The problems of metaphysics: the “new” metaphysics

It has long been recognized by philosophers that there is an important distinction to be made within the class of true propositions: the distinction between those that might have been false and those that could not have been false (or those that have to be true). Consider, for example, the proposition that Paris is the capital of France and the proposition that there is a prime between every number greater than 1 and its double. Both are true, but the former could have been false and the latter could not have been false.Philosophers have, moreover, recognized that there is a corresponding distinction to be made within the class of false propositions: between those that could have been true and those that could not have been true (or those that had to be false). That there are false propositions of both kinds is also easily proved by example.

Some Medieval philosophers supposed that the fact that true propositions are of the two sorts “necessarily true” and “contingently true” (and the corresponding fact about false propositions) showed that there were two “modes” in which a proposition could be true (or false): the mode of contingency and the mode of necessity—hence the term ‘modality’. Few modern philosophers if any would regard this as a useful thing to say. In current philosophy, ‘modality’ is a mere label, a word that reflects no particular theory. It means no more than ‘pertaining to possibility and necessity’. The modality of propositions is called modality de dicto (‘dictum’ means ‘proposition’, or close enough). If modality were—and this has been a popular view—coextensive with modality de dicto, it would be at least a defensible position that the topic of modality belongs to logic rather than to metaphysics. But modality would seem to be an undeniably metaphysical topic if one admits the existence of modality de re—the modality of things. (The modality of substances, certainly, and perhaps of things in other ontological categories.) We assign modality de re to the “new metaphysics” because, although one can ask modal questions about things that do not change—God, for example, or universals—, a large proportion of the work that has been done in this area concerns the modal features of changing things, of “ordinary objects.”

Consider first the existence of things—of human beings, for example. If Sally, an ordinary human being, says, “I might not have existed,” almost everyone will take her to have stated an obvious truth. (Anyone who does not will almost certainly be a metaphysician with a theory.) And if what she has said is indeed true, then she exists contingently. That is to say, she is a contingent being: a being who might not have existed. And if there is such an idea as the idea of a contingent being—if ‘contingent being’ is a meaningful phrase—, then there would seem to be such an idea as the complement of that idea, the idea of a necessary being, the idea of a being of which it is false that it might not have existed. (Which is not to say that this idea would be a possible idea—after all, there is such an idea as “a method of trisecting the angle by Euclidian means,” but it can be shown that nothing in reality could correspond to this idea.)

Consider next the properties of things. Like the existence of things, the possession of properties by things is subject to modal qualification. If Sally, who speaks English, says, “I might have spoken only French,” almost everyone will take that statement to be no less obviously true than her statement that she might not have existed. And if what she has said is indeed true, then “speaking English” is a property that she has only contingently or (the more usual word) only accidentally. And if there is such an idea as “having a property accidentally,” there is such an idea as having a property but not having it accidentally: the idea of having a property essentially. (A thing has a property essentially if it could not exist without having that property.) The examples that philosophers have offered of a thing's having a property essentially tend to be controversial, but this is largely because the most plausible examples of a certain object's possessing a property essentially are only as plausible as the thesis that that object possesses those properties at all. For example, if Sally is a physical object, as physicalists suppose, then it is very plausible for them to suppose further that she is essentially a physical object—but it is controversial whether they are right to suppose that she is a physical object. And, of course, the same thing can be said, mutatis mutandis, concerning dualists and the property of being a non-physical object. It would seem, however, that Sally is either essentially a physical object or essentially a non-physical object. And many would find it plausible to suppose that (whether she is physical or non-physical) she has the property “not being a poached egg” essentially.

The most able and influential enemy of modality (both de dicto and de re) was W. V. Quine, who vigorously defended both of the following theses: That modality de dicto can be understood only in terms of the concept of analyticity (a problematical concept in his view), and that modality de re cannot be understood in terms of analyticity and therefore cannot be understood at all. If modality de re makes any sort of sense, Quine contended ((1960) 199-200), cyclists must be regarded as essentially bipedal—for ‘Cyclists are bipedal’ would be regarded as an analytic sentence by those who believe in analyticity—, and mathematicians as accidentally bipedal (‘Mathematicians are bipedal’ is not analytic by anyone's lights). What then, Quine proceeded to ask, of someone who is both a mathematician and a cyclist?—is that person bipedal essentially or only accidentally? Most philosophers are now convinced, however, that Quine's “mathematical cyclist” argument has been adequately answered by Saul Kripke (1972) and Alvin Plantinga (1974) and various other defenders of modality de re. (Plantinga pointed out, moreover, that if modality de re makes sense, then modality de dicto certainly makes sense as well: a necessarily true proposition is a proposition that has the property “truth” essentially.)

The arguments of Kripke and Plantinga in defense of modality are paradigmatically metaphysical (except insofar as they directly address Quine's linguistic argument). Both turn on the concept of a possible world. Leibniz was the first philosopher to use ‘possible world’ as a philosophical term of art, but Kripke's and Plantinga's use of the phrase is different from his. For Leibniz, a possible world was a possible creation: God's act of creation consists in his choosing one possible world among many to be the one world that he creates—the “actual” world. For Kripke and Plantinga, however, a possible world is a possible “whole of reality.” For Leibniz, God and his actions “stand outside” all possible worlds. For Kripke and Plantinga, no being, not even God, could stand outside the whole system of possible worlds. A Kripke-Plantinga (KP) world is an abstract object of some sort. Let us suppose that a KP world is a possible state of affairs (this is Plantinga's idea; Kripke says nothing so definite). Consider any given state of affairs; let us say, Socrates' being snub-nosed. This state of affairs obtains, since Socrates was snub-nosed. By contrast, the state of affairs “Socrates' having a long straight nose” does not obtain. The latter state of affairs does, however, exist, for there is such a state of affairs. (Obtaining thus stands to states of affairs as truth stands to propositions: although the proposition that Socrates has a long straight nose is not true, there nevertheless is such a proposition.) The state of affairs x is said to include the state of affairs y if it is impossible for x to obtain and y not to obtain. If it is impossible for both x and y to obtain, then each precludes the other. A possible world is simply a possible state of affairs that for every state of affairs x either includes or precludes x, and the actual world is the one such state of affairs that obtains.

Having the concept of a possible world at our disposal, we may define any modal concept. For example, a necessarily true proposition is a proposition that would be true no matter what possible world was actual. Socrates is a contingent being if there is some possible world such that he would not exist if that world were actual, and he has the property “being human” essentially if every possible world that includes his existence also includes his being human. Kripke and Plantinga have greatly increased the clarity of modal discourse (and particularly of modal discourse de re), but at the expense of introducing a modal ontology, an ontology of possible worlds.

Theirs is not the only modal ontology on offer, however. The modal ontology of David Lewis (Lewis (1986)) stands in stark opposition to the KP modal ontology. Lewis's modal ontology also appeals to objects called possible worlds, but these “worlds” are concrete objects. What most of us call the universe is just exactly what Lewis calls “the actual world.” Non-actual worlds are other universes, “non-actual” only in that we are not among their inhabitants, for two “worlds” share no part. (There is, Lewis contends, a vast array of non-actual “worlds,” an array that contains at least those worlds that are generated by an ingenious “principle of recombination,” a principle that can be stated without the use of modal language ((1986), 87).) For Lewis, ‘actual’ is an indexical term: when I speak of the actual world, I refer to the world of which I am an inhabitant—and so for any speaker who is “in” (who is a part of) any world.

In the matter of modality de dicto, Lewis's theory proceeds in a manner that is at least parallel to the KP theory: there could be flying pigs if there are flying pigs in some possible world (if some world has flying pigs as parts). But the case is otherwise with modality de re. Since every ordinary object is in only one world, Lewis must either say that each such object has all its properties essentially or else adopt a treatment of modality de re that is not parallel to the KP treatment. He chooses the latter alternative. Although Socrates is in only the actual world, Lewis holds, he has “counterparts” in some other worlds, objects that play the role in those worlds that he plays in this world. If all Socrates' counterparts are human, then we may say that he is essentially human. If one of Hubert Humphrey's counterparts won (the counterpart of) the 1968 presidential election, it is correct to say of Humphrey that he could have won that election.

In addition to the obvious stark ontological contrast between the two theories, they differ in two important ways in their implications for the philosophy of modality. First, if Lewis is right, then modal concepts can be defined in terms of paradigmatically non-modal concepts, since “world” and all the Lewis's other technical terms can be defined using only ‘is spatio-temporally related to’, ‘is a part of’ and the vocabulary of set theory. For Kripke and Plantinga, however, modal concepts are sui generis, indefinable or having only definitions that appeal to other modal concepts. Secondly, Lewis's theory implies a kind of anti-realism concerning modality de re. This is because there is no one relation that is the counterpart relation, for there are various ways or respects in which one could say that objects in two worlds “play the same role” in their respective worlds. Socrates, therefore, may well have non-human counterparts “under” one counterpart relation and no non-human counterparts under another. And the choice of a counterpart relation is a pragmatic or interest-relative choice. But on the KP theory, it is an entirely objective question whether Socrates fails to be human in some world in which he exists: the answer must be Yes or No and is independent of human choices and interests.

Whatever one may think of these theories when one considers them “in their own right” (as theories of modality, as theories with various perhaps objectionable ontological commitments), one must concede that they are paradigmatically metaphysical theories. They bear witness to the “resurgence” of metaphysics in analytical philosophy in the last third of the twentieth century

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