Modality, Philosophy and Metaphysics of

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MODALITY, PHILOSOPHY AND METAPHYSICS OF

Some things are true; some are false. Some are true, but might have been false. Some are true but could not have been false. Some are false, but might have been true. Some are false but could not have been true. Thus, there are at least these different modes of truth and falsity: necessity and possibility. A truth bearer—a proposition, a statement, or an interpreted sentence—is necessarily true if and only if (iff) it is not possible that it be false; it is possibly true iff it is not necessary that it be false. A contingency is what is possibly true as well as possibly false. The study of the ways in which truth and falsity interact with necessity and possibility is the subject of modal logics.

If there are modal distinctions to be made about truth bearers—because, say, while the sum of seven and five could not fail to be twelve, there might have been twelve planets orbiting the sun even though there are not—arguably there are modal distinctions to be made regarding the attributes objects possess. While Socrates could have failed to be snub-nosed, he could not have failed to be human or perhaps a person. Modality as it pertains to the bearers of truth is de dicto modality; modality that concerns the way in which an object possesses an attribute is de re. Conventionally, □ and ◊ express necessity and possibility, respectively.

Kinds of Necessity

Necessities may be distinguished according to their scope or, perhaps, their subject matter. Some concern the limits of meaning and inference and are systematized by formal logical systems. Classical logicians maintain that meaning and inference are best understood in terms of a two-valued logic according to which truth bearers may take only the values of true or false and that exactly one of a truth bearer and its negation is true. These ideas are encoded by, though not strictly equivalent to, the laws of excluded middle, P v ¬P, and noncontradiction, ¬(P & ¬P). Where objects and their attributes are concerned, there are analogous laws: Each thing either has or lacks a given attribute and neither both has and lacks the same attribute, formally represented as ∀x(Fx v ¬Fx) and ∀x¬(Fx & ¬Fx). Some nonclassical logics have correspondingly different foundational laws. Such laws of logic are treated as necessary truths, though usually they are stated without any de dicto modal qualifier. Logical truths, the truths that follow validly from the axioms of logic, are the logical necessities. Whatever is consistent with the laws of logic are the logical possibilities and if the falsity of something follows from the laws of logic, then it is a logical impossibility.

Disputes about which of the many logical systems is the single correct system that formalizes valid inference are, then, disputes about what the logical necessities are. Disputes about whether there is a single such correct system are disputes about whether there is a plurality of sets of logical necessities, one corresponding to each system of logic. Broader notions of logical necessity are sometimes given by adding linguistic or conceptual truths. Analytic or conceptual necessities are those that follow from the laws of logic plus the linguistic or conceptual truths. That all bachelors are unmarried is a favorite example of such an analytic truth.

Laws of nature and their associated counterfactual conditionals are often thought to be necessary in one sense and contingent in another. There are many true universal generalizations and many unbroken sequences of types of events. Not all of these, however, form part of some scientific theory; some generalizations and patterns are accidental. Those that are not accidental and constitute the fundamentals of a scientific theory are the laws of nature and whatever follows from those laws are the natural necessities. Whatever is consistent with the laws of nature are the natural possibilities. It is sometimes useful to make distinctions among the natural necessities and separate the physical, chemical, biological, psychological, and perhaps other necessities.

The natural necessities are not logical truths, however. Orthodoxy has it that logical truth is known a priori, without any specific experiences, while scientific truth is knowable only a posteriori, on the basis of experience. That empirical investigation is required for scientific knowledge is taken to show that the natural necessities are contingent; they might have been otherwise. Certainly, they are not analytic and cannot be known simply by reflecting on their contents. If one takes the most central laws of physics to be the axioms of physics, then what follows from those laws are the physical necessities. That the basic physical laws are required to infer the physical necessities demonstrates more conclusively that the physical necessities are not logical truths and, so, are not logical necessities. If laws of nature are necessary in some legitimate sense, then the meaning of □ when applied to laws of nature must differ from its meaning when it is applied to laws of logic.

Somewhat more controversial is the idea that there is an intermediate modality between the logical and the natural: the metaphysical. Like natural necessities, metaphysical necessities are not logical truths and yet, unlike the natural necessities, the central metaphysical principles are to be known a priori even if knowledge of some particular metaphysical necessities requires some empirical knowledge. While there is no contradiction in denying such metaphysical principles, their proponents maintain that they are, nevertheless, necessary and that they express limits on genuine possibilities for existence. Accordingly, logical possibilities that fail to be metaphysical possibilities would be merely formal possibilities.

Thus, if there are two distinct attributes that are essentially related, then while there is no contradiction in asserting that an object could possess the one without the other, it would be, strictly speaking, impossible for any object to possess the one without the other. There might be attributes such that if an object even possibly possesses it, then that object possesses that attribute essentially. Arguably, if something is a concrete object such as a brick, then it must be concrete and could not be an abstract object such as the power set of the real numbers. Those who embrace this intermediate modality think that metaphysical principles state nontrivially what is at least part of the essence of an object—that without which it could not be—and, so, they are known as essentialists or sometimes Aristotelian essentialists since Aristotle advocated a form essentialism.

While the philosophy of modality is dominated by controversies about whether there are the three modalities mentioned and, if so what their relations are, there are others of interest. If one takes up the general pattern used earlier and recognizes that a common way to characterize the content of a modality is to formulate a set of axioms and define a sense of □ so that it applies to all and only whatever follows from those axioms, then there are indefinitely many kinds of modality. For each formally characterized system of logic there is a candidate for logical necessity, not all of which are equivalent. Such a plurality cascades down through any modality that relies on logical consequence for its own characterization.

Among the most commonly discussed of the other modalities are the epistemic, doxastic, and moral necessities. Epistemic necessity can be thought of as whatever follows from what is known and the scope of the known can be specific to an individual or to a community. Doxastic necessity is what follows from what is believed. Moral necessities are the relevant moral obligations and duties. Whether any of the modalities mentioned is nothing but a special form of any of the others is a substantial question, but the only clear connection, given the way they have been characterized, is that all the nonlogical modalities tacitly embed the logical. The axiom-theorem structure demands this, making each of them an extension of the logical and not a special case of it.

Sources of Necessity

For any recognized kind of necessity there is the substantive question of what accounts for the fact that some truths, and not some others, are necessary in the relevant sense. As with other forms of discourse, there are deep philosophical questions about whether one has any knowledge involving modality. These questions have at least two forms. The first form is a standard challenge from the skeptic who does not deny, in this context, that there are necessary truths but who denies either that one has any knowledge of which truths are necessary or that nonskeptics are entitled to their knowledge claims according to their own standards of knowledge. The second form comes from the modal antirealist, one who either denies that there are any modal truths or who claims that modal truth is so closely bound to cognizers that statements involving modality lack significant objectivity, making them more like statements of taste or preference than statements of fact. Modal noncognitivists maintain that modal discourse is used not to make assertions but to, perhaps, express an attitude or a commitment toward some nonmodal truths. David Hume (1739) adopted a kind of noncognitivism about the relation of cause and effect. Simon Blackburn (1986) and Crispin Wright (1980, 1989) advanced contemporary defenses of versions of modal antirealism.

Realist interpretations of modal discourse treat some statements involving modality as true in some person-independent manner. If modal truth is to be a species of truth more generally then, thinks the realist about modal discourse, modal truth must concern sufficiently determinate and objective facts. This is the question of what grounds modal truth or, perhaps, what the truth conditions are for modal claims. Common suggestions have been that something is possible iff it is conceivable, iff it implies no contradiction, iff it is true in at least one mathematical model, or iff it is true in at least one possible world.

The success conditions for a theory of modality depend on the purpose of that theory. Any successful theory should be extensionally adequate; it should declare as necessary all and only what is necessary. Philosophical theories are often put forward as being more than merely extensionally adequate, sometimes because they are intended as linguistic or conceptual analyses. A conceptual analysis would state not only the appropriate biconditionals that fix the extension of necessary, it would do so in such a way that analyzed the meaning of that term. Successful conceptual analyses must not only be extensionally adequate, they must also be noncircular by avoiding the use of what is to be analyzed in the analysis or definition. Analyses of modal notions would need to avoid analyzing necessary in terms of any modal notions like necessary, possible, or their cognates. When empirical confirmation of the extensional adequacy of a theory is impossible to obtain, conceptual analyses are attractive. The conceptual analysis guarantees extensional adequacy because the analysis given means nothing more and nothing less than that for which it is a theory. Theories not intended as conceptual analyses must involve some other warrant for the thesis that the theory is extensionally adequate.

If proposed as an analysis, a conceivability theory faces difficulties regarding both extensional adequacy and circularity. If it is formulated in terms of conceivers who are not perfect conceivers, then extensional adequacy is not guaranteed; there may be possibilities of which no one is capable of conceiving or else conceivers may be capable of conceiving what is impossible without noticing that it is impossible. Formulating the theory in terms of what is merely conceivable, whether by an ideal or fallible conceiver, renders the analysis circular because the semantic analysis of possible is given in terms of what it is possible to conceive. Formulating it in terms of what is actually conceived by an omniscient being avoids this circularity but brings metaphysical commitments that few want to make on the basis of their philosophy of modality alone.

The logical positivists wished to maintain that logical and mathematical truths were necessary, but they resisted all substantive metaphysics as distinct from the ontologies of the sciences. Alfred J. Ayer (1936) developed a version of conventionalism about modality. By dividing propositions into the classes of those that concern ideas or concepts only and those that concern facts, Ayer maintained that only propositions regarding ideas were both necessary and knowable a priori. They make no claims about the empirical world and, so, are not subject to empirical falsification and are either necessarily true or necessarily false. These propositions are analytically true or analytically false according to Ayer because they are true or false due solely to the definitions or analyses of their constituent symbols, both logical and nonlogical. It is necessarily true that all bachelors are unmarried not because of the way the world is but because of what is meant by all, bachelors, unmarried, and tacitly, if, then.

Willard Van Orman Quine provided what has become the received critique of attempts to ground necessary truth and falsehood in the facts of language. In "Two Dogmas of Empiricism" (1951) Quine argued that there is no hard and fast distinction between propositions that are about the world and those that are not and, so, that no proposition is immune from refutation on partly empirical grounds. Thus, he argued that there is no interesting analytic-synthetic distinction on which the positivist program depends. In "Truth by Convention" (1948) he argued that stipulations regarding the meanings of expressions cannot be a general source of necessity, since at most they can transform obvious logical truths into more convenient but less obvious truths.

So, it is a logical truth that all unmarried males are unmarried and if bachelors just are, by definition, unmarried males, then the logical truth plus the definition of bachelor is sufficient for the truth of "all bachelors are unmarried." However, this transforming work of definitions requires something to begin with that is already necessarily true: the relevant logical truth. Linguistic conventions are unable to account for the necessity of the logical truths. Rudolf Carnap (1954) tried to solve this problem by avoiding the semantic foundation of meaning, thus avoiding Quine's critique, and by relying on syntactic facts of grammar and rules of logical proof. He understood logical truth as what is derivable from the null class of sentences.

While not relying on meanings, the standard problems regarding extensional adequacy and circularity arise. Standard understandings of logical systems have it that there are infinitely many sentences that may be derived from the null set, not all of which have been derived. Framing the theory in terms of what has actually been derived renders the account extensionally inadequate, while framing it in terms of facts of derivability renders it circular. A successful form of the linguistic theory of modality might retreat from the positivist's rejection of all metaphysics and appeal to facts about concepts or propositions in a Platonic Heaven of abstract objects. Alternatively, there could be a stipulation by a kind of ostention according to which necessary is stipulated to apply to some already established classes of truths, say logical, mathematical, and analytic truths. This would give one a kind of conventional basis for necessity, but not for the truth of what is by this convention called necessary. This account assumes that there are logical, mathematical, and analytic truths before the stipulation. While each account avoids the problems posed for Ayer's (1936) and Carnap's, they do not deliver what the positivists wanted: a general theory that demonstrates why logical, mathematical, and analytic truths are completely immune from empirical refutation while at the same time avoiding all metaphysics that they found philosophically distasteful. Alan Sidelle (1989) attempted to present a more defensible version of conventionalism.

Possible Worlds and Modal Logic

Before and during the time that the positivists were developing their philosophical approach to modality and Quine (1948, 1951) was subjecting it to critical scrutiny, elementary first-order predicate logic was being extended with the use of modal operators, most famously by Clarence Irving Lewis (1918) and Lewis and Cooper Harold Langford (1932). Unlike the developments of nonmodal logics up to that time, about which there was widespread agreement that alternative axiom systems were equivalent, there were many inequivalent axiomatic systems of modal logic. Worse, standard first-order logics had been provided with mathematical semantic foundations from which the systems of proof could be shown to be adequate for proving all theorems of first-order logic and for never permitting the derivation of any nontheorems. Modal logics lacked a similar semantic framework. The many inequivalent systems made it impossible, on formal grounds alone, to determine which logic was the proper formalization of modal concepts that, in turn, caused some to wonder whether modal concepts were sufficiently respectable to be given systematic treatment.

Part of the difficulty arose because the modal expressions in formal languages, □ and ◊, were treated like the negation symbol, ¬. Thus, if P were a sentence of the formal language, ¬P, □P, and ◊P would also be sentences of the language. Like negation, the modal operators could be used in quantified sentences of the language, so that if ∀xFx and ∃xFx were sentences of the language, □∀xFx, ∀x□Fx, □∃xFx, and ∃x□Fx would be as well. The de dicto use of modality in □∀xFx and □∃xFx seemed innocent enough to those who were not convinced by Quine's (1951) critique of analyticity. More troublesome were the de re forms, ∀x□Fx and ∃x□Fx. In stating that everything is necessarily or essentially F and that something is necessarily or essentially F, these sentences seem to make metaphysical claims, about which the positivists had succeeded in raising suspicion.

In 1963 Saul Kripke made prominent some developments in the semantics of modal logic. The central idea was to mimic an important aspect of the formal semantics for first-order logic. The mathematics of model theory that had enabled logicians to define what it is for an argument to be formally valid involved appealing to a domain of objects, mathematical models, that were customarily thought to be abstract objects. In these models, one could define the extensions of predicates, intuitively the sets of objects that possessed the relevant attributes or that stood in the relevant relations to each other. Logical notions like validity could be defined in terms of these mathematical models.

Kripke and others saw that if this model-theoretic framework were extended, a similar formal semantics could be given for modal logics. Whereas standard models had concerned only everything that does exist, the extension of this approach was simply to take as the domain everything that exists not only in the actual world but also everything that exists in every possible world. The second key idea was to treat the modal operators like quantifiers. If □ was treated as ∀ and ◊ as ∃, then □P could be thought of as a expressing the claim that P is true in every possible world and ◊P could be thought of as expressing the claim that P is true in at least one such world, whether this world or not. A historical overview of developments of this general approach before Kripke's elegant presentation can be found in B. J. Copeland (1996).

Possible Worlds and Metaphysics

Those proposing this possible worlds semantics for modal logic thought of the structure quite abstractly. The suggestion to think of the main domain as the set of all possible worlds was merely a heuristic to illuminate the intuitive idea behind the abstract structure of the semantics. It was David Lewis (1973) who recommended taking this heuristic to have metaphysical significance. He argued that modal claims can be paraphrased with claims about possible worlds. Many agreed with this much, but resisted Lewis's genuine modal realism," according to which each world in this plurality was as robust and concrete as one thinks of this world. In some of these worlds there are donkeys that talk and in some there are blue swans. So, while those concerned with the semantics of modal logic were concerned with providing a formal mathematical structure according to which important logical notions like logical consequence could be precisely characterized, Lewis was concerned with the issue of the grounds for the truth values of modal claims. So, for Lewis, □P is true iff P is true in all the worlds; otherwise, not.

The formal apparatus involved an accessibility relation over this set of worlds and that relation could have variable extension. This permitted Lewis (1973) to assess counterfactual conditionals in terms of what happens not merely in some world or other, but what happens in close or sufficiently similar worlds. Thus, in some circumstances I could have done otherwise because in an appropriately similar world one similar to me does otherwise.

Lewis's (1973) genuine modal realism served as the focus of much discussion about the philosophy and metaphysics of modality, although the position has had relatively few adherents. The possible worlds theorist was able to take the mathematical results about modal logic and to find in them the grounds for modal truth. Initial discussions of the possible worlds framework, however, focused on reasons for thinking that while the framework should be adopted, Lewis's metaphysics of possible worlds should be resisted.

One serious problem for the genuine modal realist is epistemological. Suppose that there really is a plurality of concrete worlds and that it is facts about these worlds that make true or false one's modal assertions. How can this account of the truth conditions for modal claims be squared with the often-unstated starting point in the philosophy of modality: that one possesses some knowledge of modal truth that is not merely trivial? One thinks that one knows that there could be talking donkeys, blue swans, and many more things that do not actually exist. One also thinks one knows the truth of some counterfactual conditionals, such as that were the sun to cease to exist, then the earth would cool rapidly and that were a thin pane of ordinary glass to be struck by a flying rock, it would break. If the modal facts, however, really are facts about other worlds, how could one have gained any of this knowledge?

A second apparent problem is that the possible worlds framework looks ill suited to the task of philosophical analysis of modal idioms. If one says that ◊P is true iff P is true in every possible world, then the analysis certainly appears to be extensionally adequate, but at the cost of circularity. If one says, rather, that ◊P is true iff P is true in every world that there is, then obvious circularity is avoided at the cost of no longer exhibiting the extensionally adequacy of the analysis.

The epistemological problem was addressed by those who proposed accounts of the nature of possible worlds in terms of objects that, it was maintained, one already had reason to accept. Instead of thinking of truth in possible worlds as truth in or about concrete maximal spatiotemporal wholes, it was argued that truth in possible worlds is really truth in maximal states of affairs (Plantinga 1974), truth in world stories—maximal consistent sets of propositions (Adams 1974), or truth about properties of a special kind—ways the world might have been (Stalnaker 1976). Each theory was actualist in that it recognized only objects that actually exist or, to use the vocabulary of possible worlds, each recognized only objects that exist in the actual world. To that extent each of these alternatives had the advantage of locating the ground for modal truths in this world and not another. That there was a useful solution to the general form of the epistemological problem posed for Lewis's (1973) genuine modal realism depends on whether the central feature of the problem was that the modally relevant facts inhabited or constituted worlds distinct from one's own.

Arguably, the central feature of the problem was that it was hard to wed the metaphysics of concrete worlds with plausible accounts of the nature of knowledge. Lewis's account of worlds permitted no physical or causal contact with features of other worlds. To avoid this general problem, some mutually favorable accounts of the natures of states of affairs, propositions, or properties on the one hand and knowledge on the other hand are required. To the extent that these entities are abstract and to the extent that abstract entities are not spatiotemporally or causally located, these actualist theories do not solve this epistemological problem. To the extent that spatiotemporal connectedness is not necessary for access to, say, propositions, then the genuine modal realist could, perhaps, take advantage of an alternative account of knowledge to avoid this particular problem.

Lewis (1986) recognized that his theory of modality could not serve as the basis for a proper analysis of modal notions, if he could not analyze the concept of a possible world. If he could not, possible truth would be analyzed in terms of possible worlds that, while involving some philosophical advance perhaps, does not constitute a full analysis of modal concepts in nonmodal terms. Lewis (1986) argued that each world is a maximal spatiotemporally connected whole; objects inhabit the same world when they spatiotemporally connect to each other. On the reasonably safe assumption that these spatiotemporal notions are not themselves modal, obvious circularity is avoided.

Extensional adequacy must still be secured. Lewis (1986) tries to secure it by somewhat contentious means. He appeals to a Humean principle of recombination to support the thesis that there are sufficiently many possible worlds. Recombination is the denial of necessary connections between distinct existences. So long as the objects occupy distinct spatiotemporal locations, anything could exist with anything else or, strictly speaking, a duplicate of anything could exist with a duplicate of anything else. This basis for plenitude is more contentious than was the avoidance of obvious circularity because it depends on the more controversial Humean principle. Essentialists reject that principle as do those who maintain that laws of nature are metaphysically necessary.

There may yet be some hidden circularity or other theoretical impropriety as argued by Scott A. Shalkowski (1994, 2004). Of course, if there is a plurality of concrete worlds in which sufficiently much of what one takes to be possible is true, then knowing this would be sufficient warrant for declaring that possible truth just is truth in some world or other. It is knowing that there is this match between one's apparent modal knowledge and the internal workings of the worlds in the plurality that is difficult to secure in a nonquestion-begging way. Were philosophical analysis sufficient to justify not only that there are possible worlds, but that they are concrete and sufficiently plentiful for the required correlation, then all would be well for the genuine modal realist. John Divers and Joseph Melia (2002), however, argued that analysis is inadequate to establish that there are sufficiently many worlds. The danger, then, is that the grounds for genuine modal realism as a full theory of modality are question-begging or else inadequate. Furthermore, they argue that the framework may not even be extensionally adequate because there may be no complete set of all possible worlds.

Some objections to genuine modal realism concerned whether the conditions it provides really are adequate to grounding the modal claims one thinks one is entitled to make. For example, one knows that in some instances one could have behaved otherwise than one did. Strictly speaking, though, I am a world-bound individual. I inhabit only this spatiotemporal whole and not another. However, it is what goes on in other worlds that is supposed to account for the fact that I could have behaved otherwise. I could have behaved otherwise because some world contains a counterpart of me that does, in a suitably similar situation, behave otherwise. This is Lewis's counterpart theory (1968, 1986).

Kripke (1972/1980) argued that counterpart theory is inadequate precisely because the modal claim under consideration concerns what I could do. How does what someone else somewhere else does make it the case that I could have followed that alternative course of action? That someone else in this space-time does something else does not make it the case that I could have done the same, so someone else in another space-time seems no more relevant.

Though Kripke's (1972/1980) objection has intuitive appeal, arguably it is question-begging. Lewis (1986) develops counterpart theory so that the identity of individuals across worlds, transworld identity, just is a matter of having a counterpart in those other worlds. Just as there are philosophical issues about in what identity over time consists, there are philosophical issues about in what identity in modal contexts consists. According to some theories of identity over time, an object that lives for a hundred years is constituted by distinct temporal parts. There is, therefore, precedent for something like counterpart theory. What counts as a counterpart of an object in a distinct world is a matter of relevant similarity, where relevance is determined by, for example, the counterfactual conditional to be assessed. Similar remarks apply to Alvin Plantinga's (1974) objection from numerical identity.

D. M. Armstrong (1989) argued for a somewhat less ontologically ambitious modal realism: combinatorialism. According to combinatorialism possible worlds are recombinations of individuals, properties, and relations of the actual world. Like Lewis (1968), Armstrong relies on a Humean principle of recombination. A recombination of actual objects and actual properties and relations constitutes a nonactual possible world. One difference is that Lewis formulates his principle in terms of duplicates of objects, whereas Armstrong does so in terms of the objects themselves. Where Lewis has no need to countenance qualitatively indiscernible worlds as distinct, Armstrong does. That an object, a, is F and that another, b, is exactly like a except that it is G instead of F, provides for a recombination exactly like the actual world save that in this recombination it is b that is F and a that is G. This seems to involve a commitment to haecceitism, the view that there are nonqualitative differences between worlds. Though this seems to be a natural consequence of his basic combinatorial insight, Armstrong rejects haecceitism.

The are two important issues that confront the combinatorialist. First, some principled, nonmodal restriction on the principle of recombination must be given, since if there is no such restriction, impossible worlds will result and the theory will be extensionally inadequate. With no restriction, there is a recombination in which some object is both wholly red and wholly green, thus rendering it false that ◊P is true iff P is true in at least one of the combinatorialist's worlds. Armstrong (1989) attempts restrictions that arise naturally from his own theory of universals in an attempt to solve this problem.

More significant is the problem of alien properties. It is plausible that there could be objects that possess properties that no actual object possesses and that cannot be constructed from any properties that actual objects possess. Unless one is prepared to claim that one's world is maximally qualitatively rich, this consequence is unwelcome. Those who, like Armstrong (1989), wish to acknowledge the existence only of properties that are exhibited, must concede that this is a feature of the theory, in spite of strong reasons to the contrary. For other than special pleading, what reason is there for thinking that this world does not stand to another world in the relation of relative-impoverishment with respect to properties as some simpler worlds stand in relation to this one? Those who adopt a more Platonistic theory of properties and recognize uninstantiated abstract properties avoid this problem of alien properties, but at the cost of needing to solve the epistemological problems regarding one's knowledge of properties rather than one's knowledge of the genuine modal realist's worlds.

Fictionalism and Modalism

One development that at least initially promises to retain the advantages of genuine realism without this epistemological trouble is modal fictionalism. Strictly speaking, while it is possible that there be talking donkeys, there are none. However, it is also literally true that according to the fiction of possible worlds, there are worlds in which there are talking donkeys. Gideon Rosen (1990) suggested that ◊P is true iff according to the fiction of possible worlds, P or some appropriate paraphrase is true in some possible world. Possible worlds are taken to be useful fictions in the same way that scientists have found ideal gases and frictionless planes to be theoretically useful. Whether fictionalism gains any theoretical advantage over modal realism depends on the content of the operator "according to the fiction of possible worlds." It is natural to think that this should be interpreted as something like: "if the fiction of possible worlds were true, then," which is apparently modal.

Whether this is a problem for fictionalism is a matter of its point. If it is to possess all the advantages that Lewis (1986) claimed, specifically an account of all modal truth, then if the fictional operator is modal, fictionalism fails. The fictionalist also confronts a problem with incompleteness. No modal realist has given a complete specification of the contents of each world, so strictly speaking the modal fictionalist is confronted with truth value gaps for the modal claims about which the modal realist has been silent. The realist can be content with this silence since the realist need not be committed to anyone being modally omniscient. That there are gaps in the fictionalist account is a departure from orthodoxy that must be warranted by significant argument.

Kit Fine (1977), Christopher Peacocke (1978), and Graeme Forbes (1989) suggested a modalist approach that rejects the call for a reductive theory of modality in nonmodal terms. If anything, the explanation goes in the opposite direction: something is true in a possible world iff it is possibly true. For the modalist, reality is irreducibly modal and this is exhibited by the attempts to translate the whole of the possible worlds theory into a modal language, expanding the basic modal language to include an actuality operator as well as indices for the operators to permit the tracking of modal contexts. For example, if one permits oneself w₁, to be a variable ranging over worlds, w* to stand for the actual world, and E to be a two-place predicate by which one can express that an object exists in a world, then the possible worlds translation of "There could have been more things than there actually are" is:
∃w₁[∀w∀x(Exw* →Exw₁) & ∃y(¬Eyw*).
Where ◊₁ permits one to express a given possibility, A expresses actuality, and A₁ expresses what is actual in a specific possibility, the modalist translation for this is:
◊₁{[□∀x(AEx → A₁Ex)] & ∃y¬AEy}.

Melia (1992) argued that the modalist translation is not a reduction of possible worlds discourse at all, but merely a notational variant of the possible worlds statement. Even if it is granted that one has a firm grasp on the modalist's basic modal and actuality operators, once the subscripts are added and one operator is placed within the scope of others, one has no intuitive grasp of their meanings in those contexts. The only way to understand them, indeed the way the modalist explains them, is by reference to the possible worlds semantics. Contrary to the modalist claims, this makes it appear as though possible worlds discourse, not the modalist's, is semantically basic and more perspicuous.

Some assumed that modalism is to be recommended only if it can reduce possible worlds discourse in modal terms. However, why, exactly, should the modalist provide translations of all possible worlds claims? What must be determined is what, if any, possible worlds claims are merely artifacts of the possible worlds framework. It is no reason to give up modalism if it cannot accommodate mere artifacts of the possible worlds framework that is, ultimately, rejected as a literal account of modal metaphysics. For instance, according to Lewis's (1968) developments, each world is as it is. It is not essential that a world be that way, but it is essential that that specific world be that particular way. Being that way is precisely what distinguishes that world from all others. Modalists are not bound to make this essentialist claim part of their theory. So long as the modalist can say all that one has either theory-neutral or modalist grounds for asserting, the failure to translate all the modal realist's claims should not count against modalism.

Though modalism is not wedded to essentialism, Fine (1977) argued not only that reality is irreducibly modal but also that de re modality is more basic than de dicto, defending the most general aspects of essentialism defended by Kripke (1972/1980) and Hilary Putnam (1975). These works brought essentialism back into philosophical discussion among analytic philosophers. Each was concerned with the semantics for proper names and natural kinds terms. Once necessity, analyticity, and a priority were clearly separated from each other, some essentialist theses—such as that the origins/genealogy are essential to some objects and that substances have their chemical constitution essentially—became more plausible. Fine extended this so that de dicto modality, concerned as it is with the necessary truth and falsehood of some propositions, is explained by de re modal facts about the natures of truth bearers or concepts or logical functions. This provides essentialism with an explanatory role so that if objects, whether concrete or abstract, have properties without which they would not be those very objects, then modal truth is on a par with nonmodal truth. Truth, whether modal or nonmodal, depends on being. The modalist simply maintains that being is irreducibly modal.

Modality and Metaphysics

In the end, the philosophy and metaphysics of modality rests on metaphilosophical foundations. Many of the objections to the various positions have been piecemeal, showing that a theory has some consequence that is supposed to be intolerable. Lewis (1986) made quite clear that the case for genuine modal realism was a philosophical inference to the best explanation, not a single silver bullet–like argument. He claimed that when all things were considered his theory possessed the best balance of theoretical virtues and vices. Other theories might rely on less controversial ontologies or they may avoid some other counterintuitive consequences of modal realism. Nevertheless, when all things are taken into account, Lewis thinks that his theory is the best package. Those willing to engage Lewis on his own terms must provide comparable details about the relative merits and difficulties of an alternative to properly undercut the warrant that Lewis thinks that he has given for modal realism.

An alternative is to question the appropriateness of inference to the best explanation in metaphysical contexts. That argument form is typically associated with contexts in which prior experience showed that one kind of event or fact—the activity of mice—explained another—the disappearance of cheese. When one confronts another instance of missing cheese and one has been unable to observe rodents, the inference to the activity of mice might well be appropriate. In metaphysics there is no analogue to prior experience. If the legitimacy of an argument form is not knowable a priori, some a posteriori basis is needed for thinking that the argument is appropriate to a given context of application. One knows that statistical inferences are appropriate under some conditions and not others because of what one knows from empirical investigation of the world. In the absence of some general reason to think that a metaphysical theory is more likely to be true when it is the conclusion of an inference to the best explanation, the application of an inference form may be warranted in some empirical contexts but unwarranted in metaphysical contexts. Thus, warrant for a specific theory of modality depends on deeper considerations about forms of argument appropriate to metaphysics.

See also Metaphysics; Modality and Language.

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