Online research in philosophy

This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introducing objective Bayesian epistemology over propositional languages, the formalism is extended to handle predicate languages. A rather general probabilistic logic is formulated and then given a natural semantics in terms of objective Bayesian epistemology. The machinery of objective Bayesian nets and objective credal nets is introduced and this machinery is applied to provide a calculus for probabilistic logic that meshes with the objective Bayesian semantics.

The likelihood principle of Bayesian statistics implies that information about the stopping rule used to collect evidence does not enter into the statistical analysis. This consequence confers an apparent advantage on Bayesian statistics over frequentist statistics. In the present paper, I argue that information about the stopping rule is nevertheless of value for an assessment of the reliability of the experiment, which is a pre-experimental measure of how well a contemplated procedure is expected to discriminate between hypotheses. I show that, when reliability assessments enter into inquiries, some stopping rules prescribing optional stopping are unacceptable to both Bayesians and frequentists.

Bayesianism is our leading theory of uncertainty. Epistemology is defined as the theory of knowledge. So “Bayesian Epistemology” may sound like an oxymoron. Bayesianism, after all, studies the properties and dynamics of degrees of belief, understood to be probabilities. Traditional epistemology, on the other hand, places the singularly non-probabilistic notion of knowledge at centre stage, and to the extent that it traffics in belief, that notion does not come in degrees. So how can there be a Bayesian epistemology?

Bayesian epistemology addresses epistemological problems with the help of the mathematical theory of probability. It turns out that the probability calculus is especially suited to represent degrees of belief (credences) and to deal with questions of belief change, confirmation, evidence, justification, and coherence. Compared to the informal discussions in traditional epistemology, Bayesian epis- temology allows for a more precise and fine-grained analysis which takes the gradual aspects of these central epistemological notions into account. Bayesian epistemology therefore complements traditional epistemology; it does not re- place it or aim at replacing it.

In the past, few mainstream epistemologists have endorsed Bayesian epistemology, feeling that it fails to capture the complex structure of epistemic cognition. The defenders of Bayesian epistemology have tended to be probability theorists rather than epistemologists, and I have always suspected they were more attracted by its mathematical elegance than its epistemological realism. But recently Bayesian epistemology has gained a following among younger mainstream epistemologists. I think it is time to rehearse some of the simpler but still quite devastating objections to Bayesian epistemology. Most of these objections are familiar, but have never been adequately addressed by the Bayesians.

Critics of Bayesianism often assert that scientists are not Bayesians. The widespread use of Bayesian statistics in the field of radiocarbon calibration is discussed in relation to this charge. This case study illustrates the willingness of scientists to use Bayesian statistics when the approach offers some advantage, while continuing to use orthodox methods in other contexts. The case of radiocarbon calibration, therefore, suggests a picture of statistical practice in science as eclectic and pragmatic rather than rigidly adhering to any one theoretical position.

Good expresses agreement that the controversy between Bayesian and non-Bayesian statistics is more fundamental than that between Carnap and Popper, and points out that his own position is a Bayes/non-Bayes compromise.

From the outside, Bayesian statistics may seem like a closed little corner of probability. Once a prior is specified you compute! From the inside the field is filled with problems, conceptual and otherwise. This paper surveys some of what remains to be done and gives examples of the work in progress via a Bayesian peek into Feller volume I.

In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other.

In this chapter, I argue that Karl Popper was a communitarian philosopher. This will surprise some readers. Liberals often tout Popper as one of their champions. Indeed, there is no doubt that Popper shared much in common with liberals. However, I will argue that Popper rejected a central, though perhaps not essential, pillar of liberal theory, namely, individualism. This claim may seem to contradict Popper's professed methodological individualism. Yet I argue that Popper was a methodological individualist in name only. In fact, methodological individualism faded from Popper's vocabulary as he moved institutions and situational analysis more firmly to centre-stage. Popper's focus on institutions and situations constitutes what I call his communitarianism. If my interpretation is correct, then theorists in the socio logy of scientific knowledge and communitarian epistemology should reconsider their long-standing distrust of Popper's philosophy. Indeed, they may have much to gain by treating Popper as a friend rather than a foe.