A Problem for Actualism About Possible Worlds Author(S): Alan Mcmichael Source: the Philosophical Review, Vol

Philosophical Review

A Problem for Actualism About Possible Worlds Author(s): Alan McMichael Source: The Philosophical Review, Vol. 92, No. 1 (Jan., 1983), pp. 49-66 Published by: Duke University Press on behalf of Philosophical Review Stable URL: http://www.jstor.org/stable/2184521 Accessed: 09-02-2017 14:56 UTC

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This content downloaded from 128.195.69.222 on Thu, 09 Feb 2017 14:56:26 UTC All use subject to http://about.jstor.org/terms The Philosophical Review, XCII, No. 1 (January 1983)

A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDS

Alan McMichael

I. INTRODUCTION

T he notion of a possible world has many uses in the formal philosophy of language. Its primary use, of course, is in the interpretation of sentences about necessity and possibility. A proposition is necessary if and only if it is true in all possible worlds; possible if and only if true in some possible world. One advantage of the possible worlds interpretation is its extensionality. The inten- sional notions of necessity and possibility are replaced by quantifiers over possible worlds. The language in which these quantifiers appear, sometimes called "world theory," can be given an ordinary Tarski semantics. A second advantage of the possible worlds interpretation is purely heuristic. It just seems to help our modal thinking to imagine other possible worlds. However, the nature of possible worlds is the subject of a familiar controversy, the dispute between actualism and possibilism. One common position in this controversy, which I shall call atomistic actualism, seems to me the most plausible. Nevertheless, I shall show that it is open to serious objection. It fails to provide an adequate interpretation for certain modal sentences, assuming that we adopt standard rules of interpretation. Thus we must either reject atomistic actualism, even though, as I shall argue in the next section, the alternatives are not attractive, or reject the standard semantics, despite its practical successes.

II. POSSIBILISM AND ACTUALISM'

According to the possibilists, possible worlds are concrete entities. In this respect, they are like the concrete universe which we

'The possibilism-actualism distinction should not be confused with the possibilism-modalism distinction. A possibilist in the sense of the second distinction is a person who believes that necessity and possibility are ana- lyzable in terms of quantification over some kind of entities. Whether he or she is a possibilist in the first sense depends on whether those entities are taken to be actually existing or merely possible.

This content downloaded from 128.195.69.222 on Thu, 09 Feb 2017 14:56:26 UTC All use subject to http://about.jstor.org/terms ALAN MCMICHAEL inhabit. For the possibilist, this concrete universe is the actual world. (In saying that possible worlds are concrete, the possibilist is not saying that they are made of actual concrete things. Many worlds contain nonactual concrete things, such as individual dragons and unicorns.) According to the possibilism of David Lewis, this world's actuality is a merely relative matter.2 This world is indeed actual with respect to itself, but every other world is actual with respect to itself. So all worlds are on an ontological par. This postulation of ontological parity, while perhaps it can be consistently maintained, is prima facie absurd. The apparent absurdity may not be sufficient reason for dropping Lewis' theory altogether, but it is enough reason to prefer a consistent alternative. A second form of possibilism takes the notion of actuality to be absolute. Thus this world is distinguished from others by the non- relative property of actuality. In the most plausible version of this view, the property of actuality is taken to be simple and irreducible.3 Another-way to put the view is to say that all possible worlds have being, but only this world has existence or actuality. Many phi- losophers have found this two-tiered Meinongian ontology quite incomprehensible. I am inclined to reject it also, provided that some actualist alternative can be found. Actualists who believe in possible worlds view them as existing abstract entities. The actual world is not actual merely in the sense that it exists-all possible worlds exist-but rather in the sense that this concrete universe corresponds to it. Robert Stalnaker is an actualist who gives serious consideration to the view that possible worlds are irreducible abstract entities.4 He suggests that the term 'world' is in fact misleading: there is only one world, this one. However, there are many 'ways the world

2Lewis, Counterfactuals (Harvard University Press, 1973), 84-91. 3This second form of possibilism is usually adopted as a view about all possible objects, rather than merely about all possible worlds. See, for example, the theory of possibles contained in Terence Parson's Nonexistent Objects (Yale University Press, 1980). Meinong, and possibly Leibniz, held similar views. 4Stalnaker, "Possible Worlds," Nous 10 (1976), 65-75. Stalnaker does not explicitly endorse this view, but he does defend it against objections. I am grateful for his comments on this matter, in which he points out that his main theses are (a) that actualism does not require a reduction of possible worlds and (b) that reduction of propositions to possible worlds has certain advantages over the reverse reduction of possible worlds to propositions.

This content downloaded from 128.195.69.222 on Thu, 09 Feb 2017 14:56:26 UTC All use subject to http://about.jstor.org/terms A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDS might have been' or 'world-states,' and they are what we mean by the term 'possible worlds.' These world-states are abstract entities distinct from this concrete universe. We might think of them as specially determinate properties. One of the world-states is actual in the sense that it is exemplified by our concrete world. This world state is 'the way the world is.' None of the other world-states is exemplified. Thus the notion of actuality does not remain unex- plained, as it does in the absolutist form of possibilism, because in construing worlds as a kind of property, the actuality-nonactuality distinction collapses into the exemplification-nonexemplification distinction. On the view in question, possible worlds are basic properties. They are not properties that might be reduced to simpler properties, or to properties and relations. This particular aspect of the view is one I find unattractive. The decision to treat possible worlds as basic clashes with all commonly accepted patterns of reduction. Reduction proceeds from tables and chairs to atoms, not vice versa. Since this world contains tables and chairs as parts, it too is complex. But since the state of this world, the way the world is, must somehow encode the complex interrelations of this world's parts, it also is complex, a complex of properties and relations. Finally, just as the state of this world is complex, so too are the other world- states. Alvin Plantinga is an actualist who takes worlds to be complex states-of-affairs.5 A state-of-affairs is a proposition-like entity. Exam- ples are Karpov's being world chess champion and Plantinga's having climbed Mount Everest. The former state-of-affairs obtains, the latter does not. Both states-of-affairs, however, are possible. That is, each is such that it could have obtained. Not every possible state-of- affairs is a world, only those that are maximal. A state-of-affairs S is maximal if and only if for any state-of-affairs S', either it is impossible for S to obtain and S' not to obtain, or it is impossible for both S and S' to obtain. That is, S is maximal if and only if for any state-of- affairs S', S either includes S', or S precludes S'. Speaking loosely, a maximal state-of-affairs is one which is completely determinate.6 A

5Plantinga, The Nature of Necessity (Oxford University Press, 1974), IV. 1. 6This is only loosely correct because a maximal possible state-of-affairs may include a state-of-affairs of something being F without including, for any individual X, the state-of-affairs of X's being F. The importance of this point will become clear in the next section.

This content downloaded from 128.195.69.222 on Thu, 09 Feb 2017 14:56:26 UTC All use subject to http://about.jstor.org/terms ALAN MCMICHAEL possible world is a state-of-affairs which is both maximal and possible. Although all these worlds exist, just one of them is actual in the sense that it obtains. Thus the distinction between actuality and nonactuality is merely the distinction between obtaining and not obtaining. As in Stalnaker's theory, worlds, being abstract objects, exhibit a duality which accounts for the distinction. There are two other actualist theories which are very similar to Plantinga's. One, espoused by Robert Adams, says that worlds are maximal consistent sets of propositions.7 A set of propositions is consistent if and only if it is possible for all its members to be true. Such a set is maximal if and only if for every proposition p, the set contains either p or the negation of p. The actuality-nonactuality distinction is based on the true-false duality of propositions: one of the worlds is actual because it contains all the true propositions. According to the remaining actualist theory, worlds are interpreted model structures. Quine has proposed a view of this sort.8 He has construed worlds as certain set-theoretic structures represent- ing possible arrangements of physical particles. One of these structures, presumably, represents the arrangement of particles in the actual world. Quine's theory seems more parsimonious than the others. It does not, after all, refer to propositions or states-of- affairs. Nevertheless, it rests on the same ontological basis as the two other theories. Quine's model structures are interpreted. That means the features of those structures are associated with properties and relations that are taken to be fundamental. But such properties and relations are the very components of Plantinga's states- of-affairs and Adams' propositions. This agreement on an ontological basis outweighs all the differences between the views. The three views offer equally promising interpretations of modal dis- course. Consequently, I lump all three under the same title: atomistic actualism. I believe that some form of atomistic actualism is correct. For the present, I shall adopt Plantinga's version. Accordingly, our modal semantics assumes the following form:

(1) 'It is possible that A' is true if and only if there is a possible

7Adams, "Theories of Actuality," Nous 8 (1974), 211-231. 8Quine, "Propositional Objects," in Ontological Relativity (Columbia Uni- versity Press, 1968).

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world W such that W includes the state-of-affairs expressed by A.

(2) 'It is necessary that A' is true if and only if every possible world W includes the state-of-affairs expressed by A.9

It might be objected that our semantics is circular, since the notions of a possible world and of inclusion have been defined in terms of a primitive understanding of possibility. The charge of circularity is not effective, however, since we are by no means trying to define possibility and necessity. We are simply trying to give an extensional semantics for those notions, in the hope that it will prove il- luminating. It is wrong to think that definition is the only way to illuminate a notion.

III. THE ITERATED MODALITIES OBJECTION

Atomistic actualism provides adequate interpretations for many statements which seem to require quantification over nonactual possible objects. Consider:

(3) It is possible that there be someone who is not actual.

Let S be the state-of-affairs there being someone X who is not actual. Then according to the possible worlds analysis, (3) is true if and only if:-

(4) There is a possible world W which includes the state-of- affairs S.

Since the original statement is surely true, there must be such a world W. But the existence of such a world is quite compatible with atomistic actualism. S is a general state-of-afflars; no constituent of it is a merely possible object. Thus (4) does not require that W have a merely possible object as a constituent. Of course, actualists must deny that W contains any instance of the existentially generalized state-of-affairs S. On the one hand, any instance of S that involves an actual object X is a state-of-affairs

91 am interested primarily in logical necessity and logical possibility. However, if the range of possible worlds is suitably restricted, (1) and (2) can be applied to statements involving other kinds of necessity and possibility.

53o

This content downloaded from 128.195.69.222 on Thu, 09 Feb 2017 14:56:26 UTC All use subject to http://about.jstor.org/terms ALAN MCMICHAEL that could not possibly obtain. W is possible, so cannot include such an instance. On the other hand, W cannot include an instance of S that involves a nonactual object, since actualists deny that there are such things. Therefore, W includes S, but not any instance of S. This does not, contrary to appearances, contradict the maximality of W. Since the actualist denies the existence of the relevant in- stances of S, there is nothing that W is missing. There are problems, however, in the interpretation of iterated modalities. Consider the sentence:

(5) It is possible that there be a person X who does not exist in the actual world, and who performs some action Y, but who might not have performed Y.

This sentence is surely true. For example, John F. Kennedy could (logically) have had a second son who becomes a Senator, although he might have chosen to become an astronaut instead. This is an instance of iterated modality because we are talking about what is possibly possible. On the possible worlds analysis, (5) is true just in case:

(6) There is a world W which includes the state-of-affairs of there being someone X who does not exist in the actual world, and who performs some action Y, and there being a world W' which includes the state-of-affairs of X existing and not performing action Y.

Unfortunately, it is difficult to see how this truth-condition can be met. We have seen how there can be a world W which includes the state-of-affairs there being someone X who is not actual. This is a general state-of-affairs; it does not have the nonactual individual X as a constituent. But since X is not an actual individual, it is difficult to see how there can be another world W' which includes the state-of- affairs of his existing. Because X is not actual, it seems that there is no such state-of-affairs as X's existing, so nothing can include it. The reasoning is that if there were such a state-of-affairs as X's existing, then X would be a constituent of it and so, by actualist principles, be an actual individual-contrary to our hypothesis. One might object that although there is no state-of-affairs of X's existing, there indeed could be. So in this other possible world W, there is such a state-of-affairs. Also, there are maximal possible

This content downloaded from 128.195.69.222 on Thu, 09 Feb 2017 14:56:26 UTC All use subject to http://about.jstor.org/terms A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDS states-of-affairs in W which include the state-of-affairs of X's existing. But this tacitly acknowledges that the states-of-affairs existing in one world can be distinct from those in another possible world, and hence the possible worlds which exist from the point of view of one world are distinct from those which exist from the point of view of another. To acknowledge this is to give up the extensionality of possible worlds semantics, since it is being claimed that the possible worlds quantifier within the context 'there is a world W such that W includes ' does not have a range identical to that of the quantifier on the outside. That is, they don't both range over some one universal set of possible worlds. But if we have to give up the extensionality of the possible worlds approach, we might as well do without it. 1 The foregoing objection is formalized in the Appendix of this paper, using a free modal logic with quantifiers for individuals and for states-of-affairs.

IV. Do ESSENCES HELP?

Plantinga appears to avoid the iterated modalities problem by the introduction of essences. 1 1 He holds that there can be states-of- affairs of the form X exists even if there is no corresponding individual X. This doctrine is not trivial. In speaking of states-of-affairs of the form X exists, Plantinga allows only proper names to be substituted for the variable 'X', not definite descriptions. Thus while it is true that there is a state-of-affairs the present King of France exists even though there is no present King of France, this is not an instance of Plantinga's doctrine. The state-of-affairs the present King of France exists is not of the form X exists. States-of-affairs of the form X exists are states-of-affairs of genuine individual existence, not merely states-of-affairs of the existence of a unique individual satisfying such-and-such a description.

'0Kit Fine tries to do without it. See his Postscript to Worlds, Times, and Selves by Fine and A. N. Prior (Amherst, Massachusetts: University of Massachusetts Press, 1977). Fine explores some of the consequences of one of the views which is prominent in this paper, namely, that states-of-affairs that contain individuals as constituents may exist only contingently. "Essences are introduced in The Nature of Necessity, V. 2. But a more important treatment for our purposes is contained in "Actualism and Possible Worlds," Theoria 42 (1976), 139-160.

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How can there be a state-of-affairs of the form X exists in the absence of an individual X? Plantinga maintains that a state-of- affairs of the form X exists is not a compound of the property of existence and some individual X. Rather, it is a compound of the property of existence and some individual essence. Essences, according to Plantinga, exist of necessity, but an essence does not necessarily correspond to some actual individual. Yet each essence, whether there is a corresponding individual or not, enters into some one state-of-affairs of the form X exists. Plantinga takes essences to be a certain kind of property:

(7) E is an essence if and only if it is possible that something have E necessarily, and necessarily anything which has E is identical to that thing. (Possible worlds analysis: E is an essence if and only if there is some world W such that for some object X which exists in W, (1) X has the property E in every world in which X exists, and (2) for any world W' and object Y which exists in W', if Y has E in W', then Y is identical to X.)

A property E is an essence of Socrates, for example, if Socrates has the property E essentially, and necessarily anything which has E is identical to Socrates. (7) leaves room, on the other hand, for unexemplified essences, essences which are not essences of anything. An essence is a property which could have been an essence of something. Pretty clearly there are essences in the sense of (7). For example, the property of being identical to Socrates is an essence of Socrates. Socrates has this property in every world in which he exists, and it is impossible for something else to have this property. The expression for this essence, however, contains a proper name for an individual. Since on the present view this name is an expression for the essence of Socrates, the whole expression represents no analysis of that essence. The question naturally arises whether there is any interesting sense in which essences can be analyzed. More specifi- cally, we may ask: are essences qualitative in the sense that they are compounds of general properties, properties that do not themselves involve either individuals or their essences? An affirmative answer to this question would bolster Plantinga's position, for it would mean that the essences of nonactual individuals, unexemplified

This content downloaded from 128.195.69.222 on Thu, 09 Feb 2017 14:56:26 UTC All use subject to http://about.jstor.org/terms A PROBLEM FOR ACTUALISM ABOUT POSSIBLE WORLDS essences, need not be "swallowed whole," but may be understood in terms of their parts. I shall try to show, however, that individual essences cannot be qualitative. There are two strong arguments against the view that essences are qualitative. The first is the argument from symmetrical worlds: there are possible worlds that are entirely symmetrical. In each of these worlds, an individual on one side of the axis of symmetry has exactly the same general properties, both intrinsic and relational, as its correspondent on the other side of the axis of symmetry. Assuming that essences are qualitative, it follows that if the individuals in one of these pairs have individual essences, they both have the very same essence-which is impossible. We have shown, therefore, that there could have been individuals that lack individual essences. The problem for the qualitative essences view is that the possible existence of such individuals cannot be interpreted, obviously, in terms of unexemplified essences. One might object that the case of symmetrical worlds is just too special to undermine the essences theory. Two points can be made in response. First, it seems to me, on the contrary, that the theoreti- cal impossibility of adequate interpretations in the case of symmetrical worlds does suggest that the essences view yields the wrong truth-conditions for modal statements in general. Secondly, it is not clear that symmetrical worlds are only a special difficulty. Couldn't I have existed in a symmetrical world? If so, then in that world, I share all my general properties with my correspondent. So neither of us can have a qualitative individual essence there. But if I have an individual essence in the actual world, then I have it necessarily. Thus the fact that I don't have an individual essence in the symmetrical world implies that I don't have an individual essence in this world either. The same goes for other individuals: if individual essences are qualitative, then an individual that can exist in a symmetrical world has no individual essence in the actual world. 12 The second argument, which I shall call the argument from likeness, requires some new terminology. Define the role of an individual to be the conjunction of all its general properties. Recall that

'2An argument from symmetrical worlds also appears in Robert Adams' paper "Actualism and Thisness," Synthese 49 (1981), 3-42.

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general properties are ones that do not involve either individuals or individual essences. They may be either intrinsic or relational. For example, being a descendent of Abe Lincoln is not general, but there are many associated general relational properties, such as being a descendent of a famous national leader. Notice that roles are maximal in the sense that for any general property P, an individual's role includes either P or -P (Q includes P =df necessarily, anything that exemplifies Q exemplifies P). In fact, roles may be defined as maximal possible qualitative properties: R is a role if and only if (1) it is possible for something to exemplify R, and (2) for any general property P, either R includes P or R includes -P. This definition goes beyond the previous definition, for it encompasses not only the roles of actual individuals, but also roles that are not actually exemplified. In addition to an individual's actual role, there are many other roles it could have exemplified. However, since roles are maximal qualitative properties, each one of an individual's possible roles must include that individual's essence, given the assumption that roles are qualitative. It follows that the disjunction of all an individual's possible roles is an essence, since (1) the individual could not exist without filling one of the roles in the disjunction, and (2) no other individual could exemplify the disjunction without exemplifying the original individual's essence-which is impossible. Call roles R and S compossible if it is possible for there to be individuals X and Y such that both X fills role R and Y fills role S. Then the argument from likeness is: if two roles R and S are sufficiently alike, then necessarily anything that fills role R could have filled role S and vice versa. But there are compossible roles R and S such that (A) R and S are sufficiently alike, and (B) it is possible for there to be distinct individuals X and Y such that X exemplifies R and Y exemplifies S. From (A) and the first premise, it follows that if R and S include essences, then they must include the same essence. From (B), it follows that if R and S include essences, they must include distinct essences. Thus R and S cannot include essences. But assuming that essences are qualitative, and given that R and S are roles, either both R and S include essences, or necessarily, anything exemplifying R or S lacks an individual essence. Since R and S do not include essences, anything that exemplifies either R or S lacks an individual essence. But since R and

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S are possibly exemplified, it follows that there could have been individuals that lack individual essences-the same conclusion as that reached in the argument from symmetrical worlds. There are fancier versions of this argument. The roles R and S need not themselves be sufficiently alike, they need only be connected by a chain of roles R, R1, R2, . . , Rn, S such that each role is sufficiently like the next one in the chain. The intermediate roles need not be compossible with each other or with R and S.13 One might object that no such roles R and S can be found that are sufficiently alike, or that are connected by a chain of roles each of which is sufficiently like its neighbor. It seems to me, on the contrary, that it is easy to conceive of such roles. R and S might be roles of identical twins or, better yet, roles of two electrons created in the same collision of particles. Neither does it seem right to object that such roles R and S present a special case that does not undermine the essences theory. This objection can be met with the same response as the like objection to the symmetrical worlds argument. I conclude from these arguments that we must reject the idea that essences are qualitative properties. The alternative view of essences is that essences are Haecceities, properties which necessarily characterize single individuals but which are not reducible to general properties. Perhaps Plantinga's actualism can be based on essences of this sort.14 Assuming the failure of the qualitative essences view, the existence of Haecceities certainly follows. For

'31n "Identity Through Possible Worlds: Some Questions" (Nous 1 (1967), 1-8), Roderick Chisholm seems to be saying that a chain of sufficiently like roles can be constructed between the actual role of Adam and the actual role of Noah. I am not convinced that this can be done in the case of Adam and Noah. However, I think that the argument from likeness can be supported by more plausible examples. 14The term 'haecceity', however, is not Plantinga's. I derive it from David Kaplan's "How to Russell a Frege-Church," Journal of Philosophy 72 (1975), 716-729. There Kaplan says, "The doctrine that holds that it does make sense to ask-without reference to common attributes or behavior- whether this is the same individual in another possible world, . . ., I call Haecceitism." Any property which does the duty of distinguishing an individual-without reference to general attributes-I call an haecceity. This usage springs naturally from Kaplan's. However, it may not be compatible with the much older usage of Duns Scotus. Allan Back has told me that Scotus' haecceities are probably not properties.

This content downloaded from 128.195.69.222 on Thu, 09 Feb 2017 14:56:26 UTC All use subject to http://about.jstor.org/terms ALAN MCMICHAEL example, the property of being identical to Socrates is an Haec- ceity. It is an essence of Socrates, but under the present view, it is not reducible to general properties. The main problem for the Haecceitist is not that of establishing the existence of Haecceities. Rather, the problem is one of showing that Haecceities fill the modal role for which essences were introduced. That is, Haecceities must be constituents of states-of-affairs of the form X exists even in cases where there is no corresponding individual X. There must be unexemplified Haecceities. It is not easy to believe this. Since Haecceities are not reducible to general properties, expressions for Haecceities of individuals always involve proper names of individuals (or indexicals). For example, the Haecceity- expression 'being identical to Socrates' contains the proper name 'Socrates.' One can't help thinking that unless such properties can be cashed out in terms of general properties, none of them would exist if the individuals named in their expressions did not exist. Thus since Haecceities can't be cashed out in general terms, and since their expressions involve the names of the individuals they supposedly characterize, Haecceities do not exist in worlds where their corresponding individuals do not exist. Consequently, there are no unexemplified Haecceities. According to this objection, Haecceities are contingent existents. For example, the property of being identical to Socrates is a contingent existent. It exists only in worlds where Socrates exists. In reply, one might argue that Haecceities are necessary existents, because all properties are. This reply is too glib. The objector may agree that general properties are necessary existents, but point out that it is by no means obvious that others, such as identity with Socrates, are necessary existents. The set whose sole member is Socrates does not exist in worlds where Socrates does not exist. Why should identity with Socrates be different? This objection to unexemplified Haecceities is no isolated intui- tion. Once Plantinga's Haecceitism is fully spelled out, we can see that it bears a striking structural resemblance to the possibilist theories we have rejected. In place of every nonactual possible object, there stands an unexemplified Haecceity. Indeed, Plantinga's Haecceitist semantics is isomorphic to the usual Kripke semantics.

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The Kripke semantics is, on the face of it, a possibilist semantics, since we can identify within it a set of all possible objects, actual and nonactual. 15 This isomorphism is one of the signs that Plantinga is having trouble with the actualist program. Another sign is that he has departed from the usual actualist basis. Typically the actualist re- duces worlds to existing individuals, general properties, and general relations. To introduce primitive properties each of which is specific to some nonactual object seems tantamount to acceptance of possibilism. Yet this is precisely what Plantinga does. Finally, Plantinga is in the unfortunate position of being unable to give a single example of an unexemplified essence. Is the property of being identical to Sherlock Holmes, for example, such an essence? It seems not to be. From the stories, we do indeed know what some of Holmes' properties are supposed to be. But under Plantinga's Haecceitism, this knowledge seems insufficient to grasp an essence. We don't know enough of Holmes' properties to pick him out uniquely in any possible world. Hence the example fails.'6

V. MUST WE TAKE POSSIBLE WORLDS SERIOUSLY?

Atomistic actualism is threatened by the problem of iterated modalities. It is easy to see how worlds can include there being individuals other than those which there actually are. But those individuals could be otherwise than they are in their respective worlds. This suggests that there are yet other worlds which include their existence. However, it seems that a world can include the existence of something only if that thing is a constituent of that world. Since atomistic actualism holds that there are no nonactual possible individuals, nonactual possible individuals are not constituents of anything. The theory of essences promises help. According to that theory, a world can include the state-of-affairs of some nonactual possible's

'5See Plantinga's "Actualism and Possible Worlds," 155. Speaking strick- ly, Plantinga's semantics is isomorphic only to that version of the Kripke semantics which requires the extension of a predicate in a world to be a set of n-tuples of things that exist in that world. '6Plantinga himself reaches a similar conclusion. See The Nature of Neces- sity, VILL.3-4, where he discusses fictional creatures.

This content downloaded from 128.195.69.222 on Thu, 09 Feb 2017 14:56:26 UTC All use subject to http://about.jstor.org/terms ALAN MCMICHAEL existing without containing that nonactual possible as a constituent. It need only contain an unexemplified essence. Unfortunately, this maneuver fails. The theory of essences has two forms. One form, the theory of qualitative essences, is vulnerable to certain arguments. A second form, Haecceitism, seems not to solve our original problem. There is no good reason to believe that there are unexemplified Haecceities. Haecceities seem to depend for their existence on the individuals they characterize. But to remove the problem of iterated modalities, we need unexemplified essences. Haecceities will not do. My conclusion is that atomistic actualism is in conflict with standard possible world semantics, on account of the problem of iterated modalities. If we retain atomistic actualism, which I have ar- gued is the most reasonable conception of possible worlds, then we must reject the standard semantics, as represented by principles (1) and (2). I see no other way out. One might respond that the problem of iterated modalities arises only because we are discussing a particularly realistic form of actualist semantics. To be sure, an actualist must reject the idea of there really being nonactual possibles. Nevertheless, he or she is entitled to employ a semantics which includes so-called nonactual possibles. Acceptance of a possibilist's semantics does not necessarily involve commitment to the possibilist's ontology. The "nonactual possible individuals" which appear in the semantics might be construed, for example, as numbers or sets. If there are enough of these so-called possibles, and if they are related in the right ways, then the semantics which includes them may indeed prove adequate, in the sense of providing a correct distribution of truth-values, even though there really are no nonactual possibles. My main objection to this approach is that it involves unsolved difficulties. It should be clear that the construction of such a nonrealistic semantics is a sleight of hand that has never actually been accomplished. In order to give such a semantics, the number of nonactual possibles and their relationships must be determined. It is not clear how this is to be done. 17

171n "On What There Is," Quine mentions the possibilist's difficulty of determining, for example, the number of possible men in a particular doorway. The same sort of difficulty is involved in attempting to construct a nonrealistic actualist semantics.

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It is true that Saul Kripke has given a semantics for modal logic, one that can plausibly be construed as a nonrealistic actualist semantics. However, to give a semantics for modal logic is only to give the form of a semantics for modal language. What we are ultimately interested in, I believe, is to give truth-conditions for some nice modal fragment of a natural language. Kripke's semantics is useful for investigating the notion of logical validity in a modal language. It does not supply conditions for truth. When I say that to give a nonrealistic actualist semantics the number and relationships of nonactual possible individuals must be determined, I mean that it must be determined if the semantics is to provide us with truth- conditions. I agree that a semantics for modal logic has been given without such a determination.'8 My secondary objection is that questions of realism will haunt us anyway. If a nonrealistic semantics is actually constructed, then since it contains nonrealistic elements, the problem will arise of distinguishing what aspects of the semantics are of genuine significance and what aspects are purely artificial. We will want a method for "factoring out" the artificial aspects. But a nonrealistic semantics coupled with a method of "factoring out" is just a realistic semantics. An analogous situation arises in the use of spatial coordinate systems. Given a particular coordinate system, the fact that an object A has coordinates (X, Y, Z) has no significance outside that system. However, the fact that another object B with coordinates (X', Y', Z') is separated from A by the square root of (X' - X)2 + (y' - y)2 + (Z' - Z)2 units is of independent significance. It holds in all coordinate systems (assuming absolute length and discounting rela- tivistic effects). The problem of distinguishing such invariant features from artificial ones is just as important as finding a coordinate system that "works." My complaint with the approach of nonrealistic semantics is that it seems to be based on the assumption that generation of a correct distribution of truth-values is the only semantic goal. The economy sought by realistic semantics is a second semantic goal and is also worthy of pursuit. We don't just want a modal semantics that

18Compare Plantinga's distinction between pure and applied semantics, The Nature of Necessity, VII.4.

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'works." We also want one that isolates the invariant features of modal reality. In summary, I question the approach of nonrealistic semantics for two reasons: (1) It involves unsolved problems concerning the number and relationships of nonactual possibles. (2) Even if an adequate nonrealistic semantics is constructed, we will want to transform it into a realistic semantics by "factoring out" its artificial features. Given the undesirability of nonrealistic semantics, our original problem remains. We cannot retain atomistic actualism, neither Plantinga's version nor any of the others, without revising standard modal semantics.19

APPENDIX: FORMALIZATION OF THE ITERATED MODALITIES OBJECTION

I shall use 'p' and 'q' as variables for states-of-affairs, 'x' and 'y' as individual variables. Inclusion of a state-of-affairs q by a state-of affairs p will be represented using the necessity operator: LI(p -> q). Also, some symbols will be given special interpretations:

Wp: p is a possible world @: the actual world Ep: the state-of-affairs p exists Ex: the individual x exists Cxq: the individual x is a constituent of state-of-affairs q

In addition to standard axioms and rules for free quantificational S5, I shall use the following:

1. Definition of a world-

LO(Wp <-> K p & (q)[LI(p -> q) v LI(p -> -q)])

2. Constituency-

OI1(q)(x)( K q & LI[q -> Ex] -> Cxq)

191 wish to thank Marvin Belzer, James Fahey, Kit Fine, Edmund Get- tier, Alvin Plantinga, Melinda Roberts, Eleonore Stump, and the editors of The Philosophical Review for their comments on earlier versions of this paper.

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Necessarily, if a possible state-of-affairs includes the existence of some individual, then that individual is a constituent of the state-of-affairs. It is interesting to note, on the other hand, that a state-of-affairs can exclude the existence of an individual which is not a constituent of it. For example, the state-of-affairs q = there is exactly one individual and it is an electron excludes the existence of x = Socrates. We have O q (I think) and we have LI(q -> -Ex), but we do not have Cxq.

3. Actuality of Constituents-

LI(q)(x)(Cxq -> LI[@ --> Ex])

Necessarily, any constituent of a state-of-affairs must be an actually existing thing. This axiom can be regarded as a consequence of two others:

3a. Actuality of all possible constituents of an actual state- of-affairs-

(q)LI(x)(Cxq -> L[[@ --> Ex])

3b. Necessary existence of states-of-affairs- LIE-, where the blank is filled by any states-of-affairs term. This validates the Barcan formula and its converse for states-of-affairs:

(p)FE( . .p. . ) <- ~(p)( p..) AX contradiction can now be derived from (6) in the text. Letting 'Pxy' be interpreted by 'x performs action y', we may translate (6) is:

(1) (3p)(Wp & Li[p -> (3x)(3y)(-LI[@ --> Ex] & Pxy & (3q)[Wq & LI(q -> Ex & -Pxy)])])

Here '-L(@ > Ex)' is the translation of 'x does not exist in the actual world'. We may proceed:

(2) Wp & Li[p (-> x)(3 y)(-LI[@ -> Ex] & Pxy & (3q)[Wq & LI(q -> Ex & -Pxy)])] & Ep* Assumption (EI) *-In free logic, part of an El assumption is existence of the in- ;tantiated item.)

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(3) C p 2, Simp, Def World (4) p Assumption (C)

(5) Li[p -> (3x)(3y)(-][@ --> Ex] & Pxy & (3q)[Wq & Li(q -> Ex & -Pxy)])] 2, Simp

(6) (3x)(3y)(-LI1[@ -> Ex] & Pxy & (3q)[Wq & Li(q -> Ex & -Pxy)]) 4, 5, Necessity, MP

(7) -Li[@ -> Ex] & Pxy & (3q)[Wq & Li(q -> Ex & -Pxy)] & Ex & Ey Assumption (EI, EI)

(8) (3q)[Wq & Li(q -> Ex & -Pxy)] 7, Simp

(9) Wq & Li(q -> Ex & -Pxy) & Eq Assumption (EI)

(10) Li(q -> Ex) 9, Simp, . . .

(11) O q 9, Simp, Def World

(12) Cxq 10, 11, Constituency*

(*-To apply the axioms in this and the next step, we must also use 'Ex' and 'Eq'.)

(13) Li(@ -> Ex) 12, Act of Constits

(14) -Li[@ ->Ex] 7, Simp

Since the contradiction composed of (13) and (14) occurs only within El and O subproofs, it is Assumption (1) alone which is responsi- ble for the contradiction. Kit Fine avoids the contradiction by rejecting 3b, the necessary existence of states-of-affairs. In the resulting modal theory, states- of-affairs quantifiers do not commute with the modal operators (that is, the Barcan formula and its converse do not hold for states- of-affairs). Consequently, any world theory derived from this theory of states-of-affairs will contain ineliminable occurrences of the modal operators, with their attendant opaque contexts, and so it will not be truly extensional. Of course, this is no drawback at all if, because of the problems raised in the text, no satisfactory extensional world theory is possible.

Virginia Polytechnic Institute and State University

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