What does ‘Smith knows that it might be raining’ mean? Expressivism here faces a challenge, as its basic forms entail a pernicious type of transparency, according to which ‘Smith knows that it might be raining’ is equivalent to ‘it is consistent with everything that Smith knows that it is raining’ or ‘Smith doesn’t know that it isn’t raining’. Pernicious transparency has direct counterexamples and undermines vanilla principles of epistemic logic, such as that knowledge entails true belief and that something can (...) be true without one knowing it might be. I re-frame the challenge in precise terms and propose a novel expressivist formal semantics that meets it by exploiting (i) the topic-sensitivity and fragmentation of knowledge and belief states and (ii) the apparent context-sensitivity of epistemic modality. The resulting form of assertibility semantics advances the state of the art for state-based bilateral semantics by combining attitude reports with context-sensitive modal claims, while evading various objectionable features. In appendices, I compare the proposed system to Beddor and Goldstein’s ‘safety semantics’ and discuss its analysis of a modal Gettier case due to Moss. (shrink)

Sentences \(\varphi\) and \(\psi\) are _cognitive synonyms_ for one when they play the same role in one’s cognitive life. The notion is pervasive (Sect. 1 ), but elusive: it is bound to be hyperintensional (Sect. 2 ), but excessive fine-graining would trivialize it and there are reasons for some coarse-graining (Sect. 2.1 ). Conceptual limitations stand in the way of a natural algebra (Sect. 2.2 ), and it should be sensitive to subject matters (Sect. 2.3 ). A cognitively adequate individuation (...) of content may be intransitive (Sect. 3 ) due to ‘dead parrot’ series: sequences of sentences \(\varphi _1, \ldots, \varphi _n\) where adjacent \(\varphi _i\) and \(\varphi _{i+1}\) are cognitive synonyms while \(\varphi _1\) and \(\varphi _n\) are not (Sect. 3.1 ). Finding an intransitive account is hard: Fregean equipollence won’t do (Sect. 3.2 ) and a result by Leitgeb shows that it wouldn’t satisfy a minimal compositionality principle (Sect. 3.3 )._Sed contra_, there are reasons for transitivity, too (Sect. 3.4 ). In Sect. 4, we come up with a formal semantics capturing this jumble of desiderata, thereby showing that the notion is coherent. In Sect. 5, we re-assess the desiderata in its light. (shrink)

_Framing effects_ concern the having of different attitudes towards logically or necessarily equivalent contents. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We model a typical kind of framing, grounded in (i) the structural distinction between beliefs activated in working memory and beliefs left inactive in long term memory, and (ii) the topic- or subject matter-sensitivity of belief: a feature of propositional attitudes which is attracting growing research attention. We introduce (...) a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class. (shrink)

The mathematician G.F.C. Griss is known for his program of negationless intuitionistic mathematics. Although Griss’s rejection of negation is regarded as characteristic of his philosophy, this is a consequence of an executability requirement that mental constructions presuppose agents’ executing corresponding mental activity. Restoring Griss’s executability requirement to a central role permits a more subtle characterization of the rejection of negation, according to which D. Nelson’s strong constructible negation is compatible with Griss’s principles. This exposes a ‘holographic’ theory of negation in (...) negationless mathematics, in which a full theory of negation is ‘flattened’ in a putatively negationless setting. (shrink)

Schlenker (Semant Pragmat 2(3):1–78, 2009; Philos Stud 151(1):115–142, 2010a; Mind 119(474):377–391, 2010b) provides an algorithm for deriving the presupposition projection properties of an expression from that expression’s classical semantics. In this paper, we consider the predictions of Schlenker’s algorithm as applied to attitude verbs. More specifically, we compare Schlenker’s theory with a prominent view which maintains that attitudes exhibit belief projection, so that presupposition triggers in their scope imply that the attitude holder believes the presupposition (Karttunen in Theor Linguist 34(1):181, (...) 1974; Heim in J Semant 9(3):183–221, 1992; Sudo in The art and craft of semantics: a festschrift for Irene Heim, MIT Press, 2014). We show that Schlenker’s theory does not predict belief projection, and discuss several consequences of this result. (shrink)

This paper provides a rebuttal to the argument in Elohim (2018) in `Synthese'. Elohim 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)

This paper develops a question-sensitive theory of intention. We show that this theory explains some puzzling closure properties of intention. In particular, it can be used to explain why one is rationally required to intend the means to one’s ends, even though one is not rationally required to intend all the foreseen consequences of one’s intended actions. It also explains why rational intention is not always closed under logical implication, and why one can only intend outcomes that one believes to (...) be under one’s control. (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 two-dimensional hyperintensions based on Voevodsky's Univalence Axiom and function type equivalence in Homotopy Type Theory. The truth of my first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable i.e. Turing computable and the Turing machine being physically implementable. 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 paper argues that the types of intention can be modeled both as modal operators and via a multi-hyperintensional semantics. I delineate the semantic profiles of the types of intention, and provide a precise account of how the types of intention are unified in virtue of both their operations in a single, encompassing, epistemic space, and their role in practical reasoning. I endeavor to provide reasons adducing against the proposal that the types of intention are reducible to the mental states (...) of belief and desire, where the former state is codified by subjective probability measures and the latter is codified by a utility function. I argue, instead, that each of the types of intention -- i.e., intention-in-action, intention-as-explanation, and intention-for-the-future -- has as its aim the value of an outcome of the agent's action, as derived by her partial beliefs and assignments of utility, and as codified by the value of expected utility in evidential decision theory. (shrink)

We develop a theory of necessity operators within a version of higher-order logic that is neutral about how fine-grained reality is. The theory is axiomatized in terms of the primitive of *being a necessity*, and we show how the central notions in the philosophy of modality can be recovered from it. Various questions are formulated and settled within the framework, including questions about the ordering of necessities under strength, the existence of broadest necessities satisfying various logical conditions, and questions about (...) their logical behaviour. We also wield the framework to probe the conditions under which a logicist account of necessities is possible, in which the theory is completely reducible to logic. (shrink)

Modal epistemologies that rely on a fallibilism about modal claims have been gaining traction over the years. This paper critically discusses the accounts of Kung (2009; 2010; 2016) and Dohrn (2018; 2019; 2020) and argues that they are invariably susceptible to being read as entailing claims of epistemic possibility. Both Kung and Dohrn seek to ground modal intuitions on non-modal ones, and primarily appeal to the modalizing capacity of imagination to aid in the discovery of modal truths. However, insofar as (...) inference from non-modal imagination to modal truths remains fallible, then no non-ad hoc distinction can be made between substantiation of fallible metaphysically modal claims and infallible epistemically modal ones. This is because, barring an agent’s infallible knowledge of modal truths, how these truths are asserted must attend the agent’s imperfect epistemic access thereof, therefore entailing claims of modality consistent with her epistemic state – i.e., claims of epistemic possibility. If modal epistemologies in general non-modally ground their modal assertions in this fallible fashion, then they seem inevitably interpretable in terms of epistemic possibility as opposed to some non-epistemic reading of metaphysical possibility. (shrink)

This paper aims to provide a mathematically tractable background against which to model both modal and hyperintensional cognitivism and modal and hyperintensional expressivism. I argue that epistemic modal algebras, endowed with a hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics, comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are categorically dual. I examine five methods for modeling the dynamics of conceptual (...) engineering for intensions and hyperintensions. I develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. I examine then the virtues unique to the modal and hyperintensional expressivist approaches here proffered in the setting of the foundations of mathematics, by contrast to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)

This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I introduce a novel epistemic two-dimensional truthmaker semantics. I argue that the interaction between the two-dimensional framework and the mereological parthood relation, which is super-rigid, enables epistemic possibilities and truthmakers with regard to parthood to be a guide to its metaphysical profile. I specify, further, a two-dimensional formula encoding the relation between the epistemic possibility and verification of essential properties obtaining (...) and their metaphysical possibility or verification. I then generalize the approach to haecceitistic properties, and examine the Julius Caesar problem as a test case. (shrink)

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)

We study imagination as reality-oriented mental simulation (ROMS): the activity of simulating nonactual scenarios in one’s mind, to investigate what would happen if they were realized. Three connected questions concerning ROMS are: What is the logic, if there is one, of such an activity? How can we gain new knowledge via it? What is voluntary in it and what is not? We address them by building a list of core features of imagination as ROMS, drawing on research in cognitive psychology (...) and the philosophy of mind. We then provide a logic of imagination as ROMS which models such features, combining techniques from epistemic logic, action logic, and subject matter semantics. Our logic comprises a modal propositional language with non-monotonic imagination operators, a formal semantics, and an axiomatization. (shrink)

Imagining is something we use everyday in our lives and in a wide variety of ways. In spite of the amount of works devoted to its study from both psychology and philosophy, there are only a few formal systems capable of modelling it; besides, almost all of those systems are static, in the sense that their models are initially predefined, and they fail to capture the dynamic process behind the creation of new imaginary scenarios. In this work, we review some (...) influential theories of imagination and use their insights to distil an algorithm describing such process. Then, we use this algorithm to define a dynamic logical system built upon on a single-agent epistemic logic that provides the necessary tools to capture how the agent voluntarily creates new imaginary worlds; in other words, our system allows the model to be expanded dynamically at any time as a result of the agent performing an act of imagination. Furthermore, we provide an axiomatization and prove that the system is sound and complete. (shrink)

This paper endeavors to establish foundations for the interaction between hyperintensional semantics and two-dimensional indexing. I examine the significance of the semantics, by developing three, novel interpretations of the framework. The first interpretation provides a characterization of the distinction between fundamental and derivative truths. The second interpretation demonstrates how the elements of decision theory are definable within the semantics, and provides a novel account of the interaction between probability measures and hyperintensional grounds. The third interpretation concerns the contents of the (...) types of intentional action, and the semantics is shown to resolve a puzzle concerning the role of intention in action. Topic-sensitive two-dimensional truthmaker semantics can be interpreted epistemically and metasemantically. (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)

We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spin-off from a general theory of thick content, whereby the content of a sentence has two components: an intension, taking care of truth conditions; and a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities for the logic of (...) knowledge per se for arbitrary agents, and isolate three explanatory factors for them: the topic-sensitivity of content; the fragmentation of knowledge states; the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections. (shrink)

Kriegel described the problem of intentional inexistence as one of the ‘perennial problems of philosophy’, 307–340, 2007: 307). In the same paper, Kriegel alluded to a modal realist solution to the problem of intentional inexistence. However, Kriegel does not state by name who defends the kind of modal realist solution he has in mind. Kriegel also points out that even what he believes to be the strongest version of modal realism does not pass the ‘principle of representation’ and thus modal (...) realism is not an adequate solution to the problem of intentional inexistence. In this paper, I respond to Kriegel by defending a modal realist solution that he did not consider in 2007, called ‘extended modal realism’. EMR is a version of modal realism where possible worlds are not completely isolated as they are under the Lewisian model. Rather, under EMR worlds are, in a way, spatiotemporally related. The fact EMR worlds are related allows EMR to sufficiently pass the principle of representation and thus can be deemed a legitimate solution to the problem of intentional inexistence. I conclude that either EMR can pass the principle of representation in some cases or, and I think the more sensible option, we give up on the principle of representation altogether. (shrink)

Sometimes we learn through the use of imagination. The epistemology of imagination asks how this is possible. One barrier to progress on this question has been a lack of agreement on how to characterize imagination; for example, is imagination a mental state, ability, character trait, or cognitive process? This paper argues that we should characterize imagination as a cognitive ability, exercises of which are cognitive processes. Following dual process theories of cognition developed in cognitive science, the set of imaginative processes (...) is then divided into two kinds: one that is unconscious, uncontrolled, and effortless, and another that is conscious, controlled, and effortful. This paper outlines the different epistemological strengths and weaknesses of the two kinds of imaginative process, and argues that a dual process model of imagination helpfully resolves or clarifies issues in the epistemology of imagination and the closely related epistemology of thought experiments. (shrink)

We present a formal semantics for epistemic logic, capturing the notion of knowability relative to information (KRI). Like Dretske, we move from the platitude that what an agent can know depends on her (empirical) information. We treat operators of the form K_AB (‘B is knowable on the basis of information A’) as variably strict quantifiers over worlds with a topic- or aboutness- preservation constraint. Variable strictness models the non-monotonicity of knowledge acquisition while allowing knowledge to be intrinsically stable. Aboutness-preservation models (...) the topic-sensitivity of information, allowing us to invalidate controversial forms of epistemic closure while validating less controversial ones. Thus, unlike the standard modal framework for epistemic logic, KRI accommodates plausible approaches to the Kripke-Harman dogmatism paradox, which bear on non-monotonicity, or on topic-sensitivity. KRI also strikes a better balance between agent idealization and a non-trivial logic of knowledge ascriptions. (shrink)

Our topic is the theory of topics. My goal is to clarify and evaluate three competing traditions: what I call the way-based approach, the atom-based approach, and the subject-predicate approach. I develop criteria for adequacy using robust linguistic intuitions that feature prominently in the literature. Then I evaluate the extent to which various existing theories satisfy these constraints. I conclude that recent theories due to Parry, Perry, Lewis, and Yablo do not meet the constraints in total. I then introduce the (...) issue-based theory—a novel and natural entry in the atom-based tradition that meets our constraints. In a coda, I categorize a recent theory from Fine as atom-based, and contrast it to the issue-based theory, concluding that they are evenly matched, relative to our main criteria of adequacy. I offer tentative reasons to nevertheless favour the issue-based theory. (shrink)

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)

This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in category theory is identifiable with the Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. The interaction between the interpretational and objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal profile of $\Omega$-logical validity, (...) and thus the generic invariance of mathematical truth, modal coalgebras are further capable of capturing the notion of definiteness for set-theoretic truths, in order to yield a non-circular definition of indefinite extensibility. (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 essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the modal $\mu$-calculus. Via correspondence results between fixed point modal propositional logic and the bisimulation-invariant fragment of monadic second-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cognitive phenomenal properties of thoughts, and the modal operators regimenting the (...) notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via a topic-sensitive epistemic two-dimensional truthmaker semantics. (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)

Logical frameworks that are sensitive to features of sentences’ subject-matter—like Berto’s topic-sensitive intentional modals (TSIMs)—demand a maximally faithful model of the topics of sentences. This is an especially difficult task in the case in which topics are assigned to intensional formulae. In two previous papers, a framework was developed whose model of intensional subject-matter could accommodate a wider range of intuitions about particular intensional conditionals. Although resolving a number of counterintuitive features, the work made an implicit assumption that the subject-matter (...) of an intensional conditional is a function of the subject-matters of its subformulae. This assumption—which I will call a principle of topic sufficiency—runs counter to some natural intuitions concerning topic. In this paper, we will investigate topic sufficiency and offer a semantic account that is state-sensitive, providing an implementation through the introduction of topic-sensitive logics related to William Parry’s prototypical $\mathsf {PAI}$. (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.

This research is published within the project ‘The Logic of Conceivability’, funded by the European Research Council, Grant Number 681404.

Like many intensional logics, William Parry’s logic of analytic implication PAI admits extensions determined by imposing semantic conditions on its account of modality. PAI is unique, however, in its allowing a second dimension—a topic-theoretic dimension—along which extensions can be defined. The recent introduction by Francesco Berto of topic-sensitive intentional modals (TSIMs)—which disagree with PAI on this type of condition—provide further motivations to examine such topic-theoretic extensions. In this paper, we introduce, motivate, and characterize a number of such extensions of PAI, (...) paying special attention to applications to Berto’s framework and to ways in which the modal and topic-theoretic dimensions influence one another. (shrink)

The notions of subject matter and aboutness have been objects of considerable attention among philosophers over the last few years. Current theories of subject matter take sentences to be the primary bearers of subject matter: “sentences have aboutness properties if anything has” (Yablo, Aboutness, Princeton University Press, 2014). However, some subsentential expressions can also be thought of as being about something. Moreover, it appears that the subject matters of sentences depend in a systematic way on the aboutness properties of their (...) subsentential components. In this paper, we focus on the question of what predicates are about. We provide an account of predicative subject matter in which subject matters are assigned to predicates in a natural way, and which can be smoothly integrated with some existing accounts of sentential subject matter. We also argue that the notion of predicative subject matter is a worthy object of study, both within the current debate on subject matter and in its own right. (shrink)

Although the work of G.F.C. Griss is commonly understood as a program of negationless mathematics, close examination of Griss’s work suggests a more fundamental feature is its executability, a requirement that mental constructions are possible only if corresponding mental activity can be actively carried out. Emphasizing executability reveals that Griss’s arguments against negation leave open several types of negation—including D. Nelson’s strong negation—as compatible with Griss’s intuitionism. Reinterpreting Griss’s program as one of executable mathematics, we iteratively develop a pair of (...) bilateral constructive logics and argue for their adequacy as accounts of the propositional basis of Griss’s work. We conclude by observing connexive features exhibited by the two bilateral logics and by investigating the difficulties connexive principles reveal for the development of executable mathematics. (shrink)

We propose a logic of imagination, based on simulated belief revision, that intends to uncover the logical patterns governing the development of imagination in pretense. Our system complements the currently prominent logics of imagination in that ours in particular formalises (1) the algorithm that specifies what goes on in between receiving a certain input for an imaginative episode and what is imagined in the resulting imagination, as well as (2) the goal-orientedness of imagination, by allowing the context to determine, what (...) we call, the overall topic of the imaginative episode. To achieve this, we employ well-developed tools and techniques from dynamic epistemic logic and belief revision theory, enriched with a topicality component which has been exploited in the recent literature. As a result, our logic models a great number of cognitive theories of pretense and imagination [cf. Currie and Ravenscroft (Recreative minds, Oxford University Press, Oxford, 2002); Nichols and Stich (Mindreading: an integrated account of pretence, self-awareness, and understanding other minds, Oxford University Press, Oxford, 2003); Byrne (The rational imagination, The MIT Press, London, 2005); Williamson (The philosophy of philosophy, Blackwell Publishing, Oxford, 2007); Langland-Hassan (Philos Stud 159:155–179, 2012, in: Kind and Kung (eds) Knowledge through imaginaion, Oxford University Press, Oxford, 2016]. (shrink)

The notion of subject matter is a key concern of contemporary philosophy of language and logic. A central task for a theory of subject matter is to characterise the notion of sentential subject matter, that is, to assign to each sentence of a given language a subject matter that may count as its subject matter. In this paper, we elaborate upon David Lewis’ account of subject matter. Lewis’ proposal is simple and elegant but lacks a satisfactory characterisation of sentential subject (...) matter. Drawing on linguistic literature on focus and on the question under discussion, we offer a neo-Lewisian account of subject matter, which retains all the virtues of Lewis’ but also includes an attractive characterisation of sentential subject matter. (shrink)

In this paper, we review three influential theories of imagination in order to understand how the dynamics of imagination acts could be modeled using formal languages. While reviewing them, we notice that they are not detailed enough to account for all the mechanisms involved in creating and developing imaginary worlds. We claim those theories could be further refined into what we call the Common Frame for Imagination Acts, which defines a framework that can be used to study the dynamics of (...) imagination using formal languages, and we support our claim by showing how the framework allows to model certain imagination acts step by step. Then, we introduce the Rhombus of Imagination, which is a visual tool that can be used in conjunction with our framework to study the procedural structure of different kinds of imagination acts and identify their dynamic properties. (shrink)

We propose a logic of imagination, based on simulated belief revision, that intends to uncover the logical patterns governing the development of imagination in pretense. Our system complements the currently prominent logics of imagination in that ours in particular formalises (1) the algorithm that specifies what goes on in between receiving a certain input for an imaginative episode and what is imagined in the resulting imagination, as well as (2) the goal-orientedness of imagination, by allowing the context to determine, what (...) we call, the overall topic of the imaginative episode. To achieve this, we employ well-developed tools and techniques from dynamic epistemic logic and belief revision theory, enriched with a topicality component which has been exploited in the recent literature. As a result, our logic models a great number of cognitive theories of pretense and imagination [cf. Currie and Ravenscroft (Recreative minds, Oxford University Press, Oxford, 2002); Nichols and Stich (Mindreading: an integrated account of pretence, self-awareness, and understanding other minds, Oxford University Press, Oxford, 2003); Byrne (The rational imagination, The MIT Press, London, 2005); Williamson (The philosophy of philosophy, Blackwell Publishing, Oxford, 2007); Langland-Hassan (Philos Stud 159:155–179, 2012, in: Kind and Kung (eds) Knowledge through imaginaion, Oxford University Press, Oxford, 2016]. (shrink)

In frameworks in which _topic-__theoretic_ considerations—_e.g._, tracking _subject-matter_ or _topic_—are given equal importance with _veridical_ considerations, assigning topics to formulae in a satisfactory way is of critical importance. While intuitions are more-or-less solid for _extensional_ formulae in a propositional language, arriving at a compelling account of the subject-matter of _intensional_ formulae, _i.e._, formulae including intensional operators, is more challenging. This paper continues previous work on modeling topics of intensional formulae in William Parry’s logic of analytic implication, adapting the general techniques (...) to the framework of _topic-sensitive intentional modals_ (TSIMs) championed by Francesco Berto and his collaborators. As illustrations, we introduce variations on Berto and Peter Hawke’s logic of knowability relative to information ( \(\pmb {\textsf{KRI}}\) ), including a refinement sensitive to topic-theoretic distinctions between knowledge and belief and a refinement capable of internalizing its own properties. Finally, subsystems of Aybüke Ozgun and Berto’s logic of plain hyperintensional belief ( \(\pmb {\textsf{PHB}}\) ) are introduced in which fine-grained distinctions in subject-matter are possible. (shrink)

Although logical settings are typically concerned with tracking alethic considerations, frameworks exist in which topic-theoretic considerations—e.g., tracking subject-matter or topic—are given equal importance. Intuitions about extending topic through a propositional language are generally straightforward for extensional cases. For a number of reasons, arriving at a compelling account of the subject-matter of intensional operators—such as intensional conditionals—is a more difficult task. In particular, the framework of topic-sensitive intentional modals (TSIMs) championed by Francesco Berto and his collaborators leave the topics of intensional (...) formulae undefined, which artificially constricts the expressivity of the theory. This paper proposes an approach to fill in this lacuna, emphasizing an analogous problem in Parry-style containment logics. In this setting, the approach receives a proof-of-concept through the introduction of a natural and general family of subsystems of Parry’s $${\textsf{PAI}}$$ PAI —with sound and complete axiomatizations—that allow a fine degree of control over the topics of intensional conditionals. (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)

In Berto’s logic for aboutness in imagination, the output content of an imaginative episode must be part of the initial content of the episode. This condition predicts expressions of perfectly legitimate imaginative episodes to be false. Thus, this condition is too strict. Relaxing the condition to correctly model these cases requires to consider a language with predicates and constants. The paper extends Berto’s semantics for aboutness in imagination to a semantics for such a language. The new semantics models contents of (...) formulas along the lines of Hawke’s issue-based theory of topics, while remaining faithful to the validities discussed by Berto. Several relations between issues and topics are defined, which allow to overcome shortcomings of Hawke’s initial framework. These relations are then discussed with respect to their usefulness in the truth condition for the imagination operator. (shrink)

In recent work, Walton has abandoned his very influential account of the fictionality of p in a fictional work in terms of prescriptions to imagine emanating from it. He offers examples allegedly showing that a prescription to imagine p in a given work of fiction is not sufficient for the fictionality of p in that work. In this paper, both in support and further elaboration of a constitutive-norms speech-act variation on Walton’s account that I have defended previously, I critically discuss (...) his objections. In addition to answering his concerns and developing the account further, I provide additional abductive support for its explanatory virtues vis-à- institutional accounts like Walton’s, and Gricean speech-act proposals. (shrink)

The paper proposes a logical framework representing the notion of explicit knowledge as the combination of awareness of and awareness that. The setting, semantically combining neighbourhood models with ideas from awareness logic, separates the mere fact of entertaining some information (being aware of $\varphi$) from the acknowledgement that the information is indeed the case (being aware that $\varphi$ holds). The text discusses not only the main properties these concepts obtain under the given representation, but also several of the epistemic actions (...) that can be defined, and the way they affect the agent’s awareness (and thus her knowledge). (shrink)

In a recent paper Berto introduces a semantic system for a logic of imagination, intended as positive conceivability, and aboutness of imaginative acts. This system crucially adopts elements of both the semantics of conditionals and the semantics of analytical implications in order to account for the central logical traits of the notion of truth in an act of imagination based on an explicit input. The main problem left unsolved is to put forward a complete set of axioms for the proposed (...) system. In the present paper I offer a solution to this problem by providing a complete axiomatization of a generalization of the original semantics. The difficulty in proving completeness lies in the fact that the modalities that capture the notion of truth in an act of imagination are neither standard nor minimal, so that the construction of the canonical model and the proof of the truth lemma are to be substantially modified. (shrink)

Recent work in the philosophy of language attempts to elucidate the elusive notion of aboutness. A natural question concerning such a project has to do with its motivation: why is the notion of aboutness important? Stephen Yablo offers an interesting answer: taking into consideration not only the conditions under which a sentence is true, but also what a sentence is about opens the door to a new style of criticism of certain philosophical analyses. We might criticize the analysis of a (...) given notion not because it fails to assign the right truth conditions to a class of sentences, but because it characterizes those sentences as being about something they are not about. In this paper, I apply Yablo’s suggestion to a case study. I consider meta-fictionalism, the view that the content of a mathematical claim S is ‘according to standard mathematics, S’. I argue, following Woodward, that, on certain assumptions, meta-fictionalism assigns the right truth-conditions to typical assertoric utterances of mathematical statements. However, I also argue that meta-fictionalism assigns the wrong aboutness conditions to typical assertoric utterances of mathematical statements. (shrink)

Belief revision is concerned with belief change fired by incoming information. Despite the variety of frameworks representing it, most revision policies share one crucial feature: incoming information outweighs current information and hence, in case of conflict, incoming information will prevail. However, if one is interested in representing the way actual humans revise their beliefs, one might not always want for the agent to blindly believe everything they are told. This manuscript presents a semantic approach to non-prioritized belief revision. It uses (...) plausibility models for depicting an agent’s beliefs, and model operations for displaying the way beliefs change. The first proposal, semantically-based screened revision, compares the current model with the one the revision would yield, accepting or rejecting the incoming information depending on whether the ‘differences’ between these models go beyond a given threshold. The second proposal, semantically-based gradual revision, turns the binary decision of acceptance or rejection into a more general setting in which a revision always occurs, with the threshold used rather to choose ‘the right revision’ for the given input and model. (shrink)