Counterpart Theory

An intuitive objection to modal realism is that merely possible worlds and their inhabitants seem to be irrelevant to an analysis of modality. Kripke originally phrased the objection in terms of being concerned about one’s modal properties without being concerned about the properties one’s other-worldly counterparts have. The author assesses this objection in a variety of forms, and then provides his own formulation that does not beg the question against the modal realist. Finally, the author considers two potential answers to (...) the objection so understood and concludes that only one of them has a chance of succeeding. (shrink)

Bundle theories identify material objects with bundles of properties. On the traditional approach, these are the properties possessed by that material object. That view faces a deep problem: it seems to say that all of an object’s properties are essential to it. Essential bundle theory attempts to overcome this objection, by taking the bundle as a specification of the object’s essential properties only. In this paper, I show that essential bundle theory faces a variant of the objection. To avoid the (...) problem, the theory must accept the contingency of identity. I show how this can be achieved in a coherent and well-motivated way, a way that isn’t available to traditional bundle theories. (shrink)

A counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem non-trivial, most semantic theories for counterfactuals, when combined with the necessity of identity and distinctness, attribute vacuous truth conditions to such counterfactuals. In light of this, one could try to save the orthodox theories either by appealing to pragmatics or by denying that the antecedents of alleged counteridenticals really contain identity claims. Or one could reject the orthodox theory of counterfactuals in favor of a (...) hyperintensional semantics that accommodates non-trivial counterpossibles. In this paper, I argue that none of these approaches can account for all the peculiar features of counteridenticals. Instead, I propose a modified version of Lewis’s counterpart theory, which rejects the necessity of identity, and show that it can explain all the peculiar features of counteridenticals in a satisfactory way. I conclude by defending the plausibility of contingent identity from objections. (shrink)

Quine insisted that the satisfaction of an open modalised formula by an object depends on how that object is described. Kripke’s "objectual" interpretation of quantified modal logic, whereby variables are rigid, is commonly thought to avoid these Quinean worries. Yet there remain residual Quinean worries in the epistemic case. Theorists have recently been toying with assignment-shifting treatments of epistemic contexts. On such views an epistemic operator ends up binding all the variables in its scope. One might worry that this yields (...) the undesirable result that any attempt to "quantify in" to an epistemic environment is blocked. But a famous alternative to Kripke's semantics, namely Lewis' counterpart semantics, also faces this worry, since it also treats the boxes and diamonds as assignment-shifting devices. As I'll demonstrate, the mere fact that a variable is bound is no obstacle to binding it. This provides a helpful lesson for those modelling de re epistemic contexts with assignment sensitivity, and perhaps leads the way toward the proper treatment of binding in both metaphysical and epistemic contexts: Kripke for metaphysical modality, Lewis for epistemic modality. (shrink)

It is shown that counterpart theory and the duplication account of intrinsicality —two key pieces of the Lewisian package—are incompatible. In particular, the duplication account yields the result that certain intuitively extrinsic modal properties are intrinsic. Along the way I consider a potentially more general worry concerning certain existential closures of internal relations. One conclusion is that, unless the Lewisian provides an adequate alternative to the duplication account, the reductive nature of their total theory is in jeopardy.

Relativized Metaphysical Modality (RMM: Murray and Wilson, 'Relativized metaphysical modality', Oxford Studies in Metaphysics, 2012; Murray, Perspectives on Modal Metaphysics, 2017) exploits 'two-dimensionalist' resources to metaphysical, rather than epistemological, ends: the second dimension offers perspective-dependence without contingency, diverting attacks on 'Classical' analyses of modals (in effect, analyses validating S5 and the Barcan Formulae). Here, we extend the RMM program in two directions. First, we harvest resources for RMM from Lewis's 1980 'Context--Index' (CI) framework: (a) the ban in CI on binding (...) into context-arguments (akin to Kaplan's 'monstrosity' ban) projects a bright line between perspective-dependence and contingency; and (b) CI-postulated connections among meaning, content, truth, argument-structure, context, and modality collectively generate a 'Generalized Humphrey Problem' for any non-Classical analysis (examples covered include appeals to accessibility, contingent domains, and counterpart relations). Second, we sharpen the tools of RMM-based metaphysical analysis, and extend their domain of coverage across familiar anomalies for Classical modals: we revisit earlier RMM-based bulwarks for S5 (against 'Chisholm's Paradox' for moderate flexibility of essence, and nomological necessitarianism); and we now similarly shore up the Barcan Formulae (against the apparent contingency of existence and nonexistence). (shrink)

David Lewis holds that a single possible world can provide more than one way things could be. But what are possible worlds good for if they come apart from ways things could be? We can make sense of this if we go in for a metaphysical understanding of what the world is. The world does not include everything that is the case—only the genuine facts. Understood this way, Lewis's “cheap haecceitism” amounts to a kind of metaphysical anti-haecceitism: it says there (...) aren't any genuine facts about individuals over and above their qualitative roles. (shrink)

The problem of identity across possible worlds is raised with the following questions: What does it mean to say of something in one possible world that it is identical with something in another possible world? How are we to decide whether an individual in one possible world is identical with an individual in another?1 Because the questions concern meaning and verification, it appears to be the case that they presuppose that there are one or more sentences whose meaning and method (...) of verification are in need of explanation. However, although it has been generally presumed to be easy, it turns out to be very difficult to produce a sentence that enables us to formulate the problem and that is not merely supposed to say, but really does say, of an individual in one world and of an individual in another world that the first individual is identical with the second. (shrink)

Surely, it is possible that you believe falsely about this-or-that modal matter. In light of the various ways the world could be arranged, it is plausible thatthere is a nearby possible world, which would be almost identical to the actual world, if it were actualized, where you and your modal counterpart disagree over modal belief p. You might be tempted to think that your modal belief is true, while hers is not. It is not clear why this is so; after (...) all, you would each have the same evidence, cognitive abilities etc., if you were both actualized. This point generalizes to all of your modal beliefs, this seems to strongly imply that the probability that you have true modal beliefs appears inscrutable. Thus, you have some reason to withhold belief, on modal matters. (shrink)

Suppose that reality consists of parallel universes of every variety imaginable. No path through space and time leads from one to another, and each universe is causally isolated from the rest. Some physicists believe a ‘multiverse’ hypothesis not terribly distant from this one simplifies quantum mechanics and provides an elegant explanation of why our universe has its particular laws. Suppose as science advances we come to accept the multiverse hypothesis, so construed.

Jim Stone argues that one cannot combine three-dimensionalism with counterpart theory. This paper argues to the contrary.

It is widely agreed that properties play causal roles: they capture the causal powers of things. But do properties have their causal roles essentially? David Lewis did not think so. He adhered to the doctrine of quidditism, namely the doctrine that the identity of properties is primitive and that they can trade their causal roles. Quidditism is controversial. But Lewis did not see why he should want to reject it. He knew that he could avoid quidditism on the cheap by (...) treating individuals and properties alike in rejecting transworld multilocation of properties and endorsing a counterpart theory for properties. But he did not see why he should want to do so. In this article, I argue that Lewis should have wanted to endorse a counterpart theory for properties in order to reject quidditism. My argument concerns resemblance relations among properties. Another constitutive role of properties is that they capture objective resemblances between their instances. The premises of my argument are intuitive claims about resemblances among some properties that Lewis held on Humean grounds. (shrink)

I call anti-resemblism the thesis that independently of any contextual specification there is no determinate fact of the matter about the comparative overall similarity of things. Anti-resemblism plays crucial roles in the philosophy of David Lewis. For instance, Lewis has argued that his counterpart theory is anti-essentialist on the grounds that counterpart relations are relations of comparative overall similarity and that anti-resemblism is true. After Lewis committed himself to a form of realism about natural properties he maintained that anti-resemblism is (...) true about the relations of overall similarity that enter his counterpart theory and his analysis of counterfactuals. However, in this article I argue that Lewis’s account of degrees of naturalness for properties combined with his modal realism entails that anti-resemblism is false. The Lewisian must amend Lewis’s system if she aims to benefit from the alleged virtues of anti-resemblism. I consider two ways of amending it, neither of which is a free lunch. (shrink)

A number of philosophers have recently found it congenial to talk in terms of grounding. Grounding discourse features grounding sentences that are answers to questions about what grounds what. The goal of this article is to explore and defend a counterpart-theoretic interpretation of grounding discourse. We are familiar with David Lewis's applications of the method of counterpart theory to de re modal discourse. Counterpart-theoretic interpretations of de re modal idioms and grounding sentences share similar motivations, mechanisms, and applications. I shall (...) explain my motivations and describe two applications of a counterpart theory for grounding discourse. But, in this article, my main focus is on counterpart-theoretic mechanisms. (shrink)

Problems about the accidental properties of properties motivate us--force us, I think--not to identify properties with the sets of their instances. If we identify them instead with functions from worlds to extensions, we get a theory of properties that is neutral with respect to disputes over counterpart theory, and we avoid a problem for Lewis's theory of events. Similar problems about the temporary properties of properties motivate us--though this time they probably don't force us--to give up this theory as well, (...) and to identify properties with functions from world, time pairs to extensions. Again, the replacement theory is neutral with respect to a metaphysical dispute that the old theory (arguably) forces us to take a stand on--the dispute over whether objects have temporal parts. It also allows us to give a smoother semantics for predication, to better accommodate our intuitions about which objects temporary properties are properties of, and to make temporally self-locating beliefs genuinely self -locating. (shrink)

It follows from David Lewis's counterpart-theoretic analysis of modality and his counterfactual theory of causation that causal claims are relativized to a set of counterpart relations. Call this Shlewis's view. I show how Shlewis's view can provide attractively unified solutions to similar modal and causal puzzles. I then argue that Shlewis's view is better motivated, by his own lights, than the view Lewis actually held, and also better motivated than a similar approach which relativizes causal claims to sets of ‘contrast (...) events’. (shrink)

The standard conception of God is that of a necessary being. On a possible worlds semantics, this entails that God exists at every possible world. According to the modal realist account of David Lewis, possible worlds are understood to be real, concrete worlds—no different in kind from the actual world. Some have argued that Lewis’s view is incompatible with classical theism (e.g., Sheehy, 2006). More recently, Ross Cameron (2009) has defended the thesis that Lewisian modal realism and classical theism are (...) in fact compatible. I argue that this is not the case. Modal realism, I argue, is equipped to accommodate necessary beings in only one of three ways: (1) By way of counterpart theory, or (2) by way of a special case of trans-world identity for causally inert necessary beings (e.g., pure sets), or else (3) causally potent ones which lack accidental intrinsic properties. However, each of these three options entails unacceptable consequences—(1) and (2) are incompatible with theism, and (3) is incompatible with modal realism. I conclude that (at least) one of these views is false. (shrink)

Two criteria for rigid designation are distinguished; one according to which 'e' is rigid if 'e might not have been e' is false and the other according to which 'e' is rigid if it designates the same thing in all possible worlds in which it designates anything at all. Such criteria are not equivalent since 'x could not but be f' is not entailed by 'nothing other than x could be f'. I illustrate the latter lack of entailment.

Non-Identity arguments have a pervasive but sometimes counter-intuitive grip on certain key areas in ethics. As a result, there has been limited success in supporting the alternative view that our choices concerning future generations can be considered harmful on any sort of person-affecting principle. However, as the Non-Identity Problem relies overtly on certain metaphysical assumptions, plausible alternatives to these foundations can substantially undermine the Non-Identity argument itself. In this paper, I show how the pervasive force and nature of Non-Identity arguments (...) rely upon a specific adoption of a theory of modality and identity and how adopting an alternative account of modality can be used to reject many conclusions formed through Non-Identity type arguments. By using Lewis’s counterpart-theoretic account to understand ways we might have been, I outline the basis of a modal account of harm that incorporates a person-affecting aspect. This, in turn, has significant implications for ethical decision-making in areas such as reproductive choice and the welfare of future generations. (shrink)

This chapter is concerned with the coextension difficulty for nominalist theories of properties that reject tropes alongside universals. After carefully explaining the coextension difficulty and describing the theories it targets, the chapter describes different solutions to the difficulty. These solutions differ with respect to how much involved they are into a dualist approach to coextension. A dualist approach to a case of coextension consists in agreeing with the realist that the relevant ascriptions of properties are numerically distinct. A monist approach (...) to a case of coextension consists in contending that the relevant ascriptions of properties are identical. In this chapter, I defend a monist approach to cases of coextension that appeals to a counterpart theory for propositions. (shrink)

David Lewis proposed to deal with the semantics of sentences that state what is possible for an individual in terms of possible individuals that are in ways the first individual might have been, so called counterparts of the individual. In this book, I defend counterpart semantics as an approach to the semantics of modality and natural language semantics in particular. Counterpart semantics has a rival, the standard Kripkean semantics that deals with the same sentences in terms of an accessibility relation (...) between possible worlds. While counterpart semantics appears to be more flexible and carries less metaphysical presuppositions (it does not presuppose that I myself exist in various possible worlds, e.g.), Kripkean semantics has some advantages of its own. Most importantly, it incorporates the core assumptions of what may be called standard possible-worlds semantics; i.e. the core assumptions of the most successful framework within linguistic semantics. Counterpart semantics, on the other hand, does not conform to these assumptions, or so I will argue. In this book I opt for a synthesis of these two approaches that allows to combine their advantages. In Chap.1 I introduce the basic idea of counterpart semantics. I defend counterparts against the charge, made by Kripke, that counterparts are irrelevant for the analysis of modality. In Chap. 2 I present the classical version of counterpart semantics, i.e. David Lewis's translation of the language of quantified modal logic into counterpart theory. I discuss some well-known problems and opt for a revision of that translation that is able to solve the problems. Lewis's translation indirectly defines semantical values for expressions of quantified modal logic. In Chap.3 I evaluate counterpart semantics with respect to basic features of possible-worlds semantics. I conclude that the semantical values indirectly assigned to sentences by Lewis's translation are not sets of possible worlds, and that they do not meet certain intuitive demands on notions of meaning and content. (The revisions proposed in Chap.2 do not change this.) In Chap.4 I discuss various versions of a combination of counterpart semantics with Kripkean semantics found in the literature. But I conclude that here, the benefits of the latter are achieved by forfeiting the advantages of the former. Chap.5 finally contains my own proposal how to combine the two approaches in a more satisfactory way. The core semantical notion is truth according to a maximal complete representation, where representations now play the role of worlds. It is an important feature of the counterpart relation that it is qualitative, i.e. a relation in which things stand in virtue how they are. In Chap.1 I point out why it is qualitative, and why it ought to be. In Chap.6 I show how to make the notion of a qualitative property or relation precise. Finally, in Chap.7 I show how to extend this and related notions to predicates and propositions. For counterpart semantics to work at all we have to assume that everything that can be said at all can in principle be expressed in a language with qualitative predicates only (and perhaps, additionally, names, treated directly referentially). In Chap.7 I show how this assumption allows to maintain that the representations of our semantics deserve their name. (shrink)

It is commonly assumed that causation is transitive and in this paper I aim to reconcile this widely-held assumption with apparent evidence to the contrary. I will discuss a familiar approach to certain well-known counterexamples, before introducing a more resistant sort of case of my own. I will then offer a novel solution, based on Yablo’s proportionality principle, that succeeds in even these more resistant cases. There is a catch, however. Either proportionality is a constraint on which causal claims are (...) true, and the solution works, or it is not and causation is not transitive after all. I will argue that the first horn has unacceptable consequences and should be rejected, but that the second horn is less costly than it might initially appear. (shrink)

This paper argues that a counterpart-theoretic treatment of events, combined with a counterfactual theory of causation, can help resolve three puzzles from the causation literature. First, CCT traces the apparent contextual shifts in our causal attributions to shifts in the counterpart relation which obtains in those contexts. Second, being sensitive to shifts in the counterpart relation can help diagnose what goes wrong in certain prominent examples where the transitivity of causation appears to fail. Third, CCT can help us resurrect the (...) much-maligned fragility response to the problems of late pre-emption by understanding fragility in counterpart-theoretic terms. Some reasons to prefer this CCT approach to rivals are discussed. (shrink)