We propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducing the logical omniscience phenomena affecting standard doxastic/epistemic logic as well as AGM belief revision theory. Our agents don’t know all a priori truths; their belief states are not closed under classical logical consequence; and their belief update policies are such that logically or necessarily equivalent contents can lead to different revisions. We model both plain and conditional belief, then focus on dynamic belief revision. The key idea (...) we exploit to achieve non-omniscience focuses on topic- or subject matter-sensitivity: a feature of belief states which is gaining growing attention in the recent literature. (shrink)

In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing semantic (...) distinctions between sentences that, from a Fregean perspective, do not differ in meaning. This is what we call the ‘new problem’ of hyperintensionality to distinguish it from the ‘old problem’ that faced the intensional theory. We show that our semantic framework offers a joint solution to both these problems by virtue of satisfying a version of Frege’s so-called ‘equipollence principle’ for sense individuation. Frege’s principle, we argue, not only captures the semantic intuitions that give rise to the old and the new problem of hyperintensionality, but also points the way to an independently motivated solution to both problems. (shrink)

This paper investigates propositional hyperintensionality in counterfactuals. It starts with a scenario describing two children playing on a seesaw and studies the truth-value predictions for counterfactuals by four different semantic theories. The theories in question are Kit Fine’s truthmaker semantics, Luis Alonso-Ovalle’s alternative semantics, inquisitive semantics and Paolo Santorio’s syntactic truthmaker semantics. These predictions suggest that the theories that distinguish more of a given set of intensionally equivalent sentences (Fine and Alonso-Ovalle’s) fare better than those that do not (inquisitive semantics (...) and Santorio’s). Then we investigate how inquisitive semantics and Santorio can respond to these results. They can respond to them by helping themselves to considerations from Hurford disjunctions, disjunctions whose disjuncts stand in an entailment relation to one another. I argue that considerations from Hurford disjunctions are ad hoc modifications merely to predict the expected results. I conclude that the scenarios suggest a need for more fine-grained theories of sentential meaning in general. (shrink)

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without (...) resorting to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents. (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.

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)

In this work, we illustrate applications of a semantic framework for non-congruential modal logic based on hyperintensional models. We start by discussing some philosophical ideas behind the approach; in particular, the difference between the set of possible worlds in which a formula is true (its intension) and the semantic content of a formula (its hyperintension), which is captured in a rigorous way in hyperintensional models. Next, we rigorously specify the approach and provide a fundamental completeness theorem. Moreover, (...) we analyse examples of non-congruential systems that can be semantically characterized within this framework in an elegant and modular way. Finally, we compare the proposed framework with some alternatives available in the literature. In the light of the results obtained, we argue that hyperintensional models constitute a basic, general and unifying semantic framework for (non-congruential) modal logic. (shrink)

It is widely thought that grounding is a hyperintensional phenomenon. Unfortunately, the term ‘hyperintensionality’ has been doing double-duty, picking out two distinct phenomena. This paper clears up this conceptual confusion. We call the two resulting notions hyperintensionalityGRND and hyperintensionalityTRAD. While it is clear that grounding is hyperintensionalGRND, the interesting question is whether it is hyperintensionalTRAD. We argue that given well-accepted constraints on the logical form of grounding, to wit, that grounding is irreflexive and asymmetric, grounding is hyperintensionalTRAD only if (...) one endorses a sentential operator view of grounding. We argue that proponents of the sentential operator view will need to distinguish two importantly different kinds of hyperintensionalityTRAD—weak and strong—and we offer them a way to do so. (shrink)

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...) predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE’s logical connectives. Furthermore, HYPE’s first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. (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)

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)

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)

This paper presents an original semantic theory of proper names that aims to cover both non-empty and empty proper names. According to the theory, proper names have simple assignable hyperintensions as their content. This content provides the referent (if there is one) for which the proper name stands. The paper further describes the role of the proposed content of (empty) proper names within the compositional semantics of problematic sentences. I stress the difference between the content of a sentence (i.e. (...) its hyperintension) and the proposition (i.e. a mapping from possible worlds to truth values) denoted by that sentence. (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 \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 cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (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} are 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 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 $\Omega$-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. 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 \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 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 \textbf{13} examines modal responses to the alethic paradoxes. 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)

Hyperintensionality – the failure of substitutivity salva veritate of intensionally equivalent expressions – is one of the most debated topics in recent philosophy of language. Being a phenomenon that affects a wide variety of different sentential contexts, a question concerning its source arises: is hyperintensionality something that can originate from actual features of the world, or it is simply some kind of representational phenomenon, which entirely depends on our conceptual faculties and preferred semantics? After a brief general introduction to the (...) topic from the semantic standpoint, in the present work I defend a view developed by Daniel Nolan, according to which hyperintensionality can be a worldly, non-representational phenomenon. I first reconstruct Nolan’s view and argument for worldly hyperintensionality, understood through the comparison with de re intensional modality. Then, I address the main criticism that has been raised against it, developing three objections. Evidence for worldly hyperintensionality is thereby presented, by focusing on a paradigmatic trigger: counterpossible conditionals. I provide two jointly sufficient criteria for a counterpossible to be a genuine instance of worldly hyperintensionality, then illustrate three case studies from scientific practices that all rely on counterpossible reasoning: reducibility in relative computability theory; scientific explanation of certain substances’ essential properties; and emergent molecular structure in chemistry. Each of them is evaluated by checking if it satisfies the criteria for worldly hyperintensionality, leading to the detection of patterns of counterpossible dependence occurring in at least some specific instances of the case studies discussed. Finally, I suggest a possible realist reading of such dependence relation, locating its relata in the world, independently from our representations. (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 \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 cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (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} are 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 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 $\Omega$-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. 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 \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 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 \textbf{13} examines modal responses to the alethic paradoxes. 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)

Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of independent evidence and inadmissible evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. (...) While there is strong reason to think that rational credence cannot make such hyperintensional distinctions, our intuitive judgements about certain cases seem to demand that it does. (shrink)

Real human agents, even when they are rational by everyday standards, sometimes assign different credences to objectively equivalent statements, such as “George Orwell is a writer” and “Eric Arthur Blair is a writer”, or credences less than 1 to necessarily true statements, such as not-yet-proven theorems of arithmetic. Anna Mahtani calls this the phenomenon of “opacity” (a form of hyperintensionality). Opaque credences seem probabilistically incoherent, which goes against a key modelling assumption of probability theory. I sketch a modelling strategy for (...) capturing opaque credence assignments without abandoning probabilistic coherence. I draw on ideas from judgment-aggregation theory, where we face similar challenges of defining the “objects of judgment”. (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.

Frege puzzles exploit cognitive differences between co-referential terms. Traditionally, they were handled by some version of Frege’s distinction between sense and reference, which avoided disruptive consequences for epistemology. However, the Fregean programme did not live up to its original promise, and was undermined by the development of theories of direct reference; for semantic purposes, its prospects now look dim. In particular, well-known analogues of Frege puzzles concern pairs of uncontentious synonyms; attempts to deal with them by distinguishing idiolects or postulating (...) ‘narrow contents’ or elaborate forms of context-sensitivity are inadequate or semantically implausible. Although ascriptions of knowledge, belief, and other attitudes are ubiquitous in epistemology, epistemologists have not properly come to terms with the surprising consequences of anti-Fregean semantic accounts of attitude ascriptions. In ‘A Puzzle about Belief ’, Saul Kripke shows that natural-seeming disquotational principles for ascribing belief lead to apparently unacceptable consequences, including outright contradictions, in problem cases. Such disquotation principles, I argue, are best regarded not as conceptual connections but just as heuristics in the psychological sense, quick and easy ways of assessing belief ascriptions, usually accurate under normal conditions but far from 100% reliable. I discuss similar heuristics for ascribing knowledge and other attitudes. That the principles have a merely heuristic status need not be pre-theoretically manifest to their users. This view vindicates Kripke’s conclusion that it would be wrong-headed to draw semantic conclusions from Frege puzzles. I discuss the epistemological consequences of an anti-Fregean approach to Frege puzzles, including for Kripke’s cases of the contingent a priori and the necessary a posteriori, but also for evidence, for epistemic modalities, and for epistemic and subjective conceptions of probability. Anna Mahtani’s recent identification of Frege puzzles for the ex ante Pareto Principle as used in welfare economics provides an interesting example. I suggest a model-building methodology as the most promising way of handling at least some of the difficulties. A final issue is the choice between different anti-Fregean approaches to semantics, from very coarse-grained intensional approaches on which sentences express functions from possible worlds to truth-values to more fine-grained hyperintensional approaches on which sentences express functions from possible or impossible worlds to truth-values or else Russellian structured propositions. Some of the hyperintensional theories violate semantic compositionality. More generally, since our attitude ascriptions rely on heuristics, they should be expected to exhibit some level of error; although hyperintensional approaches may be able slightly to reduce the level of postulated error, they do so at the cost of vastly increased theoretical complexity, and so have weak explanatory power. Methodologically, a simple intensional approach does better. (shrink)

The problem of hyperintensional contexts, and the problem of logical omniscience, shows the severe limitation of possible-worlds semantics which is employed also in standard epistemic logic. As a solution, we deploy here hyperintensional semantics according to which the meaning of an expression is an abstract structured algorithm, namely Tichý's construction. Constructions determine the denotata of expressions. Propositional attitudes are modelled as attitudes towards constructions of truth values. Such a model of belief is, of course, inferentially restrictive. We therefore (...) also propose a model of implicit knowledge, which is the collection of a possible agent's explicit beliefs which are related through a derivation system mastered by the agent. A derivation system consists of beliefs and derivation rules by means of which the agent may derive beliefs different from the beliefs she is actually related to. Conditions imposed on the set of base beliefs and the set of rules capture the limitations of the agent's deriving capabilities. (shrink)

In recent years, a new dispute has risen to prominence: the dispute between realists and anti-realists about causal powers. Albeit sometimes overlooked, the meta-ontological features of this “question of realism for powers” are quite peculiar. For friends and foes of causal powers have characterized their contrasting views in a variety of different ways; as existence claims, as semantic or truth-making claims, as fundamentality claims, as claims about the nature of certain properties. Not only does this multiplicity of interpretations make it (...) unclear what the genuine bone of contention is, if there is one; some of them appear to be mutually exclusive. Some light can be shed on this apparent yet widespread confusion by distinguishing three degrees of ontological involvement in dispositional truths; viz., three ways, of increasing robustness, to read ontological commitments from dispositional truths. Relatedly, by exploring the literature, and focusing on some selected examples of power realism and anti-realism, we can observe that power realists vastly disagree over the intrinsic nature ad make-up of dispositional properties. Such examples furthermore invite the thought that the question of realism for powers is best understood not as the debate around the existence of properties with a distinctive identity, but rather as a debate about metaphysical hierarchy. Finally, some anti-realists positions are indistinguishable from realist ones, using merely intensional resources: power realism is best appreciated by going hyperintensional. (shrink)

You and I can differ in what we say, or believe, even though the things we say, or believe, are logically equivalent. Discussing what is said, or believed, requires notions of content which are finer-grained than sets of (metaphysically or logically) possible worlds. In this paper, I develop the approach to fine-grained content in terms of a space of possible and impossible worlds. I give a method for constructing ersatz worlds based on theory of substantial facts. I show how this (...) theory overcomes an objection to actualist constructions of ersatz worlds and argue that it naturally gives rise to useful notions of fine-grained content. (shrink)

We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the leading philosophical (...) theories of meaning, these phenomena are an unfathomable mystery. To understand these concepts, we need a metaphysical, logical, and conceptual grasp of situations that could not possibly exist: Impossible Worlds. This book discusses the metaphysics of impossible worlds and applies the concept to a range of central topics and open issues in logic, semantics, and philosophy. It considers problems in the logic of knowledge, the meaning of alternative logics, models of imagination and mental simulation, the theory of information, truth in fiction, the meaning of conditional statements, and reasoning about the impossible. In all these cases, impossible worlds have an essential role to play. (shrink)

An influential argument against the possibility of truth by linguistic convention holds that while conventions can determine which proposition a given sentence expresses, they (conventions) are powerless to make propositions true or false. This argument has been offered in the literature by Lewy, Yablo, Boghossian, Sider and others. But despite its influence and prima facie plausibility, the argument: (i) equivocates between different senses of “making true”; (ii) mistakenly assumes hyperintensional contexts are intensional; and (iii) relies upon an implausible vision (...) of the way that language works. (shrink)

The principle of plenitude says that every material object coincides with abundantly many further objects that differ in their modal profiles. A necessarily unmanifested disposition is a disposition that necessarily does not manifest. This paper argues that if the principle of plenitude holds, then there are some necessarily unmanifested dispositions. These necessarily unmanifested dispositions will be argued to evade some objections against the cases of necessarily unmanifested dispositions put forward by Carrie Jenkins and Daniel Nolan.

There are two ways to characterize symmetric relations. One is intensional: necessarily, _Rxy_ iff _Ryx_. In some discussions of relations, however, what is important is whether or not a relation gives rise to the same completion of a given type (fact, state of affairs, or proposition) for each of its possible applications to some fixed relata. Kit Fine calls relations that do ‘strictly symmetric’. Is there is a difference between the notions of necessary and strict symmetry that would prevent (...) them from being used interchangeably in such discussions? I show that there is. While the notions coincide assuming an intensional account of relations and their completions, according to which relations/completions are identical if they are necessarily coinstantiated/equivalent, they come apart assuming a hyperintensional account, which individuates relations and completions more finely on the basis of relations’ real definitions. I establish this by identifying two definable relations, each of which is necessarily symmetric but nonetheless results in distinct facts when it applies to the same objects in opposite orders. In each case, I argue that these facts are distinct because they have different grounds. (shrink)

Francesco Berto proposed a logic for imaginative episodes. The logic establishes certain (in)validities concerning episodic imagination. They are not all equally plausible as principles of episodic imagination. The logic also does not model that the initial input of an imaginative episode is deliberately chosen.Stit-imagination logic models the imagining agent’s deliberate choice of the content of their imagining. However, the logic does not model the episodic nature of imagination. The present paper combines the two logics, thereby modelling imaginative episodes with deliberately (...) chosen initial input. We use a combination ofstit-imagination logic and a content-sensitive variably strict conditional à la Berto, for which we give a Chellas–Segerberg semantics. The proposed semantics has the following advantages over Berto’s: (i) we model thedeliberate choiceof initial input of imaginative episodes (in a multi-agent setting), (ii) we showframe correspondencesfor axiomatic analogues of Berto’s validities, which (iii) allows thepossibility to disregard axiomsthat might be considered not plausible as principles concerning imaginative episodes. We do not take a definite stance on whether theseshouldbe disregarded but give reasons for why one might want to disregard them. Finally, we compare our semantics briefly with recent work, which aims to model voluntary imagination, and argue that our semantics models different aspects. (shrink)

A number of philosophers have recently claimed that intrinsicality can be analysed in terms of the metaphysical notion of grounding. Since grounding is a hyperintensional notion, accounts of intrinsicality in terms of grounding, unlike most other accounts, promise to be able to discriminate between necessarily coextensive properties that differ in whether they are intrinsic. They therefore promise to be compatible with popular metaphysical theories that posit necessary entities and necessary connections between wholly distinct entities, on which it is plausible (...) that there are such properties. This paper argues that this promise is illusory. It is not possible to give an analysis of intrinsicality in terms of grounding that is consistent with these theories. Given an adequate analysis should be compatible with these theories, it follows that it is not possible to analyse intrinsicality in terms of grounding. (shrink)

Role realism is a promising realist theory of fictional names. Different versions of this theory have been suggested by Gregory Currie, Peter Lamarque, Stein Haugom Olsen, and Nicholas Wolterstorff. The general idea behind the approach is that fictional characters are to be analysed in terms of roles, which in turn can be understood as sets of properties. I will discuss several advantages and disadvantages of this approach. I will then propose a novel hyperintensional version of role realism, according to (...) which fictional names are analysed in terms of individual concepts that cannot be matched by a reference. I will argue that this account avoids the main disadvantages of standard role realism. (shrink)

A number of philosophers have recently claimed that intrinsicality can be analysed in terms of the metaphysical notion of grounding. Since grounding is a hyperintensional notion, accounts of intrinsicality in terms of grounding, unlike most other accounts, promise to be able to discriminate between necessarily coextensive properties that differ in whether they are intrinsic. They therefore promise to be compatible with popular metaphysical theories that posit necessary entities and necessary connections between wholly distinct entities, on which it is plausible (...) that there are such properties. This paper argues that this promise is illusory. It is not possible to give an analysis of intrinsicality in terms of grounding that is consistent with these theories. Given an adequate analysis should be compatible with these theories, it follows that it is not possible to analyse intrinsicality in terms of grounding. (shrink)

This paper provides an overview of the history of the notion of essence in 20th century analytic philosophy, focusing on views held by influential analytic philosophers who discussed, or relied on essence or cognate notions in their works. It in particular covers Russell and Moore’s different approaches to essence before and after breaking with British idealism, the (pre- and post-)logical positivists’ critique of metaphysics and rejection of essence (Wittgenstein, Carnap, Schlick, Stebbing), the tendency to loosen the notion of logical necessity (...) to accommodate certain metaphysical truths in Wittgenstein and others, Quine’s logical rehabilitation of metaphysics and criticism of de re modality, the modal view of essence promoted by the development of quantified modal logic (C. I. Lewis, Barcan Marcus, Kripke) and direct reference theory (Barcan Marcus, Kripke, Putnam), and the emergence of the notion of metaphysical necessity (Kneale, Kripke), and finally Fine’s re-establishment of a Neo-Aristotelian, hyperintensional notion of essence in contemporary metaphysics. (shrink)

This paper addresses the mereological problem of the unity of structured propositions. The problem is how to make multiple parts interact such that they form a whole that is ultimately related to truth and falsity. The solution I propose is based on a Platonist variant of procedural semantics. I think of procedures as abstract entities that detail a logical path from input to output. Procedures are modeled on a function/argument logic, but are not functions. Instead they are higher-order, fine-grained structures. (...) I identify propositions with particular kinds of molecular procedures containing multiple sub-procedures as parts. Procedures are among the basic entities of my ontology, while propositions are derived entities. The core of a structured proposition is the procedure of predication, which is an instance of the procedure of functional application. The main thesis I defend is that procedurally conceived propositions are their own unifiers detailing how their parts interact so as to form a unit. They are not unified by one of their constituents, e.g., a relation or a sub-procedure, on pain of regress. The relevant procedural semantics is Transparent Intensional Logic, a hyperintensional, typed λ-calculus, whose λ-terms express four different kinds of procedures. While demonstrating how the theory works, I place my solution in a wider historical and systematic context. (shrink)

Abstract Impossible fictions have lessons to teach us about linguistic representation, about mental content and concepts, and about uses of conceivability in epistemology. An adequate theory of impossible fictions may require theories of meaning that can distinguish between different impossibilities; a theory of conceptual truth that allows us to make useful sense of a variety of conceptual falsehoods; and a theory of our understanding of necessity and possibility that permits impossibilities to be conceived. After discussing these questions, strategies for resisting (...) the picture of impossible fictions presented here and in Part I are discussed. Perhaps apparently impossible fictions describe possibilities after all; or perhaps impossible fictions are all trivial; or perhaps some apparently intelligible impossible fictions are unintelligible after all. (shrink)

A lot of research has recently been done on the topic of ground, and in particular on the logic of ground. According to a broad consensus in that debate, ground is hyperintensional in the sense that even logically equivalent truths may differ with respect to what grounds them, and what they ground. This renders pressing the question of what we may take to be the ground-theoretic content of a true statement, i.e. that aspect of the statement’s overall content to (...) which ground is sensitive. I propose a novel answer to this question, namely that ground tracks how, rather than just by what, a statement is made true. I develop that answer in the form of a formal theory of ground-theoretic content and show how the resulting framework may be used to articulate plausible theories of ground, including in particular a popular account of the grounds of truth-functionally complex truths that has proved difficult to accommodate on alternative views of content. (shrink)

This paper develops a theory of propositional identity which distinguishes necessarily equivalent propositions that differ in subject-matter. Rather than forming a Boolean lattice as in extensional and intensional semantic theories, the space of propositions forms a non-interlaced bilattice. After motivating a departure from tradition by way of a number of plausible principles for subject-matter, I will provide a Finean state semantics for a novel theory of propositions, presenting arguments against the convexity and nonvacuity constraints which Fine (2016, 2017a,b) introduces. I (...) will then move to compare the resulting logic of propositional identity (PI) with Correia’s (2016) logic of generalised identity (GI), as well as the first degree fragment of Angell’s (1989) logic of analytic containment (AC). The paper concludes by extending PI to include axioms and rules for a subject-matter operator, providing a much broader theory of subject-matter than the principles with which I will begin. (shrink)

A lot of research has recently been done on the topic of ground, and in particular on the logic of ground. According to a broad consensus in that debate, ground is hyperintensional in the sense that even logically equivalent truths may differ with respect to what grounds them, and what they ground. This renders pressing the question of what we may take to be the ground-theoretic content of a true statement, i.e. that aspect of the statement’s overall content to (...) which ground is sensitive. I propose a novel answer to this question, namely that ground tracks how, rather than just by what, a statement is made true. I develop that answer in the form of a formal theory of ground-theoretic content and show how the resulting framework may be used to articulate plausible theories of ground, including in particular a popular account of the grounds of truth-functionally complex truths that has proved difficult to accommodate on alternative views of content. (shrink)

R. Suszko’s Sentential Calculus with Identity \( SCI \) results from classical propositional calculus \( CPC \) by adding a new connective \(\equiv \) and axioms for identity \(\varphi \equiv \psi \) (which we interpret here as ‘propositional identity’). We reformulate the original semantics of \( SCI \) using Boolean prealgebras which, introduced in different ways, are known in the literature as structures for the modeling of (hyper-) intensional semantics. We regard intensionality here as a measure for the discernibility of (...) propositions (and hyperintensionality as a high degree of intensionality). As concrete examples of \( SCI \) -based intensional modeling, we review and study algebraic semantics of some Lewis-style modal logics in the vicinity of \( S3 \) and present conditions under which those modal systems can be restored, in a precise sense, as certain axiomatic extensions of \( SCI \). This generalizes work of Suszko which is focused on the modal systems \( S4 \) and \( S5 \). Our approach is particularly intended as a proposal to consider and to further study \( SCI \) (and its extensions) as a general framework for the modeling of (hyper-) intensional semantics. (shrink)

Some twenty years ago, semanticists of natural language came to be overwhelmed by the problem of semantic analysis of belief sentences (and sentences reporting other kinds of propositional attitudes): the trouble was that sentences of the shapes X believes that A and X believes that B appeared to be able to have different truth values even in cases when A and B shared the same intension, i.e. were, from the viewpoint of intensional semantics, synonymous 1 . Thus, taking intensional semantics (...) for granted, belief sentences appeared to violate the principle of intersubstitutivity of synonyms. The verdict of the gurus of intensional semantics was that hence intensional semantics is inadequate, or at least insufficient for the purposes of analysis of propositional attitudes; and that we need a kind of a ‘hyperintensional semantics’. (shrink)

I follow Giordani in distinguishing between a situational and informational conception of subject-matter and consider some of the different ways in which it might be explained within both an intensional and an hyperintensional account of propositional identity.

This book concerns the foundations of epistemic modality. 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 relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of large cardinal axioms, undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal profile of rational intuition; and (...) to the types of intention, when the latter is interpreted as a modal 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. Chapter 3 provides an abstraction principle for epistemic intensions. Chapter 4 advances a 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 $\mu$-calculus in order to account for the iteration of epistemic states, by contrast to availing of modal axiom 4. 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 epistemic two-dimensional truthmaker semantics developed in chapter 4 is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapter 8 examines the modal commitments of abstractionism, in particular necessitism, and epistemic modality and the epistemology of abstraction. Chapter 9 examines the modal profile of $\Omega$-logic in set theory. Chapter 10 examines the interaction between epistemic two-dimensional semantics and absolute decidability. Chapter 11 avails of modal coalgebraic automata to interpret the defining properties of indefinite extensibility, and avails of epistemic two-dimensional semantics in order to account for the interaction of the interpretational and objective modalities thereof. The hyperintensional, epistemic two-dimensional truthmaker semantics developed in chapter 4 is applied in chapters 8, 10, and 11. Chapter 12 provides a modal logic for rational intuition. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

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)

We introduce a general representation of unary hyperintensional modalities and study various hyperintensional modal logics based on the representation. It is shown that the major approaches to hyperintensionality known from the literature, that is state-based, syntactic and structuralist approaches, all correspond to special cases of the general framework. Completeness results pertaining to our hyperintensional modal logics are established.

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)