*Towards an accuracy-first approach to judgment aggregation*

British Academy Mid-Career Fellowship

September 2021 – August 2022

In this project, I bring a new methodology to bear on the problem of judgment aggregation, which asks how we should take the judgments of each member of a group and aggregate them to give the group’s judgment. How should we combine the conclusions of individual jurors to give the jury’s verdict? How should we aggregate the predictions of different climate models to give the ensemble’s prediction? The new methodology is the accuracy-first approach to epistemology, and it promises to break a stalemate that arises from the axiomatic methodology that is currently used. It furnishes us with ways of measuring the accuracy of judgments, and explores how to produce collective judgments that are most accurate when measured that way. This project holds significant interest for policymakers and bodies, like IPCC, that produce summaries of expert judgment to guide policy decisions.

*Epistemic Utility Theory: Foundations and Applications*

European Research Council Starting Researcher Grant

January 2013 – December 2016

This project aims to apply the powerful tools of decision theory to provide novel arguments for the epistemic norms that we take to govern what it is rational to believe; and to discover new epistemic norms. We treat the possible epistemic states of an agent as if they were epistemic actions between which that agent must choose. And we consider how we should measure the purely epistemic utility of being in such a state. We then apply the general apparatus of decision theory to determine which epistemic states are rational in a given situation from a purely epistemic point of view; and how our epistemic states should evolve over time. This allows us, often for the first time, to give formal justifications of epistemic norms without appealing to pragmatic considerations that seem intuitively irrelevant to the norms in question. These formal arguments have the great advantage that their assumptions are made mathematically precise and their conclusions are deduced from their assumptions by means of a mathematical theorem. We call their study epistemic utility theory.

*The Scientific Approach to Epistemology*

Leverhulme Trust Network Grant

June 2015 – May 2018

The scientific approach to epistemology is a novel and exciting methodology. It supplements traditional methods, such as conceptual analysis, by means of three innovative techniques: (i) formal mathematical modeling, e.g., by means of Bayesian nets; (ii) empirical experimentation; (iii) computer simulations, e.g. agent-based models. These techniques extend the range of questions that can be fruitfully asked, make the addressed problems more precise, and gauge theoretical results against empirical or simulation-based tests. Apart from incorporating insights from formal sciences such as mathematics, statistics, and computer science, the scientific approach makes (socio-)epistemological research more relevant to related disciplines, e.g. psychology or sociology.

*Accuracy and Epistemic Deference*

AHRC Early Career Fellowship

October 2011 – September 2012

The primary objective of the research is to investigate the possibility of accuracy domination arguments for such principles of epistemic deference as David Lewis’ Principal Principle and Bas van Fraassen’s Reflection Principle. The research will build on preliminary work I have already carried out on the project, which demonstrates that the approach is viable and promising: that is, such arguments can be given providing certain philosophical assumptions are made.

*Finding the Foundations for Natural and Real Number Arithmetic in a Theory of Finite Sets*

British Academy Postdoctoral Fellowship

September 2008 – August 2011

My research seeks foundations for the arithmetics of the natural and real numbers. The traditional foundations lie in a theory of *transfinite* sets. In this theory, there is not just one system of natural numbers, nor just one system of real numbers, but infinitely many systems of both. However, the assumptions that underpin the theory guarantee that these many different natural number systems are all structurally identical, and similarly for the many real number systems. These results are Dedekind’s isomorphism theorems.

I offer an alternative foundation for natural and real arithmetic in a theory of *finite*sets, and gives a philosophical motivation for this foundation. What is of especial philosophical interest is that, in this theory, Dedekind’s theorems fail. With this conclusion comes the possibility of natural number systems that are not structurally identical; for instance, a natural number system ‘longer’ than another. Also, it opens the door to a revival of the infinitesimal calculus of the seventeenth century.