
9Ramsey on Judgment: The Theory of “Facts and Propositions”Dialectica 58 (4): 499516. 2004.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…Read more

7Rules for Reasonable Belief ChangeIn Radu J. Bogdan & Ilkka Niiniluoto (eds.), Logic, Language, and Probability, D. Reidel Pub. Co.. pp. 129142. 1973.

25Some remarks on coherence and subjective probabilityPhilosophy of Science 32 (1): 3238. 1965.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

74I believe it, but soon I'll not believe it any more: Scepticism, empiricism, and reflectionSynthese 124 (2): 155174. 2000.

37On successors of Jónsson cardinalsArchive for Mathematical Logic 39 (6): 465473. 2000.We show that, like singular cardinals, and weakly compact cardinals, Jensen's core model K for measures of order zero [4] calculates correctly the successors of Jónsson cardinals, assuming $O^{Sword}$ does not exist. Namely, if $\kappa$ is a Jónsson cardinal then $\kappa^+ = \kappa^{+K}$ , provided that there is no nontrivial elementary embedding $j:K \longrightarrow K$ . There are a number of related results in ZFC concerning $\cal{P}(\kappa)$ in V and inner models, for $\kappa$ a Jónsson or s…Read more

219Logic, probability, and coherencePhilosophy of Science 68 (1): 95110. 2001.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. Thi…Read more

2Chance and Structure: An Essay on the Logical Foundations of ProbabilityOxford University Press. 1988.Discussing the relations between logic and probability, this book compares classical 17th and 18thcentury theories of probability with contemporary theories, explores recent logical theories of probability, and offers a new account of probability as a part of logic.

72Ramsey on judgment: The theory of "facts and propositions"Dialectica 58 (4). 2004.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…Read more

23Definability and logical structure in FregeJournal of the History of Philosophy 17 (3): 291308. 1979.

239On elementary embeddings from an inner model to the universeJournal of Symbolic Logic 66 (3): 10901116. 2001.We consider the following question of Kunen: Does Con(ZFC + ∃M a transitive inner model and a nontrivial elementary embedding j: M $\longrightarrow$ V) imply Con (ZFC + ∃ a measurable cardinal)? We use core model theory to investigate consequences of the existence of such a j: M → V. We prove, amongst other things, the existence of such an embedding implies that the core model K is a model of "there exists a proper class of almost Ramsey cardinals". Conversely, if On is Ramsey, then such a j, M…Read more

Chance and Structure: An Essay on the Logical Foundations of ProbabilitySynthese 91 (3): 337346. 1992.

12On Elementary Embeddings from an Inner Model to the UniverseJournal of Symbolic Logic 66 (3): 10901116. 2001.We consider the following question of Kunen: Does Con imply Con? We use core model theory to investigate consequences of the existence of such a j : M $\rightarrow$ V. We prove, amongst other things, the existence of such an embedding implies that the core model K is a model of "there exists a proper class of almost Ramsey cardinals". Conversely, if On is Ramsey, then such a j, M are definable. We construe this as a negative answer to the question above. We consider further the consequences of s…Read more