Forthcoming in Richard M. Gale (ed.), Blackwell Guide to Metaphysics, Oxford: Blackwell.
Copyright © 2001 Blackwell Publishing.
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The Actual and the Possible
Alexander R. Pruss
We use alethic modal language all the time. For instance, we say that someone did not do something she could have done, or that the existence of unicorns is possible, or that 2+2=4 could not have failed to be true. We make counterfactual assertions such as “Were I to drop this glass, which in fact I do not, it would fall.” We think it might have been the case that Hitler had never existed. In these locutions we are speaking about situations and things that are not actual, of ways the universe might have been but was not.
Moreover, alethic modal language could not play the kind of role it has in our lives if we did not take a realist stance towards it. For instance, to decide rationally between alternatives, we often need to consider what consequences would result from each alternative. To decide questions of moral responsibility we often need to decide what else could have been done. The laws of nature by which we navigate the world have counterfactual force. If we did not take our alethic modal claims to express objective truths, modal language could not play the role it does in these cases.
A useful way of clarifying modal discourse is to introduce the notion of a possible world, or world for short, which is a complete way that a universe might have been. The term “possible” refers here not to physical possibility, but to a broad notion of logical or metaphysical possibility, which lets one ask questions such as whether it would be metaphysically possible for a horse to beget an owl. Once possible worlds are introduced, one can say a proposition is possible if it is true at some world, necessary if true at all worlds, and contingent if true at some but not all, so that modal operators can be replaced by quantifiers. It is possible that there is a unicorn if and only if there is a possible world at which there are unicorns.
Many ordinary language modal claims seem local. “It might have been that Hitler had never been born” sounds like it is a claim merely about the circumstances around Hitler’s birth. However, in fact, it is a global claim. We do not simply mean that a world in which Hitler is not born is logically possible. What we mean is that there is a world like ours in relevant respects, for instance sharing the same laws of nature and initial conditions, or maybe even the same historical conditions up to the late 19th century, but in which Hitler is not born. Specifying what these relevant respects are may well be a global task, especially if laws of nature are global. So we need possible worlds for clarification and disambiguation.
Moreover, possible worlds can be used to clarify modal claims that one could not easily explicate in other ways. For instance, a claim that people’s having virtue or vice supervenes on natural facts is a claim that there are no possible worlds which share the same natural facts but which differ in respect of someone’s virtue or vice. Likewise, David Lewis has shown us how to explain counterfactuals in terms of possible worlds. Assuming I do not drop the glass, it is true that were I to drop the glass, it would fall provided that some world in which I drop the glass and it falls is more similar to our world in relevant ways, especially in nomic structure, than any world in which I drop the glass but it does not fall.
If we are to be realists about alethic modal truths, then the natural question is: What makes modal propositions true? What are they true of? In general, an objectively true proposition must be true of some aspect of reality. One way of spelling out this intuition is to say that in order for a proposition to be true, it must have a truthmaker, something in virtue of which it is true. The truthmaker is something worldly, and for propositions about concreta, it is something concrete. Thus, the truthmaker of the proposition that Smith is bald is the concrete baldness of Smith, or else Smith’s being bald.
Truthmaker-based arguments have been common in philosophy, starting with Parmenides who argued that there are no true propositions about the future on the presentist premise that future worldly states do not exist and hence the truthmakers for propositions about the future do not exist. Alternately, one could use modus tollens and argue that since it is true that tomorrow the sun will rise, some future worldly states do exist and make true propositions about the future true. Similarly, many have argued that there are no ethical truths, because the truthmakers of ethical propositions would allegedly have to be queer non-physical entities.
The claim that true propositions require truthmakers has been challenged. For instance, one might worry what existent reality can make a negative claim such as that there are no seven-legged dogs true. One could posit a negative state of affairs, such as there not being any seven-legged dogs, but that would trivialize the truthmaker theory. Alternately, one could say that what makes it true that there are no seven-legged dogs would be everything’s being either A1, or A2, … or An and A1’s having some positive property incompatible with being a seven-legged dog, A2’s having some positive property incompatible with being a seven-legged dog, … and An’s having some positive property incompatible with being a seven-legged dog.
What, then, are the truthmakers of alethic modal claims? This question is deeply puzzling, since many alethic modal claims prima facie concern non-existent things such as unicorns. One proposed answer is that the truthmakers of alethic modal claims are possible worlds, and we have already seen that we have good reason to believe in possible worlds even apart from this. So this brings us to the second question: What are possible worlds?
In his paper in this volume, William Lycan discusses six approaches to the problem of how to make sense of talk of non-existent possibilia, grouped into two wide groups. The actualist accounts reject any non-actual entities, any entities not found in the actual world, and thus must provide an account of the truth of modal claims in terms of this-worldly actual entities. The concretist accounts, on the other hand, say that there are concrete non-actual entities, such as unicorns existing concretely in concrete physical worlds different from ours, which serve as the truthmakers of modal propositions.
I will critically evaluate the most prominent contemporary concretist account, that of David Lewis, according to which possible worlds are just concrete physical universes on a par with ours, and the most promising contemporary actualist account, that of Robert M. Adams (1974) and Alvin Plantinga (1974), which claims that possible worlds are Platonic entities constructed from abstracta such as propositions or properties. I will argue that both of these kinds of accounts fail to provide an adequate theory of the truthmakers of alethic modal propositions, and sketch an alternate actualist account based on ideas of Aristotle and Leibniz. Interestingly, the actualist account I will sketch will make the truthmakers be concrete entities.
David Lewis has an elegant and thoroughly worked out concretist answer to both the problem of truthmakers of modal claims and the problem of what possible worlds are. A Lewisian world is, by definition, a maximal physical spatio-temporally connected aggregate. Every way that a world could have been is a way that some existing, physical world really is. This I call “Extreme Modal Realism.” According to the Extreme Modal Realist, there are infinitely many existing island universes, and unicorns and witches do exist, but not in our world. What makes it true to say that something could happen is just that it does happen in one of these island universes.
Lewis has a two-fold argument for positing the infinitude of physical universes that he needs. The first is a cost-benefit theoretic-utility argument. Supposing there are such universes solves the problem of what makes true modal statements true, and Lewis thinks is useful for many other philosophical purposes, such as for saying that a proposition is nothing but the set of worlds at which it is true. Given the usefulness of the theory, Lewis concludes that it is probably true.
The second argument for the theory is to argue that like indexical terms such as “I”, “here” and “now”, the word “actual” and its cognates depend for their reference on the context in which they are tokened. If someone says “There actually exist horses”, according to Lewis she is saying that there exist horses in the universe in which she is speaking. This makes the word “actual” and its cognates into indexical terms. But all the referents of indexical terms are ontologically on par. All referents of “I” are ontologically on par with me: there is no absolute property of I-ness that accrues to me and me alone. (This is not so obvious in the case of “now”, though it will be true even there on Lewis’s way of looking at time.) By analogy, all the referents of “actual” are also ontologically on par. Thus, the universe which is actual is not ontologically special. It must be ontologically on par with all the other non-actual universes, and hence all possible non-actual universes must exist, Lewis concludes, and must be ontologically on par.
Note, then, that considering “actual” to be an indexical gives one a good argument for believing in Extreme Modal Realism. Conversely, if one accepts Extreme Modal Realism, there is good reason to consider “actual” to be an indexical term, or at least a term that is relevantly similar to an indexical term. To see this, Lewis argues as follows. According to Extreme Modal Realism, every way that a world could have been is a way some concretely existing world is. Now, if actuality were an absolute property of a world, then there would be exactly one world which had that property. But “[s]urely it is a contingent matter which world is actual. A contingent matter is one that varies from world to world. At one world, the contingent matter goes one way; at another, another. So at one world, one world is actual; and at another, another. How can this be absolute actuality? — The relativity is manifest!” (Lewis, 1986, p. 94). Next, however, one can argue that our best account of something actuality’s being relative in this way is to suppose that actuality is indexical, or at least relevantly similar to indexical claims.
All this means that Extreme Modal Realism goes hand-in-hand with a relative, indexical theory of actuality. But is “actual” an indexical? Richard Gale (1996, Chapter 5) has noted that the indexical account of actuality fails to give correct truth values for various sentences. For example, the sentence “I might not have been I” is false, because an indexical like “I” is a rigid designator, that is a term which has the same referent in counterfactual as in non-counterfactual contexts. On the other hand, Gale has argued that “the actual world” is a definite description just like “the tallest person in the world.” Just as the tallest person in the world might not have been the tallest person in the world, likewise it is true to assert: “The actual world might not have been the actual world,” which is disanalogous to the indexical case and shows that “the actual world” is non-indexical. In the latter sentence, “the actual world” is used non-rigidly: its second occurrence refers to the world that would be actual in the counterfactual case.
A defender of Lewis might say that the above is a non-central use of “the actual world” and point to the central use as occurring in sentences like: “It could have been the case that Smith was taller than she is in the actual world.” In this sentence, “the actual world” is indeed used rigidly the way an indexical is, since it refers not to the counterfactual world where Smith is taller, but to the world in which the sentence is tokened. However, first of all, the very existence of a non-rigid use, even if non-central, already shows a crucial disanalogy between indexicals and “actual.” Secondly, ordinary definite descriptions also have an analogous rigidified use. For instance, one can say, with only a little awkwardness: “It could have been the case that John was faster than the fastest person alive.” Here, “the fastest person alive” acts as rigid designator: in the counterfactual context it refers to the same person who in our world is the fastest person alive, though this person is obviously not the fastest person alive in the counterfactual world.
Thus the presence of both a non-rigid and a rigid use make “the actual world” much more closely analogous to definite descriptions. This and other logico-linguistic disanalogies between “the actual world” and paradigmatic indexical terms undercut the argument for Extreme Modal Realism from the supposed indexicality of actuality. However, if one accepts Extreme Modal Realism for other reasons, such as theoretic utility, one will see a crucial analogy between actuality and indexical terms, namely the systematic shift in reference between different contexts of use: what “the actual world” refers to when used by a speaker in one world is not what it refers to when used by a speaker in another. The Lewisian will then say that “the actual world” is an indexical term, albeit one that is sometimes linguistically treated differently from paradigmatic ones. What will be decisive as an argument against this claim will be that in addition to the linguistic disanalogies, we will see that there is a crucial analogy in the way we treat actuality and ordinary indexicals in our inductive reasoning.
Now, if we do accept the plausibility of Lewis’s account of actuality, the Extreme Modal Realist account attractively answers the two basic questions of the nature of possible worlds and modality. Possible worlds are not queer ghostly might-have-beens but are full-blooded physical beings, universes like ours. And we have an apparently reductive physicalist account of possibility: A proposition is possible if and only if there is a maximal spatio-temporally connected aggregate of which it is true.
When we say that unicorns can exist, there is no semantic problem of explaining what we are doing when talking of unicorns given there are no unicorns. We are simply saying that somewhere in the totality of all physical universes there are unicorns. But of course the unicorns are not actual; they are not a part of the aggregate of all physical objects spatiotemporally related to my present tokening of this sentence.
Lewis’s theory radically revises our notions of the range of things that exist to include the things that we thought to be merely possible. Not surprisingly, this creates a number of unacceptable paradoxes.
The first of these shows that if Lewis’s theory of actuality is right, then we are never justified in making any inductive inferences about the future. But certainly we are justified in inferring on the basis of past data that, e.g., something approximately like the universal law of gravitation will continue to hold tomorrow. If tomorrow I drop a glass, it will fall—and Lewis will surely not want to deny I have reason to believe this. However, I will show that if Lewis is right that actuality is indexical, then this is an unjustified inference. Since the inference that gravity will hold tomorrow is a justified one, pace the sceptics, by modus tollens it follows that actuality is not indexical, and so this argument is a reductio of Lewis’s claims about the indexicality of actuality.
To see this, suppose for a reductio that actuality is indexical. Let D be a complete description of the actual world up to the present, that is t0, in non-future-involving terms. Intuitively, a non-truth-functionally complex sentence about a time t is “non-future-involving” provided it does not entail the existence of any instants of time after t and is compatible with the truth of an arbitrary number of tokenings of that sentence after t. Now, there are at least as many possible worlds satisfying D but at which the law of gravitation fails a day after t0 as there are worlds satisfying D but at which gravity continues to work a day after t0. This is just a statement about logical space, one that David Lewis certainly accepts, and one that both sides in the Humean debate on induction can accept.
Suppose then I have a possible world w about which the only thing I know is that it satisfies D. I am not justified in inferring just from this information that gravity will work a day after t0 in w. Since I am only talking about possible worlds at this point, this is merely a statement about logical space, and my claim follows from the fact that there are at least as many worlds satisfying D at which gravity will fail a day after t0 as there are ones at which it will continue to hold. This, too, is a statement that people on both sides of the Humean debate can accept, and should not be controversial. The mere facts that w is possible and w satisfies D do not give one reason to think gravity will continue to hold in w.
Before continuing, we need to observe one crucial fact about theoretical reason, and specifically about inductive reason. Theoretical reason is impartial with regard to merely indexical facts. If some set of non-indexical facts did not justify an inference to some further non-indexical proposition, then adding a purely indexical claim to the evidence, such as “The time described is now” or “This took place here” cannot by itself give justification for inferring the non-indexical proposition we could not infer before. Purely indexical data is irrelevant for objective reason. If, for instance, I cannot infer from some non-indexical inductive data about people that Alexander Pruss will do the right thing under some circumstances, then neither can I infer it when I add the additional premiss that I am Alexander Pruss—to do so would be to commit a fallacy of partiality.
Now suppose I find out one more piece of information about w in addition to knowing that it satisfies D: I find out that w is actual. If I take the claim that actuality is indexical seriously, then just as merely learning that t0 is now does not give me any information relevant for inferring that gravity will continue to function a day after t0, analogously, learning that w is actual will not give me any information relevant for inferring that the law of gravitation will be true in w a day after t0. Therefore, if actuality is indexical, I cannot infer from the fact that w satisfies D and w is actual that gravity will hold a day after t0. Since in fact we do not have any further relevant information about our world beyond D and the fact that this world is actual, neither can we infer that gravity will function tomorrow, assuming that actuality is indexical. But this conclusion is absurd: we certainly are justified in inferring that if we drop something tomorrow, it will fall. By modus tollens, it follows that actuality is not indexical.
More formally, the reductio is as follows:
(1) Let D be a complete non-indexical description of the actual world up to the present (t0) in non-future-involving terms. (Definition.)
(2) D contains the claim that gravity has always held prior to t0. (Premise.)
(3) Conclusions about the actual world reached by reasoning in accordance with the canons of inductive reasoning are justified, and in particular knowing that gravity has always actually held prior to t0 justifies one in believing it will continue to hold after t0. (Premise.)
(4) There are at least as many worlds satisfying D in which the law of gravitation fails after t0 as there are worlds in which it continues to hold. (Premise.)
(5) * Therefore, knowing that an entity w is a world satisfying D does not by itself epistemically justify inferring that w is a world at which gravity holds after t0. (Premise, justified intuitively by appeal to (4).)
(6) * Theoretical reason is impartial with respect to merely indexical facts: If knowing that x is F (where F is purely non-indexical and x is a definite description or proper name) does not epistemically justify inferring that x is G (where G is purely non-indexical), then neither does knowing x is F and that x is I (now, here, etc.: any pure indexical will do) justify inferring that x is G. (Premise.)
(7) * Actuality is indexical. (Premise.)
(8) Therefore, knowing that an entity w is a world satisfying D and w is actual does not epistemically justify inferring that w is a world at which gravity holds after t0. (By (5)-(7).)
(9) * But knowing that the actual world satisfies D and w is actual epistemically justifies inferring that gravity holds in w after t0. (By (2) and (3).)
(10) Therefore, knowing that the actual world satisfies D and w is actual both does and does not epistemically justify inferring that gravity holds in w after t0, which is absurd. (By (8) and (9).)
The premises marked with an asterisk form an inconsistent quadruple. All of them, except (7), are highly plausible, and hence we need to reject the premise (7) that actuality is indexical. Another way to look at this argument is to see it as showing that if actuality is indexical, then inductive reasoning violates (6) and hence is guilty of the fallacy of partiality. But in fact we take inductive scientific reasoning to be a paradigm of impartial reason, and hence actuality is not indexical.
Note that a pragmatic will-to-believe argument for accepting inductive consequences such as that gravity will continue to function cannot help Lewis. Will-to-believe arguments presuppose that we have reason to think that one belief will be more beneficial than another, and if inductive reasoning about gravity is undercut as above, likewise we do not have any information either way which beliefs are more likely to be beneficial.
Identity versus counterpart theory
A proposition is possible if and only if it is true at some world. Taking this at face value, it is possible that I be a biologist if and only if there is some world at which I am a biologist. Since I was never a biologist in the actual world, the true claim that it was possible for me to have been a biologist seemingly implies that at some non-actual world I am a biologist, which in turn implies that I exist not only at the actual world but at at least one non-actual world as well. Moreover, prima facie, for grounding the truth of the claim that it is possible that I be a biologist it is irrelevant whether other people at this or other worlds are biologists or not.
There are now two different kinds of possible world theories. An identity theorist like Saul Kripke insists on taking these intuitions at face value. Thus, I myself, exist at a number of possible worlds, at one of which I am a biologist. David Lewis, on the other hand, is a counterpart theorist and holds that each concrete entity exists in only one world. What makes it true, however, to say that I could have been a biologist is that there is a possible world at which my counterpart is a biologist, where my counterpart in a given world is (roughly) that person there, if he exists, who resembles me most in the relevant respects and whose resemblance to me is sufficiently close. The identity theorist will, of course, insist that what people very similar to me do in other worlds does not make it true that I could do those things. Although their doings would be evidence for my being able to do it, these doings would not be a truthmaker for the proposition that I can do it.
Lewis’s Extreme Modal Realism now faces a dilemma. Either counterpart theory, as Lewis himself thinks, is right, or identity theory is right. Each horn of the dilemma leads to two problems: one ethical and one metaphysical.
Suppose both identity theory and Extreme Modal Realism are true. Then the following paradox results. Whatever I choose to do, in the sum total of reality, I perform all the choices that it is logically possible for me to perform. I claim that this means that what I do overall does not matter and ethics breaks down.
First of all, as has often been have noted, on Lewisian grounds what I choose does not matter for the totality of reality at large, since according to Extreme Modal Realism the totality of all real worlds is fixed, as this totality corresponds to the logical space of all possibilities. However, this is not itself enough to generate the breakdown of ethics, as Lewis has argued. According to a non-consequentialist like Lewis, what matters is not that the sum total of all reality should be positively affected by one’s actions, but that one’s own actions be the right ones, that one be oneself virtuous, even if there are infinitely many vicious people who undo the good effects of one’s actions.
However, if one adds identity theory to Extreme Modal Realism, then the ethical paradox becomes much more formidable. For then my actions do not even affect overall what kind of a person I am, because I really exist in infinitely many worlds, and I cannot change which ones I exist in. In some worlds I am a mass murderer, in others I am a great philanthropist, and in yet others I am a venal liar. Whatever I do, facts like this will not change. I know that if I choose between a virtuous and a vicious action in favor of a virtuous action, I will do the vicious one anyway, in worlds equally real as ours and in a way that is as real as the one in which I do the virtuous action. Hence, moral choice does not have significance for building one’s moral character, since one’s overall character as a person is fixed. This is paradoxical, and hence we cannot have both identity theory and Extreme Modal Realism.
Note that this argument does not apply under counterpart theory. It is true that if I act virtuously, then infinitely many counterparts of mine will act viciously. But they are not literally I, and hence a non-consequentialist can still insist that I should do my duty, not minding them, for what they do is not my business. On the identity theory, however, what they do is literally my business, since they are I.
Besides paradox, there is a serious metaphysical difficulty for Extreme Modal Realism if identity theory is adopted. We have seen that Extreme Modal Realism cannot tolerate an absolute theory of actuality. Lewis’s indexical alternative, however, fails given the identity theory. Recall that on the indexical account of actuality, a given instance of a tokening of “the actual world”, at least in central cases, refers to that world in which it was tokened.
However, according to the identity theory, that very tokening occurs in more than one world. For suppose I token the sentence: “In the actual world, a cure for cancer is found in the year 2020”, and suppose that the sentence is in fact false. Nonetheless, it is logically possible that I make this very tokening in a world in which it expresses a true proposition. After all, according to the identity theorist, there will be a world in which this sentence-type expresses a true proposition, and in which I token the sentence at numerically the same place and time as I do, having the same history, and I perform the tokening in the same way. It is highly plausible to suppose that under these circumstances it follows that in that world I make numerically the same tokening.
But if the very same tokening of a sentence containing the phrase “the actual world” occurs in more than one world, then one cannot define the extension of the phrase “the actual world” as being the world in which it occurs. Nor can one allow the phrase to refer to more than one world, for then it would be the case that both a world where a cure for cancer is found in 2020 is actual and a world where such a cure is not found is actual, and this entails the self-contradictory statement that actually the cure for cancer is both found and not found in 2020. Therefore the indexical theory of actuality is not available on the identity variant of Extreme Modal Realism, and it is difficult to see what could replace it, given the unavailability for a Lewisian of an absolutist theory of actuality.
However the counterpart horn of the dilemma is no more congenial. First of all, we have to contend with the strong Kripkean metaphysical intuitions that what my counterparts might do in other worlds cannot be what makes it true that I could have been a biologist. Facts about people other than I are irrelevant interlopers with respect to questions about my capabilities.
Secondly, a variant ethical paradox can also be given, albeit one which for technical reasons has to be run in a counterfactual world and which needs the plausible technical assumption that there are no indiscernible worlds, a question Lewis himself remains agnostic about. It is indeed plausible that there are no indiscernible possible worlds. First of all, the usual tool for individuating indiscernible objects is by their spatio-temporal relations. But possible worlds do not stand in spatio-temporal relations to one another. Moreover, if there were indiscernible possible worlds, one could ask the question: How many indiscernible copies of a given possible world are there? Whatever answer one gave would seem arbitrary: even if the number were infinite, it would seem arbitrary that it has the precise cardinality it does.
Imagine then that I am in a possible world containing a number of persons, but only one of the persons ever makes a free choice, and suppose this choice is nondeterministic and is the only nondeterministic event physically possible in that world. The choice in question is whether I should stick my wet thumb in a light socket. Suppose I know this would not kill me and would have no ethically significant consequences for anybody in that world other than that it would cause severe pain for a while to me. It would clearly be irrational, indeed crazy, of me to perform that action.
However, if a counterpart version of Extreme Modal Realism is true, then this would not only not be crazy, but it would be heroic. For supposing that the world described above is actual, there is a non-actual world which shares the same initial conditions and laws of nature, but in which my counterpart makes the choice opposite to mine. If I stick my thumb in the light socket, my counterpart does not. If I do not stick my thumb in the light socket, my counterpart does. Therefore, there is a real sense in which by sticking my thumb in the light socket, I save someone else from horrible pain. This then is a heroic act of supererogation rather than a crazy act. Therefore, the counterpart version of Extreme Modal Realism is absurd.
Thus, Lewis’s Extreme Modal Realism leads to ethical paradoxes, albeit different ones, whether one adopts identity theory or counterpart theory. Both horns of the identity-vs.-counterpart theory dilemma involve other difficulties for Lewis’s Extreme Modal Realism. Moreover, the argument from inductive reasoning applies on either horn of the dilemma. Therefore, we have a strong cumulative case against Extreme Modal Realism on the basis of paradoxical conclusions. One paradox does not completely destroy a theory, but a large number of serious ones puts it in grave doubt.
The most promising contemporary realist alternative to Lewis’s account of possible worlds are the abstract worlds accounts promoted by Robert M. Adams and Alvin Plantinga. On their accounts, worlds turn out to be abstract Platonic entities, exactly one of which is instantiated by the universe, where “the universe” is defined to be the aggregate of all existing or occurring concrete entities, and this is the world that is absolutely actual. I will focus primarily on the Adams permutation of this account.
We thus start off by introducing propositions as theoretical abstract entities that are the bearers of truth-values and are needed to explain what it is that sentences express, what the objects of beliefs and propositional attitudes are and what paraphrases preserve, somewhat as electrons are needed to explain various physical phenomena. Some propositions, namely the true ones, are related to things and events in the universe, with the relation being one of the propositions being made true by or representing these things and events in the universe. If things in the universe were otherwise than they are, then different propositions would stand in these relations to things in the universe—if there were unicorns, then the proposition that there are unicorns would stand in the relation of being made true by to some things, namely the unicorns in the universe.
Note that the theoretical reason for believing in these Platonic propositions is largely independent of issues of modality. Adams then constructs a possible world as a maximal consistent collection of propositions. (An argument is needed that such collections exist, but as a matter of fact an argument can be supplied.) Exactly one world is then absolutely actual: it is the one all of whose propositions are true. A proposition can be said to be true at a world providing it is one of the propositions that are a member of the collection of propositions that the world is identical with. Note that because the worlds are Platonic entities, I had to distinguish between the concrete universe, which we physically inhabit, and the actual world which is the collection of all true propositions.
One might object to the Platonic approaches on the grounds that they all involve queer entities. Not only are we required to believe in Platonic beings, but, as Lewis notes, we are to believe that there is a magical relation of representation holding between Platonic beings such as propositions and the concrete entities that make them true, with it being contingent which propositions enter into those relations since it is contingent which propositions are true. What is it, then, that picks out one relation in the Platonic heaven rather than another as the relation of representation?
The proponent of these Platonic worlds can argue, however, that she has no need to answer this question. The relation of representation is one of the primitive terms in her theory, and it is not even a primitive chosen ad hoc to explain possible worlds, but a primitive needed for other explanatory purposes, such as of making sense of our practices of claiming, believing and paraphrasing. Nonetheless, if we had some way of pointing out this relation within the Platonic universe of all relations, then we would be happier as theorists.
Secondly, the Platonic theories are expressly non-reductive as accounts of possibility, unlike Lewis’s theory. For Adams, a possible world is a maximal consistent collection of propositions, which is just the same as saying it is a maximal compossible collection of propositions. On this theory, there is a primitive abstract property of possibility or consistency that applies to individual propositions and to collections of them. One could also take necessity to be the primitive concept, but this would not change anything substantially.
That the Platonic accounts are non-reductive is only a problem if a reductive account of possibility is available. However, the most plausible account claiming to be reductive is Lewis’s, which is too paradoxical to accept. But while a complete reduction is probably impossible, it would be desirable to give at least a partial reduction, on which the whole realm of alethic possibility would be seen to have its root in some more comprehensible subclass. The Platonic accounts do not succeed in performing this more limited reduction either.
Adams’ theory as an actualist one. His possible worlds are built up out of things that are actual. These abstracta actually exist—indeed, necessarily so—and an actualist theory is one that grounds possibility in actually existent realities. On the other hand, Lewis’s other worlds are not actual entities by Lewis’s indexical criterion, as they are not the world in which my tokening of the word “actual” in this sentence occurred. If we think of possible worlds as possibilities for our universe, then there is a sense in which Adams and Plantinga have grounded possibilities in actuality, thereby answering to the Aristotelian maxim that actuality is prior to possibility.
However, in a deeper way, the Platonic approach is not faithful to what the Aristotelian maxim affirms. When an Aristotelian says a possibility is grounded in an actuality, she means that the actuality has some powers, capacities or dispositions capable of producing that possibility, which of course once produced would no longer be a mere possibility. This is clearest in the paradigm case where the actuality is temporally prior to the possibility. Aristotle’s favorite illustration is how the actuality of one man makes possible the existence of a future man through the first man’s capability for begetting a descendant. If we find attractive the idea that possibilities should be grounded in actuality in the stronger Aristotelian sense, then the Platonic approach will be unsatisfactory, because Platonic entities, in virtue of their abstractness, are categorially barred from entering into causal relations, and hence cannot make possibilities possible by being capable of producing them.
Moreover, the Aristotelian can argue that in fact there are capabilities and dispositions sufficient to ground the truth of at least some possibility claims. That I could have been a biologist is very plausibly made true by my capacities and dispositions and those of various persons and things in my environment. These capacities and dispositions are concrete real-worldly things, albeit ones having modal force. Hence, in fact, we do not need a Platonic realm to make at least some possibility claims true. Indeed, the facts about the Platonic realm—about propositions having or not having some primitive property—are interlopers here. Just as the statement that I could have been a biologist was not made true by what my Lewisian counterparts in other worlds do, so too it is not made true by abstract properties of Platonic abstracta. The common intuition behind both cases is that it is something in me and my concrete environment that makes the statement true.
This, however, creates a major problem for the Platonic approach. On the Platonic approach, what makes it possible that I was a biologist is that the abstract proposition—which is an entity in the Platonic heaven—that I was a biologist has the abstract property of possibility. But we have just seen that there are concrete capacities and dispositions in the universe that are by themselves sufficient to make it possible that I was a biologist. We thus have two different ways of characterizing possibility: one is via concrete this-worldly Aristotelian properties of concreta which really do exist—the Platonist should not deny this—and the other is via some abstract Platonic primitive properties of abstracta. Moreover, anything that is possible on the Aristotelian grounds will be physically possible, and hence also logically possible, and hence possible on Platonist grounds (though prima facie perhaps not conversely). But now we can ask: Why is this so? Why is it there this apparent coincidence that anything made possible by this-worldly powers and capacities and dispositions happens to correspond to a proposition in the Platonic realm that has a certain abstract property? The Platonist is unable to explain this coincidence between powers in our universe and abstract facts about the Platonic realm, given the lack of causal interaction between the two realms.
If one shares the Aristotelian intuition that this-worldly capacities, powers and dispositions can make modal statements true, one might opt for a fully Aristotelian definition of mere possibility: A non-actual state of affairs is possible if there actually was a substance capable of initiating a causal chain, perhaps non-deterministic, that could lead to the state of affairs that we claim is possible. We can then say that something is possible if it is either actual or merely possible.
An approach like this has a number of benefits. Capacities, powers and dispositions are probably the concepts closest to ordinary language notions of possibility. They are things we arguably have direct experiential knowledge of, pace Hume, by ourselves being capable of producing effects, and we can at least point out by ostension what, say, a capacity is. Moreover, though while having modal force, they are concrete. Reducing all possibility to this subclass of modal notions would thus increase the comprehensibility of what we mean in saying something is possible—at least if one finds Aristotelian intuitions appealing. The account is not a full reduction, since powers and capacities are modal notions, but it does reduce all of modality to a more basic subclass.
There are, however, two closely related difficulties facing any such approach. The first is that while this works fine for local possibilities, such as of my having been a biologist, it is difficult to see how one could get possible worlds out of it.
The second problem is the following argument. Consider the set of all contingent beings in the universe, namely beings that could have failed to exist. It is highly plausible that if we have a set of beings, every member of which is contingent, then it is a contingent fact that any of the beings in the set exist. But if this is right, the Aristotelian has a problem. For the possibility that none of those contingent beings that exist in the universe had existed cannot be grounded in the causal powers of any actual contingent being. Note that we are talking here not about the controversial possibility that there should exist no contingent beings, but about the much less controversial one that those contingent beings that exist might not exist, though perhaps other ones might then exist in their stead.
Neither is it clear how the Aristotelian could account for the possibility of the laws of nature having been different. Again, we see that the Aristotelian account has trouble with global possibilities.
Consider now a somewhat different answer to the question of what possible worlds are. Leibniz, who started the whole debate about possible worlds, argued that necessary truths, including modal truths such as that unicorns are possible, must exist somewhere. Finding Platonic entities too queer, he wanted to locate these truths as acts of thought or ideas in the mind of an omniscient, necessarily existent God who contemplates them. He then gave an account of possible worlds that matched this. A Leibnizian possible world is a maximally specific consistent thought in the mind of God of a way for the world to be.
These acts of thought are actual entities, then, and so Leibniz has an answer as to what possible worlds are. Moreover, one might argue that Leibniz’s account makes some progress with respect to the question of how it is that the entities which are possible worlds represent concrete things. Recall that one difficulty with the Platonic approach was that of picking out which relation between concrete things and propositions was to count as the relation of representation. If one takes the controversial view that our thoughts are innately representative, the Leibnizian account may get around this problem by saying that that relation between divine thoughts and concrete things counts as the relation of representation which is the relation produced by that faculty in God’s mind which is analogous to the faculty of intentionality in us, and we can perhaps point out which of our faculties is the faculty of intentionality by ostension. There are many difficulties here, including first of all the Leibnizian’s very controversial commitment to thoughts being innately representative or to a faculty of intentionality. But if we find appealing the intuition that we can have a better grasp of what thoughts are, even divine thoughts, than we can of Platonic entities, because thoughts are something that we after all have direct experiential knowledge of, then we might prefer the Leibnizian account.
However, this does not solve the main problem with the Platonic approach which was its failure to give an adequate account of what makes possibilities possible. The Leibnizian account does not help there at all, since those divine ideas that are singled out for being dubbed “worlds” are singled out in virtue of being consistent, that is possible. Their possibility is prior in the order of explanation to their being known by God to be possible (cf. Adams, 1994, p. 191). And so this approach is not relevantly different from singling out some collections of propositions for being dubbed “worlds” on the grounds of their being consistent. Positing a God who contemplates possible worlds as described above does not in any way help with Aristotelian intuitions about possibility being grounded in actuality, since, as far as the account goes, the thoughts could be just as causally inert as Platonic abstracta.
But now go back to one of the arguments against the Aristotelian view. The argument was that the Aristotelian cannot posit a contingent substance that would ground the possibility of our whole past history having been different. But if the Aristotelian is brave enough, she can say that what this shows is that if the Aristotelian notion of possibility is correct, and if we accept the intuition that none of those contingent beings that exist might have existed, then we are committed to the claim that there is a non-contingent being which grounds the possibility of none of the contingent beings having existed. In fact, with a little work, this argument can be extended to show that the Aristotelian notion of possibility commits one to the existence of a necessary first cause (perhaps a non-unitary cause which is an aggregate of causes) that non-deterministically produces the historical universe and grounds the possibility of other histories, and indeed of there being other laws of nature.
A sketch of the argument is as follows. Let S be the set of all actually existing contingent beings, and let w0 be the actual world. Then, let w1 be a possible world in which no member of S exists. It is then true at w1 (technically, by the axiom S5 of modal logic) that it might have been that w0 was actual. Then, by the Aristotelian account, there is a substance x in w1 which could have initiated a causal chain that could lead to w0 being actual. But x cannot start any chain of causes that can lead to actuality’s not including x. Therefore, x must also exist in w0. Thus, x exists both in w0 and w1. Since no member of S exists in w1 while x exists in w0, it follows that it is true at w0 that x is not a member of S and hence is a necessary being. A further argument along similar lines can be used to show that in fact x must be the first cause of all contingent beings in w0.
To some, of course, this will count as a reductio ad absurdum of the Aristotelian approach. However, if we do not count it as such, there is a natural way to combine this account with Leibniz’s, by identifying the Aristotelian first cause with Leibniz’s necessarily existent God. Then, one could have both possible worlds, namely certain thoughts in the mind of God, and an answer to the problem of what makes these worlds possible, namely God’s power for initiating a causal chain capable of leading to their existence. The God of this theory would not only be omniscient but also omnipotent, then. Of course how attractive one will find this account will depend on one’s assessment of other evidence for and against the existence of such a God.
If one decides not to take this theistic route, one might well have to go with a Platonic account of what possible worlds are, at the cost of having possibility be a primitive property of abstracta and of not being able to do justice to the Aristotelian intuition that actuality is prior to possibility, or else with an Aristotelian account of possibility, at the cost of not having possible worlds or global possibilities. Alternately, as far as a theory of possibility goes, one might give up on possible worlds, but allow for global possibilities such as of the laws of nature being different or of none of the actual contingent beings existing by invoking a non-theistic first cause for history, such as some event prior to the Big Bang in some superuniverse.
There is hope, however, that the theistic account, once elaborated sufficiently, would end up combining the strengths of the Platonic, Aristotelian and Leibnizian accounts while avoiding most of their weaknesses. Of course this requires that there be an essentially omniscient and omnipotent necessary being, but just as Lewis thinks that the theoretical usefulness of his Extreme Modal Realism is an argument for the existence of his concrete physical worlds, so too one can argue that the theoretical usefulness of a theistic account like this provides some grounds for thinking it is true, and in particular that there is a God.
Adams, Robert M. “Theories of Actuality”, Noûs, 8 (1974), pp. 211-31.
Adams, Robert M. Leibniz: Determinist, Theist, Idealist. Oxford University Press, 1994.
Gale, Richard M. On the Nature and Existence of God. Cambridge University Press, 1991.
Lewis, David. On the Plurality of Worlds. Basil Blackwell, 1986.
Plantinga, Alvin. The Nature of Necessity. Oxford University Press, 1974.
 Technical note: It might be argued that in fact even in this example “the actual world” is not used rigidly but simply has wide scope within the sentence it is tokened in. To see this, consider the following dialogue (with a slight change of example). A: “It could have been the case that Smith was less intelligent than she is in the actual world.” B: “This is true, but it might not have been true.” In this dialogue, B makes the arguably true claim that it might have been the case that Smith had such a level of intelligence that she could not have had a lower (this would be true if it was possible for Smith to have had no intelligence at all). However, if “in the actual world” were a rigid designator, and the actual world were w0, then B would be making the claim that although it could have been the case that Smith was less intelligent than she is in w0, it could have been the case that it could not have been the case that Smith was less intelligent than she is in w0, a claim that is evidently false if S5 is true (i.e., if the possibly possible is necessarily possible). If we take it that B’s claim is not evidently false, then we have to grant that although “in the actual world” has wide scope relative to the rest of A’s assertion, it is not rigid.
 I am grateful to Robert Brandom, James Dreier, Richard Gale, Jeremy Heis, David Manley, Thane Naberhaus, Alvin Plantinga, Nicholas Rescher, Ernest Sosa and Peter van Inwagen for encouragement, discussions, comments and/or suggestions.