Evaluating Credence Change

Chapter 7 shows how the rationality measures we established in previous chapters can be used to evaluate changes in a thinker’s credences. The focus is on how we can evaluate credence changes in thinkers who reason from irrational starting points. I consider three types of changes: cases in which the thinker revises their credences (i) without learning new information or adding new attitudes; (ii) without learning new information, but adding new attitudes; (iii) as a response to learning new evidence. Examining those cases leads to some interesting discoveries: An incoherent thinker can always form new credences based on their existing incoherent credences without becoming more incoherent. Also, the identification of good patterns of reasoning is of very limited benefit in dealing with irrational thinkers.

De-Idealizing Bayesianism

Chapter 2 is concerned with the question of how we should develop a comprehensive normative theory of the epistemic rationality of credences. Its aim is twofold: (i) to familiarize readers with the basics of the Bayesian framework that are essential for understanding the arguments in subsequent chapters, and (ii) to offer an interpretation of the goals and methods of the Bayesian framework that reveals its shortcomings when applied to non-ideal thinkers. It is argued that the Bayesian view of ideal norms that is currently being developed lacks the capacity to distinguish between better and worse ways of being imperfectly epistemically rational. Moreover, it lacks the resources to substantiate a central Bayesian claim, namely that ideal epistemic norms apply to the beliefs of non-ideal thinkers as aims that should be approximated.

Matters to Be Settled

Chapter 10 summarizes the main results from each of the previous chapters. For each chapter, it points to questions that were left open in the discussion, and avenues for further research. The results of the book have the potential to inform both descriptive and normative research paradigms going forward.

Approximation Measures

The focus of Chapter 3 is the central Bayesian tenet that a thinker’s unconditional credences should be probabilistically coherent. Plausibly, thinkers who don’t have coherent credences can be more or less incoherent, i.e. their credences can diverge from complying with the probability axioms only a little, or quite substantially. We can capture this intuitive idea by representing a thinker’s credence function as a vector, and measuring its distance to the closest probabilistically coherent credence function that is defined over the same set of propositions. The problem that arises in this context is that there are many possible measures we can use to determine the distance from coherence, and those measures can deliver incompatible rankings. I present a representative range of such measures and illustrate the ways in which they differ.

Introduction

The Introduction motivates the main theme of the book: that proponents of theories of ideal rationality must give an account of why, on their views, it is beneficial for non-ideal thinkers to approximate ideal rationality. These theories need to explain what it means to be more or less irrational, and also why reducing irrationality is epistemically valuable. A survey of the content of each chapter is provided, as well as an overview of basic assumptions and modeling choices. A Bayesian theory of epistemic rationality is presupposed, and credences are represented as precise numbers between 0 and 1. Yet, the main arguments also extend to other frameworks and modeling choices.

How Do Beliefs Simplify Reasoning?

Chapter 9 examines how the proposed theory of epistemic rationality can accommodate outright beliefs, and what role such outright beliefs play in our epistemic conduct. It is argued that people need outright beliefs in addition to credences to simplify their reasoning. Outright beliefs do this by allowing thinkers to ignore small error probabilities. What is outright believed can change between contexts. When our beliefs change, we have to ask how related other beliefs, including beliefs representing uncertainties, change in light of this. It has been claimed that our beliefs change via an updating procedure resembling conditionalization. However, conditionalization is notoriously complicated. This claim is thus in tension with the explanation that the function of beliefs is to simplify our reasoning. We can resolve this puzzle by endorsing a different hypothesis about how beliefs change across contexts that better accounts for the simplifying role of beliefs.

Approximating Ideal Rationality with Multiple Norms

Chapter 6 considers views on which being ideally rational requires more than just being coherent. While extreme subjective Bayesians think that the coherence norm is the only requirement of epistemic rationality, more moderate proponents defend further requirements, such as versions of the Indifference Principle or the Principal Principle. This raises the question of how we can measure approximations to rationality, when being ideally rational requires thinkers to comply with multiple different epistemic norms. Different approaches to justifying norms of rationality are distinguished by whether they assume that there is a single epistemic value or good that explains the various requirements of rationality, or whether there are multiple epistemic values or goods that have to be aggregated somehow in evaluating the rationality of epistemic states. Each view of how epistemic values give rise to norms of rationality is then paired with a suitable strategy for measuring approximations to ideal rationality.

A Small Piece of the Puzzle

Chapter 8 examines how the proposed view of rationality fits in with other related approaches to theorizing about rationality. The view is best seen as a small piece of a bigger puzzle, and it is therefore important to ensure that there is no tension between this view and nearby puzzle pieces. Five topics are discussed in particular: the relationship between propositional and doxastic rationality, the relationship between ideal and ecological/bounded rationality, the relationship between evaluative and ameliorative approaches to theorizing about rationality, the relationship between epistemological and semantic perspectives on rationality, and the relationship between rational evaluations, permissions, and obligations. The view proposed in this book is best understood as an account of the propositional epistemic rationality of credences. It not only harmonizes with the ways in which rationality is theorized in related domains, but is often a necessary ingredient for developing theories of these aspects of rationality.

Why Approximate Coherence?

Chapter 5 continues to answer the question of how Bayesians can justify the claim that approximating probabilistic coherence is beneficial for non-ideal thinkers. Another popular argument for why coherence is rationally required is the accuracy dominance argument for probabilism. If we use an appropriate measure of distance to coherence, reducing incoherence leads to improved accuracy in every possible world. We can show, moreover, that for any incoherent credence function, it is always possible to measure distance from coherence in such a way that there is a series of less incoherent credence functions that are both more accurate in every possible world and less Dutch book-vulnerable.

Why Approximate Coherence?

Chapter 4 begins to answer the question of how Bayesians can justify the claim that approximating probabilistic coherence is beneficial for non-ideal thinkers. Dutch book arguments are often put forth to argue that ideal rationality requires being coherent. I show that we can justify that it is better to be less incoherent by showing that decreased incoherence is associated with decreased losses from Dutch books. While incoherent thinkers can never be immune from Dutch book losses, the amount they stand to lose, given that we standardize bet sizes, is greater the more incoherent their credences are.