Relational Semantics and Domain Semantics for Epistemic Modals

The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account of attitude verbs and conditionals. It can be shown the the relational account handles the same data equally well if it too is supplemented with a non-standard account of such expressions.     

Lewis,Wilson, Hume: A Response to Jessica Wilson on Lewisian Plenitude and Hume’s Dictum

According to David Lewis’s Modal Realism, other possible worlds really exist as concrete, spatiotemporal systems, and every way that a world could be is a way that some world is. To establish this plenitude of concrete possible worlds, Lewis presents his ‘principle of recombination,’ which is meant to guarantee that there exists a possible world, or part of a possible world, for every possibility. Jessica Wilson has recently argued that Lewis’s principle of recombination fails to generate enough worlds to account for the plenitude of possibilities. Namely, Wilson argues that the principle of recombination cannot account for the possibility of spatially overlapping but distinct fundamental entities, as well as certain macroscopic entities. In this paper, I will defend Lewis’s principle of recombination against these charges, arguing that Wilson’s objections overlook features of Lewisian metaphysics that can solve the problems at hand.     

Tracing and heavenly freedom

A new version of the ontological argument for the existence of God is outlined and examined. After giving a brief account of some traditional ontological arguments for the existence of God, where their defects are identified, it is explained how this new argument is built upon their foundations and surmounts their defects. In particular, this version uses the resources of impossible worlds to plug the common escape route from standard modal versions of the ontological argument. After outlining the nature of impossible worlds, and motivating the need for positing them, the new argument is delineated and its premises justified. It is taken for granted that the argument cannot be sound, since it would prove too much. However, its premises are all plausible, and their denial promises to have significant ramifications. Several intuitive lines of objections are then explored in order to illuminate their shortcomings. The puzzle that the argument poses is therefore not whether the argument is sound, for it clearly cannot be. Rather, it is to place pressure on its plausible premises, so some plausible account of how the argument fails can be identified, and that the devising of such an account promises to be insightful. In the process, we should gain an improved understanding of how such ontological arguments work.     

Propositions,Numbers, And The Problem Of Arbitrary Identification

Those inclined to believe in the existence of propositions as traditionally conceived might seek to reduce them to some other type of entity. However, parsimonious propositionalists of this type are confronted with a choice of competing candidates – for example, sets of possible worlds, and various neo-Russellian and neo-Fregean constructions. It is argued that this choice is an arbitrary one, and that it closely resembles the type of problematic choice that, as Benacerraf pointed out, bedevils the attempt to reduce numbers to sets – should the number 2 be identified with the set Ø or with the set Ø, Ø? An “argument from arbitrary identification” is formulated with the conclusion that propositions (and perhaps numbers) cannot be reduced away. Various responses to this argument are considered, but ultimately rejected. The paper concludes that the argument is sound: propositions, at least, are sui generis entities.

     

Thomas Kuhn on the existence of the world

This article argues that Thomas Kuhn's views on the existence of the world have undergone significant change in the course of his philosophical career. In Structure, Kuhn appears to be committed to the existence of the ordinary empirical world as well as the existence of an independent metaphysical world, but realism about the empirical world is abandoned in his later writings. Whereas in Structure the only relative worlds are the scientific worlds inhabited by the practitioners of various paradigms, the later Kuhn puts the non-scientific worlds of particular groups or cultures on the same footing as the paradigm-related scientific worlds. The article shows that, on what Ian Hacking called the “new-world problem”, the later Kuhn has moved to a more radical antirealist position. It is also argued that the earlier and later solutions to the “new-world problem” face insuperable difficulties, which render Kuhn's account of scientific change implausible.     

Exemplification and Parthood

Consider the things that exist—the entities—and let us suppose they are mereologically structured, that is, some are parts of others. The project of ontology within the bounds of bare mereology use this structure to say which of these entities belong to various ontological kinds, such as properties and particulars. My purpose in this paper is to defend the most radical section of the project, the mereological theory of the exemplification of universals. Along the way I help myself to several hypotheses: the existence of merely possible worlds; that particulars have thisnesses; and that mereology is far from classical. Moreover, the way I characterize instantiation might be judged too complicated to be plausible. At the end of the paper, I reply to these objections based on complexity.     

Centered assertion

I suggest a way of extending Stalnaker’s account of assertion to allow for centered content. In formulating his account, Stalnaker takes the content of assertion to be uncentered propositions: entities that are evaluated for truth at a possible world. I argue that the content of assertion is sometimes centered: the content is evaluated for truth at something within a possible world. I consider Andy Egan’s proposal for extending Stalnaker’s account to allow for assertions with centered content. I argue that Egan’s account does not succeed. Instead, I propose an account on which the contents of assertion are identified with sets of multi-centered worlds. I argue that such a view not only provides a plausible account of how assertions can have centered content, but also preserves Stalnaker’s original insight that successful assertion involves the reduction of shared possibilities.     

What are impossible worlds?

In this paper, I argue for a particular conception of impossible worlds. Possible worlds, as traditionally understood, can be used in the analysis of propositions, the content of belief, the truth of counterfactuals, and so on. Yet possible worlds are not capable of differentiating propositions that are necessarily equivalent, making sense of the beliefs of agents who are not ideally rational, or giving truth values to counterfactuals with necessarily false antecedents. The addition of impossible worlds addresses these issues. The kinds of impossible worlds capable of performing this task are not mysterious sui generis entities, but sets of structured propositions that are themselves constructed out of possible worlds and relations. I also respond to a worry that these impossible worlds are unable to represent claims about the shape of modal space itself.     

Ontology-free modal semantics

The problem with model-theoretic modal semantics is that it provides only the formal beginnings of an account of the semantics of modal languages. In the case of non-modal language, we bridge the gap between semantics and mere model theory, by claiming that a sentence is true just in case it is true in an intended model. Truth in a model is given by the model theory, and an intended model is a model which has as domain the actual objects of discourse, and which relates these objects in an appropriate manner. However, the same strategy applied to the modal case seems to require an intended modal model whose domain includes mere possibilia.Building on recent work by Christopher Menzel (Nous 1990), I give an account of model-theoretic semantics for modal languages which does not require mere possibilia or intensional entities of any kind. Menzel has offered a representational account of model-theoretic modal semantics that accords with actualist scruples, since it does not require possibilia. However, Menzel's view is in the company of other actualists who seek to eliminate possible worlds, but whose accounts tolerate other sorts of abstract, intensional entities, such as possible states of affairs. Menzel's account crucially depends on the existence of properties and relations in intension.I offer a purely extensional, representational account and prove that it does all the work that Menzel's account does. The result of this endeavor is an account of model-theoretic semantics for modal languages requiring nothing but pure sets and the actual objects of discourse. Since ontologically beyond what is prima facie presupposed by the model theory itself. Thus, the result is truly an ontology-free model-theoretic semantics for modal languages. That is to say, getting genuine modal semantics out of the model theory is ontologically cost-free. Since my extensional account is demonstrably no less adeguate, and yet is at the same time more ontologically frugal, it is certainly to be preferred.Special thanks to Brian Chellas, Charles Chihara, Harry Deutsch, Bernard Linsky, Kirk Ludwig, Christopher Menzel and Gila Sher for helpful discussion. My thanks also to an anonymous referee for this Journal for kind words and attention to detail. Portions of this paper were presented at the 1993 meeting of the Society for Exact Philosophy in Toronto, and at the 1994 conference of the Association for Symbolic Logic in Gainesville, Florida. Thanks to all who attended those sessions.     

Impossible Worlds

Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds‐based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds‐based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of impossible and as well as possible worlds. So what are impossible worlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossible worlds, too. But far from it. I'll argue that impossible worlds cannot be genuine worlds, of the kind proposed by Lewis, McDaniel or Yagisawa. Nor can they be ersatz worlds on the model proposed by Melia or Sider. Constructing impossible worlds, it turns out, requires novel metaphysical resources.     

Human understanding

Contemporary thinkers either hold that meanings cannot be mental states, or that they are patterns of brain functions. But patterns of social, or brain, interactions cannot be that which we understand. Wittgenstein had another answer (not the one attributed to him by writers who ignore his work in psychology): understanding, he said, is seeing an item as embodying a type Q, thus constraining what items will be seen as the same. Those who cannot see things under an aspect are meaning-blind.That idea is expanded in this article. Its ontology consists of types only: entities that recur in space, time, and possible worlds. Types (Socrates, Man, Red, On, etc.) overlap; Socrates = Bald at some index and not in another. The logic used is thus that of contingent identity. Now some possible worlds are mentally represented; the entities that occur in them are meanings. But such entities may also recur in the real world. Thus the entities we experience, the phenomena, which serve as our meanings, may be identical in the real world with real things. A correspondence theory of truth is thus developed: a sentence is true iff its meaning constitutes, in a specified way, a real situation.     

What in the world are the ways things might have been?

Robert Stalnaker is an actualist who holds that merely possible worlds are uninstantiated properties that might have been instantiated. Stalnaker also holds that there are no metaphysically impossible worlds: uninstantiated properties that couldn't have been instantiated. These views motivate Stalnaker's "two dimensional" account of the necessary a posteriori on which there is no single proposition that is both necessary and a posteriori. For a (metaphysically) necessary proposition is true in all (metaphysically) possible worlds. If there were necessary a posteriori propositions, that would mean that there were propositions true in all possible worlds but which could only be known to be true by acquiring empirical evidence. Consider such a purported proposition P. The role of empirical evidence for establishing P's truth would have to be to rule out worlds in which P is false. If there were no such worlds to be ruled out, we would not require evidence for P. But by hypothesis, P is necessary and so true in all metaphysically possible worlds. And on Stalnaker's view, the metaphysically possible worlds are all the worlds there are. So there can be no proposition that is true in all possible worlds, but that we require evidence to know. In this way, the motivation for Stalnaker's two dimensional account of the necessary a posteriori rests on his denying that there are metaphysically impossible Worlds. I argue that given his view of what possible worlds are, Stalnaker has no principled reason for denying that there are metaphysically impossible worlds. If I am right, this undercuts Stalnaker's motivation for his two dimensional account of the necessary a posteriori.

No two entities without identity

In a naïve realist approach to reading an ontology off the models of a physical theory, the invariance of a given theory under permutations of its property-bearing objects entails the existence of distinct possible worlds from amongst which the theory cannot choose. A brand of Ontic Structural Realism (OSR) attempts to avoid this consequence by denying that objects possess primitive identity, and thus worlds with property values permuted amongst those objects are really one and the same world. Assuming that any successful ontology of objects is able to describe a universe containing a determinate number of them, I argue that no version of OSR which both retains objects and understands ‘structure’ in terms of relations can be successful. This follows from the fact that no set of relational facts is sufficient to fix the cardinality of the collection of objects implied by those facts. More broadly, I offer reasons to believe that no version of OSR is compatible with the existence of objects, no matter how ontologically derivative they are taken to be. Any such account would have to attribute a definite cardinality to a collection of objects while denying that those objects are possessed of a primitive identity. With no compelling reason to abandon the classical conception of cardinality, such an attribution is incoherent.     

The Metasyntactic Interpretation of Two-Dimensionalism

Robert Stalnaker contrasts two interpretations, semantic and metasemantic, of the two-dimensionalist framework. On the semantic interpretation, the primary intension or diagonal proposition associated with an utterance is a semantic value that the utterance has in virtue of the actual linguistic meaning of the corresponding sentence, and that primary intension is both what a competent speaker grasps and what determines different secondary intensions or horizontal propositions relative to different possible worlds considered as actual. The metasemantic interpretation reverses the order of explanation: an utterance has the primary intension it has because it yields the secondary intensions it yields relative to different possible worlds considered as actual. In these possible worlds, the semantic facts can be different: the metasemantic interpretation is metasemantic in the sense that the secondary intensions are determined relative to possible worlds considered as actual given the meanings the expressions have there. Stalnaker holds a causal picture of the reference of names, according to which names have no meaning over and above their unique referent, and therefore maintains that the semantic interpretation is not an option. He thus endorses the metasemantic interpretation, while insisting that this interpretation does not, contrary to what he originally thought, yield any account of a priori truth and knowledge. My double aim in this paper is to show (i) that the metasemantic interpretation, as sketched by Stalnaker, is not compatible with one natural understanding of the causal picture of reference, on which names are rigid because they have their original bearers essentially, and (ii) that a third kind of interpretation of the framework is available, the metasyntactic interpretation, which grants that names have their bearers essentially and yields some account of a priori knowledge.     

From Four‐ to Five‐Dimensionalism

Philosophers have long noticed the similarity of identity over time and identity across worlds. Despite this similarity, analogous views on these matters are not always taken equally seriously. Four‐dimensionalism is one of the most well‐known accounts of identity over time. There is a clear modal analogue of four‐dimensionalism, on which objects are modally extended and their trans‐world identity is a matter of having distinct modal parts located in different possible worlds. Yet this view, which we might call ‘five‐dimensionalism,’ is rarely discussed or defended, in comparison to its temporal counterpart. I argue that five‐dimensionalism is at least as plausible as four‐dimensionalism and deserves serious consideration as an account of trans‐world identity. The strategy is to show that arguments typically used in defence of four‐dimensionalism can be adapted to defend five‐dimensionalism as well. A powerful consideration in favour of four‐dimensionalism is the fact that it provides an elegant and unified solution to a variety of puzzles concerning material coincidence. I show that such puzzles come in equally troubling modal varieties and that five‐dimensionalism provides an equally unified and elegant solution to them. 1     

BRING BACK THE MAGIC

Abstract:  Magical ersatzism is the view that possible worlds are primitive abstract entities. In On the Plurality of Worlds , David Lewis presented what appeared to many to be a devastating argument against magical ersatzism. In this paper, I show that Lewis' central argument does not succeed. Magical ersatzism remains a viable theory of possible worlds.     

Agnosticism About Other Worlds: A New Antirealist Programme in Modality

The modal antirealist, as presented here, aims to secure at least some of the benefits associated with talking in genuine modal realist terms while avoiding commitment to a plurality of Lewisian (or ersatz) worlds. The antirealist stance of agnosticism about other worlds combines acceptance of Lewis's account of what world-talk means with refusal to assert, or believe in, the existence of other worlds. Agnosticism about other worlds does not entail a comprehensive agnosticism about modality, but where such agnosticism about modality is enforced, the aim of the agnostic programme is to show that it is not detrimental to our modal practices. The agnostic programme consists in an attempt to demonstrate the rational dispensability of that disputed class of modal beliefs which the agnostic eschews, but which are held by the realist and the folk. Here I attempt to motivate, describe, and illustrate such an agnostic antirealist programme in modal philosophy.     

Hyperintensional metaphysics

In the last few decades of the twentieth century there was a revolution in metaphysics: the intensional revolution. Many metaphysicians rejected the doctrine, associated with Quine and Davidson, that extensional analyses and theoretical resources were the only acceptable ones. Metaphysicians embraced tools like modal and counterfactual analyses, claims of modal and counterfactual dependence, and entities such as possible worlds and intensionally individuated properties and relations. The twenty-first century is seeing a hypterintensional revolution. Theoretical tools in common use carve more finely than by necessary equivalence: two pieces of language can apply to the same entities across all possible worlds but not be equivalent; thoughts can be necessarily equivalent in truth value but not synonymous. This paper argues that hyperintensional resources are valuable in metaphysics outside theories of representation, and discusses some promising areas of hyperintensional metaphysics.     

On universals: an extensionalist alternative to Quine’s resemblance theory

The notion of similarity plays a central role in Quine’s theory of Universals and it is with the help of this notion that Quine intends to define the concept of kind which also plays a central role in the theory. But as Quine has admitted, his attempts to define kinds in terms of similarities were unsuccessful and it is mainly because of this shortcoming that Quine’s theory has been ignored by several philosophers (see, e.g., Armstrong, D. M. (1978a). Nominalism and realism: Universals and Scientific realism (Vol. I). Cambridge: Cambridge University Press). In the present paper, I propose an alternative framework that accounts for the phenomena that Quine intends to explain with his resemblance theory. The framework agrees with Quine’s austere ontology; in particular, it does not assume the existence of properties and of possible worlds. (I will mention below Quine’s reason for rejecting properties and possible worlds. For a theory of Universals that assumes possible worlds, see, e.g., Rodriguez-Pereyra, G. (2002). Resemblance nominalism: A solution to the problem of Universals. Oxford: Clarendon Press.) Moreover, the framework is extensionalist since the abstract entities it assumes are classes and these can be individuated extensionally, for classes are identical if their members are identical. Finally, I will refute some of the objections to Quine’s approach that have been raised by Armstrong and Oliver [(1996). The metaphysics of properties. Mind, 105, 1–80.] and I will argue that, contrary to what has been claimed by Oliver in a comment on Lewis [(1986). On the plurality of worlds. Oxford: Blackwell.], Quine is able to specify an important set of sparse properties. Editor’s Note: Nathan Stemmer died on 6 April 2007. Due to this, the proofreading was only done by the editors. All colleagues being acquainted with Nathan Stemmers work are deeply concerned about the loss.