We argue that social deliberation may increase an agent’s confidence and credence under certain circumstances. An agent considers a proposition H and assigns a probability to it. However, she is not fully confident that she herself is reliable in this assignment. She then endorses H during deliberation with another person, expecting him to raise serious objections. To her surprise, however, the other person does not raise any objections to H. How should her attitudes toward H change? It seems plausible that (...) she should increase the credence she assigns to H and, at the same time, increase the reliability she assigns to herself concerning H. A Bayesian model helps us to investigate under what conditions, if any, this is rational. (shrink)

In order to explore the quantifiability and formalizability of uncertainty a wide range of uncertainties are investigated. They are summarized under eight main categories: factual, possibilistic, metadoxastic, agential, interactive, value, structural, and linguistic uncertainty. This includes both classical uncertainty and the uncertainties commonly called great, deep, or radical. For five of the eight types of uncertainty, both quantitative and non-quantitative formalizations are meaningful and available. For one of them (interactive uncertainty), only non-quantitative formalizations seem to be meaningful, and for two (...) (agential and structural uncertainty) neither quantitative nor non-quantitative formalization seems to be a useful approach. (shrink)

It seems obvious that when higher-order evidence makes it rational for one to doubt that one’s own belief on some matter is rational, this can undermine the rationality of that belief. This is known as higher-order defeat. However, despite its intuitive plausibility, it has proved puzzling how higher-order defeat works, exactly. To highlight two prominent sources of puzzlement, higher-order defeat seems to defy being understood in terms of conditionalization; and higher-order defeat can sometimes place agents in what seem like epistemic (...) dilemmas. This chapter draws attention to an overlooked aspect of higher-order defeat, namely that it can undermine the resilience of one’s beliefs. The notion of resilience was originally devised to understand how one should reflect the ‘weight’ of one’s evidence. But it can also be applied to understand how one should reflect one’s higher-order evidence. The idea is particularly useful for understanding cases where one’s higher-order evidence indicates that one has failed in correctly assessing the evidence, without indicating whether one has over- or underestimated the degree of evidential support for a proposition. But it is exactly in such cases that the puzzles of higher-order defeat seem most compelling. (shrink)

A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a proposition if and only if she considers the probability that it is false to be so close to zero that she chooses to disregard that probability. She treats such a proposition as having the probability 1, but, importantly, she is still willing and able to revise that probability assignment if she receives information (...) that gives her sufficient reasons to do so. Such a proposition is undoubted, but not undoubtable. In the formal model it is assigned a probability 1 − δ, where δ is an infinitesimal number. The proposed model employs probabilistic belief states that contain several underlying probability functions representing alternative probabilistic states of the world. Furthermore, a distinction is made between update and revision, in the same way as in the literature on belief change. The formal properties of the model are investigated, including properties relevant for learning from experience. The set of propositions whose probabilities are infinitesimally close to 1 forms a belief set. Operations that change the probabilistic belief state give rise to changes in this belief set, which have much in common with traditional operations of belief change. (shrink)

The probability that a fair coin tossed yesterday landed heads is either 0 or 1, but the probability that it would land heads was 0.5. In order to account for the latter type of probabilities, past probabilities, a temporal restriction operator is introduced and axiomatically characterized. It is used to construct a representation of conditional past probabilities. The logic of past probabilities turns out to be strictly weaker than the logic of standard probabilities.

Two types of measures of probabilistic uncertainty are introduced and investigated. Dispersion measures report how diffused the agent’s second-order probability distribution is over the range of first-order probabilities. Robustness measures reflect the extent to which the agent’s assessment of the prior (objective) probability of an event is perturbed by information about whether or not the event actually took place. The properties of both types of measures are investigated. The most obvious type of robustness measure is shown to coincide with one (...) of the major candidates for a dispersion measure, the mean square deviation measure. (shrink)