Composition as identity, as I understand it, is a theory of the composite structure of reality. The theory’s underlying logic is irreducibly plural; its fundamental primitive is a generalized identity relation that takes either plural or singular arguments. Strong versions of the theory that incorporate a generalized version of the indiscernibility of identicals are incompatible with the framework of plural logic, and should be rejected. Weak versions of the theory that are based on the idea that composition is merely analogous (...) to identity are too weak to be interesting, lacking in metaphysical consequence. I defend a moderate version according to which composition is a kind of identity, and argue that the difference is metaphysically substantial, not merely terminological. I then consider whether the notion of generalized identity, though fundamental, can be elucidated in modal terms by reverse engineering Hume’s Dictum. Unfortunately, for realists about possible worlds, such as myself,... (shrink)
It follows from Humean principles of plenitude, I argue, that island universes are possible: physical reality might have 'absolutely isolated' parts. This makes trouble for Lewis's modal realism; but the realist has a way out. First, accept absolute actuality, which is defensible, I argue, on independent grounds. Second, revise the standard analysis of modality: modal operators are 'plural', not 'individual', quantifiers over possible worlds. This solves the problem of island universes and confers three additional benefits: an 'unqualified' principle of compossibility (...) can be accepted; the possibility of nothing can be accommodated; and the identity of indiscernible worlds can be decisively refuted. (shrink)
According to David Lewis, a realist about possible worlds must hold that actuality is relative: the worlds are ontologically all on a par; the actual and the merely possible differ, not absolutely, but in how they relate to us. Call this 'Lewisian realism'. The alternative, 'Leibnizian realism', holds that actuality is an absolute property that marks a distinction in ontological status. Lewis presents two arguments against Leibnizian realism. First, he argues that the Leibnizian realist cannot account for the contingency of (...) actuality. Second, he argues that the Leibnizian realist cannot explain why skepticism about one's own actuality is absurd. In this paper, I mount a defense of Leibnizian realism. (shrink)
Humeans have a problem with quantities. A core principle of any Humean account of modality is that fundamental entities can freely recombine. But determinate quantities, if fundamental, seem to violate this core principle: determinate quantities belonging to the same determinable necessarily exclude one another. Call this the problem of exclusion. Prominent Humeans have responded in various ways. Wittgenstein, when he resurfaced to philosophy, gave the problem of exclusion as a reason to abandon the logical atomism of the Tractatus with its (...) free recombination of elementary propositions. Armstrong promoted a mereological solution to the problem of exclusion; but his account fails in manifold ways to provide a general solution to the problem. Lewis studiously avoided committing to any one solution, trusting simply that, since Humeanism was true, there had to be some solution. Abandonment; failure; avoidance: we Humeans need to do better. -/- In this paper, I present what I take to be the best account of quantities, tailoring it where needed to meet Humean demands as well as my own prior commitment to quidditism, and my own comparativist inclinations. In short: determinables, not determinates, are the fundamental properties, and freely recombine; determinates arise from the instantiation of determinables in an enhanced world structure; determinate quantities may be local (in a sense to be explained), but they are not intrinsic. Is the account I end up with Humean? Not, unfortunately, as it stands: the problem of exclusion still rears its ugly head. After dismissing a failed attempt at a solution, I consider in the final section the two viable Humean options. One attributes the source of the necessary exclusions to conventional definition, the other attributes it to logic. The first is safe and familiar, but not a response I can accept given my other commitments. The second is more radical and less familiar; but I am convinced it is on the right track. I don’t have space to develop it much here, but I put it out for future research. (shrink)
If realism about possible worlds is to succeed in eliminating primitive modality, it must provide an 'analysis' of possible world: nonmodal criteria for demarcating one world from another. This David Lewis has done. Lewis holds, roughly, that worlds are maximal unified regions of logical space. So far, so good. But what Lewis means by 'unification' is too narrow, I think, in two different ways. First, for Lewis, all worlds are (almost) 'globally' unified: at any world, (almost) every part is directly (...) linked to (almost) every other part. I hold instead that some worlds are 'locally' unified: at some worlds, parts are directly linked only to "neighboring" parts. Second, for Lewis, each world is (analogically) 'spatio-temporally' unified; every world is 'spatio-temporally' isolated from every other. I hold instead: a world may be unified by nonspatio-temporal relations; every world is 'absolutely' isolated from every other. If I am right, Lewis's conception of logical space is impoverished: perfectly respectable worlds are missing. (shrink)
Which mathematical structures are possible, that is, instantiated by the concrete inhabitants of some possible world? Are there worlds with four-dimensional space? With infinite-dimensional space? Whence comes our knowledge of the possibility of structures? In this paper, I develop and defend a principle of plenitude according to which any mathematically natural generalization of possible structure is itself possible. I motivate the principle pragmatically by way of the role that logical possibility plays in our inquiry into the world.
David Lewis's book 'On the Plurality of Worlds' mounts an extended defense of the thesis of modal realism, that the world we inhabit the entire cosmos of which we are a part is but one of a vast plurality of worlds, or cosmoi, all causally and spatiotemporally isolated from one another. The purpose of this article is to provide an accessible summary of the main positions and arguments in Lewis's book.
The article explicates a notion of prudence according to which an agent acts prudently if he acts so as to satisfy not only his present preferences, but his past and future preferences as well. A simplified decision-theoretic framework is developed within which three analyses of prudence are presented and compared. That analysis is defended which can best handle cases in which an agent's present act will affect his future preferences.
Some argue, following Bertrand Russell, that because general truths are not entailed by particular truths, general facts must be posited to exist in addition to particular facts. I argue on the contrary that because general truths (globally) supervene on particular truths, general facts are not needed in addition to particular facts; indeed, if one accepts the Humean denial of necessary connections between distinct existents, one can further conclude that there are no general facts. When entailment and supervenience do not coincide (...) it is only failure of supervenience, not failure of entailment, that carries ontological import. (shrink)
Modal sentences of the form "every F might be G" and "some F must be G" have a threefold ambiguity. in addition to the familiar readings "de dicto" and "de re", there is a third reading on which they are examples of the "plural de re": they attribute a modal property to the F's plurally in a way that cannot in general be reduced to an attribution of modal properties to the individual F's. The plural "de re" readings of modal (...) sentences cannot be captured within standard quantified modal logic. I consider various strategies for extending standard quantified modal logic so as to provide analyses of the readings in question. I argue that the ambiguity in question is associated with the scope of the general term 'F'; and that plural quantifiers can be introduced for purposes of representing the scope of a general term. Moreover, plural quantifiers provide the only fully adequate solution that keeps within the framework of quantified modal logic. (shrink)
The most commonly heard proposals for reducing possible worlds to language succumb to a simple cardinality argument: it can be shown that there are more possible worlds than there are linguistic entities provided by the proposal. In this paper, I show how the standard proposals can be generalized in a natural way so as to make better use of the resources available to them, and thereby circumvent the cardinality argument. Once it is seen just what the limitations are on these (...) more general proposals, it can be clearly seen where the real difficulty lies with any attempt to reduce possible worlds to language. Roughly, the difficulty is this: no actual language could have the descriptive resources needed to represent all the ways things might have been. I conclude by arguing that this same difficulty spells doom for any nominalist or conceptualist proposal for reducing possible worlds. (shrink)
Reality and Humean Supervenience confronts the reader with central aspects in the philosophy of David Lewis, whose work in ontology, metaphysics, logic, probability, philosophy of mind, and language articulates a unique and systematic foundation for modern physicalism.
In this discussion of Colin McGinn's book, 'Logical Properties', I comment first on the chapter "Existence", then on the chapter "Modality." With respect to existence, I argue that McGinn's view that existence is a property that some objects have and other objects lack requires the property of existence to be fundamentally unlike ordinary qualitative properties. Moreover, it opens up a challenging skeptical problem: how do I know that I exist? With respect to modality, I argue that McGinn's argument that quantificational (...) analyses of modality in terms of possible worlds are inevitably circular does not apply to modal theorists who hold that the notion of an impossible world is incoherent. (shrink)
I am a realist of a metaphysical stripe. I believe in an immense realm of "modal" and "abstract" entities, of entities that are neither part of, nor stand in any causal relation to, the actual, concrete world. For starters: I believe in possible worlds and individuals; in propositions, properties, and relations (both abundantly and sparsely conceived); in mathematical objects and structures; and in sets (or classes) of whatever I believe in. Call these sorts of entity, and the reality they comprise, (...) metaphysical. In contrast, call the actual, concrete entities, and the reality they comprise, physical. Physical and metaphysical reality together comprise all that there is. In this paper, it is not my aim to defend realism about any particular metaphysical sort of entity. Rather, I ask quite generally whether and how any brand of realism about metaphysical sorts of entity could be justified? (shrink)
Walter Sinnott-Armstrong, Diana Raffman, Nicholas Asher, Modality, Morality, and Belief, Essays in Honor of Ruth Barcan Marcus.Terence Parsons, Ruth Barcan Marcus and the Barcan Formula.Robert Stalnaker, The Interaction of Modality with Quantification and Identity.Maxwell J. Cresswell, S1 is not so Simple.David Kaplan, A Problem in Possible-world Semantics.Charles Parsons, Structuralism and the Concept of Set.
In sections 1 through 5, I develop in detail what I call the standard theory of worlds and propositions, and I discuss a number of purported objections. The theory consists of five theses. The first two theses, presented in section 1, assert that the propositions form a Boolean algebra with respect to implication, and that the algebra is complete, respectively. In section 2, I introduce the notion of logical space: it is a field of sets that represents the propositional structure (...) and whose space consists of all and only the worlds. The next three theses, presented in sections 3, 4, and 5, respectively, guarantee the existence of logical space, and further constrain its structure. The third thesis asserts that the set of propositions true at any world is maximal consistent; the fourth thesis that any two worlds are separated by a proposition; the fifth thesis that only one proposition is false at every world. In sections 6 through 10, I turn to the problem of reduction. In sections 6 and 7, I show how the standard theory can be used to support either a reduction of worlds to propositions or a reduction of propositions to worlds. A number of proposition-based theories are developed in section 6, and compared with Adams's world-story theory. A world-based theory is developed in section?, and Stalnaker's account of the matter is discussed. Before passing judgment on the proposition based and world-based theories, I ask in sections 8 and 9 whether both worlds and propositions might be reduced to something else. In section 8, I consider reductions to linguistic entities; in section 9, reductions to unfounded sets. After rejecting the possibility of eliminating both worlds and propositions, I return in section 10 to the possibility of eliminating one in favor of the other. I conclude, somewhat tentatively, that neither worlds nor propositions should be reduced one to the other, that both worlds and propositions should be taken as basic to our ontology. (shrink)