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  1. Epistemic Modality, Mind, and Mathematics.Hasen Khudairi - 2020 - Dissertation, University of St Andrews
    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; deontic 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 (...)
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  2. Abstracta and Possibilia: Modal Foundations of Mathematical Platonism.Hasen Khudairi - manuscript
    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 (...)
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  3. Absolute Decidability and Mathematical Modality.Hasen Khudairi - manuscript
    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 (...)
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  4.  94
    An Epistemicist Solution to the Alethic Paradoxes.Hasen Khudairi - manuscript
    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 (...)
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  5. A Modal Logic for Gödelian Intuition.Hasen Khudairi - manuscript
    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 augments GL with the modal μ-calculus. Via correspondence results between modal logic and first-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 (...)
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  6.  45
    Algebraic Metaphysical Semantics.Hasen Khudairi - manuscript
    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 (...)
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  7. Cognitivism About Epistemic Modality.Hasen Khudairi - manuscript
    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, (...)
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  8.  21
    Conceivability and Haecceitism.Hasen Khudairi - manuscript
    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 two-dimensional intensional framework and the mereological parthood relation enables epistemic possibilities to target the haecceitistic properties of individuals. I outline the elements of plural logic, and I specify, then, a two-dimensional intensional formula encoding the relation between the epistemic possibility of haecceity comprehension and its metaphysical possibility. I examine the Julius Caesar problem as (...)
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  9. Conceivability and Haecceitism.Hasen Khudairi - manuscript
    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 conclude by addressing objections from the indeterminacy (...)
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  10.  95
    Epistemic Democracy - Chapter Outline.Hasen Khudairi - manuscript
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  11. Grounding, Conceivability, and the Mind-Body Problem.Hasen Khudairi - 2018 - Synthese 195 (2):919-926.
    This paper challenges the soundness of the two-dimensional conceivability argument against the derivation of phenomenal truths from physical truths in light of a hyperintensional regimentation of the ontology of consciousness. The regimentation demonstrates how ontological dependencies between truths about consciousness and about physics cannot be witnessed by epistemic constraints, when the latter are recorded by the conceivability—i.e., the epistemic possibility—thereof. Generalizations and other aspects of the philosophical significance of the hyperintensional regimentation are further examined.
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  12. Grothendieck Universes and Indefinite Extensibility.Hasen Khudairi - manuscript
    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 (...)
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  13.  18
    Modal Cognitivism and Modal Expressivism.Hasen Khudairi - manuscript
    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. 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 (...)
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  14. Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism.Hasen Khudairi - 2019 - In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Springer. pp. 65-82.
    This essay examines the philosophical significance of Ω-logic in Zermelo-Fraenkel set theory with choice (ZFC). The dual isomorphism between algebra and coalgebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of Ω-logical validity can then be countenanced within a coalgebraic logic, and Ω-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of Ω-logical validity correspond to those of (...)
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  15.  30
    Nomic Necessitism.Hasen Khudairi - manuscript
    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 (...)
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  16. Non-Transitive Self-Knowledge: Luminosity Via Modal Μ-Automata.Hasen Khudairi - manuscript
    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 μ-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 μ-automaton permits the iterations of the transition functions (...)
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  17.  40
    Two-Dimensional Truthmaker Semantics.Hasen Khudairi - manuscript
    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 (...)
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