Probabilistic models of cognition: Conceptual foundations

Remarkable progress in the mathematics and computer science of probability has led to a revolution in the scope of probabilistic models. In particular, ‘sophisticated’ probabilistic methods apply to structured relational systems such as graphs and grammars, of immediate relevance to the cognitive sciences. This Special Issue outlines progress in this rapidly developing field, which provides a potentially unifying perspective across a wide range of domains and levels of explanation. Here, we introduce the historical and conceptual foundations of the approach, explore how the approach relates to studies of explicit probabilistic reasoning, and give a brief overview of the field as it stands today.

Introduction

The history of probabilistic models of thought is, in a sense, as old as probability theory itself. Probability theory has always had a dual aspect, serving both as a normative theory for ‘correct’ reasoning about chance events, but also as a descriptive theory of how people reason about uncertainty – as providing an analysis, for example, of the mental processes of an ‘intelligent’ juror. The title of Bernouilli's great book, Ars Conjectandi [1], ‘The Art of Conjecture’, nicely embodies this ambiguity, suggesting both a ‘how-to’ guide for better reasoning, and a survey of how the ‘art’ is actually practiced. That is, from its origins, probability theory was viewed as both mathematics and psychology.

From a modern perspective, this conflation seems anomalous. Mathematics has shaken free of its psychological roots, and become an autonomous, and highly formal, discipline. The philosophical thesis of ‘psychologism’, that mathematics (including probability) is a description of thought, fell from favour by the end of the nineteenth century. Moreover, the mathematics and psychology of probability have become divorced. The normative mathematical theory has seen spectacular developments in rigor, generality, and sophistication, going far beyond unaided intuition (see Griffiths and Yuille, Technical Introduction: Supplementary material online). Yet the descriptive study of how people judge probabilities has focussed on apparently systematic patterns of fallacious reasoning about chance [2].

This Special Issue is based on the premise that reconciliation is long overdue and that the mathematics of probability is a vital tool in building theories of cognition. The articles in this issue illustrate how probability provides a rich framework for vision and motor control, learning, language processing, reasoning, and beyond. Moreover, probabilistic models can be applied in various ways – ranging from analyzing a problem that the cognitive system faces, to explicating the function of the specific neural processes that solve it. Rather than advocating a monolithic and exclusively probabilistic view of the mind, we suggest instead that probabilistic methods have a range of valuable roles to play in understanding cognition. We hope that this Special Issue will help further inspire researchers in the cognitive and brain sciences to join the project of illuminating cognition from a probabilistic standpoint; and encourage mathematicians, statisticians and computer scientists to deploy the recent remarkable conceptual and computational armoury that they have developed to help understand cognition.