Counterparts, Essences and Quantified Modal Logic

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.

Tolerance and Counterpart Theory

Many philosophers have thought that Tolerance Puzzles can be easily dissolved by adopting some form of counterpart theory, which is roughly the view that being possibly a certain way is having a counterpart that is that way. This chapter shows how standard versions of counterpart theory involve radical departures from standard modal logic (going far beyond Iteration-denial) which we claim are unacceptable, and argues that once counterpart theory is developed in such a way as to avoid such logical revisionism, it has no special capacity to resolve the puzzles.

Grounding Personal Persistence

Modal counterpart theory identifies a thing’s possibly being F with its having a counterpart that is F at another possible world; temporal counterpart theory identifies a thing’s having been F or going to be F, with its having a counterpart that is F at another time. Benovsky, J. 2015. “Alethic Modalities, Temporal Modalities, and Representation.” Kriterion: Journal of Philosophy 29: 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.

The Problem of Transworld Identity: in Defence of Essentialism

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.

Counterpart Theories: The Argument from Concern

Modal counterpart theory identifies a thing’s possibly being F with its having a counterpart that is F at another possible world; temporal counterpart theory, the stage view, according to which people and other ordinary objects are instantaneous stages, identifies a thing’s having been F or going to be F, with its having a counterpart that is F at 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 for me—not how they go for other people at other possible worlds; I care about my prospects—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.

In Memoriam

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.

Counterpart theories for everyone

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.

Two Geometrical Models for Pixelism

Pixelism is the combination of three metaphysical thesis, namely a radical form of exdurantism, mereological nihilism and counterpart theory. Pixelism is a theory that evaluates all the metaphysical phenomena of persistence, composition and modality in a homogeneous and consistent manner. In a pixel world, there is no identity over time and over possible worlds and nothing persists over more than an instant or a world. Entities can be univocally identified by a five-coordinates system (the three spatial dimensions, the temporal one and the possible worlds), and their relation is a counterpart relation both in different worlds and at different times or different regions of space. In this paper I will provide two models for pixelism: the first one takes pixels to be hypercubes, i. e. four-dimensional cubes, the acceptance of which is conditional on the acceptance of extended simples. The second one considers pixels as points in a four-dimensional space.