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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 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 the goalorientedness of imagination, by allowing the context to determine, what we call, (...) 

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 (...) 

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 (...) 

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 statebased, syntactic and structuralist approaches, all correspond to special cases of the general framework. Completeness results pertaining to our hyperintensional modal logics are established. 

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 (...) 

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 (...) 

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 settheoretic truths in the category of sets is identifiable with the Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. A modal coalgebraic automata's mappings are further argued to account for both reinterpretations of quantifier domains as well as the ontological expansion effected by the elementary embeddings in the category of sets. The interaction (...) 

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 (...) 

We investigate synonymy in the strong sense of content identity. This notion is central in the philosophy of language and in applications of logic. We motivate, uniformly axiomatize, and characterize several “benchmark” notions of synonymy in the messy class of all possible notions of synonymy. This class is divided by two intuitive principles that are governed by a nogo result. We use the notion of a scenario to get a logic of synonymy which is the canonical representative of one division. (...) 

Our topic is the theory of topics. My goal is to clarify and evaluate three competing traditions: what I call the waybased approach, the atombased approach, and the subjectpredicate 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 (...) 

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 spinoff 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 (...) 

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 (...) 

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 constitutivenorms speechact variation on Walton’s account that I have defended previously, I critically discuss (...) 

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 (...) 

Imagination has received a great deal of attention in different fields such as psychology, philosophy and the cognitive sciences, in which some works provide a detailed account of the mechanisms involved in the creation and elaboration of imaginary worlds. Although imagination has also been formalized using different logical systems, none of them captures those dynamic mechanisms. In this work, we take inspiration from the Common Frame for Imagination Acts, that identifies the different processes involved in the creation of imaginary worlds, (...) 

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 (...) 

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 (...) 

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 (...) 

We study imagination as realityoriented mental simulation : 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 (...) 

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

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. 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 (...) 

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 nonmonotonicity of knowledge acquisition while allowing knowledge to be intrinsically stable. Aboutnesspreservation models (...) 

This paper develops a questionsensitive 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 (...) 

Francesco Berto proposed a logic for imaginative episodes. The logic establishes certain 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. Stitimagination 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 (...) 

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 (...) 

We develop a theory of necessity operators within a version of higherorder logic that is neutral about how finegrained 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 (...) 

This paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras, endowed with a hyperintensional, topicsensitive epistemic twodimensional 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 (...) 

This paper aims to contribute to the analysis of the nature of mathematical modality, and to the applications of the latter to unrestricted quantification and 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 twodimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the (...) 

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 twodimensional truthmaker semantics. I argue that the interaction between the twodimensional framework and the mereological parthood relation, which is superrigid, enables epistemic possibilities and truthmakers with regard to parthood to be a guide to its metaphysical profile. I specify, further, a twodimensional formula encoding the relation between the epistemic possibility and verification of essential properties obtaining (...) 

This paper endeavors to establish foundations for the interaction between hyperintensional semantics and twodimensional 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 (...) 

I argue that the twodimensional intensions of epistemic twodimensional semantics provide a compelling solution to the access problem. 

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 axioms of a dynamic provability logic, which embeds GL within the modal $\mu$calculus. Via correspondence results between modal logic and the bisimulationinvariant fragment of secondorder logic, a precise translation can then be provided between the notion of 'intuitionof', i.e., the cognitive phenomenal properties of (...) 

This paper aims to provide modal 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 (...) 

This paper argues that the types of intention can be modeled both as modal operators and via a multihyperintensional 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 (...) 

