Ideal agents are role models whose perfection in some normative domain we try to approximate. But which form should this striving take? It is well known that following ideal rules of practical reasoning can have disastrous results for non-ideal agents. Yet, this issue has not been explored with respect to rules of theoretical reasoning. I show how we can extend Bayesian models of ideally rational agents in order to pose and answer the question of whether non-ideal agents should form new (...) degrees of belief in the same way as their ideal counterparts. I demonstrate that the epistemic and the practical case are parallel: following ideal rules does not always lead to optimal outcomes for non-ideal agents. (shrink)

According to an increasingly popular epistemological view, people need outright beliefs in addition to credences to simplify their reasoning. Outright beliefs simplify reasoning by allowing thinkers to ignore small error probabilities. What is outright believed can change between contexts. It has been claimed that thinkers manage shifts in their outright beliefs and credences across contexts by an updating procedure resembling conditionalization, which I call pseudo-conditionalization (PC). But conditionalization is notoriously complicated. The claim that thinkers manage their beliefs via PC is (...) thus in tension with the view that the function of beliefs is to simplify our reasoning. I propose to resolve this puzzle by rejecting the view that thinkers employ PC. Based on this solution, I furthermore argue for a descriptive and a normative claim. The descriptive claim is that the available strategies for managing beliefs and credences across contexts that are compatible with the simplifying function of outright beliefs can generate synchronic and diachronic incoherence in a thinker’s attitudes. Moreover, I argue that the view of outright belief as a simplifying heuristic is incompatible with the view that there are ideal norms of coherence or consistency governing outright beliefs that are too complicated for human thinkers to comply with. (shrink)

We investigate an approach for drawing logical inference from inconsistent premisses. The main idea in this approach is that the inconsistencies in the premisses should be interpreted as uncertainty of the information. We propose a mechanism, based on Kinght’s [14] study of inconsistency, for revising an inconsistent set of premisses to a minimally uncertain, probabilistically consistent one. We will then generalise the probabilistic entailment relation introduced in [15] for propositional languages to the first order case to draw logical inference from (...) a probabilistic set of premisses. We will show how this combination can allow us to limit the effect of uncertainty introduced by inconsistent premisses to only the reasoning on the part of the premise set that is relevant to the inconsistency. (shrink)

Lewis’ analysis of modality faces a problem in that it appears to confer unintended truth values to certain modal claims about the pluriverse: e.g. ‘It is possible that there are many worlds’ is false when we expect truth. This is the problem of advanced modalizing. Divers presents a principled solution to this problem by treating modal modifiers as semantically redundant in some such cases. However, this semantic move does not deal adequately with advanced de re modal claims. Here, we motivate (...) and detail a comprehensive semantics for advanced modalizing de dicto and de re. The generalized semantic feature of the initial solution is not redundancy but absence from counterpart-theoretic translations of world-constrictions. (shrink)

Bayesians defend norms of ideal rationality such as probabilism, which they claim should be approximated by non-ideal thinkers. Yet, it is not often discussed exactly in what sense it is beneficial for an agent’s credence function to approximate probabilistic coherence. Some existing research indicates that approximating coherence leads to improvements in accuracy, whereas other research suggests that it decreases Dutch book vulnerability. Yet, the existing results don’t settle whether there is a way of approximating coherence that delivers both benefits at (...) once. We show that there is. (shrink)

In this paper, we ask: how should an agent who has incoherent credences update when they learn new evidence? The standard Bayesian answer for coherent agents is that they should conditionalize; however, this updating rule is not defined for incoherent starting credences. We show how one of the main arguments for conditionalization, the Dutch strategy argument, can be extended to devise a target property for updating plans that can apply to them regardless of whether the agent starts out with coherent (...) or incoherent credences. The main idea behind this extension is that the agent should avoid updating plans that increase the possible sure loss from Dutch strategies. This happens to be equivalent to avoiding updating plans that increase incoherence according to a distance-based incoherence measure. (shrink)

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. (shrink)