J M Keynes’s 1931 Comment, “…I Yield to Ramsey, I Think He Is Right” Refers to Ramsey’s Work on Precise Probability and Degrees of Belief, Not to Imprecise Probability and Degrees of Rational Belief: 20th and 21st Century Philosophers and Economists Simply Are Ignorant About Keynes’s Imprecise Theory of Probability Contained in Part II of the A Treatise on Probability

Rational belief

Behavioral and Brain Sciences ◽

10.1017/s0140525x00015661 ◽

1983 ◽

Vol 6 (2) ◽

pp. 231-245 ◽

Cited By ~ 152

Author(s):

Henry E. Kyburg

Keyword(s):

Inductive Logic ◽

Bayes Theorem ◽

Rational Belief ◽

Degrees Of Belief ◽

Probability Calculus ◽

Probabilistic Rule ◽

New Evidence ◽

Normative Content ◽

Interval Valued ◽

Made In

AbstractThere is a tension between normative and descriptive elements in the theory of rational belief. This tension has been reflected in work in psychology and decision theory as well as in philosophy. Canons of rationality should be tailored to what is humanly feasible. But rationality has normative content as well as descriptive content.A number of issues related to both deductive and inductive logic can be raised. Are there full beliefs – statements that are categorically accepted? Should statements be accepted when they become overwhelmingly probable? What is the structure imposed on these beliefs by rationality? Are they consistent? Are they deductively closed? What parameters, if any, does rational acceptance depend on? How can accepted statements come to be rejected on new evidenceShould degrees of belief satisfy the probability calculus? Does conformity to the probability calculus exhaust the rational constraints that can be imposed on partial beliefs? With the acquisition of new evidence, should beliefs change in accord with Bayes' theorem? Are decisions made in accord with the principle of maximizing expected utility? Should they be?A systematic set of answers to these questions is developed on the basis of a probabilistic rule of acceptance and a conception of interval-valued logical probability according to which probabilities are based on known frequencies. This leads to limited deductive closure, a demand for only limited consistency, and the rejection of Bayes' theorem as universally applicable to changes of belief. It also becomes possible, given new evidence, to reject previously accepted statements.

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Probabilistic justification logic

Journal of Logic and Computation ◽

10.1093/logcom/exaa011 ◽

2020 ◽

Vol 30 (1) ◽

pp. 257-280

Author(s):

Ioannis Kokkinis ◽

Zoran Ognjanović ◽

Thomas Studer

Keyword(s):

Rational Belief ◽

Satisfiability Problem ◽

Uncertain Reasoning ◽

Justification Logic ◽

Lottery Paradox ◽

Degrees Of Belief ◽

Strong Completeness ◽

Probabilistic Justification ◽

Insight Into

Abstract We present a probabilistic justification logic, $\mathsf{PPJ}$, as a framework for uncertain reasoning about rational belief, degrees of belief and justifications. We establish soundness and strong completeness for $\mathsf{PPJ}$ with respect to the class of so-called measurable Kripke-like models and show that the satisfiability problem is decidable. We discuss how $\mathsf{PPJ}$ provides insight into the well-known lottery paradox.

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Probability theory and epistemology

Routledge Encyclopedia of Philosophy ◽

10.4324/9780415249126-p040-1 ◽

2018 ◽

Author(s):

Barry Loewer

Keyword(s):

Probability Theory ◽

Rational Belief ◽

Bayesian Epistemology ◽

Dutch Book ◽

Degrees Of Belief ◽

Rational Person ◽

Degree Of Belief ◽

New Evidence ◽

Probabilistic Epistemology ◽

Instrumental Goal

The primary uses of probability in epistemology are to measure degrees of belief and to formulate conditions for rational belief and rational change of belief. The degree of belief a person has in a proposition A is a measure of their willingness to act on A to obtain satisfaction of their preferences. According to probabilistic epistemology, sometimes called ‘Bayesian epistemology’, an ideally rational person’s degrees of belief satisfy the axioms of probability. For example, their degrees of belief in A and -A must sum to 1. The most important condition on changing degrees of belief given new evidence is called ‘conditionalization’. According to this, upon acquiring evidence E a rational person will change their degree of belief assigned to A to the conditional probability of A given E. Roughly, this rule says that the change should be minimal while accommodating the new evidence. There are arguments, ‘Dutch book arguments’, that are claimed to demonstrate that failure to satisfy these conditions makes a person who acts on their degrees of belief liable to perform actions that necessarily frustrate their preferences. Radical Bayesian epistemologists claim that rationality is completely characterized by these conditions. A more moderate view is that Bayesian conditions should be supplemented by other conditions specifying rational degrees of belief. Support for Bayesian epistemology comes from the fact that various aspects of scientific method can be grounded in satisfaction of Bayesian conditions. Further, it can be shown that there is a close connection between having true belief as an instrumental goal and satisfaction of the Bayesian conditions. Some critics of Bayesian epistemology reject the probabilistic conditions on rationality as unrealistic. They say that people do not have precise degrees of belief and even if they did it would not be possible in general to satisfy the conditions. Some go further and reject the conditions themselves. Others claim that the conditions are much too weak to capture rationality and that in fact almost any reasoning can be characterized so as to satisfy them. The extent to which Bayesian epistemology contributes to traditional epistemological concerns of characterizing knowledge and methods for obtaining knowledge is controversial.

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