Taking Up Thagard’s Challenge: A Formal Model of Conceptual Revision

Thagard (1992) presented a framework for conceptual change in science based on conceptual systems. Thagard challenged belief revision theorists, claiming that traditional belief-revision systems are able to model only the two most conservative types of changes in his framework, but not the more radical ones. The main aim of this work is to take up Thagard’s challenge, presenting a belief-revision-like system able to mirror radical types of conceptual change. We will do that with a conceptual revision system, i.e. a belief-revision-like system that takes conceptual structures as units of revisions. We will show how our conceptual revision and contraction operations satisfy analogous of the AGM postulates at the conceptual level and are able to mimic Thagard’s radical types of conceptual change.

Belief revision as a problem of scientific epistemology

The fundamental question that must be answered by any theory of knowledge that claims to be adequate is the question of how it is possible to change our knowledge. The very fact of change undoubtedly takes place, and the problem is to theoretically explicate this fact. The methodological significance of this issue is due to the fact that changing knowledge means nothing more than its development, namely, the question of the ways and means of developing our knowledge is of central importance both for the logic and methodology of science, and for general epistemology. This work is of a review character, and aims to draw the reader’s attention to a new promising direction in the modern theory of knowledge called “belief revision”.

Awareness Growth and Belief Revision

The problem of awareness growth, also known as the problem of new hypotheses, is a persistent challenge to Bayesian theories of rational belief and decision making. Cases of awareness growth include coming to consider a completely new possibility (called expansion), or coming to consider finer distinctions through the introduction of a new partition (called refinement). Recent work has centred on Reverse Bayesianism, a proposal for rational awareness growth due to Karni and Vierø. This essay develops a "Reserve Bayesian" position and defends it against two challenges. The first, due to Anna Mahtani, says that Reverse Bayesian approaches yield the wrong result in cases where the growth of awareness constitutes an expansion relative to one partition, but a refinement relative to a different partition. The second, due to Steele and Stefánsson, says that Reverse Bayesian approaches cannot deal with new propositions that are evidentially relevant to old propositions. I argue that these challenges confuse questions of belief revision with questions of awareness change. Mahtani’s cases reveal that the change of awareness itself requires a model which specifies how propositions in the agent’s old algebra are identified with propositions in the new algebra. I introduce a lattice-theoretic model for this purpose, which resolves Mahtani’s problem cases and some of Steele and Stefánsson’s cases. Applying my model of awareness change, then Reverse Bayesianism, and then a generalised belief revision procedure, resolves Steele and Stefánsson’s remaining cases. In demonstrating this, I introduce a simple and general model of belief revision in the face of new information about previously unknown propositions.

A Semantics for Hyperintensional Belief Revision Based on Information Bases

I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided.

Dare to Think?

The previous two chapters argued that beliefs are pervasively outsourced to other people and to the environment, and that belief revision often occurs in response to changes in the cues that scaffold our beliefs. In light of these facts, we need to ensure the scaffolding of better beliefs. We need, that is, to manage the epistemic environment. Many people are uncomfortable with this suggestion, and urge that instead we should improve beliefs by promoting better reasons. This chapter examines the prospects for better individual reason, focusing on virtue epistemology. It argues that individual cognition is extremely unreliable, however virtuously it is conducted. Focusing on Quassim Cassam’s recent book on intellectual vices, it works through case studies, from climate denial and from historical scholarship, to show just how limited individual cognition is. It argues that even genuine experts are at severe risk of error when they stray outside their own sphere of expertise, and that spheres of expertise are much narrower than we tend to think.

Belief Revision

This chapter first introduces the AGM theory of belief revision. Then it focuses on the problem of iterated belief revisions.

Belief First

This chapter first discusses which agents this book focuses on and which ends they are assumed to have. Then it briefly describes how this relates to conditional belief and belief revision.

Belief and Counterfactuals

This book is the first of two volumes on belief and counterfactuals. It consists of six of a total of eleven chapters. The first volume is concerned primarily with questions in epistemology and is expository in parts. Among other theories, it provides an accessible introduction to belief revision and ranking theory. Ranking theory specifies how conditional beliefs should behave. It does not tell us why they should do so nor what they are. This book fills these two gaps. The consistency argument tells us why conditional beliefs should obey the laws of ranking theory by showing them to be the means to attaining the end of holding true and informative beliefs. The conditional theory of conditional belief tells us what conditional beliefs are by specifying their nature in terms of non-conditional belief and counterfactuals. In addition, the book contains several novel arguments, accounts, and applications. These include an argument for the thesis that there are only hypothetical imperatives and no categorical imperatives; an account of the instrumentalist understanding of normativity, or rationality, according to which one ought to take the means to one’s ends; as well as solutions to the problems of conceptual belief change, logical learning, and learning conditionals. A distinctive feature of the book is its unifying methodological approach: means-end philosophy. Means-end philosophy takes serious that philosophy is a normative discipline, and that philosophical problems are entangled with each other. It also explains the importance of logic to philosophy, without being a technical theory itself.

An Epistemological Study of Theory Change

Belief Revision is a well-established field of research that deals with how agents rationally change their minds in the face of new information. The milestone of Belief Revision is a general and versatile formal framework introduced by Alchourrón, Gärdenfors and Makinson, known as the AGM paradigm, which has been, to this date, the dominant model within the field. A main shortcoming of the AGM paradigm, as originally proposed, is its lack of any guidelines for relevant change. To remedy this weakness, Parikh proposed a relevance-sensitive axiom, which applies on splittable theories; i.e., theories that can be divided into syntax-disjoint compartments. The aim of this article is to provide an epistemological interpretation of the dynamics (revision) of splittable theories, from the perspective of Kuhn's inuential work on the evolution of scientific knowledge, through the consideration of principal belief-change scenarios. The whole study establishes a conceptual bridge between rational belief revision and traditional philosophy of science, which sheds light on the application of formal epistemological tools on the dynamics of knowledge.