2022: Tacking by conjunction, genuine confirmation and convergence to certainty (original) (raw)

2020: Genuine Confirmation and Tacking by Conjunction

2020

Tacking by conjunction is a deep problem for Bayesian confirmation theory. It is based on the insight that to each hypothesis h that is confirmed by a piece of evidence e one can 'tack' an irrelevant hypothesis h 0 so that h6h 0 is also confirmed by e. This seems counterintuitive. Existing Bayesian solution proposals try to soften the negative impact of this result by showing that although h6h 0 is confirmed by e, it is so only to a lower degree. In this article we outline some problems of these proposals and develop an alternative solution based on a new concept of confirmation that we call genuine confirmation. After pointing out that genuine confirmation is a necessary condition for cumulative confirmation we apply this notion to the tacking by conjunction problem. We consider both the question of what happens when irrelevant hypotheses are added to a hypothesis h that is confirmed by e as well as the question of what happens when h is disconfirmed. The upshot of our discussion will be that genuine confirmation provides a robust solution for each of the different perspectives.

A Classic of Bayesian Confirmation Theory

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

Bayesian Confirmation by Uncertain Evidence: A Reply to Huber [2005]

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.

Chapter 7 Towards a Grammar of Bayesian Confirmation

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...

STUDIES IN BAYESIAN CONFIRMATION THEORY

2001

According to Bayesian confirmation theory, evidence E (incrementally) confirms (or supports) a hypothesis H (roughly) just in case E and H are positively probabilistically correlated (under an appropriate probability function Pr). There are many logically equivalent ways of saying that E and H are correlated under Pr.

An objective Bayesian account of confirmation

This paper revisits Carnap's theory of degree of confirmation, identifies certain shortcomings, and argues that a new approach based on objective Bayesian epistemology can overcome these shortcomings.

Unfolding the Grammar of Bayesian Confirmation: Likelihood and Antilikelihood Principles

We explore the grammar of Bayesian confirmation by focusing on some likelihood principles , including the Weak Law of Likelihood. We show that none of the likelihood principles proposed so far is satisfied by all incremental measures of confirmation, and we argue that some of these measures indeed obey new, prima facie strange, antilikelihood principles. To prove this, we introduce a new measure that violates the Weak Law of Likelihood while satisfying a strong antilikelihood condition. We conclude by hinting at some relevant links between the likelihood principles considered here and other properties of Bayesian confirmation recently explored in the literature.

A Bayesian account of establishing

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.

On Bayesian Measures of Evidential Support: Theoretical and Empirical Issues

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.

The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity

Philosophy of Science, 1999

Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity.