In the last few decades of the twentieth century there was a revolution in metaphysics: the intensional revolution. Many metaphysicians rejected the doctrine, associated with Quine and Davidson, that extensional analyses and theoretical resources were the only acceptable ones. Metaphysicians embraced tools like modal and counterfactual analyses, claims of modal and counterfactual dependence, and entities such as possible worlds and intensionally individuated properties and relations. The twenty-first century is seeing a hypterintensional revolution. Theoretical tools in common use carve more (...) finely than by necessary equivalence: two pieces of language can apply to the same entities across all possible worlds but not be equivalent; thoughts can be necessarily equivalent in truth value but not synonymous. This paper argues that hyperintensional resources are valuable in metaphysics outside theories of representation, and discusses some promising areas of hyperintensional metaphysics. (shrink)

This paper argues for a particular view about in what metaphysical equivalence consists: namely, that any two metaphysical theories are metaphysically equivalent if and only if those theories are strongly hyperintensionally equivalent. It is consistent with this characterisation that said theories are weakly hyperintensionally distinct, thus affording us the resources to model the content of propositional attitudes directed towards metaphysically equivalent theories in such a way that non-ideal agents can bear different propositional attitudes towards metaphysically equivalent theories.

An overview of hyperintensionality is provided. Hyperintensional languages have expressions with meanings that are more fine-grained than necessary equivalence. That is, the expressions may necessarily co-apply and yet be distinct in meaning. Adequately accounting for theories cast in hyperintensional languages is important in the philosophy of language; the philosophy of mind; metaphysics; and elsewhere. This entry presents a number of areas in which hyperintensionality is important; a range of approaches to theorising about hyperintensional matters; and a (...) range of debates that attention to hyperintensional constructions has generated. (shrink)

Propositions play a central role in contemporary semantics. On the Russellian account, propositions are structured entities containing particulars, properties and relations. This contrasts sharply with the sets-of-possible-worlds view of propositions. I’ll discuss how to extend the sets-of-worlds view to accommodate fine-grained hyperintensional contents. When this is done in a satisfactory way, I’ll argue, it makes heavy use of entities very much like Russellian tuples. The two notions of proposition become inter-definable and inter-substitutable: they are not genuinely distinct accounts of (...) how propositions represent what they represent. Semantic theorists may move freely between the two conceptions of what propositions are. Nevertheless, the two approaches give different accounts of the metaphysical nature of propositions. I argue that the sets-of-worlds view provides an adequate account of the nature of propositions, whereas the Russellian view cannot. (shrink)

The received view says that possibility is the dual of necessity: a proposition is (metaphysically, logically, epistemically etc.) possible iff it is not the case that its negation is (metaphysically, logically, epistemically etc., respectively) necessary. This reading is usually taken for granted by modal logicians and indeed seems plausible when dealing with logical or metaphysical possibility. But what about epistemic possibility? We argue that the dual definition of epistemic possibility in terms of epistemic necessity generates tension when reasoning about non-idealized (...) agents and is a problem of concern for most hyperintensional epistemic logics that alleviate the problem of logical omniscience. The tension is particularly evident when knowledge is taken as a primitive to define other epistemic concepts, such as justification and belief, as done in the knowledge-first tradition. We propose a non-dual interpretation of epistemic possibility, employing a hyperintensionality filter similar to the one that makes the corresponding epistemic necessity operator hyperintensional. We employ the proposed semantics to model Stalnaker's belief as epistemic possibility of knowledge and provide a sound and complete axiomatization for a hyperintensional version of his bimodal logic of knowledge and belief. (shrink)

This paper provides a rebuttal to the argument in Bowen (2018) in `Synthese'. Bowen provides a novel hyperintensional, ground-theoretic regimentation of the proposals in the metaphysics of consciousness. He then argues that Chalmers' (2010) intensional two-dimensional conceivability argument against physicalism is unsound, in light of the hyperintensional metaphysics of consciousness. Thus, intensional conceivability cannot be a guide to hyperintensional metaphysics. This paper demonstrates that a multi-hyperintensional version of epistemic two-dimensional semantics can be countenanced, (...) and is sufficient for conceivability to be a guide to metaphysics in the hyperintensional setting such that Chalmers' argument, hyperintensionally construed, is in fact sound. (shrink)

Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in (...) related fields get up to speed on open research-level problems. (shrink)

The standard counterexamples to David Lewis’s account of intrinsicality involve two sorts of properties: identity properties and necessary properties. Proponents of the account have attempted to deflect these counterexamples in a number of ways. This paper argues that none of these moves are legitimate. Furthermore, this paper argues that no account along the lines of Lewis’s can succeed, for an adequate account of intrinsicality must be sensitive to hyperintensional distinctions among properties.

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed (...) by Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

Theories of structured meanings are designed to generate fine-grained meanings, but they are also liable to overgenerate structures, thus drawing structural distinctions without a semantic difference. I recommend the proliferation of very fine-grained structures, so that we are able to draw any semantic distinctions we think we might need. But, in order to contain overgeneration, I argue we should insert some degree of individuation between logical equivalence and structural identity based on structural isomorphism. The idea amounts to forming an equivalence (...) class of different structures according to one or more formal criteria and designating a privileged element as a representative of all the elements, i.e., a first among equals. The proposed method helps us to a cluster of notions of co-hyperintensionality. As a test case, I consider a recent objection levelled against the act theory of structured propositions. I also respond to an objection against my methodology. (shrink)

I argue that the two-dimensional hyperintensions of epistemic topic-sensitive two-dimensional truthmaker semantics provide a compelling solution to the access problem. I countenance an abstraction principle for epistemic hyperintensions based on Voevodsky's Univalence Axiom and function type equivalence in Homotopy Type Theory. I apply, further, modal rationalism in modal epistemology to solve the access problem. Epistemic possibility and hyperintensionality, i.e. conceivability, can be a guide to metaphysical possibility and hyperintensionality, when (i) epistemic worlds or epistemic hyperintensional states are interpreted as (...) being centered metaphysical worlds or hyperintensional states, i.e. indexed to an agent, when (ii) the epistemic (hyper-)intensions and metaphysical (hyper-)intensions for a sentence coincide, i.e. the hyperintension has the same value irrespective of whether the worlds in the argument of the functions are considered as epistemic or metaphysical, and when (iii) sentences are said to consist in super-rigid expressions, i.e. rigid expressions in all epistemic worlds or states and in all metaphysical worlds or states. I argue that (i) and (ii) obtain in the case of the access problem. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine 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 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 cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-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 μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-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 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 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 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters 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 8 examines the interaction between my 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 Ω-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 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that 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 hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 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 the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent 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 while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 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)

Let an X/Y distinction be a distinction between kinds of properties, such as the distinctions between qualitative and non-qualitative, intrinsic and extrinsic, perfectly natural and less-than-perfectly natural or dispositional and categorical properties. An X/Y distinction is hyperintensional iff there are cointensional properties P and Q, such that P is an X-property, whereas Q is a Y-property. Many accounts of metaphysical distinctions among properties presuppose that such distinctions are non-hyperintensional. In this paper, I call this presupposition into question. I (...) develop a sufficient condition for the hyperintensionality of X/Y distinctions and argue that this condition is satisfied by a number of standard classifications of properties. It follows that non-hyperintensional analyses of distinctions among properties are harder to defend than is often assumed. (shrink)

This paper aims to contribute to the analysis of the nature of mathematical modality and hyperintensionality, and to the applications of the latter to absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of two-dimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the priority (...) and relation between epistemic mathematical modality and metaphysical mathematical modality. The discrepancy between the modal systems governing the parameters in the two-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I also advance a topic-sensitive epistemic two-dimensional truthmaker semantics, if hyperintensional approaches are to be preferred to possible worlds semantics. I examine the relation between two-dimensional hyperintensional states and epistemic set theory, providing two-dimensional hyperintensional formalizations of the modal logic of ZFC, large cardinal axioms, $\Omega$-logic, and the Epistemic Church-Turing Thesis. (shrink)

Modal accounts of knowledge, mind, and language, as prominently defended by Lewis, leave no room for enquiry into non-contingent matters. According to Lewis, there is only one necessarily true proposition, and it is vacuously known by everyone. What, then, are we doing when we do metaphysics, which often seems to deal with non-contingent questions? Lewis never gave a satisfactory answer, or even acknowledged the problem. I explore some options. Can we understand the relevant parts of metaphysics as dealing (...) with contingent questions about our concepts? Can we understand them in terms of a hyperintensional conception of “explicit” knowledge? Both options have some promise. Ultimately, however, I don’t think they succeed at squaring Lewis’s empiricist epistemology with his metaphysical realism. (shrink)

In this paper we propose and defend the Synonymy account, a novel account of metaphysical equivalence which draws on the idea (Rayo in The Construction of Logical Space, Oxford University Press, Oxford, 2013) that part of what it is to formulate a theory is to lay down a theoretical hypothesis concerning logical space. Roughly, two theories are synonymous—and so, in our view, equivalent—just in case (i) they take the same propositions to stand in the same entailment relations, and (ii) they (...) are committed to the truth of the same propositions. Furthermore, we put our proposal to work by showing that it affords a better and more nuanced understanding of the debate between Quineans and noneists. Finally we show how the Synonymy account fares better than some of its competitors, specifically, McSweeney’s (Philosophical Perspectives 30(1):270–293, 2016) epistemic account and Miller’s (Philosophical Quarterly 67(269):772–793, 2017) hyperintensional account. (shrink)

An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as (...) primitive the notion of a substitution on a proposition (property, etc.) and, among other things, uses this idea to elucidate a number of theoretically important distinctions. A class of structures are identified which can be used to model a wide range of positions about the granularity of reality; certain of these structures are seen to receive a natural treatment in the category of M-sets. (shrink)

Variabilism is the view that proper names (like pronouns) are semantically represented as variables. Referential names, like referential pronouns, are assigned their referents by a contextual variable assignment (Kaplan 1989). The reference parameter (like the world of evaluation) may also be shifted by operators in the representation language. Indeed verbs that create hyperintensional contexts, like ‘think’, are treated as operators that simultaneously shift the world and assignment parameters. By contrast, metaphysical modal operators shift the world of assessment only. Names, (...) being variables, refer rigidly in the latter merely intensional contexts, but may vary their reference in hyperintensional contexts. This conforms to the intuition that the content of attitude ascriptions encapsulates referential uncertainty. Furthermore, names in hyperintensional contexts are ambiguous between de re* and de dicto* interpretations. This fact is used to account for asymmetric mistaken identity attributions (for example, Biron thinks Katherine is Rosaline, but he doesn’t think Rosaline is Katherine). -/- The variable theory compares favourably with its alternatives, including Millianism and descriptivism. Millians cannot account for the behaviour of names in hyperintensional contexts, while descriptivists cannot generate a necessary contrast between intensional and hyperintensional contexts. No other theory can capture the facts pertaining to the existentially bound use of names. (shrink)

The author reviews and summarizes, in as jargon-free way as he is capable of, the form of anti-platonist anti-nominalism he has previously developed in works since the 1980s, and considers what additions and amendments are called for in the light of such recently much-discussed views on the existence and nature of mathematical objects as those known as hyperintensional metaphysics, natural language ontology, and mathematical structuralism.

A principle endorsed by many theories of objective chance, and practically forced on us by the standard interpretation of the Kolmogorov semantics for chance, is the principle that when a proposition P has a chance, any proposition Q that is necessarily equivalent to P will have the same chance as P. Call this principle SUB (for the substitution of necessary equivalents into chance ascriptions). I will present some problems for a theory of chance, and will argue that the best way (...) to resolve these problems is to reject SUB, and similar principles e.g. for the chances of outcomes or the chances of events. Objective chance, it turns out, carves things more finely than necessary equivalence does. (shrink)

The aim of this paper is to provide a systematic account of the metaphysically important distinction between haecceitistic properties, such as being David Lewis or being acquainted with David Lewis, and qualitative properties, such as being red or being acquainted with a famous philosopher. I first argue that this distinction is hyperintensional, that is, that cointensional properties can differ in whether they are qualitative. Then I develop an analysis of the qualitative/haecceitistic distinction according to which haecceitistic properties are relational (...) in a certain sense. I argue that this analysis can capture the hyperintensionality of the qualitative/haecceitistic distinction and is generally in accordance with the use of the notion of a qualitative property in philosophical debates. (shrink)

Propositions are often aligned with truth-conditions. The view is mistaken, since propositions discriminate where truth conditions do not. Propositions are hyperintensional: they are sensitive to necessarily equivalent differences. I investigate an alternative view on which propositions are truthmaker conditions, understood as sets of possible truthmakers. This requires making metaphysical sense of merely possible states of affairs. The theory that emerges illuminates the semantic phenomena of samesaying, subject matter, and aboutness.

A property is intrinsic iff individuals have it in virtue of how they themselves are, not in virtue of their relations to other individuals; a property is extrinsic iff it is not intrinsic. Being a cube and being an electron are intrinsic properties; being next to a cube, and being repelled by an electron are extrinsic properties. The debate about the distinction between intrinsic and extrinsic properties revolves around the following two questions: (1) Can the distinction be analysed in terms (...) of other, better understood notions, and if so, what should such an analysis should look like? (2) What are the general characteristics of the intrinsic/extrinsic distinction? I first describe several attempts to define the intrinsic/extrinsic distinction: the loneliness test proposed by Langton and Lewis, combinatorial accounts, and approaches based on the notion of grounding. I point out that any successful analysis of the intrinsic/extrinsic distinction invokes notions based on substantial metaphysical assumptions, such as the notions of grounding or natural property. I then discuss the general features of the intrinsic/extrinsic distinction and argue that the distinction is hyperintensional and vague. (shrink)

Theories of content are at the centre of philosophical semantics. The most successful general theory of content takes contents to be sets of possible worlds. But such contents are very coarse-grained, for they cannot distinguish between logically equivalent contents. They draw intensional but not hyperintensional distinctions. This is often remedied by including impossible as well as possible worlds in the theory of content. Yet it is often claimed that impossible worlds are metaphysically obscure; and it is sometimes claimed that (...) their use results in a trivial theory of content. In this paper, I set out the need for impossible worlds in a theory of content; I briefly sketch a metaphysical account of their nature; I argue that worlds in general must be very fine-grained entities; and, finally, I argue that the resulting conception of impossible worlds is not a trivial one. (shrink)

Grounding is a hyperintensional notion: necessarily equivalent sentences need not be equivalent from a ground-theoretic perspective. How fine-grained, exactly, is grounding? There is a striking lack of consensus on this question. In this chapter, I try to systematize and review the main options that have been put forward in the literature. For reasons that have to do with both naturalness and convenience, I for the most part take the question to be about what is sometimes called, following Kit Fine’s (...) (2012a) terminology, strict full grounding, and I take for granted a conception of grounding as a relation that is many-to-one and non-factive. I discuss the consequences of making alternative assumptions only in the very last section. (shrink)

This article aims to contribute to the largely neglected issue of whether metaphysical grounding – the relation of one fact’s obtaining in virtue of the obtaining of some other (or others) – can be given a reductive account. I introduce the notion of metaphysically opaque grounding, a form of grounding which constitutes a less metaphysically intimate connection than in standard cases. I then argue that certain important and interesting views in metaphysics are committed to there being cases of opaque (...) grounding and demonstrate that four representative accounts of grounding available in the literature are unable to accommodate such cases. This is argued to constitute a problem for those accounts that is likely to extend to other possible reductive accounts of grounding that employ the popular strategy of explaining grounding in terms of other hyperintensional phenomena. Unless the reductionist is willing to opt for some sophisticated modalist account, the possibility of opaque grounding cases thus provides indirect support for primitivism about grounding, a view that has previously been widely embraced but rarely supported by argument. (shrink)

This paper aims to introduce Meinongian Abstractionism (MA), i.e. a view on the metaphysics of truthmaking and modality. This approach is based on the notion of objectives—one of the key elements of Alexius Meinong’s Theory of Objects. In the light of it, worlds are interpreted in terms of sets of subsistent and non-subsistent objectives. This—along with Meinong’s characterization of objectives—provides a ground for possible as well as impossible worlds. One of the consequences of Meinongain Abstractionism is a reformulation of (...) the relation of truthmaking in modal terms. Importantly, this reformulation avoids the problem of too-coarse grained analysis of truthmakers. This makes MA a metaphysically–oriented supporter of the so-called ‘hyperintensional revolution.’. (shrink)

The consensus among spacetime substantivalists is to respond to Leibniz's classic shift arguments, and their contemporary incarnation in the form of the hole argument, by pruning the allegedly problematic metaphysical possibilities that generate these arguments. Some substantivalists do so by directly appealing to a modal doctrine akin to anti-haecceitism. Other substantivalists do so by appealing to an underlying hyperintensional doctrine that implies some such modal doctrine. My first aim in this paper is to pose a challenge for all extant (...) forms of this consensus position. My second aim is to show what form substantivalism must take in order to uphold the consensus while addressing this challenge. The result is a novel "plenitudinous" substantivalist view, which predicts that certain modal facts about spacetime are vague or indeterminate. I then argue against this view on independent grounds, concluding that substantivalists should reject the consensus position. The paper also discusses the way forward for substantivalists in light of this conclusion. (shrink)