•  9
    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
  • Belief and Probability
    Mind 89 (355): 452-454. 1980.
  • Hans Sluga, "Gottlob Frege" (review)
    Journal of the History of Philosophy 21 (1): 123. 1983.
  •  7
    Rules for Reasonable Belief Change
    In Radu J. Bogdan & Ilkka Niiniluoto (eds.), Logic, Language, and Probability, D. Reidel Pub. Co.. pp. 129--142. 1973.
  •  162
    Some features of theories of belief
    Journal of Philosophy 63 (8): 197-201. 1966.
  •  25
    Gottlob Frege (review)
    Journal of the History of Philosophy 21 (1): 123-124. 1983.
  •  12
    On Elementary Embeddings from an Inner Model to the Universe
    with P. D. Welch
    Journal of Symbolic Logic 66 (3): 1090-1116. 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
  •  25
    Some remarks on coherence and subjective probability
    Philosophy of Science 32 (1): 32-38. 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
  •  39
    Belief and Probability
    with J. P. Day
    Philosophical Quarterly 28 (111): 171. 1978.
  •  37
    On successors of Jónsson cardinals
    with P. D. Welch
    Archive for Mathematical Logic 39 (6): 465-473. 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 non-trivial 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
  •  51
    Characteristics of projectible predicates
    Journal of Philosophy 64 (9): 280-286. 1967.
  •  219
    Logic, probability, and coherence
    Philosophy of Science 68 (1): 95-110. 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
  •  2
    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.
  •  72
    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
  •  239
    On elementary embeddings from an inner model to the universe
    with P. D. Welch
    Journal of Symbolic Logic 66 (3): 1090-1116. 2001.
    We consider the following question of Kunen: Does Con(ZFC + ∃M a transitive inner model and a non-trivial 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