Research

Overview

My research focuses principally on the philosophical foundations and applications of formal theories of rational choice and inference, spanning topics in the philosophy of science, epistemology, philosophical logic, artificial intelligence and decision theory.

Current project

I have recently been awarded a Future Fellowship by the Australian Research Council, for a project titled `Qualitative Models of Rationality: Philosophical Foundations and Applications‘. This project will be my main focus until June 2021. Further details below.

Short summary

Mathematical models of rationality, which aim to formalise the rules of good reasoning and decision making, have
traditionally proceeded on the assumption that people’s beliefs and desires are always given to us in terms of
precise, quantifiable degrees of confidence and value. This assumption has been noted to be implausibly strong
and alternative, qualitative frameworks, such as belief revision theory, have been developed to handle the
frequent situations in which it fails. These, however, remain critically incomplete and their foundations poorly
understood. The project will address their key omissions, secure their conceptual underpinnings and put them to
work in clarifying and resolving a range of long-standing philosophical problems.

Long summary

A wide variety of academic disciplines share a keen interest in elucidating the laws that govern correct theoretical and practical reasoning, i.e. in understanding the conditions under which a given set of data would warrant the drawing of a given conclusion, or the choice of a given course of action. The motivations for this preoccupation are varied. It may stem from a desire to improve our standards of scientific inquiry or policy choice (statistics, operations research,…), to design artificial agents or automated decision aids (artificial intelligence, robotics,…), or again to predict the behaviour of agents that are assumed to be approximately rational (microeconomics, psychology,…). But the issue is also a fascinating one in its own right, and the multitude of puzzles and paradoxes with which it is associated has long captivated the attention of the philosophical community.

For reasons of clarity and precision, contemporary theories of rational choice and inference typically take the form of abstract mathematical representations of rational reasoners, much in the same way that contemporary physical theories take the form of abstract mathematical representations of the material world. This model-building project has however come to find itself split into two distinct traditions, di ffering fundamentally in terms of the way that they conceive of the psychological states of the agents that they depict.

The first, so-called quantitative, approach takes agents to hold extremely precise numerical degrees of belief and desire–aka ‘subjective probabilities’ and ‘subjective utilities’, respectively–with respect to each of the various states of aff airs that they can conceive of (e.g. believing to degree 0.746 that it will rain tomorrow or desiring to degree 3.741 not to miss the next number 38 bus). A number of ‘rationality constraints’ are then imposed on these mental states, their evolution through time and the possible decisions that they give rise to.

This type of framework, the most influential variant of which is known as the ‘Bayesian’ approach, has historically been the dominant tradition in most disciplines. It has been worked out in great detail, over the course of many decades. Its philosophical foundations have been carefully scrutinised and a significant amount of work has been carried out with respect to the justification of its normative commitments, with a whole spectrum of arguments having been marshalled in their favour. Having long enjoyed a hegemonic status in the philosophical literature on rational choice, this approach has also become increasingly deeply entrenched in the subdisciplines of epistemology and philosophy of science.

This more recent development owes much to the emergence of ‘Bayesian confirmation theory’, which o ffers a precise analysis of the concept of evidential support–the relation that obtains between a given hypothesis and the considerations that motivate its endorsement (e.g. the hypothesis that a patient has developed a particular ailment and the positive result of a relevant diagnostic test)–in terms of shifts in rational degrees of belief.

The second way of proceeding, the qualitative approach, eschews the complex, and some would claim somewhat unrealistic, psychological picture painted by its quantitative counterpart in favour of the more familiar talk of unqualified beliefs and desires (e.g. believing that it will rain tomorrow or desiring not to miss the next number 38 bus) that is commonplace in everyday folk-psychology. More recent in origin, and currently less thoroughly worked out, these qualitative models have yet to gain influence outside their native disciplines of logic and artificial intelligence. This is true, most notably, of AGM ‘Belief Revision Theory’ (BRT), an extremely powerful and elegant model of belief dynamics based on an entirely non-numerical representation of the agent’s opinions.

Indeed, whilst this framework has generated a fair amount of attention in computer science, where it has immediate applications to database management, its impact on the philosophical literature remains comparatively minor. There are a few noteworthy exceptions here, but, overall, it is fair to say that BRT has nowhere near achieved the kind of philosophical impact enjoyed by its Bayesian counterpart.

It is admittedly true that BRT is still in a state of comparative theoretical immaturity. Both the finer details and the philosophical underpinnings of the approach remain to be worked out. There remains for instance a striking lack of consensus regarding the appropriate rules governing sequences of changes of opinion. Furthermore, those features of the account on which there is consensus typically only stand justified by brute appeals to intuition.

In spite of this, however, the marginal status of BRT, and of qualitative frameworks more generally, still remains somewhat of a surprising fact. Bayesian confirmation theory, for instance, for all its popularity, remains plagued by a number of well-known diculties, including a notorious issue known as the ‘problem of old evidence’, flagged out in Glymour’s classic paper titled ‘Why I am not a Bayesian’. As was aptly put to me in a recent anonymous referee report: ‘Bayesians are somewhat like the drunk looking for his watch under the street lantern, because there is more light there than at the place where he lost it.’. BRT o ffers a fresh opportunity to return to the drawing board and radically rethink the way in which formal philosophers approach the issue of evidential support.

More fundamentally, the vast majority of the classical debates in philosophy, be they in the philosophy of science, in epistemology or elsewhere, have been conducted in terms of the everyday qualitative mental ontology of folk psychology, with no consideration paid to the somewhat less familiar concepts of numerical degrees of belief or degrees of desire. This would clearly suggest that qualitative modelling is a particularly apposite approach, o ffering a natural formal tool to clarify and investigate traditional philosophical controversies.

The present project will firmly establish the qualitative approach as a viable and attractive choice by pursuing three lines of inquiry, whose strategic importance will have been made clear by the preceding section. Building on previously published research of mine, it will deliver:

  1. a critical examination of various foundational issues concerning qualitative models of rationality, including the elaboration of an entirely fresh approach to the handling of sequences of belief change and a justification of this approach in terms of objective performance measures,
  2. the development of concrete philosophical applications, of which most notably a highly innovative, BRT-based, approach to the analysis of the concept of evidential relevance, o ffering an attractive qualitative alternative to Bayesian confirmation theory,
  3. an investigation into the relation that these frameworks bear to their quantitative counterparts, resolving a number of critical open questions recently flagged out in my published work.

The project will, in the first instance, focus on models of rational belief dynamics, although the scope will later be broadened to cover preference dynamics, as well as qualitative accounts of rational decision-making.

Publications

Articles in peer-reviewed conference proceedings:

  1. (with R. Booth) Extending the Harper Identity to Iterated Belief Change, Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI 2016) (2016). pdf (IJCAI short version) pdf (arXiv long version with proofs)

Articles in peer-reviewed journals:

  1. (with R. Booth) The Irreducibility of Iterated to Single Revision. Journal of Philosophical Logic 46(4) (2017): 405–418. pdf
  2. Preservation, Commutativity and Modus Ponens: Two recent triviality results. Mind, 126(502) (2017): 579–602. pdf
  3. Subjective Probabilities Need Not Be Sharp. Erkenntnis, 79(6) (2017): 1273–1286. pdf
  4. Contrastive Confirmation: Some Competing Accounts. Synthèse, 190(1) (2013): 129–138. pdf
  5. Acceptance, Aggregation and Scoring Rules. Erkenntnis, 78(1) (2013): 201–217. pdf
  6. Defeat Reconsidered. Analysis, 73(1) (2013): 49–51. pdf
  7. Transmission Failure, AGM style. Erkenntnis, 78(2) (2013): 383–398. pdf
  8. (with A. Rieger) Self-Respect Regained, Proceedings of the Aristotelian Society, CXI(3) (2011): 1–8. pdf
  9. The Lottery Paradox Generalised?, British Journal for the Philosophy of Science, 61(3) (2010): 667–679. pdf
  10. The Transmission of Support: A Bayesian Reanalysis, Synthèse, 176(3) (2009): 333–343. pdf
  11. Solving the Tacking Problem with Contrast Classes, British Journal for the Philosophy of Science, 58(3) (2007): 489–502. pdf
  12. Whyte on Desire Fulfillment Conditions: a Simple Problem, Disputatio , II(21) (2006): 65–68. pdf

Book chapters:

  1. Descriptive Decision Theory. In E. Zalta (ed.) The Stanford Encyclopaedia of Philosophy (Winter 2017 Edition) (2017). Metaphysics Research Lab, Stanford University. pdfhtml
  2. (with V. Harrison) Probability in the Philosophy of Religion: Introduction, In Chandler & Harrison (2012). pdf

Edited volumes:

  1. (with V. Harrison) Probability in the Philosophy of Religion, Oxford University Press (2012).

Miscellaneous:

  1. Review of Spohn’s The Laws of Belief, Dialectica 71(1) (2017): 141–146. pdf
  2. Review of Huber & Schmidt-Petri’s (eds.) Degrees of Belief, Philosophy in Review, 29(6) (2009): 422–424. pdf
  3. On Being Inexplicit. University of Sussex Cognitive Science Research Papers, #516 (2000).
Work in progress
  1. (with R. Booth) Two New Constraints on the Aggregation of Moral Judgments.
  2. (with R. Booth) BOIs, BOIs, BOIs! Basic Ordinal Interval Revision Operators.
  3. A Problem for Ranking Theory.
  4. (with R. Booth, S.O. Hansson, E. Fermé & R. Wasserman) A Survey of Recent Work on Iterated Belief Change.
  5. Modelling Modal Agnosticism. pdf (slides, with proofs)
  6. Contrastive Support in the AGM Framework. pdf (slides) pdf (handout, incl. proofs)