Likelihoodism, Bayesianism, and relational confirmation

Philosophical Perspectives, 2005

Many philosophers think of Bayesianism as a theory of practical rationality. This is not at all surprising given that the view's most striking successes have come in decision theory. Ramsey (1931), Savage (1972), and De Finetti (1964) showed how to interpret subjective degrees of belief in terms of betting behavior, and how to derive the central probabilistic requirement of coherence from reflections on the nature of rational choice. This focus on decision-making can obscure the fact that Bayesianism is also an epistemology. Indeed, the great statistician Harold Jeffries (1939), who did more than anyone else to further Bayesian methods, paid rather little heed to the work of Ramsey, de Finetti, and Savage. Jeffries, and those who followed him, saw Bayesianism as a theory of inductive evidence, whose primary role was not to help people make wise choices, but to facilitate sound scientific reasoning. 1 This paper seeks to promote a broadly Bayesian approach to epistemology by showing how certain central questions about the nature of evidence can be addressed using the apparatus of subjective probability theory. Epistemic Bayesianism, as understood here, is the view that evidential relationships are best represented probabilistically. It has three central components: Evidential Probability. At any time t, a rational believer's opinions can be faithfully modeled by a family of probability functions C t , hereafter called her credal state, 2 the members of which accurately reflect her total evidence at t. Learning as Bayesian Updating. Learning experiences can be modeled as shifts from one credal state to another that proceed in accordance with Bayes's Rule. Confirmational Relativity. A wide range of questions about evidential relationships can be answered on the basis of information about structural features credal states. The first of these three theses is most fundamental. Much of what Bayesians say about learning and confirmation only makes sense if probabilities in credal

The British Journal for the Philosophy of Science, 2021

When a proposition is established, it can be taken as evidence for other propositions. Can the Bayesian theory of rational belief and action provide an account of establishing? I argue that it can, but only if the Bayesian is willing to endorse objective constraints on both probabilities and utilities, and willing to deny that it is rationally permissible to defer wholesale to expert opinion. I develop a new account of deference that accommodates this latter requirement.

Nous, 2001

Philosophy of Science, 2007

Epistemologists and philosophers of science have often attempted to express formally the impact of a piece of evidence on the credibility of a hypothesis. In this paper we will focus on the Bayesian approach to evidential support. We will propose a new formal treatment of the notion of degree of confirmation and we will argue that it overcomes some limitations of the currently available approaches on two grounds: (i) a theoretical analysis of the confirmation relation seen as an extension of logical deduction and (ii) an empirical comparison of competing measures in an experimental inquiry concerning inductive reasoning in a probabilistic setting.

Philosophy of statistics, handbook of …, 2011

Wheeler, Gregory and Williamson, Jon (2011) Evidential probability and objective Bayesian epistemology. In: Philosophy of statistics. Handbook of the Philosophy of Science . Elsevier, pp. 307-331. ... The full text of this publication is not available from this repository.

Philosophical Foundations of Evidence Law, 2021

While the laws of probability are rarely disputed, the question of how we should interpret probability judgments is less straightforward. Broadly, there are two ways to conceive of probability—either as an objective feature of the world, or as a subjective measure of our uncertainty. Both notions have their place in science, but it is the latter subjective notion (the Bayesian approach) that is crucial in legal reasoning. This chapter explains the advantages of using Bayesian networks in adjudicative factfinding. It addresses a number of common objections to the Bayesian approach, such as “There is no such thing as a probability of a single specified event”; “The Bayesian approach only works with statistical evidence”; “The Bayesian approach is too difficult for legal factfinders to comprehend”; and “A Bayesian network can never capture the full complexity of a legal case.” Fenton and Lagnado offer rebuttals to each of these objections.

The British Journal for the Philosophy of Science, 2008

Bayesian epistemology postulates a probabilistic analysis of many sorts of ordinary and scientific reasoning. Huber ([2005]) has provided a novel criticism of Bayesianism, whose core argument involves a challenging issue: confirmation by uncertain evidence. In this paper, we argue that under a properly defined Bayesian account of confirmation by uncertain evidence, Huber's criticism fails. By contrast, our discussion will highlight what we take as some new and appealing features of Bayesian confirmation theory.

Artificial Intelligence, 1992

Belief functions are mathematical objects defined to satisfy three axioms that look somewhat similar to the Kolmogorov axioms defining probability functions. We argue that there are (at least) two useful and quite different ways of understanding belief functions. The first is as a generalized probability function (which technically corresponds to the inner measure induced by a probability function). The second is as a way of representing evidence. Evidence, in turn, can be understood as a mapping from probability functions to probability functions. It makes sense to think of updating a belief if we think of it as a generalized probability. On the other hand, it makes sense to combine two beliefs (using, say, Dempster's rule of combination) only if we think of the belief functions as representing evidence. Many previous papers have pointed out problems with the belief function approach; the claim of this paper is that these problems can be explained as a consequence of confounding these two views of belief functions.

2011

A long standing tradition in epistemology and the philosophy of science sees the notion of confirmation as a fundamental relationship between a piece of evidence E and a hypothesis H. A number of philosophical accounts of confirmation, moreover, have been cast or at least could be cast in terms of a formally defined model c.H; E/ involving evidence and hypothesis.1 Ideally, a full-fledged and satisfactory confirmation model c.H; E/ would meet a series of desiderata, including the following: (1) c.H; E/ should be grounded on some simple and intuitively appealing “core intuition”; (2) c.H; E/ should exhibit a set of properties which formally express sound intuitions; (3) it should be possible to specify the role and relevance of c.H; E/ in science as well as in other forms of inquiry. In what follows we will focus on accounts of confirmation arising from the Bayesian framework and we will mainly address issues (1) and (2). Bayesianism arguably is a major theoretical perspective in con...

Book review of Paul Horwich, Probability and Evidence (Cambridge Philosophy Classics edition), Cambridge: Cambridge University Press, 2016, 147pp, £14.99 (paperback).