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A Philosophical Introduction to Higher-order LogicsRoutledge. 2023.This is the first comprehensive textbook on higher order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages -- their model theory and proof theory, the theory of λ-abstraction and its generalizations -- and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, makin…Read more
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A Case For Higher-Order MetaphysicsIn Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics, Oxford University Press. 2024.Higher-order logic augments first-order logic with devices that let us generalize into grammatical positions other than that of a singular term. Some recent metaphysicians have advocated for using these devices to raise and answer questions that bear on many traditional issues in philosophy. In contrast to these 'higher-order metaphysicians', traditional metaphysics has often focused on parallel, but importantly different, questions concerning special sorts of abstract objects: propositions, pro…Read more
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A Theory of NecessitiesJournal of Philosophical Logic 51 (1): 151-199. 2022.We develop a theory of necessity operators within a version of higher-order logic that is neutral about how fine-grained reality is. The theory is axiomatized in terms of the primitive of *being a necessity*, and we show how the central notions in the philosophy of modality can be recovered from it. Various questions are formulated and settled within the framework, including questions about the ordering of necessities under strength, the existence of broadest necessities satisfying various logic…Read more
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ClassicismIn Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics, Oxford University Press. pp. 109-190. 2024.This three-part chapter explores a higher-order logic we call ‘Classicism’, which extends a minimal classical higher-order logic with further axioms which guarantee that provable coextensiveness is sufficient for identity. The first part presents several different ways of axiomatizing this theory and makes the case for its naturalness. The second part discusses two kinds of extensions of Classicism: some which take the view in the direction of coarseness of grain (whose endpoint is the maximal…Read more
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Prior to Kripke's seminal work on the semantics of modal logic, McKinsey offered an alternative interpretation of the necessity operator, inspired by the Bolzano-Tarski notion of logical truth. According to this interpretation, `it is necessary that A' is true just in case every sentence with the same logical form as A is true. In our paper, we investigate this interpretation of the modal operator, resolving some technical questions, and relating it to the logical interpretation of modality a…Read more
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A paradox for supertask decision makersPhilosophical Studies 153 (2): 307. 2011.I consider two puzzles in which an agent undergoes a sequence of decision problems. In both cases it is possible to respond rationally to any given problem yet it is impossible to respond rationally to every problem in the sequence, even though the choices are independent. In particular, although it might be a requirement of rationality that one must respond in a certain way at each point in the sequence, it seems it cannot be a requirement to respond as such at every point for that would be to …Read more
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Logical CombinatorialismPhilosophical Review 129 (4): 537-589. 2020.In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentenc…Read more
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Is reality fundamentally qualitative?Philosophical Studies 176 (1): 259-295. 2019.
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Inductive KnowledgeNoûs 54 (2): 354-388. 2018.This paper formulates some paradoxes of inductive knowledge. Two responses in particular are explored: According to the first sort of theory, one is able to know in advance that certain observations will not be made unless a law exists. According to the other, this sort of knowledge is not available until after the observations have been made. Certain natural assumptions, such as the idea that the observations are just as informative as each other, the idea that they are independent, and that th…Read more
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The Logic of OpacityPhilosophy and Phenomenological Research 99 (1): 81-114. 2019.We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show that some of…Read more
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Vagueness and ThoughtOxford University Press. 2018.
Los Angeles, California, United States of America
Areas of Specialization
Metaphysics |
Philosophy of Language |
Logic and Philosophy of Logic |
Areas of Interest
Epistemology |
Metaphysics |
Philosophy of Language |
Logic and Philosophy of Logic |