The dogma that the propositional logic of metaphysical modality is S5 is rebutted in related installments (previously published and unpublished essays).

An exploration of the details of counterpart theory, and some applications of the view. In Chapter 1, I set out the view and clarify the most important features: that the counterpart relation is a context dependent similarity relation, and that individuals are world-bound entities. I then set out what I take to be the most promising methods of filling in important details. Chapter 2 is a discussion of an alternative view, lump theory. I attempt to distinguish lump theory from counterpart (...) theory, and argue that several attempt to do so fail. Chapter 3 is an attempt to apply counterpart theory for individuals to properties. I attempt to stay as close to the standard view as possible, but find it necessary to modify the world-bound condition. I suggest a version of property counterpart theory that overcomes the obstacles I have identified. The final chapter is a discussion of a recent attempt to apply counterpart theory to the comparativist view of quantitative properties. I argue that an attempt to rely on counterpart theory to overcome an objection is unsuccessful. (shrink)

It has been claimed that counterpart theory cannot support a theory of actuality without rendering obviously invalid formulas valid or obviously valid formulas invalid. We argue that these claims are not based on logical flaws of counterpart theory itself, but point to the lack of appropriate devices in first-order logic for “remembering” the values of variables. We formulate a mildly dynamic version of first-order logic with appropriate memory devices and show how to base a version of counterpart theory with actuality (...) on this. This theory is, in special cases, equivalent to modal first-order logic with actuality, and apparently does not suffer from the logical flaws that have been mentioned in the literature. (shrink)

David Lewis’s counterpart theory is often seen as involving a radical departure from the standard, Kripke-style semantics for modal logic, suggesting that we are dealing with deeply divergent accounts of our modal talk. However, CT captures but one version of the relevant semantic intuition, and does so on the basis of metaphysical assumptions that are ostensibly discretionary. Just as ML can be translated into a language that quantifies explicitly over worlds, CT may be formulated as a semantic theory in which (...) world quantification is purely metalinguistic. And just as Kripke-style semantics is formally compatible with the doctrine of world-boundedness, a counterpart-based semantics may in principle allow for cases of trans-world identity. In fact, one may welcome a framework that is general enough to include both Lewis’s counterpart-based account and Kripke’s identity-based account as distinguished special cases. There are several ways of doing so. The purpose of this paper is to outline a fully general option and to illustrate its philosophical significance, showing how the large variety of intermediate relations that lie between Lewisian counterparthood and Kripkean identity yield a corresponding variety of modal theories that would otherwise remain uncharted. (shrink)

Counterpart theory is often advertised by its track record at solving metaphysical puzzles. Here I focus on puzzles of occasional identity, wherein distinct individuals at one world or time appear to be identical at another world or time. To solve these puzzles, the usual interpretation rules of counterpart theory must be extended beyond the simple language of quantified modal logic. I present a more comprehensive semantics that allows talking about specific times and worlds, that takes into account the multiplicity and (...) sortal-dependence of counterpart relations, and that does not require names to denote actual or present individuals. In addition, the semantics I defend does not identify ordinary individuals with world-bound or time-bound stages and thereby avoids the most controversial aspect of counterpart theory. Humphrey’s counterpart at other worlds or times is none other than Humphrey himself. (shrink)

The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

The counterpart theorist has a problem: there is no obvious way to understand talk about actuality in terms of counterparts. Fara and Williamson have charged that this obstacle cannot be overcome. Here I defend the counterpart theorist by offering systematic interpretations of a quantified modal language that includes an actuality operator. Centrally, I disentangle the counterpart relation from a related notion, a ‘representation relation’. The relation of possible things to the actual things they represent is variable, and an adequate account (...) of modal language must keep track of the way it is systematically shifted by modal operators. I apply my account to resolve several puzzles about counterparts and actuality. In technical appendices, I prove some important logical results about this ‘representational’ counterpart system and its relationship to other modal systems. (shrink)

David Lewis’s counterpart-theoretic semantics for quantified modal logic is motivated originally by worries about identifying objects across possible worlds; the counterpart relation is grounded more cautiously on comparative similarity. The possibility of contingent identity is an unsought -- and in some eyes, unwelcome -- consequence of this approach. In this paper I motivate a Kripkean counterpart theory by way of defending the prior, pre-theoretical, coherence of contingent directness. Contingent identity follows for free. The theory is Kripkean in that the counterpart (...) relation is in a sense stipulated rather than grounded on similarity, and is such that no object has more than one counterpart at a world. This avoids a number of objections Fara and Williamson have recently levelled against counterpart theory generally; their other objections are addressed by enriching the theory with special quantifiers and actuality operators. (shrink)

Lewis’s [1968] counterpart theory (LCT for short), motivated by his modal realism, made its appearance within a year of Chisholm’s modal paradox [1967]. We are not modal realists, but we argue that a satisfactory resolution to the paradox calls for a counterpart-theoretic (CT-)semantics. We make our case by showing that the Chandler–Salmon strategy of denying the S4 axiom [◊◊ψ →◊ψ] is inadequate to resolve the paradox – we take on Salmon’s attempts to defend that strategy against objects from Lewis and (...) Williamson. We then consider three substantially different CT-approaches: Lewis’s LCT, Forbes’s (FCT), including his fuzzy version, and Ramachandran’s (RCT). We argue that the best approach is a mish-mash of FCT and RCT. (shrink)

Lewis (1968) claims that his language of Counterpart Theory (CT) interprets modal discourse and he adverts to a translation scheme from the language of Quantifed Modal Logic (QML) to CT. However, everybody now agrees that his original translation scheme does not always work, since it does not always preserve the ‘intuitive’ meaning of the translated QML-formulas. Lewis discusses this problem with regard to the Necessitist Thesis, and I will extend his discourse to the analysis of the Converse Barcan Formula. Everyone (...) also agrees that there are CT-formulas that can express the QMLcontent that gets lost through the translation. The problem is how we arrive to them. In this paper, I propose new translation rules from QML to CT, based on a suggestion by Kaplan. However, I will claim that we cannot have ‘the’ translation scheme from QML to CT. The reason being that de re modal language is ambiguous. Accordingly, there are diferent sorts of QML, depending on how we resolve such ambiguity. Therefore, depending on what sort of QML we intend to translate into CT, we need to use the corresponding translation scheme. This suggests that all the translation problems might just disappear if we do what Lewis did not: begin with a fully worked out QML that tells us how to understand de re modal discourse. (shrink)

Antihaecceitists believe that all facts about specific individuals—such as the fact that Fred exists, or that Katie is tall—globally supervene on purely qualitative facts. Haecceitists deny that. The issue is not only of interest in itself, but receives additional importance from its intimate connection to the question of whether all fundamental facts are qualitative or whether they include facts about which specific individuals there are and how qualitative properties and relations are distributed over them. Those who think that all fundamental (...) facts are qualitative are arguably committed to antihaecceitism. The goal of this paper is to point out some problems for antihaecceitism (and therefore for the thesis that all fundamental facts are qualitative). The article focuses on two common assumptions about possible worlds: (i) Sets of possible worlds are the bearers of objective physical chance. (ii) Counterfactual conditionals can be defined by appeal to a relation of closeness between possible worlds. The essay tries to show that absurd consequences ensue if either of these assumptions is combined with antihaecceitism. Then it considers a natural response by the antihaecceitist, which is to deny that worlds play the role described in (i) and (ii). Instead, the reply continues, we can introduce a new set of entities that are defined in terms of worlds and that behave the way worlds do on the haecceitist position. That allows the antihaecceitist to formulate antihaecceitist friendly versions of (i) and (ii) by replacing the appeal to possible worlds with reference to the newly introduced entities. This maneuver invites an obvious reply, however. If the new entities are the things that play the role we typically associate with worlds, as partially described by (i) and (ii), then it is natural to conclude that they really are the entities we talk about when we speak of worlds, so that haecceitism is true after all. (shrink)

This paper is about two puzzles, or two versions of a single puzzle, which deserve to be called paradoxes, and develops some apparatus in terms of which the apparently conflicting principles which generate the puzzles can be rendered consistent. However, the apparatus itself is somewhat controversial: the puzzles are modal ones, and the resolution to be advocated requires the adoption of a counterpart theoretic semantics of essentially the kind proposed by David Lewis, which in turn requires qualified rejection of certain (...) modal theses about identity which are valid in S5. (shrink)

The delicate point in the formalistic position is to explain how the non-intuitionistic classical mathematics is significant, after having initially agreed with the intuitionists that its theorems lack a real meaning in terms of which they are true (S. C. Kleene, 1952).

Many philosophers, following David Lewis, believe that we should look to counterpart theory, not quantified modal logic, as a means of understanding modal discourse. We argue that this is a mistake. Significant parts of modal discourse involve either implicit or explicit reference to what is actually the case, raising the question of how talk about actuality is to be represented counterpart-theoretically. By considering possible modifications of Lewis's counterpart theory, including actual modifications due to Graeme Forbes and Murali Ramachandran, we argue (...) that no coherent version of counterpart theory can provide a plausible representation of talk about actuality, and so, we conclude, counterpart theory should be rejected. (shrink)

We propose a novel interpretation of Lewis on the analysis of modality that is constructed from primary sources, comprehensive and unprecedented. Our guiding precepts are to distinguish semantics from metaphysics, while respecting the inter-relations between them, and to discern whatever may be special, semantically or metaphysically, about the modal case. Following detailed presentation, we amplify and advocate our interpretation by providing a conforming genealogy of Lewis’s theory of modality and applying it to construct a detailed and newly illuminating version of (...) the Lewisian theory of modality de re. (shrink)

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

This article includes a basic overview of possible world semantics and a relatively comprehensive overview of three central philosophical conceptions of possible worlds: Concretism (represented chiefly by Lewis), Abstractionism (represented chiefly by Plantinga), and Combinatorialism (represented chiefly by Armstrong).

I defend counterpart theory against post-Kripkean objections. Trenton Merricks objects that no construction of ersatz counterparts is uniquely and intrinsically suitable; I reply that metaphysical constructions need not have these features. Sarah Moss refutes my solution (from "All the world's a stage") to the problem of timeless counting for temporal counterpart theory; I offer a new solution. Hazen, Fara, Williamson, and others have objected that counterpart theory generates an unacceptable logic for an actuality operator; I attempt to give a better (...) semantics. (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)

Modal realists face a puzzle. For modal realism to be justified, modal realists need to be able to give a successful reduction of modality. A simple argument, however, appears to show that the reduction they propose fails. In order to defend the claim that modal realism is justified, modal realists therefore need to either show that this argument fails, or show that modal realists can give another reduction of modality that is successful. I argue that modal realists cannot do either (...) of these things and that, as a result, modal realism is unjustified and should be rejected. (shrink)