Julia Staffel

This paper is about teaching probability to students of philosophy who don’t aim to do primarily formal work in their research. These students are unlikely to seek out classes about probability or formal epistemology for various reasons, for example because they don’t realize that this knowledge would be useful for them or because they are intimidated by the material. However, most areas of philosophy now contain debates that incorporate probability, and basic knowledge of it is essential even for philosophers whose work isn’t primarily formal. In this paper, I explain how to teach probability to students who are not already enthusiastic about formal philosophy, taking into account the common phenomena of math anxiety and the lack of reading skills for formal texts. I address course design, lesson design, and assignment design. Most of my recommendations also apply to teaching formal methods other than probability theory.

Epistemologists routinely distinguish between two kinds of justification or rationality – the propositional and the doxastic kind – in order to characterize importantly different ways in which an attitude can be justified or rational for a person. I argue that these notions, as they are commonly understood, are well suited to capture rationality judgments about the attitudes that agents reach as conclusions of their reasoning. Yet, these notions are ill-suited to capture rationality judgments about attitudes that agents form while their reasoning is still in progress. In fact, we currently lack any suitable theory of rationality that lets us capture the ways in which we evaluate the rationality of such transitional attitudes, even though they are ubiquitous. I propose to capture these rationality judgments by introducing a new notion of rationality that is orthogonal to the propositional/doxastic distinction, which I call pro tem rationality. This new notion can be integrated with both traditional and formal ways of characterizing rationality or justification. It can be used to enlighten debates about logical and empirical learning, higher-order evidence, and the epistemology of philosophy, among others.

Active reasoning is the kind of reasoning that we do deliberately and consciously. In characterizing the nature of active reasoning and the norms it should obey, the question arises which attitudes we can reason with. Many authors take outright beliefs to be the attitudes we reason with. Others assume that we can reason with both outright beliefs and degrees of belief. Some think that we reason only with degrees of belief. In this paper I approach the question of what kinds of beliefs can participate in reasoning by using the following method: I take the default position to be maximally permissive – that both graded and outright beliefs can participate in reasoning. I then identify some features of active reasoning that appear at first glance to favor a more restrictive position about which types of belief we can reason with. I argue that the arguments based on these features ultimately fail.

In his new book "The Importance of Being Rational", Errol Lord aims to give a real definition of the property of rationality in terms of normative reasons. If he can do so, his work is an important step towards a defense of ‘reasons fundamentalism’ – the thesis that all complex normative properties can be analyzed in terms of normative reasons. I focus on his analysis of epistemic rationality, which says that your doxastic attitudes are rational just in case they are correct responses to the objective normative reasons you possess. For some fact to be an objective normative reason to do something that you possess, you have to be in a position to know this fact and be able to competently use it as a reason to do that thing. Lord’s view is thus a knowledge-first view about possessing normative reasons. Throughout the book, Lord conceptualizes belief in the traditional tripartite way – if you take any attitude at all towards a proposition, then you either believe it, or disbelieve it, or you suspend judgment about it. Lord doesn’t discuss cases in which we’re uncertain. Yet, those cases are ubiquitous. I explore how his view can be extended to them. I first discuss whether his strategy for vindicating coherence requirements in terms of normative reasons can be applied to credences. I then ask how Lord can conceive of the doxastic attitudes that encode uncertainty .

This chapter is a philosophical survey of some leading approaches in formal epistemology in the so-called ‘Bayesian’ tradition. According to them, a rational agent’s degrees of belief—credences—at a time are representable with probability functions. We also canvas various further putative ‘synchronic’ rationality norms on credences. We then consider ‘diachronic’ norms that are thought to constrain how credences should respond to evidence. We discuss some of the main lines of recent debate, and conclude with some prospects for future research.

Bayesian epistemology provides a popular and powerful framework for modeling rational norms on credences, including how rational agents should respond to evidence. The framework is built on the assumption that ideally rational agents have credences, or degrees of belief, that are representable by numbers that obey the axioms of probability. From there, further constraints are proposed regarding which credence assignments are rationally permissible, and how rational agents’ credences should change upon learning new evidence. While the details are hotly disputed, all flavors of Bayesianism purport to give us norms of ideal rationality. This raises the question of how exactly these norms apply to you and me, since perfect compliance with those ideal norms is out of reach for human thinkers. A common response is that Bayesian norms are ideals that human reasoners are supposed to approximate – the closer they come to being ideally rational, the better. To make this claim plausible, we need to make it more precise. In what sense is it better to be closer to ideally rational, and what is an appropriate measure of such closeness? This article sketches some possible answers to these questions.

I argue that in order to account for normative uncertainty, an expressivist theory of normative language and thought must accomplish two things: Firstly, it needs to find room in its framework for a gradable conative attitude, degrees of which can be interpreted as representing normative uncertainty. Secondly, it needs to defend appropriate rationality constraints pertaining to those graded attitudes. The first task – finding an appropriate graded attitude that can represent uncertainty – is not particularly problematic. I tackle the second task by exploring whether we can devise expressivist versions of the standard arguments used to support rationality constraints on degrees of uncertainty, Dutch book arguments and accuracy-dominance arguments. I show that we can do so, but that the resulting arguments don’t support the same rationality constraints as the original versions of the arguments.