Accuracy, probabilism, and the insufficiency of the alethic

The best and most popular argument for probabilism is the accuracy-dominance argument, which purports to show that alethic considerations alone support the view that an agent’s degrees of belief should always obey the axioms of probability. I argue that extant versions of the accuracy-dominance argument face a problem. In order for the mathematics of the argument to function as advertised, we must assume that every omniscient credence function is classically consistent; there can be no worlds in the set of dominance-relevant worlds that obey some other logic. This restriction cannot be motivated on alethic grounds unless we’re also willing to accept that rationality requires belief in every metaphysical necessity, as the distinction between a priori logical necessities and a posteriori metaphysical ones is not an alethic distinction. To justify the restriction to classically consistent worlds, non-alethic motivation is required. And thus, if there is a version of the accuracy-dominance argument in support of probabilism, it isn’t one that is grounded in alethic considerations alone.

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.

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.

The Aggregate Utility Solution II: The Solution Itself

The previous chapter concluded that we should aggregate credences and utilities first. This chapter considers how we should aggregate them. It claims that we should use the individual’s current credence function together with a weighted average of the utility functions of the individual’s past, present, and future selves. It then responds to an objection based on the partition sensitivity of the proposed solution. It proposes that an individual should aggregate the utilities assigned to those states of the world that specify everything that any of the individual’s various selves care about.

ACCURACY UNCOMPOSED: AGAINST CALIBRATIONISM

ABSTRACTPettigrew offers new axiomatic constraints on legitimate measures of inaccuracy. His axiom called ‘Decomposition’ stipulates that legitimate measures of inaccuracy evaluate a credence function in part based on its level of calibration at a world. I argue that if calibration is valuable, as Pettigrew claims, then this fact is an explanandum for accuracy-first epistemologists, not an explanans, for three reasons. First, the intuitive case for the importance of calibration isn't as strong as Pettigrew believes. Second, calibration is a perniciously global property that both contravenes Pettigrew's own views about the nature of credence functions themselves and undercuts the achievements and ambitions of accuracy-first epistemology. Finally, Decomposition introduces a new kind of value compatible with but separate from accuracy-proper in violation of Pettigrew's alethic monism.