This paper presents and motivates a counterpart theoretic semantics for quantifi ed modal logic based on a fleshed out account of Lewis's notion of a `possibility.' According to the account a possibility consists of a world and some haecceitistic information about how each possible individual gets represented de re. A semantics for quanti ed modal logic based on evaluating formulae at possibilities is developed. It is shown that this framework naturally accommodates an actuality operator, addressing recent objections to counterpart theory, (...) and is equivalent to the more familiar Kripke semantics for quanti fied modal logic with an actuality operator. (shrink)

Leibniz has enjoyed a prominent place in the history of thought about possible worlds.' I shall argue that on the feading interpretation of Leibniz's account of contingency — an ingenious interpretation with ample textual support — possible worlds may be invoked by Leibniz only on pain of inconsistency. Leibnizian contingency, as reconstructed in detail by Robert C. Sleigh, Jr.,z will be shown to preclude propositions with different truth-values in different possible worlds.

Physicalists about the mind are committed to claims about property identities. Following Kripke's well-known discussion, modal arguments have emerged as major threats to such claims. This paper argues that modal arguments can be resisted by adopting a counterpart theoretic account of modal claims, and in particular modal claims involving properties. Thus physicalists have a powerful motive to adopt non-Kripkean accounts of the metaphysics of modality and the semantics of modal expressions.

In this paper I argue that Gareth Evans’ famous proof of the impossibility of de re indeterminate identity fails on a counterpart-theoretic interpretation of the determinacy operators. I attempt to motivate a counterpart-theoretic reading of the determinacy operators and then show that, understood counterpart-theoretically, Evans’ argument is straightforwardly invalid.

Recently Carolyn Brighouse and Jeremy Butterfield have argued that David Lewis's counterpart theory makes it possible both to believe in the reality of spacetime points and to consider general relativity to be a deterministic theory, thus avoiding the ‘hole argument’ of John Earman and John Norton. Butterfield's argument relies on Lewis's own counterpart-theoretic analysis of determinism. In this paper, I argue that this analysis is inadequate. This leaves a gap in the Butterfield–Brighouse defence against the hole argument.

The paper shows – contra what has been argued by Trenton Merricks – that counterpart theory, when conjoined with composition as identity, does not entail mereological essentialism. What Merrick’s argument overlooks is that contingent identity is but one of the effects of grounding identity across possible worlds on similarity.

David Lewis advised essentialists to judge his counterpart theory a false friend. He also argued that counterpart theory needs natural properties. This essay argues that natural properties are all essentialists need to find a true friend in counterpart theory. Section one explains why Lewis takes counterpart theory to be anti-essentialist and why he thinks it needs natural properties. Section two establishes the connection between the natural properties counterpart theory needs and the essentialist consequences Lewis disavows. Section three answers two objections: (...) the first attempts to block the consequences of adding natural properties to counterpart theory; the second grants the consequences, but denies that they amount to essentialism. –Correspondence to: Todd_Buras@baylor.edu. (shrink)

Jim Stone has argued that a multiversal version of Modal Realism together with Counterpart Theory cannot account for a certain intuitive possibility. Roughly, it is the possibility that all free moral choices of a certain sort are the right choices in all cases in the multiverse. The present work offers an explanation of how the metaphysics in question can account for the intuitive possibility in question.

In this paper, I examine the putative incompatibility of three theses: (1) Haecceitism, according to which some maximal possibilities differ solely in terms of the non-qualitative or de re possibilities they include; (2) Modal correspondence, according to which each maximal possibility is identical with a unique possible world; (3) Counterpart theory, according to which de re modality is analyzed in terms of counterpart relations between individuals. After showing how the modal realism defended by David Lewis resolves this incompatibility by rejecting (...) modal correspondence, I defend modal correspondence and develop an alternative strategy for reconciling these theses. Specifically, I examine Lewis’s arguments against non-qualitative counterpart theory and undermine them by developing a novel version of non-qualitative counterpart theory that appeals to a metaphysics of bare particulars. I then indicate how this version of non-qualitative counterpart theory accommodates both haecceitism and modal correspondence. (shrink)

David Lewis's modal realism claims that nothing can exist in more than one world or time, and that statements about how something would have been are to be analysed in terms of its counterpart . I first explain why the counterpart relation depends on de re modal statements in an intensional language, so that intuitive properties of similarity relations cannot be used to show that the counterpart relation is not an equivalence relation. I then look at test sentences in (the (...) intensional) natural language, and show that none of them provide compelling evidence that a counterpart semantics is needed. (shrink)

David Lewis's modal realism claims that nothing can exist in more than one world or time, and that statements about how something would have been are to be analysed in terms of its counterpart . I first explain why the counterpart relation depends on de re modal statements in an intensional language, so that intuitive properties of similarity relations cannot be used to show that the counterpart relation is not an equivalence relation. I then look at test sentences in (the (...) intensional) natural language, and show that none of them provide compelling evidence that a counterpart semantics is needed. (shrink)

David Lewis's modal realism claims that nothing can exist in more than one world or time, and that statements about how something would have been are to be analysed in terms of its counterpart . I first explain why the counterpart relation depends on de re modal statements in an intensional language, so that intuitive properties of similarity relations cannot be used to show that the counterpart relation is not an equivalence relation. I then look at test sentences in (the (...) intensional) natural language, and show that none of them provide compelling evidence that a counterpart semantics is needed. (shrink)

In 'Four-Dimensional Objects' Peter van Inwagen gives two arguments for the claim that proponents of four-dimensionalism have to be counterpart theorists. Recently Jack Copeland, Heather Dyke, and Diane Proudfoot, echoing in part points made by Mark Heller in this journal in 1993, have sought to rebut one of van Inwagen's arguments. In this paper I shall criticize their discussion and by implication certain points made by Heller. In so doing I shall also rebut a possible objection to van Inwagen's second (...) argument. While I shall conclude that Copeland et al . fail to make their case, I nevertheless argue that van Inwagen's argument can be resisted, provided that the four-dimensionalist is willing to adopt a certain conception of transworld identity. Moreover, I shall argue that to the extent that van Inwagen's paper highlights something problematic for four-dimensionalism in this particular conception of transworld identity, the paper highlights something equally problematic for three-dimensionalism. (shrink)

This paper investigates the form a modal realist analysis of possibility and necessity should take. It concludes that according to the best version of modal realism, the notion of a world plays no role in the analysis of modal claims. All contingent claims contain some de re element; the effect of modal operators on these elements is described by a counterpart theory which takes the same form whether the de re reference is to a world or to something else. This (...) fully general counterpart theory can validate orthodox modal logic, including the logic of 'actually'. (shrink)

I argue that there is a conflict between two positions defended by David Lewis: counterpart theory, and the identification of propositions with sets of possible worlds. There is no adequate answer to the question whether a world where Humphrey has one winning and one losing counterpart is or is not a member of the set that is the proposition that Humphrey wins. If one says it is, it will follow that it is possible for that proposition to be true without (...) Humphrey winning; if one says that it is not, it will follow that it is possible for Humphrey to win without that proposition being true. (shrink)

Recently, Jim Stone has argued that counterpart theory is incompatible with the existence of temporal parts. I demonstrate that there is no such incompatibility.

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)

This paper is an informal presentation of the ideas presented formally in (”Relative-Sameness Counterpart Theory”. Relative-sameness relations -- such as being the same person as -- are like David Lewis’s “counterpart” relations in the following respects: (i) they may hold over time or across worlds between objects that aren’t cross-time or cross-world identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different contexts. They differ from his counterpart relations, however, (...) in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis’s Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). The use of sameness as opposed to similarity relations in the analysis of de-re temporal and modal predication renders the resulting truth conditions as statable in terms that proponents of Kripke’s identity-based analysis can accept. (shrink)

If a counterpart theorist's understanding of the counterpart relation precludes haecceitist differences between possible worlds, as David Lewis's does, how can he admit haecceitist possibilities, as Lewis wants to? Lewis (Philosophical Review 3-32, 1983; On the Plurality of Worlds, 1986) devised what he called a 'cheap substitute for haecceitism,' which would allow for haecceitist possibilities while preserving the counterpart relation as a purely qualitative one. The solution involved lifting an earlier (Journal of Philosophy 65(5): 113-126, 1968; 68(7): 203-211, 1971) ban (...) on there being multiple intra-world counterparts. I argue here that serious problems for 'cheap haecceitism' lurk very close to its surface, and they emerge when we consider the effect of using an actuality operator in our language. Among the most serious of the problems is the result that being the case in some possible world does not always suffice for possibly being the case. The result applies to any counterpart theory that employs a purely qualitative counterpart relation. The upshot is that if we are to admit haecceitist possibilities, as we should, then we must reject any purely qualitative relation as the one involved in the analysis of what might have been for an individual. (shrink)

If a counterpart theorist’s understanding of the counterpart relation precludes haecceitist differences between possible worlds, as David Lewis’s does, how can he admit haecceitist possibilities, as Lewis wants to? Lewis (Philosophical Review 3–32, 1983; On the Plurality of Worlds, 1986) devised what he called a ‘cheap substitute for haecceitism,’ which would allow for haecceitist possibilities while preserving the counterpart relation as a purely qualitative one. The solution involved lifting an earlier (Journal of Philosophy 65(5):113–126, 1968; 68(7):203–211, 1971) ban on there (...) being multiple intra-world counterparts. I argue here that serious problems for ‘cheap haecceitism’ lurk very close to its surface, and they emerge when we consider the effect of using an actuality operator in our language. Among the most serious of the problems is the result that being the case in some possible world does not always suffice for possibly being the case. The result applies to any counterpart theory that employs a purely qualitative counterpart relation. The upshot is that if we are to admit haecceitist possibilities, as we should, then we must reject any purely qualitative relation as the one involved in the analysis of what might have been for an individual. (shrink)

Here I propose a coherent way of preserving the identity of material objects with the matter that constitutes them. The presentation is formal, and intended for RSL. An informal presentation is in preliminary draft! -/- Relative-sameness relations—such as being the same person as—are like David Lewis's "counterpart" relations in the following respects: (i) they may hold between objects that aren't identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different (...) contexts. They differ from counterpart relations, however, in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis's Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). (shrink)

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)

In a recent article in Analysis, Graeme Hunter and William Seager (1981) attempt to rescue counterpart theory (CT) from some objections of Hazen 1979. They see these objections as arising from ‘uncritical use of the translation scheme originally proposed by Lewis’, and intend to meet them by refraining from use of that scheme. But they do not offer a new scheme; they say ‘…it is no more necessary to have one to capture the sense of modal idiom than it is (...) to capture the sense of quantificational idiom…Appeal to truth value is the single most important criterion of correct translation’ (Hunter and Seager 1981:72). Thus, where the scheme of Lewis (1968) translates a truth by a falsehood or conversely, Hunter and Seager simply produce a sentence which they claim to be a better translation, without articulating any structural principles they employ to arrive at their candidate. A friend of CT should not be happy with this procedure. Let Lm be first-order modal language and Lc be the language of counterpart theory. Sentences of Lc are intended to interpret or elucidate the meanings of Lm-sentences in the strong sense that they should be the outputs of an adequate theory of meaning, which we can formulate as a model theory, for Lm, written in Lc plus set theory. The interest of CT resides in its potential to provide an alternative approach to the model theory of modal logic, and from the clauses of any such alternative model theory we should be able to read off a translation scheme for Lm into Lc, just as we can in the standard case. If CT’s motivation is sound, which Hunter and Seager do not dispute, yet there is no translation scheme and so no counterpart-theoretic model theory, one might suspect some defect in the original language Lm. And in fact, Hunter and Seager find certain Lm-sentences multiply ambiguous with respect to Lc; but if a counterpart-theoretic model theory is possible, to say.. (shrink)

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

In this paper I consider Saul Kripke’s famous Humphrey objection to David Lewis’s views on de re modality and argue that responses to this objection currently on the market fail to mitigate its force in any significant way.

Fara and Williamson (Mind, 2005) argue that counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.

Comparative overall similarity lies at the basis of a lot of recent metaphysics and epistemology. It is a poor foundation. Overall similarity is supposed to be an aggregate of similarities and differences in various respects. But there is no good way of combining them all.

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)

A not-unpopular position in the metaphysics of material objects (Ted Sider's, for instance) combines realism about what objects there are and the conditions of objecthood with conventionalism about de re modality. I argue that this is not a coherent combination of views: one must go fully conventionalist, or fully realist. The central argument displays the difficulty for the modal conventionalist/object realist in specifying the object that satisfies de re modal predicates. I argue that if this is a mind-independent object, contradictions (...) arise when we consider the possibility or actuality of non-equivalent conventions both applying to 'the same object'. (shrink)

Counterpart theory has come a long way since the seventies. Its virtues are now generally appreciated. It has been extended to temporal discourse.1 And it is less often dismissed out of hand, now that Saul Kripke’s scornful words are no longer regarded as the last on the subject. But new critics have appeared, equally formidable if less dismissive. Counterpart theorists, both modal and temporal, owe them answers.

(No abstract is available for this citation).

It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are (...) adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis' counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics. (shrink)

I introduce and defend the semantic notion of counterfactual identity, distinguishing it from the metaphysical notion of transworld identity. After showing that Lewis's counterpart theory misconstrues counterfactual identity facts, I outline and motivate a ‘Leibnizian counterpart theory’ where the notion of counterfactual identity is adequately modelled. Finally, I show that counterfactual identity can be characterized without relying on some implausible features of Lewis's theory of conditionals.

Lewis proposed to test the validity of a modal thesis by checking whether its possible-world translation is a theorem of counterpart theory. However, that criterion fails to validate many standard modal laws, thus raising doubts about the logical adequacy of the Lewisian framework. The present paper considers systems of counterpart theory of increasing strength and shows how each can be motivated by exhibiting a suitable intended model. In particular, perfect counterpart theory validates all the desired modal laws and therefore provides (...) a way out of the logical objection. Finally, a weakening of perfect counterpart theory is put forward as a response to some metaphysical objections. (shrink)

The paper investigates the link between the theory of modal occurrents (where individuals are allowed to stretch across possible worlds) and Lewis’s counterpart theory (where all individuals are world-bound but have counterparts in other worlds). First I show how to interpret modal talk extensionally within the theory of modal occurrents. Then I show that the assumption that worlds be pairwise discrete is all that is needed to reconstruct the bulk of counterpart theory (i.e., to define the concept of a counterpart (...) and to derive the standard postulates governing that concept) in terms of the theory of modal occurrents. Finally, I argue that this reconstruction allows us to view the indeterminacy of our modal intuitions as being part and parcel with the indeterminacy of our criteria for individuating modal occurrents, and that this indeterminacy is naturally explained in terms of linguistic (as opposed to ontic) vagueness. (shrink)

David Lewis adopts a counterpart theory of individuals to account for how it is that Humphrey has the modal property of ‘could have won the election.’ Once counterpart theory is taken on board, however, I think that the motivation for having a plurality of worlds is untenable. I will claim that counterpart theory with respect to individuals invites counterpart theory with respect to properties1, which in turn invites an analysis of modality that involves only one possible world, viz., the actual (...) world. (shrink)

(No abstract is available for this citation).