Julia Staffel

Many philosophers hold that the probability axioms constitute norms of rationality governing degrees of belief. This view, known as subjective Bayesianism, has been widely criticized for being too idealized. It is claimed that the norms on degrees of belief postulated by subjective Bayesianism cannot be followed by human agents, and hence have no normative force for beings like us. This problem is especially pressing since the standard framework of subjective Bayesianism only allows us to distinguish between two kinds of credence functions—coherent ones that obey the probability axioms perfectly, and incoherent ones that don’t. An attractive response to this problem is to extend the framework of subjective Bayesianism in such a way that we can measure differences between incoherent credence functions. This lets us explain how the Bayesian ideals can be approximated by humans. I argue that we should look for a measure that captures what I call the ‘overall degree of incoherence’ of a credence function. I then examine various incoherence measures that have been proposed in the literature, and evaluate whether they are suitable for measuring overall incoherence. The competitors are a qualitative measure that relies on finding coherent subsets of incoherent credence functions, a class of quantitative measures that measure incoherence in terms of normalized Dutch book loss, and a class of distance measures that determine the distance to the closest coherent credence function. I argue that one particular Dutch book measure and a corresponding distance measure are particularly well suited for capturing the overall degree of incoherence of a credence function

This paper investigates the relationship between two evaluative claims about agents’ de- grees of belief: (i) that it is better to have more, rather than less accurate degrees of belief, and (ii) that it is better to have less, rather than more probabilistically incoherent degrees of belief. We show that, for suitable combinations of inaccuracy measures and incoherence measures, both claims are compatible, although not equivalent; moreover, certain ways of becoming less incoherent always guarantee improvements in accuracy. Incompatibilities between particular incoherence and inaccuracy measures can be exploited to argue against particular ways of measuring either inaccuracy or incoherence.

Sorensen offers the following definition of a ‘knowledge-lie’: ‘An assertion that p is a knowledge-lie exactly if intended to prevent the addressee from knowing that p is untrue but is not intended to deceive the addressee into believing p.’ According to Sorensen, knowledge-lies are not meant to deceive their addressee, and this fact is supposed to make them less bad than ordinary lies. I will argue that standard cases of knowledge-lies, including almost all the cases Sorensen considers, do in fact involve deception, contrary to what Sorensen claims. And while there are cases of non-deceptive knowledge-lies, such cases are deviant, either because it is only incidental that the knowledge-preventing assertion is a lie, or because it is only incidental that the lie doesn't deceive. Here's an example of a knowledge-lie: Dr Head is considering firing Dr Appendix because of his weak research. But he doesn't want to fire Appendix unless he knows that Appendix's research isn't good, and so he consults Dr Heart. Head knows that if Appendix's research is good, then Heart will tell the truth and say so, whereas if Appendix's work isn't good, then Heart may or may not …