Reasoning with degrees of belief

2013-04-08In this dissertation, I lay the groundwork for developing a comprehensive theory of reasoning with degrees of belief. Reasoning, as I understand it here, is the mental activity of forming or revising one’s attitudes based on other attitudes. I argue that we need such a theory, since degrees of belief, also called credences, play an important role in human reasoning. Yet, this type of reasoning has so far been overlooked in the philosophical literature. Discussions of reasoning, understood as a mental activity of human beings, focus almost exclusively on the traditional notion of outright belief, according to which an agent can believe, disbelieve, or suspend judgment about a proposition. The philosophical literature on degrees of belief, on the other hand, acknowledges that this model of belief is too coarse grained: agents can have different levels of confidence in a proposition, and hence we should think of belief as a graded notion. Yet, the literature on degrees of belief is hardly concerned with the question of how agents should reason. The leading research paradigm is subjective Bayesianism, a theory according to which the probability axioms constitute the norms of rationality for degrees of belief. However, the norms of subjective Bayesianism should not be construed as principles of reasoning, and so this theory does not provide an account of reasoning with degrees of belief. ❧ One important constraint on a comprehensive theory of reasoning with degrees of belief is that it must apply to non-ideal reasoners, who have incoherent degrees of belief. This constraint provides one of the reasons why subjective Bayesianism cannot be viewed as a theory of reasoning: it is widely criticized for applying at best to ideal agents, since the coherence norms on degrees of belief it postulates seem impossibly demanding for human agents. ❧ I argue that when we try to establish principles of reasoning that apply to incoherent agents, a condition of adequacy on such principles is that they should minimize increases in incoherence. In order to evaluate whether a principle of reasoning meets this condition of adequacy, we need to be able to measure the degree to which an agent’s credence function is incoherent. Yet, the standard Bayesian theory provides no way of measuring degrees of incoherence. This theory allows us to distinguish between coherent and incoherent credence functions, but it does not allow us to distinguish between credence functions with higher and lower degrees of incoherence. I propose a way of extending the standard Bayesian framework by developing and defending a formal measure of such incoherence. I then show how this measure can be applied to formulate constraints on adequate rules of reasoning for incoherent agents. In particular, I use the measure to ascertain whether it is advisable for non-ideal agents to follow the same reasoning strategies as their ideal counterparts. I show that this is not always a good idea, because doing so can sometimes make an agent more incoherent than following some alternative reasoning strategy