Epistemic Modality and Hyperintensionality in Mathematics
Ph.D. Dissertation, Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology, University of St Andrews.
Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism. In Don Berkich and Matteo Vincenzo d'Alfonso (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence -- Themes from IACAP 2016. Springer (2019).
Grounding, Conceivability, and the Mind-Body Problem. Synthese 195 (2):919–926 (2018), doi:10.1007/s11229-016-1254-2
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, ground-theoretic 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.
Philosophy of Mathematics:
Abstracta and Possibilia: Modal Foundations for Mathematical Platonism
Modality and Hyperintensionality in Mathematics
Grothendieck Universes and Indefinite Extensibility
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 the category of sets is identifiable with the elementary embeddings of large cardinal axioms. 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 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 coalgebraic automata are further capable of capturing the notion of definiteness for set-theoretic truths, in order to yield a non-circular definition of indefinite extensibility.
A Modal Logic for Gödelian Intuition
A Two-dimensionalist Solution to the Access Problem
Entanglement, Modality, and Indeterminacy
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.
Philosophy of Mind and Cognitive Science:
Consciousness, Haecceitism, and Grounding
Hyperintensional Conceivability, Grounding, and Consciousness
This paper provides a rebuttal to the argument in Khudairi (2018) in `Synthese'. Khudairi 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
Epistemicism and Moral Vagueness
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 value-theoretic concepts adduces in favor of an epistemic interpretation of the indeterminacy thereof.
Intention: Hyperintensional Semantics and Decision Theory
Books in Progress
'Imagination and Knowledge of Necessary Existence'. Evidence and Imagination, University of Graz, November 2016. (Refereed) [declined, owing to illness]
'Modal Cognitivism and Modal Expressivism'. History and Philosophy of Logic and Mathematics, Arché, October 2016.
'Grothendieck Universes and Indefinite Extensibility'. Salzburg Conference for Young Analytic Philosophy, University of Salzburg, September 2016. (Refereed) [declined, owing to illness]
'Imagination and Knowledge of Necessary Existence'. The Logics of Image, International Symmetry Society Congress (Santorini, Greece), July 2016. (Refereed)
'Grounding, Conceivability, and the Mind-Body Problem'. Grounding and Consciousness, University of Birmingham, June 2016. (Refereed)
'Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism'. International Association for Computing and Philosophy -- Annual Meeting, University of Ferrara, June 2016. (Refereed)
'Goodness and Moral Obligation'. Kant, Metaethics, and Value, Trinity College Dublin, May 2016. (Refereed)
'Grounding, Conceivability, and the Mind-Body Problem'. The Science of Consciousness, University of Arizona, April 2016. (Refereed)
'Logical and Epistemic Modality'. Postgraduate Friday Seminar, Departments of Logic and Metaphysics and of Moral Philosophy, University of St Andrews, April 2016.
'Algebraic Metaphysical Semantics'. Uehiro Graduate Philosophy Conference, University of Hawai‘i at Mānoa, March 2016. (Refereed)
'Grounding and Fundamentality'. Metaphysics: Identity, Existence, and Structure, Arché, November 2015.
'Rules and Evolution' and 'Inference in Logic'. History and Philosophy of Logic and Mathematics, Arché, October 2015.
'Modal Saturations via Ultrafilter Extensions'. Arché Logic Group, May 2015.
'Grounding beyond the Image of Causation'. Metaphysics: Identity, Existence, and Structure, Arché, April 2015.
'Bisimulations'. Arché Logic Group, April 2015.
'An Epistemicist Solution to the Alethic Paradoxes'. Postgraduate Friday Seminar, University of St Andrews, March 2015.
'Bayesian Apriority'. Models, Modality, and Meaning Research Group, Arché, December 2014.
'Consciousness, Haecceitism, and Grounding'. Metaphysics: Identity, Existence, and Structure, Arché, November 2014.
'Haecceitism, Chance, and Counterfactuals'. Metaphysics: Identity, Existence, and Structure, Arché, November 2014.
'On Oliver and Smiley's Mid-plural Logic'. Arché Logic Group, November 2014.
'On Gradational Accuracy Measures for 4-valued Logic'. Arché Graduate Conference, November 2014.
'Imagination and Knowledge of Necessary Existence'. Postgraduate Friday Seminar, University of St Andrews, October 2014.
'On Second-order Logic and Mathematics'. Arché Logic Group, October 2014.
Awards and Honors
St Leonard's College PhD Research Scholarship. University of St Andrews, 2014 - 2017.
Departmental Honors in Philosophy. Johns Hopkins University, 2008.
University Honors. Johns Hopkins University, 2008.