Logic for Justice is an introductory textbook which covers propositional logic and first-order logic, and which connects both of those logical systems to social justice.
The higher-order languages, on which philosophers have focused, are not nearly higher-order enough: as I argue, for the purposes of metaphysical theorizing about identity, existence, and more, we should use the calculus of constructions, which allows for quantifying over types.
After explicating pure type systems which allow for quantification into type position—and so which are far more expressive than the typed languages on which philosophers have focused—I use those systems to formulate highly general principles of grounding.
Facts about explanation are, I argue, prior to facts about causation: the fact that c causes e is grounded in the facts that (i) the occurrence of c explains the occurrence of e, and (ii) c and e are wholly distinct.
I develop three different accounts of why it is more objectively valuable theorize in terms of natural properties than to theorize in terms of non-natural properties.
I argue that possible worlds are pluralities of sentences in an extremely large language, and I raise a cardinality problem for views which identify worlds with sets rather than pluralities.
I propose and defend the view that groups are pluralities at times, and I compare that view to both (i) other views of groups in the literature, and (ii) analogous views of objects.
I argue that a single relation (i) backs all cases of explanation, and (ii) explains why other relations—causation, grounding, and so on—are explanation-backing.
I propose a theory of how identity facts explain by using (i) explanatory counterfactuals, (ii) counterpart theory, (iii) impossible worlds, and (iv) structural equation models.
I formulate and defend a functional characterization of chance based on the law of large numbers: roughly, to be a chance is to be typically approximated by physically possible frequencies in the way that the law of large numbers describes.
This paper offers an empiricist answer, based largely on observations of frequencies, to the question of what justifies using one mathematical measure over others to express typicality facts.
Boltzmann Brains (forthcoming). In S. O. Hansson and A. Wilson, eds., Comprehensive Philosophy of Science. Elsevier.
This paper surveys philosophical issues surrounding Boltzmann Brains, focusing in particular on explicating connections between entropy, energy distributions, abilities to do work, and order/disorder.
We explore whether Humeans should identify their best system laws with sentences, unstructured propositions, structured propositions, or something else entirely.
The Typical Principle (2025). The British Journal for the Philosophy of Science 76: 1059-1076.
I propose and defend a precise version of the following principle: if a proposition is typically true, given your evidence, then you are rationally required to believe it.
When used to model physical systems, the law of large numbers, I argue, is best interpreted as asserting that the probability of an event typically—rather than probably—approximates the frequency with which that event occurs.
Explanatory Circles (2024). Studies in History and Philosophy of Science 108: 84-92.
By appealing to non-recursive structural equation models in the special sciences, I argue that there are perfectly legitimate circles of explanation.
I make three comments about Bird's Knowing Science: one concerning science's goals, one criticizing an epistemic principle, and one proposing a new version of the No Miracles Argument for realism.
I use causation to formulate existence conditions, identity conditions, and parthood conditions for mechanisms.
Wavefunction Mereology (forthcoming). The British Journal for the Philosophy of Science.
Wavefunctions stand in parthood relations to each other which, I argue, can be analyzed in terms of projection operators; this analysis has implications for standard debates in the mereological literature.
Centering Cosmological Calculations (forthcoming). In K. Kraay and D. Rubio, eds., The Blackwell Companion to Philosophy and the Multiverse. Blackwell.
I critically evaluate the calculations, and assumptions underlying those calculations, of first-person probabilities in cosmology: among other things, I argue that attempted reductions of those first-person probabilities to third-person probabilities do not succeed.
I propose an account of the Everett interpretation which, by invoking centered chances—objective chances, that is, of centered propositions—suggests that fundamental physical laws can include indexical information about us.
I argue that a new research methodology, currently emerging in the fields of astronomy and spacecraft trajectory design, solves several epistemological problems posed by chaotic dynamics in the solar system.
Centering Update (forthcoming). The Journal of Philosophy.
To be rational, when updating on centered propositions, I argue that agents should adopt credences which—among all credences compatible with their evidence—are closest to their original credences.
I show that centered propositions pose a serious problem for Lewis's Principal Principle, and I solve the problem by proposing that centered propositions can be objectively chancy.
The Logic of Typicality (2020). In V. Allori, ed., Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature (pp. 173-229). World Scientific. (with Harry Crane)
I propose a formal system, based on propositional modal logic, for reasoning about typicality.
I prove that if an agent's set of beliefs satisfies Scott's axiom, then that set of beliefs can be formally represented by a probability function.
Articles by Research Project
(some papers contribute to multiple projects)
Centering Update (forthcoming). The Journal of Philosophy.
To be rational, when updating on centered propositions, I argue that agents should adopt credences which—among all credences compatible with their evidence—are closest to their original credences.
Centering Cosmological Calculations (forthcoming). In K. Kraay and D. Rubio, eds., The Blackwell Companion to Philosophy and the Multiverse. Blackwell.
I critically evaluate the calculations, and assumptions underlying those calculations, of first-person probabilities in cosmology: among other things, I argue that attempted reductions of those first-person probabilities to third-person probabilities do not succeed.
I propose an account of the Everett interpretation which, by invoking centered chances—objective chances, that is, of centered propositions—suggests that fundamental physical laws can include indexical information about us.
I show that centered propositions pose a serious problem for Lewis's Principal Principle, and I solve the problem by proposing that centered propositions can be objectively chancy.
Facts about explanation are, I argue, prior to facts about causation: the fact that c causes e is grounded in the facts that (i) the occurrence of c explains the occurrence of e, and (ii) c and e are wholly distinct.
I develop three different accounts of why it is more objectively valuable theorize in terms of natural properties than to theorize in terms of non-natural properties.
Explanatory Circles (2024). Studies in History and Philosophy of Science 108: 84-92.
By appealing to non-recursive structural equation models in the special sciences, I argue that there are perfectly legitimate circles of explanation.
I argue that a single relation (i) backs all cases of explanation, and (ii) explains why other relations—causation, grounding, and so on—are explanation-backing.
I propose a theory of how identity facts explain by using (i) explanatory counterfactuals, (ii) counterpart theory, (iii) impossible worlds, and (iv) structural equation models.
The higher-order languages, on which philosophers have focused, are not nearly higher-order enough: as I argue, for the purposes of metaphysical theorizing about identity, existence, and more, we should use the calculus of constructions, which allows for quantifying over types.
After explicating pure type systems which allow for quantification into type position—and so which are far more expressive than the typed languages on which philosophers have focused—I use those systems to formulate highly general principles of grounding.
I argue that possible worlds are pluralities of sentences in an extremely large language, and I raise a cardinality problem for views which identify worlds with sets rather than pluralities.
I make three comments about Bird's Knowing Science: one concerning science's goals, one criticizing an epistemic principle, and one proposing a new version of the No Miracles Argument for realism.
I argue that a new research methodology, currently emerging in the fields of astronomy and spacecraft trajectory design, solves several epistemological problems posed by chaotic dynamics in the solar system.
I prove that if an agent's set of beliefs satisfies Scott's axiom, then that set of beliefs can be formally represented by a probability function.
Wavefunction Mereology (forthcoming). The British Journal for the Philosophy of Science.
Wavefunctions stand in parthood relations to each other which, I argue, can be analyzed in terms of projection operators; this analysis has implications for standard debates in the mereological literature.
We explore whether Humeans should identify their best system laws with sentences, unstructured propositions, structured propositions, or something else entirely.
Bohmian Collapse (2024). In A. Bassi, S. Goldstein, R. Tumulka, and N. Zanghì, eds., Physics and the Nature of Reality (pp. 63-70). Springer.
I present and explain the Bohmian account of collapse in quantum mechanics.
I propose and defend the view that groups are pluralities at times, and I compare that view to both (i) other views of groups in the literature, and (ii) analogous views of objects.
I formulate and defend a functional characterization of chance based on the law of large numbers: roughly, to be a chance is to be typically approximated by physically possible frequencies in the way that the law of large numbers describes.
This paper offers an empiricist answer, based largely on observations of frequencies, to the question of what justifies using one mathematical measure over others to express typicality facts.
Boltzmann Brains (forthcoming). In S. O. Hansson and A. Wilson, eds., Comprehensive Philosophy of Science. Elsevier.
This paper surveys philosophical issues surrounding Boltzmann Brains, focusing in particular on explicating connections between entropy, energy distributions, abilities to do work, and order/disorder.
The Typical Principle (2025). The British Journal for the Philosophy of Science 76: 1059-1076.
I propose and defend a precise version of the following principle: if a proposition is typically true, given your evidence, then you are rationally required to believe it.
When used to model physical systems, the law of large numbers, I argue, is best interpreted as asserting that the probability of an event typically—rather than probably—approximates the frequency with which that event occurs.
I argue that facts about what is typical—for instance, the fact that gases typically evolve to equilibrium—can explain.
Honourable mention, 2022 BJPS Popper Prize.
Featured in the OUP "Best of Philosophy 2019" article collection.
The Logic of Typicality (2020). In V. Allori, ed., Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature (pp. 173-229). World Scientific. (with Harry Crane)
I propose a formal system, based on propositional modal logic, for reasoning about typicality.
