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)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

When some objects are the parts of another object, they compose that object and that object is composite. This article is intended as an introduction to the central questions about composition and a highly selective overview of various answers to those questions. In §1, we review some formal features of parthood that are important for understanding the nature of composition. In §2, we consider some answers to the question: which pluralities of objects together compose something? As we will see, the (...) dominant answers are all of them and none of them. In §§3-4, we examine one of the main arguments that has driven philosophers to these extreme answers: the argument from vagueness. In §5, we turn to the question of whether composition is unique: is it sometimes the case that some things compose more than one thing? Finally, in §6, we turn from the question of which composites exist to the question of which composites exist fundamentally. (shrink)

An encyclopedia entry which covers various revisionary conceptions of which macroscopic objects there are, and the puzzles and arguments that motivate these conceptions: sorites arguments, the argument from vagueness, the puzzles of material constitution, arguments against indeterminate identity, arguments from arbitrariness, debunking arguments, the overdetermination argument, and the problem of the many.

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)

This paper aims to demonstrate that the ontology of consciousness is consistent with both the modal and the metaphysical versions of Haecceitism. I examine the varieties of Haecceitism, and I specify the intended versions that the arguments will vindicate. I define the property of 'being purely qualitative', and examine its relation to the properties of phenomenal consciousness. I draw, inter alia, on Bayesian perceptual psychology, in order to specify the identity-conditions of phenomenal properties in detail. I provide two, abductive arguments (...) for the claim that the identity-conditions on some individuals are metaphysically haecceitistic, in virtue of the relations that hold between those individuals and the phenomenal properties that they instantiate. The first argument is corroborated by empirical results concerning the phenomenological effects of attention. The second argument is corroborated by empirical results from the study of color in vision science. The arguments vindicate a version of Metaphysical Haecceitism, because the individuals are shown to be typed by the phenomenal properties that they instantiate, although quantification over the individuals is an ineliminable condition on their identity and distinctness. I provide, then, a regimentation of the extant proposals in the ontology of consciousness, using the logic of hyperintensional ground, as augmented by the Bayesian probability calculus. The hyperintensional regimentation vindicates a version of Modal Haecceitism, because the probabilistic ontological dependence of the parts of worlds on other parts thereof provides an ineliminable condition on the identity and distinctness of worlds. (shrink)

A growing consensus in the literature on agentive modals has it that ability modals like ‘can’ or ‘able to’ have a _dual_, i.e. interpretations of ‘must’ or ‘cannot but’ which stand to _necessity_ as ability stands to _possibility_. We argue that this thesis (which we call ‘Agentive Duality’) is much more controversial than meets the eye. While Agentive Duality follows from the orthodox possibility analysis of ability given natural assumptions, it sits uneasily with a wide range of alternative proposals which (...) are unified by the idea that ability requires _control_. In particular, we show that against the background of a control requirement on ability, Agentive Duality can be used to derive absurd predictions featuring this dual. Far from being a purely definitional thesis, Agentive Duality thus affords a new lens through which to assess the long-standing debate between possibility analyses of ability and their discontents. (shrink)

The purpose of this paper is to provide a new system of logic for existence and essence, in which the traditional distinctions between essential and accidental properties, abstract and concrete objects, and actually existent and possibly existent objects are described and related in a suitable way. In order to accomplish this task, a primitive relation of essential identity between different objects is introduced and connected to a first order existence property and a first order abstractness property. The basic idea is (...) that possibly existent objects are completely determinate and that essentially identical objects are just different individuations of the same individual essence. Accordingly, essential properties are defined as properties that are invariant with respect to this kind of identity, while abstract objects are determined by being characterized by essential properties only. Once such ideas are implemented, a number of classical intuitions about objects, their essence, and their way of existence can be consistently interpreted. (shrink)

In 2008, Graff Fara presented relative-sameness semantics, a semantics for a first-order modal and temporal language with the explicit aim of being able to render true certain contingent/temporary identity claims (relative to certain contexts). Graff Fara achieves this aim by abandoning a straightforward analysis of de re modal/temporal claims in terms of identity. Instead, such a claim is analyzed in terms of her relative-sameness relations (which need not be the identity relation), with the relevant relative-sameness relations in play determined by (...) context and individual terms occurring in the claim. However, there is a significant problem for relative-sameness semantics concerning (i) iterated modality/temporality, and (ii) existence that renders it an inappropriate account of our modal and temporal talk. In this paper, I present that problem and a solution to it. (shrink)

Philosophers distinguish between having a property essentially and having it accidentally. The way the distinction has been drawn suggests that it is modal in character, and so that it can be captured in terms of necessity, or cognate notions. The present chapter takes the suggestion at face value by considering a number of modal characterizations of the essential/accidental distinction that have been articulated and discussed since the early 20th century, as well as some of the challenges that they face.

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)

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)

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)

Anti-haecceitism is the thesis that things cannot differ from actuality in a purely non-qualitative fashion. Anti-haecceitism being a modal notion, we would expect it to be explicable in terms of possible worlds. Bradford Skow denied that, arguing that alternative conceptions of possible worlds prompt non-equivalent characterizations of anti-haecceitism. Therefore, the haecceitism debate should take place in the modal language, rather than in the language of possible worlds. The aim of this paper is to provide a metaphysically neutral possible-world characterization of (...) anti-haecceitism, i.e. one compatible with alternative understandings of the nature of possible worlds. (shrink)

Natural language provides motivation for studying modal backwards-looking operators such as “now”, “then” and “actually” that evaluate their argument formula at some previously considered point instead of the current one. This paper investigates the expressive power over models of both propositional and first-order basic modal language enriched with such operators. Having defined an appropriate notion of bisimulation for first-order modal logic, I show that backwards-looking operators increase its expressive power quite mildly, contrary to beliefs widespread among philosophers of language and (...) formal semanticists. That in turn presents a strong argument for the use of operator-based systems in the semantics of natural language, instead of systems with explicit quantification over worlds and times that have become a de-facto standard for such applications. The popularity of such explicit-quantification systems is shown to be based on the misinterpretation of a claim by Cresswell, which led many philosophers and linguists to assume that introducing “now” and “then” is expressively equivalent to explicitly quantifying over worlds and times. (shrink)