In the general problem of verisimilitude, we try to define the distance of a statement from a target, which is an informative truth about some domain of investigation. For example, the target can be a state description, a structure description, or a constituent of a first-order language. In the problem of legisimilitude, the target is a deterministic or universal law, which can be expressed by a nomic constituent or a quantitative function involving the operators of physical necessity and possibility. The (...) special case of legisimilitude, where the target is a probabilistic law, has been discussed by Roger Rosenkrantz and Ilkka Niiniluoto. Their basic proposal is to measure the distance between two probabilistic laws by the Kullback–Leibler notion of divergence, which is a semimetric on the space of probability measures. This idea can be applied to probabilistic laws of coexistence and laws of succession, and the examples may involve discrete or continuous state spaces. In this paper, these earlier studies are elaborated in four directions. First, even though deterministic laws are limiting cases of probabilistic laws, the target-sensitivity of truthlikeness measures implies that the legisimilitude of probabilistic laws is not easily reducible to the deterministic case. Secondly, the Jensen-Shannon divergence is applied to mixed probabilistic laws which entail some universal laws. Thirdly, a new class of distance measures between probability distributions is proposed, so that their horizontal differences are taken into account in addition to vertical ones. Fourthly, a solution is given for the epistemic problem of estimating degrees of probabilistic legisimilitude on the basis of empirical evidence. (shrink)

This article connects recent work in formal epistemology to work in economics and computer science. Analysing the Dutch Book Arguments, Epistemic Utility Theory and Objective Bayesian Epistemology we discover that formal epistemologists employ the same argument structure as economists and computer scientists. Since similar approaches often have similar problems and have shared solutions, opportunities for cross-fertilisation abound.

There is a well-known equivalence between avoiding accuracy dominance and having probabilistically coherent credences (see, e.g., de Finetti 1974, Joyce 2009, Predd et al. 2009, Pettigrew 2016). However, this equivalence has been established only when the set of propositions on which credence functions are defined is finite. In this paper, I establish connections between accuracy dominance and coherence when credence functions are defined on an infinite set of propositions. In particular, I establish the necessary results to extend the classic accuracy (...) argument for probabilism to certain classes of infinite sets of propositions including countably infinite partitions. (shrink)

There is an ongoing debate about which rule we ought to use for scoring probability estimates. Much of this debate has been premised on scoring-rule monism, according to which there is exactly one best scoring rule. In previous work, I have argued against this position. The argument given there was based on purely a priori considerations, notably the intuition that scoring rules should be sensitive to truthlikeness relations if, and only if, such relations are present among whichever hypotheses are at (...) issue. The present paper offers a new, quasi-empirical argument against scoring-rule monism. This argument uses computational simulations to show that different scoring rules can have different economical consequences, depending on the context of use. (shrink)