Research

Roughly half of my work is about bringing pure math together with important issues in general philosophy of science, metaphysics and epistemology. I’m especially interested in noncausal explanations, their role in mathematical and scientific practice, and what they can teach us about things like explanation, understanding, intertheoretic reduction, modeling and representation.

More recently I've worked on several issues in philosophy of AI, including the promise of ethical AI as a safety strategy, the use of large language models in psychology research and the contribution of AI tools to biorisk.

I'm also interested in various issues in aesthetics and ethics, including truth in fiction and partner choice.

Peer-reviewed Publications

1. "Deontology and Safe Artificial Intelligence" (Philosophical Studies special issue on AI safety, forthcoming)

   • Explores some ways in which prominent deontological theories (including moderate, contractualist and non-aggregative deontology) may lead to unsafe outcomes when implemented by autonomous AI systems. Also discusses the conceptual relationship between morally alignment and safety, arguing that these properties need not coincide and that we should prefer safe systems in the event of possible conflicts. Take-home message: the ethical AI program is likely not a straightforward solution to AI risk mitigation.

2. "Artificial Intelligence: Arguments for Catastrophic Risk" (Philosophy Compass, 2024; with Adam Bales and Cameron Domenico Kirk-Giannini)

   • Some people think we should be worried about future AI systems' potential to cause us great harm. We survey discussions around two influential and interrelated arguments. One argument claims that sufficiently advanced AI systems might be expected to engage in dangerous power-seeking behavior in the course of pursuing their goals. The second argument suggests that, once we've developed human-level AI technology, subsequent systems might improve very quickly, culminating in a "singularity" far beyond human capabilities.

3. "Large Language Models and Biorisk" (American Journal of Bioethics, 2023; with Harry Lloyd and Nate Sharadin)

   • A commentary piece discussing some ways in which AI technology might facilitate the development and malicious misuse of dangerous biochemical material (e.g. by helping with the discovery of novel bioagents, or by serving as a highly effective lab assistant and thus lowering the barrier to entry for the relevant bench work). Also suggests some policy strategies for mitigating these risks.

4. "AI Language Models Cannot Replace Human Research Participants" (AI & Society, 2023; with Jacqueline Harding, N.G. Laskowski and Rob Long)

   • A short piece responding to Dillion et al.'s "Can AI Language Models Replace Human Participants?", which notes the strong correlation between average human and LLM moral judgments and speculates optimistically about the possible roles of language models in psychology research. We argue that this optimism is either overstated or misplaced.

5. "Unrealistic Models in Mathematics" (Philosophers' Imprint, forthcoming)

   • Shows that mathematicians, like empirical scientists, use unrealistic models to gain better understanding of the complex phenomena they study. I present a pair of case studies and draw three morals. First: that unrealistic models have important uses in pure mathematics, and their epistemic benefits include improving our understanding of their target phenomena. Second: that the understanding gained from these models (and hence from unrealistic models in general) need not flow from explanations of the target phenomena. Third: that it need not flow from counterfactual knowledge either.

6. "Transferable and Fixable Proofs" (Episteme, forthcoming)

   • Explores a tension between two plausible conditions on acceptable proofs: (1) that proofs containing significant mistakes may be acceptable, so long as the mistakes are fixable in a certain sense; (2) that acceptable proofs must be transferable, meaning that the information they contain is enough to convince a typical expert. I argue that these conditions conflict, and that the transferability condition is the problem. Acceptable proofs only have to satisfy a pair of weaker constraints, which I call evaluability and corrigibility. 

7. "Is It Bad to Prefer Attractive Partners?" (Journal of the American Philosophical Association, forthcoming)

   • Argues that there are prima facie similarities between the preference for physically attractive partners and various forms of wrongful discrimination, and that some obvious strategies for justifying the former don't work. I suggest that the most defensible version of the preference is one that links attractive aspects of personal style to desirable personality traits and values. Lots of discussion of the psychology and social science literature on attractiveness.

   • This paper was discussed on an episode of the popular philosophy and psychology podcast Very Bad Wizards.

8. "Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth" (Synthese, 2021)

   • Analyzes a long-running disagreement among mathematicians about how best to explain Gauss's quadratic reciprocity theorem. I argue that some explanatory proofs of QR are "transparent", while others are "deep"; the disagreement arises because some mathematicians prefer one type of explanation over the other. Closes by raising a problem for Marc Lange's theory of mathematical explanation.

   • This paper is based on my math MS thesis, supervised by Ramin Takloo-Bighash. 

9. "Viewing-as Explanations and Ontic Dependence" (Philosophical Studies, 2020)

   • Explores the phenomenon of “viewing one object as another”. I show that “viewing-as” lies at the heart of a distinctive type of explanation. Viewing-as cases are interesting in many ways, notably because they seem to defy the popular ontic and counterfactual conceptions of explanation. What’s needed instead, I suggest, is a “cognitivist” account that understands explanatory success in terms of benefits to thinking and reasoning.

   • This paper received the APA's 2019 Routledge, Taylor and Francis article prize for best publication by a pre-tenure-track philosopher. The selection committee called it "an excellent, original and important contribution to the philosophy of science".

10. "Mathematical Explanation beyond Explanatory Proof" (British Journal for the Philosophy of Science, 2020)

    • Argues that not all mathematical explanations involve proofs. Considers in detail Galois's explanation of the unsolvability of the quintic, which has been claimed to rest on an explanatory proof; I try to show that this is mistaken.

    • This paper was a BJPS Editor's Choice selection and is freely available to read on the journal website.

11. "Explanation in Mathematics: Proofs and Practice" (Philosophy Compass, 2019)

    • Surveys recent work on explanatory proofs and their role in mathematical practice.

    • I also made an accompanying Teaching and Learning Guide with suggestions for further reading and ideas for class activities and projects.

12. "Arithmetic, Set Theory, Reduction and Explanation" (Synthese, 2018)

    • Argues that viewing the natural numbers and arithmetical operations as sets has no explanatory value. Thus, contrary to received wisdom, there are bona fide intertheoretic reductions that are nevertheless unexplanatory.

13. "Explicitism about Truth in Fiction" (British Journal of Aesthetics, 2016)

    • Challenges "implicitism", a widespread view about truth in fiction according to which there are truths in some stories that aren't explicitly asserted anywhere in the relevant texts. (E.g., "Holmes is human".)

    • This paper was a runner-up in the British Society for Aesthetics 2014 Essay Prize contest.

Other Writing

“What’s Hot in Mathematical Philosophy” column for The Reasoner magazine

• The Reasoner 16: 2 (March-April 2022, on purity of methods)

• The Reasoner 16: 1 (January-February 2022, on mathematical understanding)

• The Reasoner 15: 5 (September-October 2021, on the error-tolerance of proofs)

• The Reasoner 15: 4 (July-August 2021, on enumerative induction and mathematical justification)

• The Reasoner 15: 3 (May-June 2021, on the necessity of mathematics)

• The Reasoner 15: 1 (January-February 2021, on counterfactuals and mathematical explanation)

Guest editorial and interview with Kenny Easwaran

• The Reasoner 15:2 (March-April 2021), 9-12 

• I talk to Kenny about fractal music, Zoom conferences, journal refereeing, teaching in math and philosophy, the rationalist community and its relationship to academia, decision-theoretic pluralism, and the city of Manhattan, Kansas.

“Extraversion, Happiness, and the Pandemic”

• Blog of the APA (Mar. 18, 2021)

• About the nature of extraversion,  the relationship between personality and happiness, and what this can tell us about the surprising fact that extraverts were happier than introverts during early COVID lockdowns.

Dissertation

Dimensions of Mathematical Explanation,  UIC, 2017.

Committee: Daniel Sutherland (chair), Mahrad Almotahari, Dave Hilbert, Marc Lange, Kenny Easwaran.

• I did a three-paper dissertation, the parts of which would become "Arithmetic, Set Theory, Reduction and Explanation", "Mathematical Explanation beyond Explanatory Proof", and "Viewing-as Explanations and Ontic Dependence".