ABSTRACT An alternative to the classical Stalnaker–Lewis account of subjunctive conditionals is outlined. A distinction is drawn between a basic notion of ‘wouldness’ and a more full‐bloodedly modal variant, each with its own logic. Previous philosophers have challenged the alleged vacuity of counterpossibles using logico‐mathematically impossible worlds. Here the vacuity thesis as well as other orthodox alleged logical principles are challenged more forcefully through consideration of a logico‐mathematically possible world. The impossible‐world theorist's Strangeness of Impossibility Condition is also challenged using the same logico‐mathematically possible world. The dogma that the truth‐condition of a subjunctive invokes the antecedent worlds sufficiently ‘closest’ to (most like) the actual world is also challenged through consideration of the same logico‐mathematically possible world. The dogma is a variation on David Lewis's counterpart theory, and is flawed in the same way.

ABSTRACT Soames attributes to Kripke the theory of epistemic possibility that uses metaphysical impossibilities in explaining necessary a posteriori truths. I attribute to Kripke a theory from epistemic counterparthood. I develop an epistemic accessibility based on Kripke’s appeal to Lewis’ counterpart theory that is reflexive, non-transitive, and non-symmetric. I also propose an epistemic counterpart function and a description function.

Abstract Many philosophers and linguists have been attracted to counterpart theory as a framework for natural language semantics. I raise a novel problem for counterpart theory involving simple declarative sentences with proper names. To resolve this problem, counterpart theorists must introduce the notion of a counterpart in the semantics of the non‐modal fragment of language. I develop my preferred solution: a novel theory of proper names as counterpart‐theoretic individual concepts. The resulting view highlights a hitherto unnoticed fact: counterpart theorists should formulate their theory, not by modifying the standard semantics for modal operators, but by modifying the standard semantics for names and variables.

Lewis (The Journal of Philosophy, 65(5), 113–126, 1968) attempts to provide an account of modal talk in terms of the resources of counterpart theory, a first-order theory that eschews transworld identity. First, a regimentation of natural language modal claims into sentences of a formal first-order modal language L is assumed. Second, a translation scheme from L-sentences to sentences of the language of the theory is provided. According to Hazen (The Journal of Philosophy, 76(6), 319–338, 1979) and Fara & Williamson (Mind, 114(453), 1–30, 2005), the account cannot handle certain natural language modal claims involving a notion of actuality. The challenge has two parts. First, in order to handle such claims, the initial formal modal language that natural language modal claims are regimented into must extend L with something like an actuality operator. Second, certain ways that Lewis’ translation scheme for L might be extended to accommodate an actuality operator are unacceptable. Meyer (Mind, 122(485), 27–42, 2013) attempts to defend Lewis’ approach. First, Meyer holds that in order to handle such claims, the formal modal language L∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^*$$\\end{document} that we initially regiment our natural language claims into need not contain an actuality operator. Instead, we can make do with other resources. Next, Meyer provides an alternative translation scheme from L∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^*$$\\end{document}-sentences to sentences of an enriched language of counterpart theory. Unfortunately, Meyer’s approach fails to provide an appropriate counterpart theoretic account of natural language modal claims. In this paper, I demonstrate that failure.

The infamous Hole Argument has led philosophers to develop various versions of substantivalism, of which metric essentialism and sophisticated substantivalism are the most popular. In this journal, Trevor Teitel has recently advanced novel arguments against both positions. However, Teitel does not discuss the position of Jeremy Butterfield, which appeals to Lewisian counterpart theory in order to avoid the Hole Argument. In this note I show that the Lewis-Butterfield view is immune to Teitel’s challenges.

ABSTRACT In this paper, I argue that not only is metaphysical modal normativism an attractive view but that, as a matter of fact, many of us have, all along, been metaphysical modal normativists of a particular stripe. Namely, we have been the kinds of modal normativists, in the form of counterpart theorists, who are robust realists about possibility simpliciter. Having introduced modal normativism as Thomasson does in Norms and Necessity, I go on to recast it in somewhat different terms. With this re-casting in place we can see that while the view offers a pleasingly deflationary account of metaphysical necessity and possibility it does so only against the backdrop of robust realism about possibility simpliciter. If that is right, then Lewis’ counterpart theory turns out to be a potent version of metaphysical modal normativism. So many of us have, all along, been metaphysical modal normativists, and so much the better for it.

Abstract One of the primary interests in understanding biological systems is the interaction between noise and cellular regulation. Noise levels can be altered by rate constant perturbations, which may result in an imbalance of important biological functions. Although the theory of noise localization can estimate noise perturbation response, it is currently limited to open systems, where the majority of biological networks belong. However, during their lifetime, some components of biological systems participate in reactions that can be categorized under a closed system. Therefore, a counterpart theory for closed systems is desirable. In this work, steady‐state perturbations of monomolecular closed systems and ways to estimate the response of noise as (co)variances are explored. We extend the structural sensitivity analysis for analyzing noise response patterns by using additional clues derived from multinomial assumptions. We identified scenarios in which this combination might fail in noise prediction, which we call noise flip, arising from the nonlinear dependence of variance upon composition. Nevertheless, theoretical intuition and simulation show that noise flip diminishes with increasing system size. This work provides an efficient and scalable means to estimate noise responses with potential applications in model discrimination, network‐wide response scanning, and reconstruction.

Abstract In this paper, I develop a “safety result” for applied mathematics. I show that whenever a theory in natural science entails some non-mathematical conclusion via an application of mathematics, there is a counterpart theory that carries no commitment to mathematical objects, entails the same conclusion, and the claims of which are true if the claims of the original theory are “correct”: roughly, true given the assumption that mathematical objects exist. The framework used for proving the safety result has some advantages over existing nominalistic accounts of applied mathematics. It also provides a nominalistic account of pure mathematics.

ABSTRACTDavid Lewis argues at length against haecceitism and goes as far as claiming that, on a certain counterpart‐theoretic construal, the doctrine is unintelligible or inconsistent. I argue, contra Lewis, that both qualitative and non‐qualitative counterpart theory are in fact committed to haecceitism, but that this commitment is harmless since what is really at stake for a counterpart theorist such as Lewis are more general supervenience claims that are independent of haecceitism. I further argue that Lewis's formulation of the doctrine suffers from two important defects that, once remedied, free counterpart theory of its haecceitistic commitments. Along the way I discuss an objection to the effect that the cheap substitute is inconsistent in the presence of an ‘actually’ operator. This paper therefore brings together important critical discussion on haecceitism and counterpart theory.

Lewis (1968) claims that his language of Counterpart Theory (CT) interprets modal discourse and he adverts to a translation scheme from the language of Quantified 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 QML-content 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 different 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.

Abstract David Lewis’ contemplations regarding divine foreknowledge and free will, along with some of his other more substantial work on modal realism and his counterpart theory can serve as a springboard to a novel solution to the foreknowledge and metaphysical freedom puzzle, namely a proposal that genuine metaphysical freedom is compatible with determinism, which is quite different from the usual compatibilist focus on the compatibility between determinism and moral responsibility. This paper argues that while Lewis opens the doors to such a possibility, in order to fully elucidate a genuinely metaphysical compatibilist account, Lewis’ own counterpart theory must be abandoned in favour of an account of trans-world identity that is theoretically framed by a modified version of Robert Nozick’s closest continuer theory.

It is commonplace to formalize propositions involving essential properties of objects in a language containing modal operators and quantifiers. Assuming David Lewis’s counterpart theory as a semantic framework for quantified modal logic, I will show that certain statements discussed in the metaphysics of modality de re, such as the sufficiency condition for essential properties, cannot be faithfully formalized. A natural modification of Lewis’s translation scheme seems to be an obvious solution but is not acceptable for various reasons. Consequently, the only safe way to express some intuitions regarding essential properties is to use directly the language of counterpart theory without modal operators.

Standard accounts of counterfactuals with metaphysically impossible antecedents take them to by trivially true. But recent work shows that nontrivial countermetaphysicals are frequently appealed to in scientific modeling and are indispensable for a number of metaphysical projects. I focus on three recent discussions of counterpossible counterfactuals, which apply counterpossibles in both scientific and metaphysical modeling. I show that a sufficiently developed modal counterpart theory can provide a semantics for a wide range of counterpossibles without any inconsistent possibilities or other forms of impossible worlds. But such a view faces problems: in order for the metaphysical views I discuss to bear weight, there must be a significant difference between the metaphysical possibilities and impossibilities. I will show how the counterpart-theoretic view delineates the possible from impossible, while still making room for the impossible.

Abstract In two‐dimensional semantics in the tradition of Davies and Humberstone, whether a singular term receives an epistemically shifted reading in the scope of a modal operator depends on whether the world considered as actual is shifted. This means that epistemically shifted readings should be available only in environments where an explicit contrast between the actual world and some counterfactual worlds cannot be made. In this paper, I argue that this is incorrect. Whether a singular term receives an epistemically shifted reading is independent of whether the world treated as actual is shifted. This, I argue, undermines the two‐dimensionalist account of epistemic shift. I then turn to the question how a positive view should handle these two phenomena separately. I argue for treating singular terms with a version of counterpart theory in which the difference between epistemically shifted and other readings is determined in the context of utterance.

Abstract Modal counterpart theory identifies a thing’spossibly being Fwith its having a counterpart that isFat another possible world; temporal counterpart theory identifies a thing’shaving been Forgoing to be F, with its having a counterpart that isFat another time.Benovsky, J. 2015. “Alethic Modalities, Temporal Modalities, and Representation.”Kriterion: Journal of Philosophy29: 18–34 in this journal endorses modal counterpart theory but holds that temporal counterpart theory is untenable because it does not license the ascription of the intuitively correct temporal properties to ordinary objects, and hence that we should understand ordinary objects, including persons, as transtemporal ‘worms’. I argue that the worm theory is problematic when it comes to accounting for what matters in survival and that temporal counterpart theory provides a plausible account of personal persistence.

In this article, the problem of transworld identity – that is the question, if and how it is possible to ground the intuition that the same individual exists in more than one possible world – is solved by arguing that individuals have essences. First of all, it is claimed that the concept of transworld identity is desirable since it betters both global pan-essentialism and counterpart theory. Then, necessary terminology for successful understanding of the transworld identity problem is introduced. Afterwards, it is contended that the well-known Chisholm’s paradox for transworld identity can be resolved by appealing to individual essences. It is argued that if extreme haecceitism is true, then essences of individuals are non-qualitative and hence haecceitist switches are ontologically grounded. On the other hand, if reductionism is true, then essences of individuals are qualitative and hence haecceitist switches are impossible. Finally, it is shown that by referring to individual essences across possible worlds it is possible to solve the problem of cross-world identification.

Abstract Modal counterpart theory identifies a thing’spossibly being Fwith its having a counterpart that isFat another possible world; temporal counterpart theory, thestage view, according to which people and other ordinary objects are instantaneous stages, identifies a thing’shaving been Forgoing to be F, with its having a counterpart that isFat another time. Both counterpart theories invite what has been called ‘the argument from concern’ (Rosen, G. 1990. “Modal Fictionalism.” Mind 99 (395): 327–54). Why should I be concerned about my counterparts at other possible worlds or other times? I care about how things might have gone forme—not how they go for other people at other possible worlds; I care aboutmyprospects—not the way go for other people at other times. Jiri Benovsky has argued that while modal counterpart theory can be defended against this style of argument, temporal counterpart theory cannot (Benovsky, J. 2015. “Alethic Modalities, Temporal Modalities, and Representation.” Kriterion: Journal of Philosophy 29: 18–34). I argue that temporal counterpart theory, like modal counterpart theory, resists the argument from concern.

I remember distinctly the moment I learned that David Lewis had died. It was during my years as a postdoctoral fellow, when I was more than a little isolated, and so it turned out to have been some time—months, maybe—since the event. I recall thinking: the world in which I thought I was living, during those months, turned out not to be the actual world, and so I turned out not to be the person I thought I was, but merely a counterpart of that person. And thus arose the half-formed thought (still only half-formed now, alas) that therein lay some insight into what is actually at stake in the conflict between counterpart theory and transworld identity.

David Lewis (Papers in metaphysics and epistemology: volume 2. Cambridge University Press, Cambridge, pp 164–182, 1993) offers two solutions to the problem of the many, one of which relies on supervaluationism and the other on the notion of “almost-identity” for the most part. In this paper, I argue that Lewis’ other metaphysical views constitute reasons to prefer his second solution to the first one. Specifically, Lewis’ theory of propositions and his counterpart theory give rise to two similar problems of the many, which I call “the problem of many propositions” and “the problem of many counterparts” respectively. While both Lewis’ solutions may solve the problem of the many with respect to objects in the actual world, I argue that only his second solution can solve the problem of many propositions and the problem of many counterparts. Therefore, for anyone who accepts Lewis’ metaphysical views on propositions and counterparts, they should embrace Lewis’ second solution to the problem of the many for the reason of unification.

David Lewis’s counterpart theory (CT) is often seen as involving a radical departure from the standard, Kripke-style semantics for modal logic (ML), 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 (all worlds are equally real, individuals are world-bound) 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.