Deference principles for imprecise credences

Forthcoming. In The Journal of Philosophy. Winner of the Isaac Levi Prize 2024. [DRAFT]

This essay gives an account of epistemic deference for agents with imprecise credences. I look at the two main imprecise deference principles in the literature, known as Identity Reflection and Pointwise Reflection. I show that Pointwise Reflection is strictly weaker than Identity Reflection, and argue that, if you are certain you will update by conditionalisation, you should defer to your future self according to Identity Reflection. Then I give a more general justification for Pointwise and Identity Reflection from the assumption that you defer to someone whenever you consider their doxastic state to be better than yours, in the sense of leading to better decision-making.

An accuracy characterisation of approximate coherence.

2024. In Synthese 203.2. [LINK]

Accuracy-first epistemologists argue that rational agents have probabilistically coherent credences. But why should we care, given that we can't help being incoherent? A common answer: probabilistic coherence is an ideal to be approximated as best one can. To spell out this answer we need to show whether, or why, it's generally better to be more rather than less approximately coherent from an accuracy-first perspective. In this essay I give a characterisation of approximate coherence in terms of accuracy. Then I use it to show that accuracy-firsters should maintain that more approximately coherent credences are better than less approximately coherent ones if and only if they accept that it's better to miss out on less rather than more guaranteed accuracy.

Trust the evidence: deference principles for imprecise probabilities.

2023. In  International Symposium on Imprecise Probability: Theories and Applications. Proceedings of Machine Learning Research. [LINK]

Our intuition that rational agents should value the evidence can be captured by a well-known theorem due to I. J. Good. However, Good’s theorem fails when agents have imprecise credences. This essay shows a different way to capture our starting intuition, as the claim that rational agents defer to their informed selves. I introduce and motivate two deference principles for imprecise probabilities, and show that rational imprecise agents defer to their informed selves according to these principles. This shows a sense in which imprecise agents value the evidence.

Towards the inevitability of nonclassical probability

2023. In The Review of Symbolic Logic 16, no. 4. [LINK] [PREPRINT]

I extend Lindley's (1982) argument for probabilism to a number of non-classical logical settings whose truth-values are in the set {0, 1}, and where logical consequence ⊨ is given the “no-drop” characterization. I show that an agent’s credence can only avoid accuracy-domination in these settings if its canonical transform is a non-classical probability function. Therefore, if an agent values accuracy as the fundamental epistemic virtue, rationality requires her credence to have some probabilistic structure. Then I show that, for a certain class of reasonable measures of inaccuracy, having such a probabilistic structure is sufficient to avoid accuracy-domination.

Imprecision and Higher-Order Uncertainty

WIP

Imprecise Bayesians claim that some of our attitudes cannot be appropriately described by precise probabilities. They are imprecise credences. This essay looks at how imprecise credences relate to two other kinds of attitudes: the attitude of doubting what one’s credences are (introspective uncertainty), and the attitude of doubting what one’s credences should be (normative uncertainty). In particular, I argue against the view that descriptively/normatively uncertain precise credences can do all the work that imprecise credences are supposed to do.

A global accuracy characterisation of trust

2023. arXiv Preprint [LINK]

Dorst et al. (2021) put forward a deference principle called Total Trust, and characterise it in terms of accuracy: an agent totally trusts an expert iff they expect the expert to be more accurate than them. This note gives a new proof of their result using a global defnition of accuracy due to Konek (Forthcoming), rather than the local one used in the original. This allows for a simpler, direct proof of the global characterisation result.

Imprecision and the representation of belief

2021. [DRAFT]

This essay is about the way three characters respond to a formal result connecting categorical (i.e. all-or-nothing) beliefs and precise credences. This result was outlined by Fitelson and Easwaran (2015, 2016) as a response to the preface paradox, but has broader implications. Each character interprets the result from a different philosophical perspective, and uses it for a different purpose. I present a similar result connecting beliefs and imprecise credences, and then evaluate how it affects the views of each character. For at least some of their views, I argue, the imprecise result is a significant improvement.

• Presented at Formal Epistemology Workshop 2022