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, differing 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 affairs 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 offers 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 offers 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, offering 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:
- 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,
- 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, offering an attractive qualitative alternative to Bayesian confirmation theory,
- 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.