Abstract
I discuss Stalnaker’s views on modality. In particular, his views on actualism, anti-essentialism, counterpart theory, and the Barcan formulas.
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Notes
Published by Oxford University Press, 2003. All quotes, unless otherwise noted, are to this work.
Adams, Kripke, and Plantinga are also actualists; Lewis is a possibilist. Some actualists, most notably Kit Fine [see, in particular, his (Fine, 1985)], also refuse to identify possible worlds with sets of propositions, although typically on different grounds than Stalnaker’s.
I shall not discuss two papers from those sections: ‘Vague identity’, originally published in 1988, and ‘Varieties of supervenience’, originally published in 1996. This is solely due to unity of topic considerations. Both papers are rich and full of theses and arguments worth discussion.
Or at least it is no more problematic than the distinction between necessity and contingency itself, as applied to proposition. Quine was, of course, skeptical of any form of modality. But he thought that there are special problems with QML. Indeed, in (Quine, 1947), he grants, even if only for the sake of argument, that we can make sense of a necessity applying to a closed sentence and argues that it is non-sense when applied to an open sentence. In his (Quine, 1955), he claims that it is the third grade, as opposed to the second grade, of modal involvement that is the problematic. Quine also claims (Quine, 1980), p. 156, that introducing a modal operators is useless if they cannot apply to open sentences as they otherwise do not increase expressive power. He in turn thought this because he took for granted that necessity had to be explicated in terms of analyticity and hence that if modal operators only applied to closed sentences one could replace ‘□p’ with ‘‘p’ is analytic’ without lose of expressive power.
Marcus distinguishes a weak and strong form of discriminating essentialism. (Marcus doesn’t use the title ‘discriminating essentialism’, which is, I think, my own.) According to the weak form, some objects necessarily have properties that others don’t have necessarily, whereas according to the strong form, some objects necessarily have properties that other objects have but don’t have necessarily. This distinction won’t play a role in my discussion.
I think that there are other anti-essentialist strategies worthy of pursuit as well. One of them is based on the first few sections of (Kaplan, 1969), where Kaplan suggests that we posit an additional, hidden quantifier that ranges over individual-concepts in the characteristic formulae of QML. (He makes a similar claim, which is developed in more detail, with respect to propositional attitude verbs.) So, for example, ∃x□Fx is expanded to ∃x∃c[c Δx & □Fc], where ‘c’ takes an individual-concept as value and ‘Δ’ is Church’s designation relation between an individual-concept and an individual. Kaplan noted that the view entailed that every property an individual has it necessarily has and every property that any individual could have every individual possibly could have, given a sufficiently loose conception of individual-concepts as any condition an individual uniquely satisfies. Kaplan found this unintuitive and so went on to seek further constrains, which he only filled out for the case of belief. (He claimed that a de re belief attribution is true only if the agent has a vivid name of the object of her belief under which she believes what she does.) I think that this is a mistake; an anti-essentialist should embrace this cheapening of de re modal properties. Any further constrains will have an essentialist backing. (One may perhaps take the sting out of this by making the further constraints be contextually determined.) I discuss this at greater length in (Nelson, ms1). Kaplan abandoned this view and developed a very different response to Quine in (Kaplan, 1986).
‘Anti-essentialism’, originally published in 1979. Stalnaker notes on p. 85n11 that it was written as a response to (Parsons, 1969).
They are not entirely without reason in making this exception. Ruth Marcus has stressed that if one accepts the standard necessitation axiom—which is, after all, an axiom of even the weakest modal logic K—and the fact that MN = MN is a theorem of standard FOL with identity, then we’re stuck with its being the case that MN is necessarily identical with MN. In response (on behalf of the anti-essentialist) I say: So much the worse for such a generous necessitation axiom. I’ll return to this below.
Thanks to Leslie Wolf for suggesting to me this vivid way of thinking of anti-essentialism.
Stalnaker calls the view “bare particular anti-essentialism.” I think that the title is apt. If for every quality F and every individual i, it is possible that i is F and it is possible that i is not-F, then, modulo some plausible even if not incontestable assumptions, i better be independent of every quality and hence better be bare.
Now this does not, I hasten to add, entail that I might not have been self-identical. I shall describe below how to keep that entailment from flowing.
Stalnaker writes: “Even if there are possible worlds in which [Babe] Ruth is a kangaroo, a tricyle, or a billiard ball, even if he has no essential nature which constrains the qualitative characteristics that he might have had, still, in all possible worlds he will have the [referential] properties mentioned above, since these properties are defined so that Babe Ruth could not lack them without lacking his own identity” (p. 73). I agree that Ruth couldn’t lack the relevant referential properties without lacking his own identity, but why think that Ruth is so tied to his own identity that he couldn’t lack that? Why would Ruth’s metaphysical nature not constrain the qualitative characteristics he could take on but would constrain the referential properties he could take on? It seems to me that an anti-essentialist ought not see a difference here.
I should make explicit that I am not claiming that there is no room for a view that denies that individuals have substantive natures—for example, denying that Ruth’s nature includes personhood which excludes being a kangaroo—and yet accepting that individuals necessarily have some referential properties. Such a view is clearly consistent. I am rather suggesting that such a view is at odds with (what seems to me to be) the motivating spirit of anti-essentialism; namely, the idea that modal predications don’t flow from nature as it is independent of our conceptualization.
If we are interested in standard objectual quantification, we’ll need to make sense of this to make sense of quantifying in. And it is surely needed to make sense of cross-modal anaphora, like ‘Jason is such that it is possible that he is honest’.
Fine distinguishes object-blind and object-sensitive conceptions of logical form in (Fine, 1989). I rely heavily upon his excellent discussion in developing indiscriminate essentialism. Fine’s purposes are different from mine. Fine was interested in a form of logical necessity. Furthermore, as I noted above, Fine goes on to develop an object-sensitive conception of logical form and argue that it too is devoid of any problematic (from the anti-essentialist’s perspective) form of essentialism.
Indeed, I think that many have thought that they must accept the necessity of identity, and thus at least some referential properties as essences, despite their attraction to anti-essentialism in general, precisely because they think that denying the necessity of identity requires denying the necessity of self-identity as well. This, as I show, is a mistake.
The proponent of the object-blind conception will also have to distinguish between \(\square (x = y) \) and \(\square (x = x). \) Even under an assignment of the same object to both variables ‘x’ and ‘y’, the first condition is false under that assignment while the second is true under every assignment. Again, this is because the universal closure of the (unmodalized version of the) first is not necessary whereas the universal closure of the (unmodalized version of the) second is necessarily true (i.e., \(\square \forall x\forall y(x = y) \) is false and \(\square \forall x(x = x) \) is true). If one is not entitled to look at the relative identities of the objects that constitute the assignment of values to variables, as a proponent of the object-blind conception insists, then it shouldn’t be surprising that the first condition fails even when we assign the same object as value to both variables. To valuate the first condition, we need to assign either two objects or one object twice over; that is, we require a pair. And, given the object-blind conception, there is no saying whether it’s an identity pair or a non-identity pair that has been assigned. But valuating the second condition requires only a singleton, so there is no worry of “their” relative identity. I have again followed (Fine, 1989) in making these points.
That sentence is true only if, necessarily, there is exactly one object and, what’s more, that object is MN.
We don’t want all intrinsic properties to be legitimate values for ‘F’ in the above schema. On any reasonably understanding of the nebulous notion of an intrinsic property, being identical with a is an intrinsic property of A. But this is just the kind of property we want to exclude. So, not all predicates that express intrinsic properties are legitimate substitution instances for ‘F’. Such a property isn’t, it would seem, purely qualitative; or at least, it isn’t purely qualitative if the identity of indiscernibles is false. So, such properties are excluded because they are non-qualitative; being intrinsic isn’t doing any real work. So, it seems to me that Stalnaker is really aiming at a characterization of qualitative properties.
‘Counterparts and identity’, originally published in 1986.
Lewis also argues for CPT on the grounds that it best solves the problem of accidental intrinsics. (See (Lewis, 1986), chapter 4.) The problem mirrors another problem that has received a lot of attention; namely, the problem of temporary intrinsics, which Lewis employs to argue that objects persist through time and persist through change not by enduring, or being wholly present at more than one time, but rather by perduring, or having different temporal parts at different times. I think that neither argument is very persuasive, but as Stalnaker relies on neither, here is not the place to discuss them.
See (Gibbard, 1975).
In this paper I shall accept that these cases motivate contingent identity. But I doubt this. In my view, the best account of the relation between a composite and its matter is one involving non-identity. I try to defend this view against its most pressing criticism—the so-called grounding problem—in (Nelson, ms2). With respect to Chisholm’s paradox, Salmon (in (Salmon, 1986, 1989)) argues that the best solution involves claiming that the accessibility relation between possible worlds is non-transitive and hence what is in fact possible (or what is possible from the perspective of the actual world) is different from what would have been possible had things been different in certain ways (or what is possible from the perspective of worlds that are possible from the perspective of the actual world). I agree.
Stalnaker discusses four sets of cases as motivation for contingent identity. See pp. 115–117.
Stalnaker describes his view thus: “The main thesis that I will, somewhat tentatively, suggest is that the actualist can coherently combine a belief in primitive thisness and genuine identity across possible worlds with a version of counterpart theory that permits one to make sense of contingent identity and distinctness—that is, of the claim that one thing might have been two, and that distinct things might have been identical” (p. 112). Stalnaker appeals to Adams’s notion of primitive thisness. (Stalnaker also uses the title ‘haecceitism’ for the view in question.) Adams, in (Adams, 1979), argued that there are primitive identities by arguing against the identity of indiscernibles (PII), according to which, for all objects x,y, if, for all qualitative properties F, x has F iff y has F, then x = y. Following and expanding on Max Black’s (Black, 1952) case of a possible world consisting of nothing but two qualitatively indiscernible but distinct spheres, Adams argued that the distinctness of objects is fundamental and is irreducible to qualitative similarity and difference. Anti-haecceitism is thus the thesis that identity and distinctness is reducible to qualitative similarity and difference.
Stalnaker sometimes seems to conflate the debate between haecceitists and anti-haecceitists with another, distinct debate between (bare) particular theorists and bundle theorists. (“The opposite doctrine—antihaecceitism—is the doctrine I cited in section 2 above as the second motivation for counterpart theory,” and, looking back to the second motivation from section 2, we see that Stalnaker has in mind here the bundle theory (p. 123). Similarily, in characterizing the bundle theory in section 2 Stalnaker writes: “According to bundle theorists, there is no thisness or individual essence underlying the qualities and relations” (p. 115).) But the two debates are independent.
First, what’s at issue in the debate between (bare) particular theorists and bundle theorists? I think two things. First is the existence (or lack of existence) of featureless substrata in which properties inhere; (bare) particular theorists are said to accept and bundle theorists to deny the existence of substrata. Second is the fundamentality of particularity; (bare) particular theorists are said to accept and bundle theorists to deny that particularity is a fundamental category. Very crudely, bundle theorists maintain that an individual is nothing over and above the qualities it instantiates; there is no “unclothed” substrata, itself featureless, in which qualities inhere. Individuals just are, bundle theorists say, bundles of properties. (I think that these two issues are distinct and also can be pulled apart. Indeed, my own view is that particularity is fundamental but there is no such thing as a featureless substratum. I won’t, however, discuss this here.)
The standard view is that bundle theory entails anti-haecceitism, in the sense that identity and diversity of individuals is reducible to qualitative similarity and difference. (See, for example, (Armstrong, 1989), p. 198.) It is probably this assumption that Stalnaker is relying on in saying that bundle theory is the “opposite doctrine” of haecceitism. But, I shall argue, this standard assumption is wrong.
Suppose we agree that Max Black universes are possible. Then anti-haecceitism (as I’ve defined it above) is false. Is bundle theory too? No. There are two options. First, the bundle theorist could continue to individuate objects in terms of the properties in the bundle but claim that in addition to purely qualitative properties there are also primitive identity properties. So, although sphere1 and sphere2 in the Max Black universe have all the same qualities and hence the bundle of which they consist is the same when one considers only qualities, there are in addition the non-qualitative property of being sphere1 which is in the bundle of which sphere1 consists but not in the bundle of which sphere2 consists and similarly the non-qualitative property of being sphere2 which is in the bundle of which sphere2 consists but not in the bundle of which sphere1 consists. Now these identity properties are not individual involving—remember, the bundle theorist insists that individuals are not ontologically prior to the properties they bear. Rather, such identity properties must be basic. (Such a conception of identity properties is employed by Plantinga in (Plantinga, 1974, 1976, 1983).) Nothing in this view runs contrary to bundle theory, but it entails haecceitism. Alternatively, the bundle theorist attracted (as we all are) by the possibility of a Black universe might give up individuating individuals in terms of the properties they bear and say that there are two brutely distinct bundles of the same properties in the Black universe. According to this view, there are only universals (and bundles thereof) and furthermore, in opposition to the view immediately above, all universals are qualitative. But the same set of qualities can and, in the Max Black world do, combine together to be two rather than one. Such a theorists will insist that there are brutely distinct bundles of the same qualities not because they inhere in brutely distinct individuals, as Adams and his followers would, but simply because the bundles are brutely distinct. Again, we have a version of bundle theory—particularity is not fundamental—that entails haecceitism.
I’ve above described two ways of being a bundle theorist and accepting haecceitism. I conclude that Stalnaker’s claim that haecceitism’s “opposite doctrine” is the bundle theory is false; anti-haecceitism is just what you would expect—namely, the negation of haecceitism and thus the thesis that the identity and diversity of individuals is reducible to qualitative similarity and distinctness.
(O’Leary-)Hawthorne (1995) argues for a distinct claim from that I have argued above. Hawthorne argues that, despite appearances, bundle theory and PII are both compatible with the possibility of Max Black universes. This is because he takes a Max Black universe to be “a world consisting solely of two indiscernible spheres at some distance to each other” (ibid., p. 191). He then argues that a bundle theorist can accept that a single bundle of qualities can be bi-located—that is, one bundle of qualities can be fully located at different places at the same time—and so can accept that there are indistinguishable spheres at some distance. (He claims that the claim of multiplicity in the description of the universe is not justified.) Even if he is correct (but see (Hughes, 1999) and (Zimmerman, 1997) for arguments that he isn’t), notice that Hawthorne’s thesis is much weaker than that for which I argued above. Hawthorne only argues that a bundle theorist can accept the possibility of a Max Black universe under one description; nothing Hawthorne says suggests that bundle theory is compatible with haecceitism and the rejection of PII. But this stronger thesis is what I have argued.
Stalnaker writes: “Our defense of actualist counterpart theory and the coherence of contingent identity requires, first, a distinction between possible individuals themselves and their essences or representatives in the domains of the various possible worlds... [This is motivated by actualism s]ince, according to actualism, there are no merely possible individuals, [and hence] we need something other than possible individuals to represent the possibility that there be things other than those that actually exist” (p. 126). Let’s grant for now that admitting the possible existence of things that don’t actually exist commits the actualist to representers in the various domains of other worlds. (I question this in the following section.) That doesn’t motivate the claim that Stalnaker needs in defending CPT. Stalnaker needs to motivate the claim that actually existing objects have surrogates in the various possible worlds that do the work of representing the ways they could have been but aren’t. Even if Stalnaker is right that an actualists needs representers for non-actual objects, that in no way suggests what he needs; namely, that actually existing objects also need representers in the various worlds. Now, this is not to say, I want to stress, that there is any tension in an actualist following Stalnaker and answering the above two questions differently; it is rather just to say that Stalnaker has done little to show that it flows naturally from actualism itself.
Michael Della Rocca pointed out to me that Stalnaker may allow us to say, for example, “Lumpl is Goliath, but there is another world such that from the perspective of that world a ≠ b.” Perhaps that suffices. I’m not sure. But we can at least say this: There are ways of being an actualist and accepting the more canonical form of contingent identity, as I describe in the text below.
One must embrace multiple CPT, according to which one object can have multiple, distinct counterparts at a single world, to account for contingent identity.
It sometimes seems that Stalnaker is thinking that haeceitism, defined as the thesis that the identity and diversity of individuals is irreducible to qualitative similarity and diversity, pushes one to accept genuine transworld identity. (This is also suggested by the quote from (Kaplan, 1975) Stalnaker cites on p. 123.) This, however, is a mistake. Haecceitism is true, remember, just in case it is possible for there to be distinct objects that are qualitatively indiscernible. One could accept this and still think that, say, my non-actual possibilities are represented by objects strictly distinct from me having different properties in different worlds and so the denial of genuine transworld identity relations.
That is, contingent identity, CPT, and genuine transworld identity, precisely because a thoroughgoing version of CPT is incompatible with genuine transworld identity.
Thanks to Michael Della Rocca for very helpful discussion of this view.
See (Marcus, 1946).
The source of this standard assessment is (Kripke, 1963). Kripke notes that BF is valid just in case one world w 1 is accessible to a world w 2 only if the domain of w 2 is a subset of the domain of w 1 ; that is, only if everything in w 2 is in w 1 . Kripke then developed variable world domains semantics, introduced a more complex proof procedure for variable world domains semantics, and proved completeness and soundness. Dissenters from the standard opinion (i.e., defenders of the validity of BF and CBF) include (Linsky & Zalta, 1994), (Parsons, 1995), and (Williamson, 1998, 1999, 2000, 2001). I shall briefly discuss Linsky and Zalta and Williamson below. Parsons appeals to his infamous doctrine of nonexistent objects to try to disarm the sting of CBF, claiming that there actually are (contingently) nonexistent talking donkeys and I might have been nonexistent, for example.
Something that is distinct from every actually existing thing? Well, if we have the necessity of distinctness, yes. From BF we get that there is something that is possibly distinct from every actually existing thing. But, if the necessity of distinctness is true, then for all x, y, if x ≠ y, then necessarily x ≠ y. So, that something that is possibly distinct from every actually existing thing is necessarily distinct from every actually existing thing and hence is distinct from every actually existing thing.
Linsky and Zalta (1994), p. 436), following (Marcus, 1986), note this too. Linsky and Zalta object to the strategy on the grounds that it conflicts with essentialism. It seems to me that they are not hardly in a position to level this complaint, as they themselves are anti-essentialists about the property being concrete. It seems less plausible to be an anti-essentialist about the property being concrete—that is, to claim that an object is in fact, say, abstract but might have been concrete—than to be an anti-essentialist about run of the mill properties like being a person or even embrace contingent identities.
Let ‘F’ in the above schema be ∃y(x = y). Then, as □∀x∃y(x = y), CBF entails ∀x□∃y(x = y), which is true only if everything that exists necessarily exists.
Again, the standard view here originates from (Kripke, 1963). Kripke notes that CBF is valid just in case world w 1 is accessible to a world w 2 only if the domain of w 1 is a subset of the domain of w 2 ; that is, only if everything in w 1 is in w 2. Kripke’s variable world domain semantics once again provides for countermodels to the formula.
There are several other attempts to in the literature to make both CBF and NE consistent with actualism. First, one might appeal to Plantinga’s conception of individual essences to try to argue that even though everything that exists necessarily exists, this doesn’t entail that every individual essence is instantiated in every possible world. In every world there are all of the individual essences that could be instantiated, but it is not the case that they are all instantiated in every world. This fact—the fact that there are worlds in which the individual essences that are in fact instantiated are not instantiated—accounts, one might claim, for our (admittedly wrong) intuition that NE is false. (I have greatly benefited from discussions with Sam Newlands on Plantinga on necessary existence. Plantinga’s conception of individual essences has come under attack, in particular in (Adams, 1981) and (Fine, 1985). In effect, both argue (I think rightly) that it doesn’t make sense to speak of individual properties that are ontologically prior to any individuals; individual properties are individual-involving and hence are constructed from, and hence ontologically posterior to, the individuals from which they are constructed. Plantinga discusses these arguments in (Plantinga, 1983).) Second, one might follow (Linsky & Zalta, 1994), briefly discussed above, and insist that every concrete particular that could be actually exists, but many of them are (in the actual world) abstract. Finally, one might follow (Williamson, 2001) and claim that there in fact are beings that being is purely modal; there in fact are possibly physical objects, where that irreducibly gives the kind they belong to. (See, in particular, p. 247.) Williamson writes: “On the view defended here, an object is essentially a locus of potential. How far it actualizes its potential may be a radically contingent matter. But the existence of that object with that potential is wholly noncontingent” (ibid., pp. 250–251). So, it would seem, Williamson’s idea is that we intuitively reject NE because we (rightly) see that the extent to which an object actualizes its potential is radically contingent, but (wrongly) mistake that with the contingency of existence. Williamson presents a very interesting argument for NE. I criticize this argument, as well as the other solutions discussed in this note, in my (Nelson, ms3), defending a view akin to that of Adams and Fine, which resolutely denies BF, CBF, and NE.
‘The interaction of modality with quantification and identity’, originally published in 1994.
He presents, initially at least, a fairly standard version of variant domains QML.
Stalnaker writes the following support of QCBF: “Whatever the relations between the domains, surely if in w it is necessary that everything that satisfies [‘F’], then anything that exists in w must satisfy [‘F’] in every accessible possible world in which that individual exists” (p. 151). Kripke countermodels to CBF and hence NE rely upon the fact, given a variable domains, a world accessible from one world might have a individuals in its domain not in the domain of the original world. But if we require, as QCBF does, that the individuals in the original world exist in all accessible worlds, then such countermodels are, as it were, excluded. And so the standard Kripkean countermodels to CBF are not countermodels to QCBF.
Thanks to Troy Cross for helpful discussion on this point.
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Acknowledgements
I would like to thank my Yale opacity course in the fall of 2004—Christopher Holownia, Sam Newlands, Gaurav Varirani, and Leslie Wolf—for extremely helpful discussions of the material in the first two sections of this paper. Thanks also to the modality reading discussions with Troy Cross, Michael Della Rocca, Sam Newlands, Geoff Pynn, Gaurav Vazirani, and Leslie Wolf. Much of what I say in the second and third sections grew out of those discussions to such an extent that it is impossible for me to detect where I am simply repeating what one of them said. Thanks also to Tom Blackson for the invitation to contribute to this symposium
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Nelson, M. Ways an actualist might be. Philos Stud 133, 455–471 (2007). https://doi.org/10.1007/s11098-006-9064-x
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DOI: https://doi.org/10.1007/s11098-006-9064-x