradox, rev. and enlarged edn, New York: Random House: 185–96. Citations to reprinting. ——. (1953b) ‘Reference and Modality’, in From a Logical Point of View , Cambridge MA: Harvard University Press: 160–67. ——. (1956) ‘Quantifiers and Propositional Attitudes’, Journal of Philosophy 53: 177–87. ——. (1961) ‘Reference and Modality’, in From a Logical Point of View , 2nd edn rev., Cambridge: Cambridge University Press: 160–67. ——. (1963) ‘Reply to Professor Marcus’ in M. W. Wartofsky (ed.), Proceedings of the Boston Colloquium for the Philosophy of Science , Dordrecht: Reidel: 97–104. ——. (1980) ‘Reference and Modality’, in From a Logical Point of View , 2nd edn rev., New York: Harper and Row: 139–59. Richard, M. (1990) Propositional Attitudes: An Essay on Thoughts and How We Ascribe Them , Cambridge: Cambridge University Press. Russell, B. (1903) The Principles of Mathematics, Cambridge: Cambridge University Press. ——. (1905) ‘On Denoting’, Mind 14: 479–93. ——. (1906) ‘On the Nature of Truth’, Proceedings of the Aristotelian Society 7: 28–49. ——. (1910) ‘Knowledge by Acquaintance and Knowledge by Description’, Proceedings of the Aristotelian Society 11: 108–28. ——. (1912) The Problems of Philosophy , Oxford: Oxford University Press. ——. (1913) Theory of Knowledge , in E. Eames (ed.), The Collected Papers of Bertrand Russell, vol. 7, London: George Allen and Unwin, 1984. Salmon, N. (1986) Frege’s Puzzle , Cambridge, MA: MIT Press. ——. (1989) ‘The Logic of What Might Have Been’, Philosophical Review 98: 3–34. Smullyan, A. (1947) Review of Quine’s ‘The Problem of Interpreting Modal Logic’, Journal of Symbolic Logic 12: 139–41. ——. (1948) ‘Modality and Description’, Journal of Symbolic Logic 13: 31–37. Strawson, P. F. (1990) Individuals: An Essay on Descriptive Metaphysics , London: Routledge. Originally published in 1959, Taylor Francis Group. Whitehead, A. N. and Russell, B. (1925) Principia Mathematica , vol. 1, 2nd edn, Cambridge: Cambridge University Press. Wiggins, D. (2001) Sameness and Substance Renewed, Cambridge: Cambridge University Press.


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Page 343 15 Points, Complexes, Complex Points, and a Yacht Nathan Salmon I comment here on two puzzling passages in Russell’s masterpiece, ‘On Denoting’.1 One is the famous ‘Gray’s Elegy argument’, as it is usually called.2 Afterward, I discuss errors in the famous discussion of the small yacht and its touchy owner. THE ‘GRAY’S ELEGY’ ARGUMENT Russell’s famous argument, as I interpret it, is aimed against a popular theory of the semantics of definite descriptions: ST : A definite description designates by virtue of the description’s semantic content, which fixes the designatum of the description to be (if anything) the individual or thing that uniquely answers to the description; further, when the definite description occurs in a declarative sentence, the description’s content represents the description’s designatum in the proposition expressed. ST fleshes out the simple and seemingly innocuous thesis that definite descriptions are singular terms. It had been held by Russell in The Principles of Mathematics. It is also held by theorists as diverse as John Stuart Mill, Gottlob Frege, Alexius Meinong, and legions of others. Here in a nutshell is Russell’s reductive argument against ST : The attempt to form a proposition directly about the content of a definite description (as by using an appropriate form of quotation) inevitably results in a proposition about the thing designated instead of the content expressed. I call this phenomenon the Collapse . In light of the Collapse, Russell argues, the ST theorist must accept that all propositions about a description’s content are about that content indirectly, representing it by means of a higher-level descriptive content. And this, according to Russell, renders our cognitive grip on definite descriptions inexplicable. On my interpretation, Russell may be seen as arguing in eight separate stages (at least), as follows: At stage ( I) he argues that there is some awkwardness in so much as stating the very theory ST . At stage ( II) he argues that once a way of stating ST is found, the theory, so stated, gives


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Page 344 rise to a peculiar phenomenon: The attempt to form a singular proposition about the content of a definite description inevitably results instead in a general proposition about the individual designated by the description. This is the Collapse. At stage ( III) the Collapse leads to a preferable formulation of ST . At stage ( IV) Russell shows that the Collapse remains a feature of the reformulated theory. At stage ( V) Russell argues that the Collapse commits ST to a very sweeping conclusion: that no singular term designating the content of a definite description can be what Russell will later call a logically proper name ; instead any such term must be itself a definite description, or function as one. As Russell puts it, on our theory ST , ‘the meaning cannot be got at except by means of denoting phrases’ (p. 486). At stage ( VI) he argues furthermore that the content of a definite description cannot be a constituent of the content of any definite description of it. Russell proceeds to complain at stage ( VII ) that the results of the preceding two stages are philosophically intolerable. At stage ( VIII ) he provides a complementary argument for the conclusion that ST ignores that which, by its own lights, is philosophically most significant about propositions. In Russell’s terminology, a denoting phrase is a noun phrase beginning with what linguists call a determiner , like ‘every’, ‘some’, or ‘the’. Both definite and indefinite descriptions are denoting phrases, in Russell’s sense. A definite description of a given language is said to mean —in a more standard terminology, it expresses—a denoting complex c as its meaning. The denoting complex c , in turn, denotes—in Church’s terminology, it is a concept of—an object as its denotation . I here translate Russell’s term ‘meaning’ as ‘content’.3 Russell does not use any special term for the binary relation between a definite description and the object of which the expression’s content in the language is a concept. Instead Russell speaks of “the denotation of the meaning”, saying that a definite description α “has a meaning which denotes” an object x. Sometimes he says that α itself (as opposed to its content) denotes x. Here I avoid Russell’s term ‘denote’ altogether. Instead I use ‘determine’ for the relation between a complex c and the object x of which c is a concept, and I call x the ‘determinatum’ of c . I use ‘designate’ for the relation between the expression α and x, and I call x the ‘designatum’ of α. Russell uses ‘ C’ as a variable ranging over determining complexes, and sometimes instead as a metalinguistic variable ranging over determiner phrases. Frequently he uses ‘ C’ as a schematic letter (a substitutional variable), sometimes standing in for an arbitrary definite description, sometimes for a term designating an arbitrary determining complex. Any sentence in which ‘ C’ occurs as schematic letter is strictly speaking a schema, of which Russell means to assert every instance. With a little finesse, Russell’s intent can often be captured by taking ‘ C’ as a variable either ranging over definite descriptions or ranging over determining complexes. I here use ‘α’ as a metalinguistic variable, and upper case ‘ D’ as a schematic letter


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Page 345 standing in for an arbitrary definite description. I use lower-case ‘ c ’ as a determining-complex variable. I use Quine’s quasi-quotation marks, ‘ ’ and ‘ ’ in combination with ‘α’. In quasi-quotation, all internal expressions are quoted, that is, mentioned (designated), except for metalinguistic variables, whose values are mentioned. I use single quotation marks for direct (expression) quotation. Following David Kaplan, I use superscripted occurrences of ‘ m ’ as indirect-quotation marks, and superscripted occurrences of ‘ M ’ as indirect-quasi-quotation marks (1971:120–21).4 In indirect-quasiquotation, the contents of all internal expressions are mentioned, except for determining-complex variables, whose values are mentioned. Here I avoid double quotation marks, except as scare-quotes when using another’s words. Departures from the original appear in boldface. Analytical Translation of the Famously Obscure Passage ( A′ ) The relation of the content to the designatum involves certain rather curious difficulties, which seem in themselves sufficient to prove that the theory which leads to such difficulties must be wrong. ( B′ ) ( I) When we wish to speak about, that is, to designate, the content of a determiner phrase, that is, of a definite description, as opposed to its designatum, the present mode of doing so is by indirect-quotation marks. Thus we say: The centre of mass of the Solar System is a point, not a determining complex; m The centre of mass of the Solar System m is a determining complex, not a point. Or again, The first line of Gray’s Elegy expresses a proposition. m The first line of Gray’s Elegym does not express a proposition. Thus taking any determiner phrase, for example, taking any definite description … , α, we wish to consider the relation between α and where the difference of the two is of the kind exemplified in the above two instances.5 ( C′ ) We say, to begin with, that when α occurs it is the designatum of α that we are speaking about; but when occurs, it is the content. Now the relation of content to designatum is not merely linguistic through the phrase, that is, it is not merely the indirect product of the semantic relations of being the content of a phrase and designating: there must be a direct, nonlinguistic, logico-metaphysical relation involved, which we express by saying that the content determines the designatum. But the difficulty which confronts us is that we cannot succeed in both preserving the connexion of content to designatum and preventing them—the content and the designatum —from being


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Page 346 one and the same; also that the content cannot be got at except by means of determiner phrases.6 This happens as follows. ( D′i) The one phrase α was to have both content and designation. But if in an effort to designate the content, we speak of , that gives us the content (if any) of the designatum of α. ‘The content of the first line of Gray’s Elegy’ designates the same complex as ‘The content of m The curfew tolls the knell of parting day m ’, and … not the same as ‘The content of m the first line of Gray’s Elegym ’. Thus in order to get the content we want, we must speak not of , but of , which designates the same as itself.7 ( D′ii ) Similarly does not designate the determinatum we want, the determinatum of α’s content, but means something, that is, expresses a determining complex, which, if it determines anything at all, determines what is determined by the determinatum we want. For example, let α be ‘the determining complex occurring in the second of the above instances’. Then and ‘The curfew tolls the knell of parting day’ are both true.8 But what we meant to have as the determinatum was m the first line of Gray’s Elegym . Thus we have failed to get what we wanted from 9 ( E′i) ( II) The difficulty in speaking of the content of a determining complex, that is, in using a phrase of the form , may be stated thus: The moment we put the complex in a proposition, the proposition is about the determinatum;10 and hence if we make a proposition in which the subject component is M the content of cM , for some determining complex c , then the subject represents the content (if any) of the determinatum of c , which was not intended.11 ( E′ii ) ( III) This leads us to say that, when we distinguish content and determinatum of a determining complex, as we did in the preceding paragraph, we must be dealing in both cases with the content: the content has a determinatum and is a determining complex, and there is not something other than the content, which can be called , and be said to have both content and a determinatum. The right phraseology, on the view in question, is that some contents have determinata. ( F′i) ( IV) But this only makes our difficulty in speaking of contents more evident. For suppose c is our target complex, and let ‘ D’ represent in what follows a determiner phrase that expresses c (for example, let c be m the centre of mass of the Solar Systemm and let ‘ D’ stand in for the phrase ‘the centre of mass of the Solar System’); then we are to say that mDm , that is, c , is the content of the phrase ‘ D’, instead of saying that mDm itself has a content. Nevertheless, whenever ‘ D’ occurs without indirect-quotation marks, what is said is not about mDm , the content of ‘ D’, but only about D, the designatum of ‘ D’, as when we say:


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Page 347 The centre of mass of the Solar System is a point. ( F′ii ) ( V) Thus to speak of mDm itself, that is, to express a proposition about the content of ‘ D’, our subject component must not be mDmitself , but something else, a new determining complex, which determines mDm .12 Thus m mDm m —which iterated indirect quotation is what we use when we want to speak of the content of ‘ mDm ’—must be not the content of ‘ D’, that is, not mDm itself, but something which determines the content. ( F′iii) ( VI) And mDm , that is, c must not be a constituent of this higher-level complex m mDm m (as it is of M the content of cM ); for if mDm occurs in the complex, it will be its determinatum, not the content of ‘ D’, that is, not mDm itself, that will be represented and there is no backward road from determinata to contents, because every object can be designated by an infinite number of different determiner phrases.13 ( G′i) ( VII ) Thus it would seem that m mDm m and mDm are altogether different entities, such that m mDm m determines mDm ; but this cannot be an explanation of m mDm m , because the relation of m mDm m to mDm remains wholly mysterious; and where are we to find the determining complex m mDm m which is to determine mDm ?14 ( G′ii ) ( VIII ) Moreover, when mDm occurs in a proposition, it is not only the determinatum that occurs (as we shall see in the next paragraph); yet, on the view in question, mDm represents only the determinatum, the content ( that is, the representing of mDm itself) being wholly relegated to m mDm m . This is an inextricable tangle, and seems to prove that the whole distinction of content and designation has been wrongly conceived. ( H′ ) That the content is relevant when a determiner phrase occurs in a sentence expressing a proposition is formally proved by the puzzle about the author of Waverley . The proposition m Scott is the author of Waverleym has a property not possessed by m Scott is Scottm , namely, the property that George IV wished to know whether it was true. Thus the two are not identical propositions; hence the content of ‘the author of Waverley ’ must be relevant to the proposition as well as the designatum, if we adhere to the point of view to which this distinction belongs. Yet, as we have seen, so long as we adhere to this point of view, we are compelled to hold that only the designatum can be relevant. Thus the point of view in question must be abandoned.15 Some previous interpreters do not so much as mention what I am calling the Collapse . Others have extracted the alleged phenomenon from ( Ei), but place little or no importance on it. Some have depicted its occurrence in the ‘Gray’s Elegy’ passage as little more than a clever observation, characteristic of Russell but one that he makes only in passing and is of limited significance in the grand sweep of the overall argument. In sharp contrast, on my interpretation the Collapse is the very linchpin of the ‘Gray’s Elegy’


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Page 348 argument, and plays a pivotal role in later stages that constitute the heart of the argument.16 At stage ( V) (the middle section of paragraph ( F )), Russell argues by means of the Collapse that on ST , m mDm m ≠ mDm , where ‘ D’ stands in for any definite description.17 We may designate a particular complex, say m the centre of mass of the Solar System m , in order to express a proposition about it. However, any proposition in which the complex itself occurs is about the centre of mass of the Solar System, that is, the determinatum of the target complex rather than the complex itself. A singular proposition about a determining complex is an evident impossibility; hence, any proposition that is about a complex must involve a second-level determining complex that determines the target complex. Hence, any term for a complex must function in the manner of a definite description. Even our indirect quotation, ‘ m the centre of mass of the Solar System m ’ (the closest thing there is to a standard name of the complex), must be a disguised definite description, expressing a second-level determining complex, m m the centre of mass of the Solar System m m , as its content. Furthermore, m m the centre of mass of the Solar System m m is distinct from, and in fact determines, m the centre of mass of the Solar System m . It is in this very concrete sense that on ST , ‘the meaning cannot be got at except by means of determiner phrases’. The only way to designate a determining complex is by expressing a higher-level determining complex.18 Russell has thus far argued that the theory ST is committed, by the Collapse, to denying the very possibility of singular propositions about contents. Some commentators have construed this argument as an objection to Frege’s theory, which rejects singular propositions.19 Such an argument would be a howler. On the contrary, Fregeans should welcome the conclusion derived at stage ( V), which provides a reductio argument against ST in conjunction with singular propositions of unrestricted subject matter— a theory like Mill’s or that of Russell’s Principles . The incoherence of these non-Fregean versions of ST may even be given a kind of proof, using the principle of Compositionality (which Russell relied on at least implicitly and Frege explicitly endorsed), according to which the content of a compound expression is an effectively computable function of the contents of the contentful components. Compositionality is subject to certain restrictions. For example, the content of a compound expression containing a standard (syntactic) quotation is a function of the content of the quotation itself, together with the contents of the surrounding subexpressions, but not of the content of the quoted expression. Subject to such restrictions as this, Compositionality evidently entails a similarly restricted principle of Synonymous Interchange , according to which substitution of a synonym within a larger expression preserves content. (I here call a pair of expressions synonymous if there is something that is the content of both.) To give the argument its sharpest focus, we consider Russell’s example:


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Page 349 (1) The centre of mass of the Solar System is a point. According to ST , the grammatical subject of (1), ‘the centre of mass of the Solar System’, expresses the determining complex m the centre of mass of the Solar System m as its English content. According to the non-Fregean version of ST , the content of the indirect quotation ‘ m the centre of mass of the Solar System m ’ itself is this same determining complex, and sentences containing the indirect quotation express singular propositions about the complex. Hence, the description and the indirect quotation are synonymous according to the non-Fregean version of ST . Therefore, by Synonymous Interchange, so also are (1) and (2) m The centre of mass of the Solar System m is a point. But (1) is true while (2) is necessarily false, indicating that they do not express the same thing. The content of (2) must invoke the second-level complex m m the centre of mass of the Solar System m m to represent the firstlevel complex. The same argument may be given using the free variable ‘ c ’ in place of the indirect quotation. On the supposition that the content of the variable under the established assignment is its value, the variable has the very same content as the definite description ‘the first line of Gray’s Elegy’. The Collapse then follows directly by Synonymous Interchange. This refutes the assumption that the variable under its assignment is a logically proper name for the complex in question. The theory ST is thus committed to extending its content/designation distinction for definite descriptions to all terms that designate determining complexes. The argument can be repeated in connection with the content of the indirect quotation itself. The argument is thus converted into an argument by mathematical induction for an infinite hierarchy of contents associated with ‘the first line of Gray’s Elegy’. Indeed, the postulated second-level complex m m the first line of Gray’s Elegym m is, for Frege, the content that the description expresses when occurring in ungerade (‘oblique’) contexts, like the contexts created by ‘believes that’ and by indirect quotation marks.20 He called this the indirect sense of ‘the first line of Gray’s Elegy’. The series beginning with ‘The curfew tolls the knell of parting day’, followed by m the first line of Gray’s Elegym , m m the first line of Gray’s Elegym m , m m m the first line of Gray’s Elegym m m , and so on, is precisely Frege’s infinite hierarchy of senses for the definite description (treating designation as the bottom level in the hierarchy). Not all of Frege’s disciples have followed the master down the garden path to Frege’s jungle. Two noteworthy deserters are Carnap and Dummett.21 But Church has followed Frege even here.22 In fact, at least one of the loyal opposition has as well. Russell’s argument via the Collapse for ST ’s commitment to the hierarchy was independently reinvented closer to the end of the previous century by Tyler Burge.23


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Page 350 Russell clarifies the nature of the hierarchy at stage ( VI ), which makes up the final third of ( F ). A feature of ( Fiii) that is typically overlooked is that it again invokes the Collapse.24 Russell observes that the target complex is not only distinct from the postulated second-level complex we seek; it is not even a constituent of the latter complex (as it is of m Russell has memorized the first line of Gray’s Elegym , and of m the content of the first line of Gray’s Elegym ). Here Russell pursues the obvious question: Given that the indirect quotation ‘ m the first line of Gray’s Elegym ’ must express a second-level complex that determines our target complex, which second-level complex does it express? The best way to identify the sought after second-level complex would be to provide a definite description of the form ‘the determining complex that is such-and-such’ which is fully understood (independently of indirectquotation), and which is synonymous with ‘ m the first line of Gray’s Elegym ’. Given Compositionality, it might be hoped that the suitable definite description will incorporate something expressing the designated target complex itself. We would thus construct the postulated second-level complex using the target complex. However, the desired description cannot be ‘the complex that determines the first line of Gray’s Elegy’, for there are infinitely many and varied complexes each of which determines the words ‘The curfew tolls … ’. Let us try a different tack. Let ‘ c ’ name the target complex, and consider: the determining complex that is c . Russell observes that this will not do either. Indeed, no description of the form ‘the determining complex that bears relation R to c ’ will succeed. Or to put the same point somewhat differently, our postulated second-level complex cannot be M the determining complex that bears R to cM , for some binary relation R. (Note the indirect-quasi-quotation marks.) For the Collapse occurs with determining complexes just as it does with propositions. The content of the description collapses into: m the determining complex that bears R to the first line of Gray’s Elegym . The problem here is that there is no ‘backward road’ from the words ‘The curfew tolls … ’ to their particular representation by m the first line of Gray’s Elegym , and likewise no backward road from the Solar System’s centre of mass to its particular representation as such. That is, there is no relevantly identifiable binary relation R whose converse is a ‘choice’ function that selects exactly our target complex, to the exclusion of all others, and assigns it, and only it, to its determinatum. If R is taken to be the relation of determining , then the collapsed second-level complex fails to determine a unique complex because there are too many complexes (infinitely many, in fact) that bear this relation to the first line of Gray’s Elegy. And if R is taken to be the relation of identity, then the resulting secondlevel complex fails to determine a unique complex because there are too few complexes that bear this relation to the first line of Gray’s Elegy. More generally, if c is our target complex, the postulated second-level complex cannot be of the form Mf ( c ) M , where ‘ f ’ designates a choice function that selects a distinguished or privileged determining complex from the class of all complexes that determine a given object. It is important to notice that


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Page 351 the missing choice function f goes not at the level from the target complex to the second-level complex, but at the bottom level from the determinatum to the complex itself. A ‘low’ backward road might enable us to construct the postulated second-level complex from the target complex. But high or low, no backward road is forthcoming. So ends stage ( VI). Because there is no backward road from ‘The curfew tolls …’ to m the first line of Gray’s Elegym , it follows via the Collapse that the second-level complex m m the first line of Gray’s Elegym m is not constructed from the target complex m the first line of Gray’s Elegym . Indirect quotations thus constitute a restriction on a principle of Strong Compositionality (also endorsed by both Frege and Russell), according to which the content of a compound expression is not only a function of, but is in fact a complex composed of, the contents of the contentful components. Russell might have taken the argument a step further. Continuing and embellishing the argument on Russell’s behalf, although the indirect quotation ‘ m the first line of Gray’s Elegym ’ expresses, and thereby uniquely fixes, the postulated second-level complex, the target complex designated by the indirect quotation does not itself uniquely single out the second-level complex. It is a serious mistake, for example, to suppose that m m the first line of Gray’s Elegym m can be described as the content of m the first line of Gray’s Elegym . (Russell believes he has shown that on ST , this description designates the target complex itself, whereas the description actually designates nothing. The alternative phrase, ‘the content of “the first line of Gray’s Elegy”’ does designate the target complex itself. Still, we do not get at the postulated second-level complex.) But neither can m m the first line of Gray’s Elegym m be described as the complex that determines m the first line of Gray’s Elegym . For any given object there are infinitely many complexes that determine it. Our target complex is also determined by such second-level complexes as m the determining complex occurring in the second of Russell’s instances m and m the determining complex that has given Russell’s readers more headaches than any other m —neither of which is suited to be the content expressed by ‘ m the first line of Gray’s Elegym ’. Thus not only is it the case, as Russell explicitly argues, that the target complex is altogether different from the postulated second-level complex. The target complex does not even uniquely fix the second-level complex. Never mind the Collapse. If there is no backward road from determinata to determining complexes, then not only is there no low road from the first line of Gray’s Elegy to m the first line of Gray’s Elegym ; there is likewise no high road from m the first line of Gray’s Elegym to m m the first line of Gray’s Elegym m . We have no way to go from the content of a definite description to the content of its indirect quotation. Our indirect quotation marks thus yield a restriction also on the weaker principle of Compositionality: The content of an indirect quotation is not even a computable function of (let alone a complex composed partly of) the content of the expression within the quotes. This result is stronger than the conclusion that Russell explicitly draws. If the


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Page 352 target complex were a constituent of the postulated second-level complex, presumably it would single out the latter complex. But the mere fact that the target complex is not a constituent of the secondlevel complex does not yet rule out the possibility that the target complex uniquely fixes the secondlevel complex in some other manner. The fact that there is a multiplicity of complexes determining any given object seems to do just that. (By contrast, the indirect quotation ‘ m the first line of Gray’s Elegym ’ singles out the second-level complex, as its English content.)25 SIZE MATTERS Having disposed of ST once and for all with his ‘Gray’s Elegy’ argument (so he believes), Russell moves on to illustrate the important distinction between primary occurrence and secondary occurrence with his famous example of the touchy yacht owner: I have heard of a touchy owner of a yacht to whom a guest, on first seeing it, remarked, ‘I thought your yacht was larger than it is’; and the owner replied, ‘No, my yacht is not larger than it is’. What the guest meant was, ‘The size that I thought your yacht was is greater than the size your yacht is’; the meaning attributed to him is, ‘I thought the size of your yacht was greater than the size of your yacht’. (p. 489) Speaking on ‘Russell’s Notion of Scope’ at Rutgers University in May 2005 (and also in conversation some years earlier), Saul Kripke pointed out a significant snag in Russell’s treatment of his yacht example. The meaning Russell attributes to the guest cannot be correct. Indeed, the guest might well have thought that the yacht was larger than it turned out to be without there being any particular size the guest thought the yacht was. Much more likely, the guest, on the basis of the owner’s boasts, had merely judged the yacht to be, at a minimum, grander than it turned out on visual inspection to be, that is, to be some size or other among a range of sizes (perhaps indeterminately delineated), each noticeably greater than the yacht’s actual size. In that case, the description, ‘the size I thought your yacht was’ is improper. Russell’s distinction of primary and secondary occurrence therefore appears to be of no help in removing the misunderstanding. Indeed, it seems that definite descriptions, as such, are entirely irrelevant to the example. In his talk Kripke said, ‘So Russell’s analysis in terms of his theory of descriptions, as stated, is incorrect … How to fix up Russell’s example is a little complicated, and not clear. Maybe it has relatively little to do with the definite descriptions themselves.’26 Any such conclusion robs Russell of credit he richly deserves. The correct conclusion is that although Russell’s theory of descriptions indeed applies to the case at hand, he misapplied it. Correctly applied, Russell’s theory


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Page 353 provides insight into an example that, at least on the surface, does not appear to invoke definite descriptions, or indeed any determiner phrases of the sort to which Russell’s theory directly applies.27 The sentence that is supposed to be subject to the primary/secondary occurrence ambiguity is: S: I thought your yacht was larger than it is. Now in general, a statement of the form, L: α is larger than β is plausibly analyses into α is greater in size than β is , which plausibly analyses into α has a greater size than β has . This last, in turn, plausibly analyses into The size that α has is greater than the size that β has , or more simply: L′: The size of α is greater than the size of β. This analysis uncovers two definite-description occurrences that remain concealed in L’s surface form. Plugging this analysis of L into S, letting both α and β be ‘your yacht’, yields the following: S′: I thought the size of your yacht was greater than the size of your yacht. Contrary to appearances, this analysis of S does not remove all ambiguity. The ambiguity is evidently preserved intact; S′ is evidently ambiguous in the same way that S is. What is significant is that the ambiguity of S′ is evidently one of scope. The definite description ‘the size of your yacht’ occurs twice in S′. Russell should probably be seen as maintaining that the same description therefore implicitly occurs twice in S itself. The touchy yacht owner deliberately misinterprets the guest’s remark, precisely as Russell indicates, by giving both the left-hand (first) and right-hand (second) description occurrences in S′ their secondary-occurrence readings: I thought: that there is a size s that was uniquely a size of your yacht and a size s ′ that was also uniquely a size of your yacht and s was greater than s ′, or more simply, S2,2 : I thought: that a unique size of your yacht was greater than a unique size of your yacht. By contrast with S2,2 , and by contrast also with Russell’s careless stab at capturing the guest’s intent (and contrary to the thrust of Kripke’s remark),


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Page 354 giving the right-hand description occurrence its primary-occurrence reading while still giving the lefthand description occurrence its secondary-occurrence reading yields precisely what the guest did mean: There is a size r that is uniquely a size of your yacht and I thought: that there is a size s that was uniquely a size of your yacht and s was greater than r, or more simply, S2,1 : There is a size r that is a unique size of your yacht and I thought: that a unique size of your yacht was greater than r. This result should not be underappreciated. It appears to vindicate Russell on two counts: ( i) the deep structure of the original problem sentence S evidently involves a definite description, ‘the size of your yacht’, hidden in the surface form; and as a result ( ii ) Russell’s theory of descriptions, with its distinction of primary and secondary occurrence, is indeed evidently applicable to the case, roughly as he says. Kripke is correct that S does not involve the improper description, ‘the size that I thought your yacht was’, but everything Russell says about the example is correct once his sloppy ascription is replaced with a more careful formulation, like ‘The size of your yacht is such that I thought the size of your yacht was greater than that’.28 There remains a problem of a sort rather different from the problem that Kripke noticed, but one that genuinely calls Russell’s theory into question. According to that theory, the left-hand description occurrence in S′ is subject to the same two options of primary and secondary occurrence. Giving both description occurrences their primary-occurrence readings yields a result, S1,1 , analogous to S2,2 .29 Giving the left-hand description occurrence its primary-occurrence reading while giving the right-hand its secondary-occurrence reading yields yet another unintended interpretation, but this one is truly bizarre: S1,2 : There is a size r that is a unique size of your yacht and I thought: that r was greater than a unique size of your yacht. This says, in effect, that the guest thought the yacht was smaller than it is! The main problem with S1,2 is not merely that it is a misinterpretation of the guest’s intent (although it is certainly that). The main problem is not even merely that it imputes to the guest exactly the opposite of the guest’s intent (although it does that as well). The main problem with S1,2 is that it is not a possible reading of the original sentence S at all. Instead, it is perhaps a natural reading of a very different sentence: S″: Your yacht is larger than I thought it was.


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Page 355 Any theory entailing that S may legitimately be read as S″ is incorrect. It remains unclear whether Russell’s is such a theory. Insofar as Russell might have held that S may be read as S′, there is ample cause for worry on this score. Perhaps Russell may avoid the difficulty by analysing L differently in terms of ‘the size of your yacht’. More promising, perhaps some argument can be provided that whereas S2,1 and S2,2 are indeed possible readings of S—and hence the ‘misunderstanding’, precisely as Russell holds—S1,2 by contrast is precluded by considerations extraneous, and complementary, to the theory of descriptions. More plausible still, S2,2 may not be a legitimate reading of S any more than S1,2 is. The ‘was’ in the original sentence S (‘ was larger’) might be seen as somehow incorporating subjunctive mood, the ‘is’ (‘than it is’) as incorporating indicative mood. The contrasting moods may be taken as indicating that the left-hand occurrence of ‘the size of your yacht’ in S′ is to be a secondary occurrence (‘the size your yacht had ’), the right-hand a primary occurrence (‘the size your yacht has ’), thereby unequivocally yielding S2,1 . Instead, the owner misreads S as ‘I thought your yacht was larger than it was ’, yielding S2,2 . NOTES 1. I have had the essentials of the interpretations provided here since 1972, but many others have greatly influenced my thought on the topic, too many others to list here. No one influenced me more than David Kaplan. The Santa Barbarians Discussion Group patiently worked through my edited version of the crucial passage in 1997. I am indebted to them, especially C. Anthony Anderson, for their comments and our efforts. By not venturing to challenge the interpretation, the group shares some responsibility for the final product—how much responsibility depending upon the success or failure of the project. I am also grateful to Alan Berger, Saul Kripke, Teresa Robertson, the participants in my seminars at UCSB and UCLA during 1998–99, notably Roberta Ballarin, Stavroula Glezakos, David Kaplan, and D. Anthony Martin, and my audience at the McMaster University 2005 conference on ‘Russell vs. Meinong: 100 Years After On Denoting ‘, for their insightful comments, notably Matt Griffin. Finally, I am grateful to Oxford University Press for permission to incorporate portions of my article ‘On Designating’. 2. Previous discussions include the following, chronologically: Alonzo Church (1943:302); Ronald J. Butler (1954); John Searle (1958); Peter Geach (1959); Ronald Jager (1960); David Kaplan (1969); A. J. Ayer (1971:30–32); Chrystine E. Cassin (1971); Michael Dummett (1973:267–68; Herbert Hochberg (1976); Simon Blackburn and Alan Code (1978); Geach (1978); Blackburn and Code (1978); A. Manser (1985); Peter Hylton (1990:249–64); Pawel Turnau (1991); Michael Pakaluk (1993); Russell Wahl (1993); Michael Kremer (1994); Harold Noonan (1996); Gregory Landini (1998); William Demopoulos (1999); Gideon Makin (2000:22–45, 206–22); James Levine (2004). 3. Fregeans may substitute the word ‘sense’ wherever I use ‘content’. 4. Kaplan there calls indirect-quotation marks meaning-quotation marks. Indirect quotation quotes not expressions but their content.


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Page 356 5. That is, we wish to consider the relation between ‘the centre of mass of the Solar System’ and ‘ m the centre of mass of the Solar System m ’, between ‘the first line of Gray’s Elegy’ and ‘ m the first line of Gray’s Elegym ’, and so on. 6. It might have been more perspicuous for Russell to formulate his objection this way: We cannot succeed in both preserving the connection of content to designatum and allowing the content and the designatum to be one and the same. Moreover, we cannot even succeed in both preserving the connection of content to designatum and disallowing the content and the designatum from being one and the same unless the content cannot be got at except by means of determiner phrases. That is, if we preserve the connection whereby the designatum of a definite description is determined by the description’s content which is distinct from the designatum itself, then the content cannot be designated by means of a ‘genuine name in the strict, logical sense’. 7. This yields the awkward result that m αm = the content of m αm is true. I am here attributing to Russell a serious equivocation, resulting from his dual use of inverted commas both as direct–quotation marks and as indirect-quotation marks. He appears to believe that he has derived from the theory that definite descriptions have a content/designation distinction the consequence that in order to designate m the centre of mass of the Solar System m , rather than using the inappropriate phrase ‘the content of the centre of mass of the Solar System’ we must use ‘the content of m the centre of mass of the Solar System m ’ (which Russell fails to distinguish from the perfectly appropriate ‘the content of ‘the centre of mass of the Solar System’’), thus ascribing a content to a determining complex itself. As a criticism of the content/designation theory, or even as a neutral description, this is a red herring. Instead, the theory entails that one may designate m the centre of mass of the Solar System m using the functor ‘the content of’ in combination with ‘the centre of mass of the Solar System’ and direct quotation, not indirect. Russell has a stronger criticism to make of the theory, though his presentation is coloured somewhat by this red herring. 8. In the original text, Russell here uses ‘ C’ as a schematic letter standing in for a term designating a determining complex. The preceding two sentences should read: For example, let ‘ C’ [stand in for] ‘the determining complex occurring in the second of the above instances’. Then C = m the first line of Gray’s Elegym , and the determinatum of C = ‘The curfew tolls the knell of parting day’. I have reformulated this in the metalinguistic mode using ‘α’, quasi-quotation, and the predicate ‘is true’. 9. Pace Russell, his apparent observation that in order to designate the designatum of α we should use the determinatum of m αm rather than the determinatum of α , though correct, provides no support whatever for his apparent conclusion that in order to designate the content of α, rather than using the content of α we must use the content of m αm , which is in fact equally inappropriate. Instead we can designate α’s content by using the content of ‘α’ or m αm . Analogously, we can equally designate α’s designatum using the designatum of ‘α’ or α itself. 10. That is, as soon as we put a determining complex in a proposition, by using a sentence involving a singular term whose content is the complex, the proposition is about the complex’s determinatum. This generates what I call the Collapse . As Russell will argue below, this same phenomenon arises even when designating the complex by using the simple indirect quotation m αm . 11. Roughly, a proposition component represents an object x in a proposition p if p is about x in virtue of that component. This marks the first use by


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Page 357 Russell of his variable ‘ C’ as ranging over determining complexes rather than definite descriptions. Moreover, the quotation marks here are indirect-quasi-quotation marks. The quotation ‘ M the content of cM ’ designates the determining complex consisting of the content of the functor ‘the content of’ joined with the complex c . Let c be the particular determining complex, m the first line of Gray’s Elegym . When we attempt to form a proposition about it by using a sentence containing the indirect quotation ‘ m the first line of Gray’s Elegym ’ (Russell supposes that one way to do this on the theory he is criticizing is by means of the sentence ‘“The content of the first line of Gray’s Elegy” is intriguing’), if the quotation functions as a logically proper name of the determining complex, then the resulting proposition is that (the content of) the first line of Gray’s Elegy is intriguing, rather than a proposition about the intended determining complex itself. This is one particular form of the Collapse: In attempting to form a proposition about a determining complex c by using a sentence containing an indirect quotation m αm , where α is a definite description that expresses c , we generate a proposition not about c but about its determinatum. We might use the content of ‘α’ instead of the indirect quotation m αm , but having assimilated this to the content of m αm , or failing to distinguish the two, Russell believes he has just shown that use of such a phrase inevitably comes to grief, via the Collapse. In any event, the objective in ( D) was to form a singular proposition about a determining complex, not a proposition in which the target complex is represented as the content of this or that phrase. 12. In this sense, “the meaning cannot be got at except by means of determiner phrases”; it cannot be genuinely named , in the strict, logical sense. 13. For example, let us attempt to name a particular complex, say m the first line of Gray’s Elegym , in order to express a proposition about it. Any proposition in which the complex itself occurs is about the first line of Gray’s Elegy, i.e. the determinatum of the target complex rather than the complex itself. And any proposition that is about the complex itself will involve a second-level determining complex that determines the target complex. For example, the indirect quotation ‘ m the first line of Gray’s Elegym ’ itself must express a second-level determining complex, m m the first line of Gray’s Elegym m , as its content. Moreover, the target complex is not a constituent of the postulated second-level complex, as it is of m the content of the first line of Gray’s Elegym . The second-level complex cannot, for example, be of the form M the determining complex that bears relation R to cM , for some relation R and where c is our target complex, m the first line of Gray’s Elegym . For the Collapse occurs here just as it does with propositions; the complex just formed collapses into m the determining complex that bears R to the first line of Gray’s Elegym . If R is the relation of determining , then this second-level complex fails to determine a unique complex because there are too many complexes that bear this relation to the first line of Gray’s Elegy (infinitely many, in fact). And if R is the relation of identity, then this second-level complex fails to determine a unique complex because there are too few complexes that bear this relation to the first line of Gray’s Elegy (none, in fact). 14. We have no idea which determining complex m mDm m is of the infinitely many complexes that determine mDm . 15. The inextricable tangle does indeed seem to prove that the whole distinction of content and designation has been wrongly conceived … by Russell. On the theory that definite descriptions are singular terms, whereas the proposition is about the description’s designatum and not about the content, the content itself is relevant to the proposition’s identity, and especially to its distinctness from other propositions involving determining


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Page 358 complexes with the same determinata. This is the very point of the theory (and Russell knows it). 16. Blackburn and Code mention the Collapse only after presenting their rival interpretation, which does not rely on the Collapse (1978a: 76; crediting David Kaplan for showing them that the Collapse refutes the earlier theory of designating in Russell’s Principles ). In sharp contrast to my interpretation, they express uncertainty whether Russell is even aware of the Collapse by the time he writes ‘On Denoting’. As against the hypothesis that he was, they say that ‘although this is a problem as to how one refers to senses [contents], the obvious solution is not to attack Frege, but rather to insist that his three-entity view [distinguishing among an expression, its content, and its designatum] applies to all referring [designating] expressions’. There are at least five problems with this. First, Russell was explicitly aware of the Collapse already in the lengthy and rambling ‘On Fundamentals’, begun not two months prior to ‘On Denoting’ and posthumously published in The Collected Papers of Bertrand Russell (1994a: 363, 382, and passim). Indeed, some passages of ‘On Fundamentals’ appear virtually verbatim in the ‘Gray’s Elegy’ argument, which is in certain respects a streamlined version of the convoluted reasonings of the former. Second, whereas one might hope to solve the problem by insisting that any singular term that designates a content always has its own content distinct from its designatum, the same distinction does not have to be extended to all terms (including names for concrete objects) in order for the solution to work. Third, though Russell was aware of the possibility of a theory like the one Blackburn and Code call ‘the obvious solution’ (as is shown by a passage they quote from Principles ), he did not unequivocally endorse it. Fourth, on the contrary, a central purpose of ‘On Denoting’ is precisely to reject Frege’s ‘three-entity view’ in regard to all singular terms, and replace it with a two-entity view. Finally, and most importantly, the very point of paragraphs ( F ) and ( G) appears to be precisely that the very proposal in question utterly fails to solve the problem. 17. The expression ‘ m mDm m ’ may stand in for the iterated indirect quotation ‘ m m the centre of mass of the Solar System m m ’, which designates the content of the indirect quotation, ‘ m the centre of mass of the Solar System m ’. 18. This does not rule out that the content can also be “got at” by means of an indefinite description, even if it is deemed not a singular term. Since ST is neutral regarding indefinite descriptions, it is equally consistent with the view that definite and indefinite descriptions alike are singular terms. The latter view makes indefinite descriptions subject to the argument from the Collapse. On the Theory of Descriptions, by contrast, a definite description is analysed as a special kind of indefinite description, neither being a singular term. The interpretation of this stage of Russell’s argument is strongly supported by the fact that he also gives this argument in writings just prior to ‘On Denoting’ (posthumously published). Cf. his ‘On Fundamentals’ and ‘On Meaning and Denotation’, also in The Collected Papers of Bertrand Russell (1994b: 322). 19. Searle (1958:139–40) depicts Russell as arguing that in order for a term to designate, the designated object must, if we are not to “succumb to mysticism”, occur in the propositions expressed with the help of the designating term; but then the Collapse excludes the possibility of designating determining complexes. Searle complains that the whole point of Frege’s theory, which Russell is attacking, is to deny Russell’s premise. It is possible that Church construes the argument similarly. 20. In ‘ Über Sinn und Bedeutung ’ (1994:149), Frege identified the indirect sense of a sentence φ with the customary sense of the thought that φ , which phrase may be presumed synonymous with m φ m .


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Page 359 21. Carnap (1947:118–37, especially 129–33) may be profitably interpreted as rejecting singular propositions about individuals, while accepting that ungerade constructions (as occur in belief attributions, modal claims, etc.) express singular propositions about the contents of their complement clauses. Cf. Dummett (1973:267–68) and Parsons (1981). 22. Church disagrees with Frege on some details, and as I argue in (Salmon 1993), he may have been inconsistent regarding the issue of the hierarchy. 23. Burge argues (1979:271–72), as follows, specifically that Frege’s theory of Sinn and Bedeutung is committed to hierarchies of sense, when coupled with Church’s methodology of eliminating ambiguityproducing devices (like ‘believes that’) that shift expressions in their scope into ungerade mode in favour of fully extensional operators applied to univocal names of senses: Suppose for a reductio that the true proposition that Bela believes that Opus 132 is a masterpiece does not contain a second-level complex that determines the proposition that Opus 132 is a masterpiece, and that instead the latter proposition represents itself in the former proposition. In accordance with Church’s methodology, we introduce an artificial extensional two-place operator ‘Believes’ for the binary relation of belief (between a believer and the object believed), so that ‘Bela Believes ( m Opus 132 is a masterpiece m )’ expresses that Bela believes that Opus 132 is a masterpiece. Then according to Frege’s theory, the quasi-artificial expression E, ‘Bela Believes (Opus 132 is a masterpiece)’, expresses the bizarre proposition that Bela believes a particular truth-value —to wit, the truth-value that is truth if Opus 132 is a masterpiece, and is falsity otherwise. But by our reductio hypothesis, E expresses a content consisting of the very components of the proposition that Bela believes that Opus 132 is a masterpiece, composed the very same way. By Compositionality, E therefore expresses our target proposition. (This collapse is obtained, in effect, from the reductio hypothesis by Synonymous Interchange.) On Frege’s extensional semantics, substitution in E of any sentence materially equivalent with ‘Opus 132 is a masterpiece’ preserves truth-value. Since E expresses that Bela believes that Opus 132 is a masterpiece, it follows on Frege’s theory that if Bela believes that Opus 132 is a masterpiece, he believes every materially equivalent proposition, which is absurd. Striking evidence that the central thrust of the ‘Gray’s Elegy’ argument has been lost on Russell’s readers is provided by Burge’s remark (280, n8) that to his knowledge, the argument presented above was nowhere explicitly stated before. Burge’s argument employs a sentence in place of a definite description, but this difference from Russell’s examples is completely inessential to the general argument. Burge also frames his argument in terms of a Fregean conception whereby an artificial notation should be used to avoid natural-language ambiguities produced by ungerade devices (e.g., ‘Believes’ in place of ‘believes that’). This introduces additional complexity, also inessential to the general point and leading to an unnecessarily restricted conclusion. Burge’s argument may be strengthened as follows: Suppose for a reductio that the true proposition that m the centre of mass of the Solar System m is a sense does not contain a second-level complex that determines m the centre of mass of the Solar System m , and that instead the complex m the centre of mass of the Solar System m represents itself in the proposition. The English sentence S, ‘The centre of mass of the Solar System is a sense’—which contains no artificial notation—then expresses a proposition consisting of the very components of the proposition that m the centre of mass of the Solar System m is a sense, and composed the very same way. By Compositionality, S therefore expresses our target proposition. But this conflicts with the fact that S is false.


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Page 360 24. A notable exception is Kremer (1994:287–88). Though my analysis of the argument differs from his, I have benefited from his meticulous probing and careful analysis of the passage. 25. The argument just given on Russell’s behalf purports to prove that, in Frege’s terminology, the sense of an indirect quotation is not an effectively computable function of the customary senses of the expressions within the indirect quotes. Frege concedes that the sense of a compound expression is not always composed of the customary senses of the component expressions. Frege would insist, however, that indirect-quotation marks do not violate Compositionality, or even Strong Compositionality as he intends these principles, since an expression does not have its customary sense when occurring within indirect-quotation marks and instead expresses its indirect sense, which does uniquely fix the sense of the indirect quotation. He says something analogous in connection with direct quotation. Direct quotations of customary synonyms are not themselves synonyms. 26. [Added after original submission of this article.] Kripke’s criticism has since been published (2005: see 1021–23). I take this opportunity to correct Kripke’s characterization there (1022) of our communication concerning Russell’s example. In my earlier discussion with Kripke I emphasized a distinction in semantic content that I draw, and of which Kripke is dubious, between the binary-relational predication ‘ a is larger than a ’ and the monadic-predicational ‘ a is a thing larger than itself’—the latter symbolized as ‘(λ x)[ x is larger than x]( a )’. I used the distinction not to solve the problem Kripke noticed in Russell’s discussion of his example, but rather to support my contention (which Kripke does not accept) that it is possible for one to believe concerning a particular yacht y, that y is larger than y is, while not thereby believing that y is self-larger (i.e., a thing x larger than itself). Cf. my ‘Reflexivity’ (1986) and my ‘Reflections on Reflexivity’ (1992). I was aware that this distinction (even if it is legitimate, as I maintain) does not solve the problem Kripke had noticed. I have known the corrected “purely Russellian” analysis, and have so interpreted Russell’s intended treatment of the example, since I first studied ‘On Denoting’ in 1971–72 (in undergraduate courses given by Alonzo Church, David Kaplan, Kripke and others). I had given the example essentially the same Russellian analysis on first reading ‘On Denoting’. Each of Kripke’s explicit misgivings (1025, n45) concerning my former proposal can be met. In particular, on my proposal, although a formula φβ and its lambda-convert (λα)[φα](β) differ in semantic content, the two remain coextensional and indeed logically equivalent (at least in the absence of nonextensional devices). The distinction in content in no way undermines the observation that there is always a fact of the matter concerning whether x = x (just as there is a fact concerning whether x is self-identical—the two matters being equivalent), any more than it undermines the observation that it is a necessary truth that x = x. Furthermore, Kripke’s claim that “Church, inventor of the lambda notation, did not intend any such distinction” in semantic content between a formula φβ and its lambda-convert (λα)[φα](β) (as between ‘a is larger than a ’ and ‘(λ x)[ x is larger than x]( a )’) is historically incorrect. On Church’s Alternative (0), which he explicitly preferred over Alternatives (1) and (2) as an explication of having the same sense , such lambda converts are, as Church recognized, although logically equivalent, not synonymous—just as the mathematical expressions ‘3!’ (alternatively, ‘(λ x)[ x!](3)’) and ‘6’ are codesignative but not synonymous. I am in agreement with Church in this. (φ-converts are regarded as synonymous on the other two alternatives.) Cf.


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Page 361 Church (1993) and Anderson (2001:421–22). (Thanks to Anderson for discussion and bibliographical references.) 27. David Kaplan and Terence Parsons have noted related difficulties in Russell’s discussion of the example. I am grateful to Kripke, Kaplan, and Parsons for discussion. Kripke is now persuaded, whereas I believe Parsons remains unconvinced, that Russell’s distinction of primary and secondary occurrence, properly applied, nevertheless provides an insightful diagnosis of the ambiguity. See the following note concerning Kaplan. Russell correctly observes in the same paragraph of ‘On Denoting’ that the primaryoccurrence reading of ‘George IV wondered whether Scott is the author of Waverley ’ is true if King George glimpses Scott at a distance and asks ‘Is that Scott?’. Russell was likely assuming, at least for the purposes of illustration, a commonsensical epistemology on which visual perception of an object is sufficient to enable one to apprehend singular propositions about it, and thus to bear de re propositional attitudes towards it. However, Russell’s observation thus seems incompatible with his claim that ‘an interest in the [reflexive] law of identity can hardly be attributed to the first gentleman of Europe’. Kaplan, Kripke, and others have independently also noticed this flaw in Russell’s presentation. (See Kripke, 2005:1023–24.) Russell’s observation can be made consistently with Russell’s insistence that King George had no interest in the reflexivity of identity by distinguishing, as I do, the singular proposition about Scott that he is Scott from the singular proposition about Scott that he is self-identical (a thing identical with itself), so that one can in fact wonder about Scott whether he is him without thereby wondering whether he is self-identical. See the preceding note. Kripke argues (1024–25) that this distinction was not available to Russell given his logical apparatus. I never asserted that Russell’s account of sentences involving λ-abstraction is compatible with my own. I believe, however, that Russell could have distinguished (even if not through his apparatus for propositional-functional abstraction) between the singular propositions about Scott that he is him and that he is selfidentical (a thing identical with itself). He might also have interpreted the reflexivity of identity as not involving the property of being self-identical. In any event, King George’s wondering about Scott whether he is him (as glimpsed from a distance) should not be misrepresented as a concern about the reflexivity of identity. King George knows about Scott all the while (even while glimpsing him from a distance) both that he is him and that he is, as with everything else, self-identical. 28. Kaplan, in (1973) observes, ‘The yacht owner’s guest who is reported by Russell to have become entangled in ‘I thought that your yacht was longer than it is’ should have said, ‘Look, let’s call the length of your yacht ‘a russell’. What I was trying to say is that I thought that your yacht was longer than a russell.’ If the result of such a dubbing were the introduction of ‘russell’ as a mere abbreviation for ‘the length of your yacht’, the whole performance would have been in vain’ (501). The measurement term ‘russell’ in Kaplan’s disambiguation of S serves much the same purpose as the anaphoric pronoun in ‘The size of your yacht is such that I thought the size of your yacht was greater than that’. So does the variable ‘ r’ in S2,1 . This suggests that Kaplan had in mind the same correction proposed here. 29. A potential difference between S1,1 and S2,2 is that one might easily come to believe of a single thing x, de re , that x is greater than x is. I take it to be clear, however, that the guest did not believe this of the yacht’s size. See n26 above.


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Page 362 REFERENCES Anderson, C. A. (2001) ‘Alternative (1*): A Criterion of Identity for Intensional Entities’, in Anderson and M. Zeleny (eds), Logic, Meaning and Computation: Essays in Memory of Alonzo Church , Boston: Kluwer: 395–427. Ayer, A. J. (1971) Russell and Moore: The Analytic Heritage, London: Macmillan. Blackburn, S. and Code, A. (1978a) ‘The Power of Russell’s Criticism of Frege: On Denoting pp. 48–50’, Analysis 38: 65–77. ——. (1978b) ‘Reply to Geach’, Analysis 38: 206–7. Burge, T. (1979) ‘Frege and the Hierarchy’, Synthese 40: 265–81. Butler, R. J. (1954) ‘The Scaffolding of Russell’s Theory of Descriptions’, The Philosophical Review 63: 350–64. Carnap, R. (1947) Meaning and Necessity , Chicago, IL: University of Chicago Press (reprinted 1970). Cassin, C. E. (1971) ‘Russell’s Discussion of Meaning and Denotation: A Re-examination’, in E. D. Klemke (ed.), Essays on Bertrand Russell, Chicago/London: University of Illinois Press: 256–72. Church, A. (1943) Review of Carnap’s Introduction to Semantics, The Philosophical Review 52: 298–304. ——. (1993) ‘A Revised Formulation of the Logic of Sense and Denotation, Alternative (1)’, Noûs , 27: 141–57. Demopoulos, W. (1999) ‘On the Theory of Meaning of On Denoting ‘, Noûs 33: 439–58. Dummett, M. (1973) Frege: The Philosophy of Language, London: Duckworth. Frege, G. (1994) ‘ Über Sinn und Bedeutung ’ (translated as ‘On Sense and Reference’), in Robert M. Harnish, (ed.), Basic Topics in the Philosophy of Language, Boston, MA: Prentice-Hall: 42–60. Geach, P. (1959) ‘Russell on Meaning and Denotation’, Analysis 19: 69–72. ——. (1978) ‘Russell on Denoting’, Analysis 38: 204–5. Hochberg, H. (1976) ‘Russell’s Attack on Frege’s Theory of Meaning’, Philosophica 18: 9–34. Hylton, P. (1990) Russell, Idealism and the Emergence of Analytic Philosophy , New York/Oxford: Oxford University Press. Jager, R. (1960) ‘Russell’s Denoting Complex’, Analysis 20: 53–62. Kaplan, D. (1969) Reviews of Butler, Searle, Geach, Jager and Garver, Journal of Symbolic Logic 34, 1: 142–45. ——. (1971) ‘Quantifying In’, in L. Linsky (ed.), Reference and Modality, New York/Oxford: Oxford University Press: 112–44. ——. (1973) ‘Bob and Carol and Ted and Alice’, in K. J. J. Hintikka, J. M. E. Moravcsik, and P. Suppes (eds), Approaches to Natural Language, Boston: Reidel: 490–518. Kremer, M. (1994) ‘The Argument of On Denoting ‘, The Philosophical Review 103, 2: 249–97. Kripke, S. (2005) ‘Russell’s Notion of Scope’, Mind 114, 456: 1005–37. Landini, G. (1998) ’ On Denoting Against Denoting’, Russell, n.s. 18, 1: 43–80. Levine, J. (2004) ‘On the Gray’s Elegy Argument and its Bearing on Frege’s Theory of Sense’, Philosophy and Phenomenological Research 69: 251–95. Makin, G. (2000) The Metaphysicians of Meaning , London: Routledge. Manser, A. (1985) ‘Russell’s Criticism of Frege’, Philosophical Investigations 8: 269–87. Noonan, H. (1996) ‘The Gray’s Elegy Argument—and Others’, in R. Monk and A. Palmer (eds), Bertrand Russell and the Origins of Analytic Philosophy , Bristol: Thoemmes Press: 65–102.


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Page 363 Pakaluk, M. (1993) ‘The Interpretation of Russell’s Gray’s Elegy Argument’, in A. D. Irvine and G. A. Wedeking (eds), Russell and Analytic Philosophy , Toronto: University of Toronto Press: 37–65. Parsons, T. (1981) ‘Frege’s Hierarchies of Indirect Senses and the Paradox of Analysis’, in P. French, T. Uehling and H. Wettstein (eds), Midwest Studies in Philosophy , Minneapolis: University of Minnesota Press: 37–58. Russell, B. (1905) ‘On Denoting’, Mind 14: 479–93. ——. (1994a) ‘On Fundamentals’, in A. Urquhart (ed.), The Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–1905, London: Routledge: 359–413. ——. (1994b) ‘On Meaning and Denotation’, in A. Urquhart (ed.), The Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–1905, London: Routledge: 314–58. Salmon, N. (1986) ‘Reflexivity’, Notre Dame Journal of Formal Logic 27, 3: 401–29. Reprinted in N. Salmon and S. Soames (eds), Propositions and Attitudes, Oxford Readings in Philosophy, Oxford: Oxford University Press, 1988: 240–74. Also reprinted in Salmon, Content, Cognition, and Communication: Philosophical Papers II, Oxford: Oxford University Press, 2007. ——. (1992) ‘Reflections on Reflexivity’, Linguistics and Philosophy 15, 1: 53–63. Reprinted in Salmon, Content, Cognition, and Communication: Philosophical Papers II, Oxford: Oxford University Press, 2007. ——. (1993) ‘A Problem in the Frege-Church Theory of Sense and Denotation’, Noûs 27, 2: 158–66. ——. (2005) ‘On Designating’, Mind 114, 456: 1069–1133. Searle, J. (1958) ‘Russell’s Objections to Frege’s Theory of Sense and Reference’, Analysis 18: 137–43. Turnau, P. (1991) ‘Russell’s Argument against Frege’s Sense-Reference Distinction’, Russell, n.s. 2: 52– 66. Wahl, R. (1993) ‘Russell’s Theory of Meaning and Denotation and On Denoting’, Journal of the History of Philosophy 31: 71–94.


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