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)

This is surely a bit of Socrates' famous irony. He draws the analogy to explain how his friends should regard poetry as they regretfully banish it from the ideal state. But lovers were no more sensible then than they are now. The advice to banish poetry, undermined already by Plato's own delight and skill in drama, is perhaps undermined still further by this evocation of a 'sensible' lover who counts love so well lost. Yet Socrates' image is one of avowed (...) rationality and prudence. The sensible lover imitates the older literary example of Ulysses' tying himself to the mast. (The example belongs therefore to the class of problems treated in Elster (1979)). Both this lover and Ulysses foresee that under certain possible future conditions, their opinions, values and preferences will or would differ from what they are now, in a very definite fashion. To what extent is such foresight possible? Correspondingly (when we do not claim foreknowledge) to what extent is such opinion reasonable, rational, coherent, or consistent in some suitably broad sense? It is not easy to understand exactly what is possible or even logically permissible in this respect. In an earlier paper, "Belief and the Will", I argued for a principle ("Reflection") to govern such deliberation. Here I will both generalize the treatment of opinion in "Belief and the Will" and respond to criticism. Critical examples mainly resembled the story of Ulysses who foresaw a period of dysfunction (at the sound 2 of the sirens) in his epistemic and/or doxastic future. Other criticism focused on the model of opinion used (precise numerical subjective probability) and on the merits of Dutch Book arguments. The present argument will not rely on Dutch Book arguments and strategies, and the Reflection principle will be formulated so as to apply also to vague opinion. (shrink)

I follow Hájek (Synthese 137:273–323, 2003c) by taking objective probability to be a function of two propositional arguments—that is, I take conditional probability as primitive. Writing the objective probability of q given r as P(q, r), I argue that r may be chosen to provide less than a complete and exact description of the world’s history or of its state at any time. It follows that nontrivial objective probabilities are possible in deterministic worlds and about the past. A very simple (...) chance–credence relation is also then natural, namely that reasonable credence equals objective probability. In other words, we should set our actual credence in a proposition equal to the proposition’s objective probability conditional on available background information. One advantage of that approach is that the background information is not subject to an admissibility requirement, as it is in standard formulations of the Principal Principle. Another advantage is that the “undermining” usually thought to follow from Humean supervenience can be avoided. Taking objective probability to be a two-argument function is not merely a technical matter, but provides us with vital flexibility in addressing significant philosophical issues. (shrink)

Kyburg’s opposition to the subjective Bayesian theory, and in particular to its advocates’ indiscriminate and often questionable use of Dutch Book arguments, is documented and much of it strongly endorsed. However, it is argued that an alternative version, proposed by both de Finetti at various times during his long career, and by Ramsey, is less vulnerable to Kyburg’s misgivings. This is a logical interpretation of the formalism, one which, it is argued, is both more natural and also avoids other, widely-made (...) objections to Bayesianism. (shrink)

The thesis that probabilities of conditionals are conditional probabilities has putatively been refuted many times by so-called ‘triviality results’, although it has also enjoyed a number of resurrections. In this paper I assault it yet again with a new such result. I begin by motivating the thesis and discussing some of the philosophical ramifications of its fluctuating fortunes. I will canvas various reasons, old and new, why the thesis seems plausible, and why we should care about its fate. I will (...) look at some objections to Lewis’s famous triviality results, and thus some reasons for the pursuit of further triviality results. I will generalize Lewis’s results in ways that meet the objections. I will conclude with some reflections on the demise of the thesis—or otherwise. (shrink)

In Belief and the Will, van Fraassen employed a diachronic Dutch Book argument to support a counterintuitive principle called Reflection. There and subsequently van Fraassen has put forth Reflection as a linchpin for his views in epistemology and the philosophy of science, and for the voluntarism (first-person reports of subjective probability are undertakings of commitments) that he espouses as an alternative to descriptivism (first-person reports of subjective probability are merely self-descriptions). Christensen and others have attacked Reflection, taking it to have (...) unpalatable consequences. We prescind from the question of the cogency of diachronic Dutch Book arguments, and focus on Reflection's proper interpretation. We argue that Reflection is not as counterintuitive as it appears — that once interpreted properly the status of the counterexamples given by Christensen and others is left open. We show also that descriptivism can make sense of Reflection, while voluntarism is not especially well suited to do so. (shrink)

Norms—that is, specifications of what we ought to do—play a critical role in the study of informal argumentation, as they do in studies of judgment, decision-making and reasoning more generally. Specifically, they guide a recurring theme: are people rational? Though rules and standards have been central to the study of reasoning, and behavior more generally, there has been little discussion within psychology about why (or indeed if) they should be considered normative despite the considerable philosophical literature that bears on this (...) topic. In the current paper, we ask what makes something a norm, with consideration both of norms in general and a specific example: norms for informal argumentation. We conclude that it is both possible and desirable to invoke norms for rational argument, and that a Bayesian approach provides solid normative principles with which to do so. (shrink)

Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of IBE. My argument focuses on (...) cases in which we are concerned with multiple levels of explanation of some phenomenon. I show that in many such cases, following IBE as an inference rule for full beliefs leads to deductively inconsistent beliefs, and following IBE as a non-Bayesian updating rule for degrees of belief leads to probabilistically incoherent degrees of belief. (shrink)

This thesis is a collection of three self-contained papers on related themes in the area of formal and social epistemology. The first paper explores the possibility of measuring the coherence of a set with multiplicative averaging. It has been pointed out that all the existing probabilistic measures of coherence are flawed for taking the relevance between a set of propositions as the primary factor which determines the coherence of the set. What I show in this paper is that a group (...) of measures, namely the confirmation-based ones, can be saved from this problem if we adopt a nonlinear averaging function to measure the coherence of a set. The second paper discusses how people should conciliate in disagreements. Some epistemologists take linear averaging as the only way of conciliating and claim that conciliating leads to fallacious results. In the paper, I show that the problem is not conciliating, but taking linear averaging as the only way to conciliate. Since there is no reason for us to insist on conciliating with linear averaging, we can adopt nonlinear averaging functions for conciliating and thereby avoid the formal deficiencies. The third paper focuses on the pragmatic results of taking conciliating as a general strategy in disagreements. There is a potential dilemma about conciliating: if everyone always conciliates, it is likely for an epistemic bubble to arise. If everyone refuses to conciliate, an epistemic echo chamber may appear. A possible way of solving the dilemma is to develop a diachronic strategy which tells people how to both conciliate and update their estimate of their interlocutors’ reliability. Although the three papers differ in the subject, they jointly offer some unifying reflections on the way we approach philosophical problems with formal tools. From 5 the first two papers, we see that a formal analysis of a philosophical position is incomplete if philosophers fail to consider a sufficiently wide range of formal tools. The third paper, on the contrary, shows that we should change the ordinary way of modelling a notion if required. This thesis concludes by proposing a pluralistic view of formal methods in formal epistemology. (shrink)