Discussing the relations between logic and probability, this book compares classical 17th- and 18th-century theories of probability with contemporary theories, explores recent logical theories of probability, and offers a new account of probability as a part of logic.

Ramsey's “Facts and Propositions” is terse, allusive, and dense. The paper is far from easy to understand. The present essay is an effort, largely following Brian Loar's account,1 to say what Ramsey's goal is, to spell out what he took to be the means to accomplish it, and to show how those means, at least in the terms of F&P, cannot accomplish that end. I also contrast Loar's own account of judgment, explicitly modeled on Ramsey's view, with the latter. The (...) exercise is not at all academic. Loar makes clear the striking depth and originality of Ramsey's insights. (shrink)

How does deductive logic constrain probability? This question is difficult for subjectivistic approaches, according to which probability is just strength of (prudent) partial belief, for this presumes logical omniscience. This paper proposes that the way in which probability lies always between possibility and necessity can be made precise by exploiting a minor theorem of de Finetti: In any finite set of propositions the expected number of truths is the sum of the probabilities over the set. This is generalized to apply (...) to denumerable languages. It entails that the sum of probabilities can neither exceed nor be exceeded by the cardinalities of all consistent and closed (within the set) subsets. In general any numerical function on sentences is said to be logically coherent if it satisfies this condition. Logical coherence allows the relativization of necessity: A function p on a language is coherent with respect to the concept T of necessity iff there is no set of sentences on which the sum of p exceeds or is exceeded by the cardinality of every T-consistent and T-closed (within the set) subset of the set. Coherence is easily applied as well to sets on which the sum of p does not converge. Probability should also be relativized by necessity: A T-probability assigns one to every T-necessary sentence and is additive over disjunctions of pairwise T-incompatible sentences. Logical T-coherence is then equivalent to T-probability: All and only T-coherent functions are T-probabilities. (shrink)

The main sources here are Hume, Husserl, and De Finetti. The problem is how phenomenological investigation has to do with partial or probabilistic judgment. Behavioristic, frequentist and subjectivistic views are briefly surveyed. A variant of Hume's account of the probability of chances is developed with the help of De Finetti's concept of exchangeability. The question of transcendental elements in or behind partial judgment is considered in the light of understanding disagreement and error in partial judgment.

In this paper I consider the question of the reality of chance. This is not what divides contemporary probabilists into the objective and subjective schools. That division is accomplished by the question whether there are objective grounds for the correctness of probability judgments. The subjectivists say that there need not be such grounds, and that probability judgments thus need not be empirically meaningful in the verificationist sense, or perhaps that they are not judgments at all, but rather expressions of attitude. (...) (See [11], pp. 156-198). The objectivists say that the truth conditions for probability judgments are such as the frequencies of traits in populations or the existence of propensities. Objectivists and subjectivists are, however, agreed that there are no objective chances. (See [2], pp. 141, 142; and [12], §16).There is a Humean argument against the reality of chance which depends mainly upon the premise that we have no experience of it. (shrink)

Ramsey's “Facts and Propositions” is terse, allusive, and dense. The paper is far from easy to understand. The present essay is an effort, largely following Brian Loar's account,1 to say what Ramsey's goal is, to spell out what he took to be the means to accomplish it, and to show how those means, at least in the terms of F&P, cannot accomplish that end. I also contrast Loar's own account of judgment, explicitly modeled on Ramsey's view, with the latter. The (...) exercise is not at all academic. Loar makes clear the striking depth and originality of Ramsey's insights. (shrink)

The interpretation of the calculus of probability as a logic of partial belief has at least two advantages: it makes the assignment of probabilities plausible in cases where classical frequentist interpretations must find such assignments meaningless, and it gives a clear meaning to partial belief and to consistency of partial belief.

Bioethics, Volume 36, Issue 1, Page 25-41, January 2022.

In Faculty Misconduct in Collegiate Teaching, higher education researchers John Braxton and Alan Bayer address issues of impropriety and misconduct in the teaching role at the postsecondary level. Braxton and Bayer define and examine norms of teaching behavior: what they are, how they come to exist, and how transgressions are detected and addressed. Do faculty members across various collegiate settings, for example, share views about appropriate and inappropriate teaching behaviors, as they share expectations regarding actions related to research? And (...) what mechanisms are utilized to correct inappropriate behavior on the part of college and university teachers? The authors' work is based on survey results obtained from faculty members at research universities, liberal arts colleges, and two-year community, junior, and technical colleges. Braxton and Bayer's focus is on undergraduate teaching in four disciplines: biology, history, mathematics, and psychology. In their analyses, the authors examine how individual, disciplinary, and institutional differences influence professorial behavior. In contrast to the more explicitly understood and enforced rules of conduct in research, the authors find that teaching norms are informally defined and observed. They argue that a formal code of ethics for undergraduate teaching would serve the dual purpose of improving undergraduate education and elevating the status of college teaching. A groundbreaking study of contemporary academe, Faculty Misconduct in Collegiate Teaching is required reading for all university and college instructors and administrators. (shrink)