A seemingly plausible application of Bayesian decision-theoretic reasoning to determine one's rational degrees of belief yields a paradoxical conclusion: one ought to jettison one's intermediate credences in favour of more extreme (opinionated) ones. I discuss various attempts to solve the paradox, those involving the acceptance of the paradoxical conclusion, and those which attempt to block its derivation.

The Stability of Belief: How Rational Belief Coheres with Probability, by LeitgebHannes. Oxford: Oxford University Press, 2017. Pp. xiv + 365.

The present article illustrates a conflict between the claim that rational belief sets are closed under deductive consequences, and a very inclusive claim about the factors that are sufficient to determine whether it is rational to believe respective propositions. Inasmuch as it is implausible to hold that the factors listed here are insufficient to determine whether it is rational to believe respective propositions, we have good reason to deny that rational belief sets are closed under deductive consequences.

This target article presents a new computational theory of explanatory coherence that applies to the acceptance and rejection of scientific hypotheses as well as to reasoning in everyday life, The theory consists of seven principles that establish relations of local coherence between a hypothesis and other propositions. A hypothesis coheres with propositions that it explains, or that explain it, or that participate with it in explaining other propositions, or that offer analogous explanations. Propositions are incoherent with each other if they (...) are contradictory, Propositions that describe the results of observation have a degree of acceptability on their own. An explanatory hypothesis is acccpted if it coheres better overall than its competitors. The power of the seven principles is shown by their implementation in a connectionist program called ECHO, which treats hypothesis evaluation as a constraint satisfaction problem. Inputs about the explanatory relations are used to create a network of units representing propositions, while coherende and incoherence relations are encoded by excitatory and inbihitory links. ECHO provides an algorithm for smoothly integrating theory evaluation based on considerations of explanatory breadth, simplicity, and analogy. It has been applied to such important scientific cases as Lovoisier's argument for oxygen against the phlogiston theory and Darwin's argument for evolution against creationism, and also to cases of legal reasoning. The theory of explanatory coherence has implications for artificial intelligence, psychology, and philosophy. (shrink)

The rule of adjunction is intuitively appealing and uncontroversial for deductive inference, but in situations where information can be uncertain, the rule is neither needed nor wanted for rational acceptance, as illustrated by the lottery paradox. Practical certainty is the acceptance of statements whose chances of error are smaller than a prescribed threshold parameter, when evaluated against an evidential corpus. We examine the failure of adjunction in relation to the threshold parameter for practical certainty, with an eye towards reinstating the (...) rule of adjunction in some restricted forms, by observing the conditions under which the overall chance of error of the joint statements can be variously bounded. (shrink)

The no-free-lunch theorems promote a skeptical conclusion that all possible machine learning algorithms equally lack justification. But how could this leave room for a learning theory, that shows that some algorithms are better than others? Drawing parallels to the philosophy of induction, we point out that the no-free-lunch results presuppose a conception of learning algorithms as purely data-driven. On this conception, every algorithm must have an inherent inductive bias, that wants justification. We argue that many standard learning algorithms should rather (...) be understood as model-dependent: in each application they also require for input a model, representing a bias. Generic algorithms themselves, they can be given a model-relative justification. (shrink)

In “What price coherence?”, Klein and Warfield put forward a simple argument that triggered an extensive debate on the epistemic virtues of coherence. As is well-known, this debate yielded far-reaching impossibility results to the effect that coherence is not conducive to truth, even if construed in a ceteris paribus sense. A large part of the present paper is devoted to a re-evaluation of these results. As is argued, all explications of truth-conduciveness leave out an important aspect: while it might not (...) be the case that coherence is truth-conducive, it might be conducive to verisimilitude or epistemic utility. Unfortunately, it is shown that the answer for both these issues must be in the negative, again. Furthermore, we shift the focus from sets of beliefs to particular beliefs: as is shown, neither is any of the extant probabilistic measures of coherence truth-conducive on the level of particular beliefs, nor does weakening these measures to quasi-orderings establish the link between coherence and truth for an important amount of measures. All in all, the results in this paper cast a serious doubt on the approach of establishing a link between coherence and truth. Finally, recent arguments that shift the focus from the relationship between coherence and truth to the one between coherence and confirmation are assessed. (shrink)

Critical Notice of Kant's Transcendental Deduction, by Henry Allison. Oxford: Oxford University Press, 2015. Pp. Xv + 477.

According to the Ramsey Test, conditionals reflect changes of beliefs: α > β is accepted in a belief state iff β is accepted in the minimal revision of it that is necessary to accommodate α. Since Gärdenfors’s seminal paper of 1986, a series of impossibility theorems (“triviality theorems”) has seemed to show that the Ramsey test is not a viable analysis of conditionals if it is combined with AGM-type belief revision models. I argue that it is possible to endorse that (...) Ramsey test for conditionals while staying true to the spirit of AGM. A main focus lies on AGM’s condition of Preservation according to which the original belief set should be fully retained after a revision by information that is consistent with it. I use concrete representations of belief states and (iterated) revisions of belief states as semantic models for (nested) conditionals. Among the four most natural qualitative models for iterated belief change, two are identified that indeed allow us to combine the Ramsey test with Preservation in the language containing only flat conditionals of the form α > β. It is shown, however, that Preservation for this simple language enforces a violation of Preservation for nested conditionals of the form α > (β > γ). In such languages, no two belief sets are ordered by strict subset inclusion. I argue that it has been wrong right from the start to expect that Preservation holds in languages containing nested conditionals. (shrink)

This paper addresses the question whether the past couple of decades of formal research in belief revision offers evidence of a new psychologism in logic. In the first part I examine five potential arguments in favour of this thesis and find them all wanting. In the second part of the paper I argue that belief revision research has climbed up a hierarchy of models for the change of doxastic states that appear to be clearly normative at the bottom, but are (...) more amenable to an empirical-descriptive interpretation on higher levels. I conclude that this observation might offer a foothold for the thesis that there is a new psychologism in logic. (shrink)

Probabilistic belief contraction has been a much neglected topic in the field of probabilistic reasoning. This is due to the difficulty in establishing a reasonable reversal of the effect of Bayesian conditionalization on a probabilistic distribution. We show that indifferent contraction, a solution proposed by Ramer to this problem through a judicious use of the principle of maximum entropy, is a probabilistic version of a full meet contraction. We then propose variations of indifferent contraction, using both the Shannon entropy measure (...) as well as the Hartley entropy measure, with an aim to avoid excessive loss of beliefs that full meet contraction entails. (shrink)

Famously, William James held that there are two commandments that govern our epistemic life: Believe truth! Shun error! In this paper, I give a formal account of James' claim using the tools of epistemic utility theory. I begin by giving the account for categorical doxastic states – that is, full belief, full disbelief, and suspension of judgment. Then I will show how the account plays out for graded doxastic states – that is, credences. The latter part of the paper thus (...) answers a question left open in Pettigrew. (shrink)

My concern in this paper is a debate between Pascal Engel and Richard Rorty documented in the book What’s the Use of Truth? Both Engel and Rorty problematize the natural suggestion that attaining truth is a goal of our inquiries. Where Rorty thinks this means that truth is not something we should aim for at all over and beyond justification, Engel maintains that truth still plays a distinct role in our intellectual and daily lives. Thus, the debate between Engel and (...) Rorty ends in a standoff. In the present paper, I question the claim that truth is not a goal of inquiry. I do so from the point of view of a systematic and general theory of rational goal-setting which has its roots in management science. I argue, in this connection, that Rorty’s central claim rests on a principle of goal-setting rationality that is generally invalid. The bottom line is that the goal of truth, like other visionary goals, is likely to have the positive effect of increasing motivation and effort, and this may offset the drawbacks which Rorty, rightly, calls attention to. In largely following Rorty in this regard, Engel is making one concession too much to his opponent. (shrink)

Susan Mills and John Beatty's propensity interpretation of fitness encountered very different philosophical criticisms by Alexander Rosenberg and Kenneth Waters. These criticisms and the rejoinders to them are both predictable and important. They are predictable as raisingkinds of issues typically associated with disposition concepts (this is established through a systematic review of the problems generated by Carnap's dispositional interpretation of all scientific terms). They are important as referring the resolution of these issues to the development of evolutionary biology. This historical (...) approach to the propensity interpretation of fitness draws attention to the precarious relation between philosophical clarification of scientific concepts and any given state of the empirical arts. (shrink)

Scientific realists use the “no miracle argument” to show that the empirical and pragmatic success of science is an indicator of the ability of scientific theories to give true or truthlike representations of unobservable reality. While antirealists define scientific progress in terms of empirical success or practical problem-solving, realists characterize progress by using some truth-related criteria. This paper defends the definition of scientific progress as increasing truthlikeness or verisimilitude. Antirealists have tried to rebut realism with the “pessimistic metainduction”, but critical (...) realists turn this argument into an optimistic view about progressive science. (shrink)

The notion of truthlikeness or verisimilitude has been a topic of intensive discussion ever since the definition proposed by Karl Popper was refuted in 1974. This paper gives an analysis of old and new debates about this notion. There is a fairly large agreement about the truthlikeness ordering of conjunctive theories, but the main rival approaches differ especially about false disjunctive theories. Continuing the debate between Niiniluoto’s min-sum measure and Schurz’s relevant consequence measure, the paper also gives a critical assessment (...) of Oddie’s new defense of the average measure and Kuipers’ refined definition of truth approximation. (shrink)