Schwitzgebel (2001) — henceforth 'S' — offers three examples in order to convince us that there are situations in which individuals are neither accurately describable as believing that p or failing to so believe, but are rather in 'in-between states of belief'. He then argues that there are no 'Bayesian' or representational strategies for explicating these, and proposes a dispositional account. I do not have any fundamental objection to the idea that there might be 'in-between states of belief'. What I (...) shall argue, rather, is that: (I) S does not provide a convincing argument that there really are such states; (II) S does not show, as he claims, that 'in-between states of belief' could not be accounted for in terms of degrees of belief; (III) S’s dispositional account of 'in-between states of belief' is more problematic than the 'degree of belief' alternative. (shrink)

Hájek has recently presented the following paradox. You are certain that a cable guy will visit you tomorrow between 8 a.m. and 4 p.m. but you have no further information about when. And you agree to a bet on whether he will come in the morning interval (8, 12] or in the afternoon interval (12, 4). At first, you have no reason to prefer one possibility rather than the other. But you soon realise that there will definitely be a future (...) time at which you will (rationally) assign higher probability to an afternoon arrival than a morning one, due to time elapsing. You are also sure there may not be a future time at which you will (rationally) assign a higher probability to a morning arrival than an afternoon one. It would therefore appear that you ought to bet on an afternoon arrival. The paradox is based on the apparent incompatibility of the principle of expected utility and principles of diachronic rationality which are prima facie plausible. Hájek concludes that the latter are false, but doesn't provide a clear diagnosis as to why. We endeavour to further our understanding of the paradox by providing such a diagnosis. (shrink)

Darrell P. Rowbottom reviews the book "In defense of objective Bayesianism" by Jon Williamson.

In his Bayesian Nets and Causality, Jon Williamson presents an ‘Objective Bayesian’ interpretation of probability, which he endeavours to distance from the logical interpretation yet associate with the subjective interpretation. In doing so, he suggests that the logical interpretation suffers from severe epistemological problems that do not affect his alternative. In this paper, I present a challenge to his analysis. First, I closely examine the relationship between the logical and ‘Objective Bayesian’ views, and show how, and why, they are highly (...) similar. Second, I argue that the logical interpretation is not manifestly inferior, at least for the reasons that Williamson offers. I suggest that the key difference between the logical and ‘Objective Bayesian’ views is in the domain of the philosophy of logic; and that the genuine disagreement appears to be over Platonism versus nominalism. (shrink)

How are we to understand the use of probability in corroboration functions? Popper says logically, but does not show we could have access to, or even calculate, probability values in a logical sense. This makes the logical interpretation untenable, as Ramsey and van Fraassen have argued. -/- If corroboration functions only make sense when the probabilities employed therein are subjective, however, then what counts as impressive evidence for a theory might be a matter of convention, or even whim. So isn’t (...) so-called ‘corroboration’ just a matter of psychology? -/- In this paper, I argue that we can go some way towards addressing this objection by adopting an intersubjective interpretation, of the form advocated by Gillies, with respect to corroboration. I show why intersubjective probabilities are preferable to subjective ones when it comes to decision making in science: why group decisions are liable to be superior to individual ones, given a number of plausible conditions. I then argue that intersubjective corroboration is preferable to intersubjective confirmation of a Bayesian variety, because there is greater opportunity for principled agreement concerning the factors involved in the former. (shrink)

Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails (...) because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief . One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective Bayesian norms are tied up in the very notion of degrees of belief. (shrink)

In this article, I present some new group level interpretations of probability, and champion one in particular: a consensus-based variant where group degrees of belief are construed as agreed upon betting quotients rather than shared personal degrees of belief. One notable feature of the account is that it allows us to treat consensus between experts on some matter as being on the union of their relevant background information. In the course of the discussion, I also introduce a novel distinction between (...) intersubjective and interobjective interpretations of probability. (shrink)