AOS:

Philosophical Logic (philosophical applications of (i) modal logic, especially modal algebra, coalgebra, and the modal $\mu$-calculus (ii) dynamic epistemic logic, (iii) hyperintensional semantics, and (iv) two-dimensional semantics)

Philosophy of Mathematics (modality and hyperintensionality in mathematics; set theory; mathematical practice)

Epistemology (epistemic logic and epistemic modal and hyperintensional semantics; modal epistemology; epistemology of mathematics; conceivability; the apriori)

Metaphysics (modal ontology; mathematical objects; consciousness; grounding; hyperintensionality; metaphysical semantics)

Philosophy of Mind (consciousness; mental representation; attention)

AOC:

Philosophy of Language and Linguistics;

Cognitive Science;

Ethics;

Feminist Philosophy

Education:

Ph.D. Student, Philosophy. Arché Philosophical Research Centre for Logic, Language, Metaphysics, and Epistemology, University of St Andrews. (2014-2017) [withdrew, owing to illness]

Research Groups:

Models, Modality, and Meaning (2014-2015)

Metaphysics (2014-2017)

Arché Logic Group (2014-2017)

History and Philosophy of Logic and Mathematics (2015-2017; Convener for the group in the Fall 2016 semester)

Visiting Ph.D. Student. Australian National University. (2017) [declined, owing to illness]

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

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

Interviews

(1) I wasn't interviewed by "What is it like to be a Philosopher?", but I thought that it would be worthwhile to answer the questions that they proffer for anyone interested in my autobiography. Their questions and my replies can be found here,

Books

Epistemic Modality and Hyperintensionality in Mathematics

Ph.D. Dissertation, Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology, University of St Andrews.

[PhilPapers][Amazon]

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 to the types of intention, when the latter is interpreted as a modal mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states, by contrast to availing of modal axiom 4 (i.e. the KK principle). Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapter \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional intensions of epistemic two-dimensional semantics solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between topic-sensitive epistemic two-dimensional truthmaker semantics, the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. Chapter \textbf{9} examines the modal profile of $\Omega$-logic in set theory. Chapter \textbf{8} examines the modal commitments of abstractionism, in particular necessitism, and epistemic modality and the epistemology of abstraction. Chapter \textbf{11} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of epistemic two-dimensional semantics in order to account for the interaction of the interpretational and objective modalities thereof. Chapter \textbf{12} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal semantics for the different types of intention and the relation of the latter to evidential decision theory. The multi-hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is applied in chapters \textbf{7}, \textbf{8}, \textbf{10}, \textbf{11}, \textbf{12}, and \textbf{14}.

Publications

Modal Ω-Logic. 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).

[preprint]

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-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 $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical. Second, the foregoing provides a modal account of the interpretation of mathematical vocabulary.

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.

Submitted Papers:

Epistemic Modality:

Modal Cognitivism and Modal Expressivism

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, topic-sensitive epistemic two-dimensional 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 hyperintensions. I develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. I examine then 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.

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

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 interpretation of a $\mu$-automaton permits fixed points to entrain a principled means by which to account for necessary conditions on self-knowledge.

A Modal Logic for Gödelian Intuition

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 modal $\mu$-calculus. Via correspondence results between modal logic and the bisimulation-invariant fragment of second-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 operators regimenting the notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via a topic-sensitive epistemic two-dimensional truthmaker semantics.

Conceivability, Essence, and Haecceities

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 two-dimensional truthmaker semantics. I argue that the interaction between the two-dimensional framework and the mereological parthood relation, which is super-rigid, enables epistemic possibilities and truthmakers with regard to parthood to be a guide to its metaphysical profile. I specify, further, a two-dimensional formula encoding the relation between the epistemic possibility and verification of essential properties obtaining and their metaphysical possibility or verification. I then generalize the approach to haecceitistic properties. I also 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.

Philosophy of Mathematics:

Abstracta and Possibilia: Modal Foundations for Mathematical Platonism

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 (2013); and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics

Modality and Hyperintensionality in Mathematics

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 two-dimensional 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 two-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I also advance a topic-sensitive epistemic two-dimensional truthmaker semantics, if hyperintensional approaches are to be preferred to possible worlds semantics. I examine the relation between two-dimensional hyperintensional states and epistemic set theory, providing two-dimensional hyperintensional formalizations of the modal logic of ZFC, large cardinal axioms, $\Omega$-logic, and the Epistemic Church-Turing Thesis.

Category Theory 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 Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. 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 coalgebras 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 Two-dimensionalist Solution to the Access Problem

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

Logic:

Truth, Modality, and Paradox: Critical Review of Scharp, Replacing Truth

This paper targets a series of potential issues for the discussion of, and modal resolution to, the alethic paradoxes advanced by Scharp (2013). I proffer four novel extensions of the theory, and detail five issues that the theory faces.

Formal Semantics:

Topic-Sensitive Two-Dimensional Truthmaker Semantics

This paper endeavors to establish foundations for the interaction between hyperintensional semantics and two-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 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 truthmakers. 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. Topic-sensitive two-dimensional truthmaker semantics can be interpreted epistemically and metasemantically as well.

Metaphysics:

Physical Necessitism

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 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 geometric setting -- merits adoption by the Necessitist.

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

This paper aims to demonstrate that the ontology of consciousness is consistent with both the modal and the metaphysical versions of Haecceitism. I examine the varieties of Haecceitism, and I specify the intended versions that the arguments will vindicate. I define the property of 'being purely qualitative', and examine its relation to the properties of phenomenal consciousness. I draw, inter alia, on Bayesian perceptual psychology, in order to specify the identity-conditions of phenomenal properties in detail. I provide two, abductive arguments for the claim that the identity-conditions on some individuals are metaphysically haecceitistic, in virtue of the relations that hold between those individuals and the phenomenal properties that they instantiate. The first argument is corroborated by empirical results concerning the phenomenological effects of attention. The second argument is corroborated by empirical results from the study of color in vision science. The arguments vindicate a version of Metaphysical Haecceitism, because the individuals are shown to be typed by the phenomenal properties that they instantiate, although quantification over the individuals is an ineliminable condition on their identity and distinctness. I provide, then, a regimentation of the extant proposals in the ontology of consciousness, using the logic of hyperintensional ground, as augmented by the Bayesian probability calculus. The hyperintensional regimentation vindicates a version of Modal Haecceitism, because the probabilistic ontological dependence of the parts of worlds on other parts thereof provides an ineliminable condition on the identity and distinctness of worlds.

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

Ethics:

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

This paper argues that the types of intention can be modeled both as modal operators and via a multi-hyperintensional 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 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.

Books in Progress

Epistemic Democracy

Research Presentations

'Imagination and Knowledge of Necessary Existence'. Evidence and Imagination, University of Graz, November 2016. (Refereed) [declined, owing to illness]

'Fritz and Goodman on Counting Incompossibles'. Arché Research Group in History and Philosophy of Logic and Mathematics, November, 2016.

'Modal Cognitivism and Modal Expressivism'. History and Philosophy of Logic and Mathematics, Arché, October 2016.

'Koslicki on Fine's Theory of Embodiments'. Metaphysics: Identity, Existence, and Structure Research Group, 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.

'On Scharp's Resolution to the Alethic Paradoxes'. Models, Modality, and Meaning, Arché, October 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.