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(2014 - 2017)    Ph.D. Research Fellow, Philosophy. Arché Philosophical Research Centre, University of St Andrews. 

                      Research Groups:
                    History and Philosophy of Logic and Mathematics (2015 - 2017)
 
                    Identity, Existence, and Structure (2014 - 2017)
 
                    Arché Logic Group (2014 - 2017)

                    Models, Modality, and Meaning (2014 - 2015)
(2017)                   Visiting Ph.D. Research Fellow, Philosophy. Australian National University.

(2010 - 2012)        M.A., Philosophy. Columbia University.
 

(2005 - 2008)        B.A. (Hons.), Philosophy. Johns Hopkins University.

General Information:
(2014 -- 2017)            Ph.D. Research Fellow.
                                   Arché Philosophical Research Centre, University of St Andrews.

(2016)                        Convener.
                                   Arché Research Group in the History and Philosophy of Logic and Mathematics.
 
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A Modal Logic for Gödelian Intuition

By: Hasen Khudairi

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 first-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cogn...

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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 epistem...

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Cognitivism about Epistemic Modality: Epistemic Modal Algebra, Hom...

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...

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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-th...

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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...

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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 interp...

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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...

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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 epist...

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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 Nec...

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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 inte...

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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 subjec...

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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...

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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 truth...

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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 un...

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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 w...

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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 ...

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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 log...

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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...

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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 settin...

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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 theo...

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