Online research in philosophy

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.

This article sketches a theory of objective probability focusing on "nomic probability", which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the "statistical syllogism". It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues.

This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues.

The first third of John Pollock’s Thinking about Acting is on the topics of pleasure, desire, and preference, and these topics are the ones on which this paper focuses. I review Pollock’s position and argue that it has at least one substantial strength (it elegantly demonstrates that desires must be more fundamental than preferences, and embraces this conclusion wholeheartedly) and at least one substantial weakness (it holds to a form of psychological hedonism without convincingly answering the philosophical or empirical objections that might be raised).

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 this paper two theories of defeasible reasoning, Pollock's account and my theory of ranking functions, are compared, on a strategic level, since a strictly formal comparison would have been unfeasible. A brief summary of the accounts shows their basic difference: Pollock's is a strictly computational one, whereas ranking functions provide a regulative theory. Consequently, I argue that Pollock's theory is normatively defective, unable to provide a theoretical justification for its basic inference rules and thus an independent notion of admissible rules. Conversely, I explain how quite a number of achievements of Pollock's account can be adequately duplicated within ranking theory. The main purpose of the paper, though, is not to settle a dispute with formal epistemology, but rather to emphasize the importance of formal methods to the whole of epistemology.

In this book Pollock deals with the subject of probabilistic reasoning, making general philosophical sense of objective probabilities and exploring their ...

Probability is sometimes regarded as a universal panacea for epistemology. It has been supposed that the rationality of belief is almost entirely a matter of probabilities. Unfortunately, those philosophers who have thought about this most extensively have tended to be probability theorists first, and epistemologists only secondarily. In my estimation, this has tended to make them insensitive to the complexities exhibited by epistemic justification. In this paper I propose to turn the tables. I begin by laying out some rather simple and uncontroversial features of the structure of epistemic justification, and then go on to ask what we can conclude about the connection between epistemology and probability in the light of those features. My conclusion is that probability plays no central role in epistemology. This is not to say that probability plays no role at all. In the course of the investigation, I defend a pair of probabilistic acceptance rules which enable us, under some circumstances, to arrive at justified belief on the basis of high probability. But these rules are of quite limited scope. The effect of there being such rules is merely that probability provides one source for justified belief, on a par with perception, memory, etc. There is no way probability can provide a universal cure for all our epistemological ills.

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.