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Intention, Modality, and Decision Theory

By: Hasen Khudairi

This paper argues that the types of intention can be modeled as modal operators. I delineate the intensional-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 modal 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....

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An Epistemicist Solution to the Alethic Paradoxes

By: Hasen Khudairi

This paper targets a series of potential issues for the discussion of, and modal resolution to, the alethic paradoxes advanced by Scharp (2013). I aim, then, to provide a novel, epistemicist treatment of the alethic paradoxes. In response to Curry's paradox, the epistemicist solution that I advance enables the retention of both classical logic and the traditional rules for the alethic predicate: truth-elimination and truth-introduction. By availing of epistemic modal logic, the epistemicist approach permits, further, of a descriptively adequate explanation of the indeterminacy that is exhibited by epistemic states concerning liar-paradoxical sentences....

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Absolute Decidability and Mathematical Modality

By: Hasen Khudairi

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 multi-dimensional intensional 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 multi-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I demonstrate, finally, how the duality axioms of the epistemic logic for the semantics can be availed of, in order to defuse the paradox of knowability....

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Hyperintensional Property Theory

By: Hasen Khudairi

This paper provides three models of hyperintensional property theory. According to the first model, two properties can be identical while being relatively discernible, if the first property bears a non-symmetric relation to the second. I argue that the non-symmetry of identity is crucial for countenancing the relation between value-theoretic properties such as goodness and non-value-theoretic, natural properties. The non-symmetry of identity is argued to be crucial, as well, for defining a relational rather than intrinsic conception of value-theoretic properties; e.g., predicate modifiers such as being a good book, and the property of being good-for a subject. The second model of hyperintensional property theory avails of an operator-based semantics for the logic of ground, according to which hyperintensional ontological dependencies between properties are definable via reflexive bijections. Finally, I present a third model of hyperintensional identity crtieria which is consistent with the operator-based semantics for ground, without having to detour through a relation-based semantics or quantification over arbitrary objects....

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Grothendieck Universes and Indefinite Extensibility

By: Hasen Khudairi

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 in the category-theoretic setting is identifiable with the Kripke functors of modal coalgebraic automata, where the automata model Grothendieck Universes and the functors are further inter-definable with the elementary embeddings of large cardinal axioms. The Kripke functors definable in Grothendieck universes are argued to account for the ontological expansion effected by the elementary embeddings in the category of sets. By characterizing the modal profile of $\Omega$-logical validity, and thus the generic invariance of mathematical truth, modal coalgebraic automata are further capable of capturing the notion of definiteness, in order to yield a non-circular definition of indefinite extensibility....

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Algebraic Metaphysical Semantics

By: Hasen Khudairi

This paper argues that metaphysically fundamental truths ought to be defined within an algebraic language. In the first part of the paper, I provide examples of the algebraic structures used to define models of physical ontology (namely, quantum mechanics and field theory); the mathematical universe (set-theory); modal logic; and the metaphysics of consciousness. I outline, then, some explanatory desiderata concerning the relation between fundamental and derivative truths. I argue that a relation of apriori material implication, i.e. 'scrutability', cannot satisfy the relevant desiderata; and I propose in turn that -- given the model-theoretic uniformity between fundamental modal truths and the derivative truths concerning mental representational states -- a novel derivability relation can be specified. The relation is unique in having a purely model-theoretic characterization, and I examine the epistemic advantages accruing to the relation's model-theoretic profile....

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Nomic Necessitism

By: Hasen Khudairi

This paper aims to provide two abductive considerations adducing in favor of the thesis of Necessitism in modal ontology. I demonstrate how instances of the Barcan formula can be witnessed, when the modal operators are interpreted 'naturally' -- i.e., as including geometric and nomological possibilities -- and the quantifiers in the formula range over a domain of natural, or concrete, entities and their contingently non-concrete analogues. I argue that, because there are considerations within physics and metaphysical inquiry which corroborate modal relationalist claims concerning the possible geometric structures of spacetime, and dispositional properties are actual possible entities, the condition of being grounded in the concrete is consistent with the Barcan formula; and thus -- in the nomological setting -- merits adoption by the Necessitist....

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Emotional Phenomenology, Desire, and Belief

By: Hasen Khudairi

This essay concerns the interaction between the emotions and sensory and cognitive phenomenal consciousness. In Section \textbf{2}, I argue that emotional phenomenology can be identified with the positively and negatively valenced information comprising a subject's memory stores, and that the valences modulate the subject's sensory and cognitive phenomenal awareness. I argue that a sufficient condition on the instantiation of emotional phenomenal properties is the subject's desires. In Section \textbf{3}, I defend the proposal from three arguments against non-reductive emotional phenomenology. In Section \textbf{4}, I argue that desire is able to modulate the cognitive intentional states at issue, by responding to Lewis' (1988, 1996) impossibility proofs concerning the identification of beliefs with desires in the setting of decision theory. The impossibility proof can be defused by availing of a norm of synchronic, rather than diachronic, conditionalization, where the latter enables the rational reassignment of preference rankings and utility values to one's probability distribution (cf. Moss, 2015: 191-192; Hedden, 2015: 8.2). Sec...

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Multi-Dimensional Truthmaker Semantics

By: Hasen Khudairi

This paper endeavors to establish foundations for the interaction between hyperintensional semantics and multi-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 interaction between the hyperintensional truthmaker semantics and modal ontology is further examined. 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....

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Abstracta and Possibilia: Modal Foundations of Mathematical Platonism

By: Hasen Khudairi

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 Hale and Wright and examined in Hale (2013a); examine cardinality issues which arise depending on whether Necessitism is accepted at first- and higher-order; and demonstrate how a multi-dimensional intensional approach to the epistemology of mathematics, augmented with Necessitism, is consistent with Hale and Wright's notion of there being epistemic entitlement rationally to trust that abstraction principles are true. Epistemic and metaphysical modality may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in explaining our possible know...

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Modal Cognitivism and Modal Expressivism

By: Hasen Khudairi

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 comprise a materially adequate fragment of the language of thought, and endeavor to show how such algebras provide the resources necessary to resolve Russell's paradox of propositions. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are dually isomorphic. I examine, in particular, the virtues unique to the modal expressivist approach 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....

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Entanglement, Modality, and Indeterminacy

By: Hasen Khudairi

This paper aims to contribute to the metaphysical foundations of the Everett or `many-worlds' interpretation of quantum mechanics (cf. Everett, 1957; Wallace, 2012). I focus on the nature of the indeterminacy countenanced by states of entanglement, and argue that an account which clarifies the nature of the possible worlds at issue might serve to elucidate both the notion of metaphysical indeterminacy as well as the status of probability in the interpretation. I endeavor to elucidate the claim that the compossible states exhibited by entangled superpositions are real. I advance, then, three interpretations of the reality of the worlds at issue, and examine their interaction with the actuality operator. Finally, I examine which combinations of the approaches are consistent, and I argue in favor of a property-based approach to possible worlds....

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Non-Transitive Self-Knowledge: Luminosity via Modal $\mu$-Automata

By: Hasen Khudairi

This essay provides a novel account of iterated epistemic states. The essay argues that states of epistemic determinacy might be secured by countenancing self-knowledge on the model of fixed points in monadic second-order modal logic, i.e. the modal $\mu$-calculus. Despite the epistemic indeterminacy witnessed by the invalidation of modal axiom 4 in the sorites paradox -- i.e. the KK principle: $\square$$\phi$ $\rightarrow$ $\square$$\square$$\phi$ -- an epistemic interpretatation of the Kripke functors of a $\mu$-automaton permits the iterations of the transition functions to entrain a principled means by which to account for necessary conditions on self-knowledge....

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Logical and Epistemic Modality

By: Hasen Khudairi

This paper examines the interaction between the philosophy and psychology of concepts and the modal characterization of the deductive concept of logical validity. The concept of logical consequence on which I focus is model-theoretic, where the concept records the property of necessary truth-preservation from the premise of an argument to its conclusion, as well as the condition that, in the class of all possible worlds in which a premise is true, a consequent formula or succedent set of formulas is true, as well. Focusing on the case of logical necessity, I argue that the ability to account for the modal properties of concepts places a desideratum on the explanatory adequacy of theories of mental representation. I outline, then, five approaches to the nature of concepts pursued in philosophy and cognitive science, and argue that the above desideratum does not appear to be satisfiable by the candidate proposals. Given the limits of the foregoing, I appeal to a sixth approach -- namely, cognitivism about epistemic modality, which takes epistemic possibilities to be intensional functions in a language of thought -- and endeavor to dem...

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Moral Vagueness and Luminosity

By: Hasen Khudairi

This essay defends an epistemicist response to the phenomenon of vagueness concerning moral terms. I outline a traditional model of -- and then two novel approaches to -- epistemicism about moral predicates, and I demonstrate how the foregoing are able to provide robust explanations of the source of moral, as epistemic, indeterminacy. The first model of epistemic indeterminacy concerns the extensions of moral predicates, as witnessed by the non-transitivity of a value-theoretic sorites paradox. The second model of moral epistemicism is induced by the status of moral dilemmas in the epistemic interpretation of multi-dimensional intensional semantics. The third model is argued to consist in the formal invalidation of modal axiom K -- and thus of epistemic closure -- in the derivation of Curry's paradox. I examine the philosophical significance of the foregoing, and compare the proposal to those of ethical expressivism, constructivism, and scalar act-consequentialism. Finally, I examine the status of moral relativism in light of the epistemicist models of moral vagueness developed in the paper, and I argue that the rigidity of ethical ...

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Cognitivism about Epistemic Modality: Epistemic Modal Algebra, Homotopy Type Theory, and the Computational Theory of Mind

By: Hasen Khudairi

This paper aims to vindicate the thesis that cognitive computational properties are abstract objects implemented in physical systems. I avail of the equivalence relations countenanced in Homotopy Type Theory, in order to specify an abstraction principle for intensional, computational properties. The homotopic abstraction principle for intensional mental functions provides an epistemic conduit into our knowledge of cognitive algorithms as abstract objects. I examine, then, how intensional functions in Epistemic Modal Algebra are deployed as core models in the philosophy of mind, Bayesian perceptual psychology, the program of natural language semantics in linguistics, and in quantum information theory, and I argue that this provides abductive support for the truth of homotopic abstraction. Epistemic modality can thus be shown to be both a compelling and a materially adequate candidate for the fundamental structure of mental representational states, comprising a fragment of the Language of Thought....

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Conceivability, Plural Quantification, and Haecceitism

By: Hasen Khudairi

This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I argue that the interaction between the multi-dimensional intensional framework and intensional plural quantification enables epistemic possibilities to target the haecceitistic properties of individuals. I outline the elements of plural logic, and I specify, then, a multi-dimensional intensional formula encoding the relation between the epistemic possibility of haecceity comprehension and its metaphysical possibility. I examine the Julius Caesar problem as a test case. I conclude by addressing objections from the indeterminacy of ontological principles relative to the space of epistemic possibilities, and from the consistency of epistemic modal space....

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Forms of Luminosity: Epistemic Modality, Mind, and Mathematics

By: Hasen Joseph Khudairi

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 phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The book demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the apriori-aposteriori distinction; to the modal profile of rational propositional intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Examining the nature of epistemic logic itself, I develop a novel approach to conditions of self-knowledge in the setting of the modal $\mu$-calculus, as well as novel epistemicist solutions to Curry's, the liar, and the knowability paradoxes. Solutions to the Julius Ca...

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Transcendental Ethics: Hyperintensional Foundations of Value Theory

By: Hasen Joseph Khudairi

This book concerns the modal and hyperintensional foundations of ethics. The book provides three metaphysical frameworks in which to examine the nature of ethical value, obligation, cognition, consciousness, and divinity. The first framework is an algebraic semantics, and provides support for the claim that truths about modality are metaphysically fundamental. The second framework is a multi-dimensional hyperintensional semantics, and is shown to provide a natural setting in which to address issues both in decision theory and which concern intentional action. The third framework is a hyperintensional property theory. The framework enables properties -- such as intrinsic goodness -- to be identical to physical properties, while demonstrating how they are yet relatively discernible; and it is flexible enough to define relational notions of goodness, such as the property of being a good book and of something being good-for an agent. Within the foregoing metaphysical frameworks, the book examines the semantics of deontic modality; the relations between values and moral obligations; the role of intuition, abductive methodology, and virtu...

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