• In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that satisf…Read more
  • Frege's Begriffsschrift is Indeed First-Order Complete
    History and Philosophy of Logic 38 (4): 342-344. 2017.
    It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the first-order comple…Read more
  • "Click!" Bait for Causalists
    with Huw Price
    In Arif Ahmed (ed.), Newcomb's Problem, Cambridge University Press. pp. 160-179. 2018.
    Causalists and Evidentialists can agree about the right course of action in an (apparent) Newcomb problem, if the causal facts are not as initially they seem. If declining $1,000 causes the Predictor to have placed $1m in the opaque box, CDT agrees with EDT that one-boxing is rational. This creates a difficulty for Causalists. We explain the problem with reference to Dummett's work on backward causation and Lewis's on chance and crystal balls. We show that the possibility that the causal facts …Read more
  • Heart of DARCness
    with Huw Price
    Australasian Journal of Philosophy 1-15. forthcoming.
    There is a long-standing disagreement in the philosophy of probability and Bayesian decision theory about whether an agent can hold a meaningful credence about an upcoming action, while she deliberates about what to do. Can she believe that it is, say, 70% probable that she will do A, while she chooses whether to do A? No, say some philosophers, for Deliberation Crowds Out Prediction (DCOP), but others disagree. In this paper, we propose a valid core for DCOP, and identify terminological causes …Read more
  • Can an agent deliberating about an action A hold a meaningful credence that she will do A? 'No', say some authors, for 'Deliberation Crowds Out Prediction' (DCOP). Others disagree, but we argue here that such disagreements are often terminological. We explain why DCOP holds in a Ramseyian operationalist model of credence, but show that it is trivial to extend this model so that DCOP fails. We then discuss a model due to Joyce, and show that Joyce's rejection of DCOP rests on terminological choic…Read more
  • The Sure-thing Principle and P2
    Economics Letters 159 221-223. 2017.
    This paper offers a fine analysis of different versions of the well known sure-thing principle. We show that Savage's formal formulation of the principle, i.e., his second postulate (P2), is strictly stronger than what is intended originally.
  • Context-dependent Utilities
    In Wiebe Van Der Hoek, Wesley H. Holliday & Wen Fang Wang (eds.), Logic, Rationality, and Interaction, Springer. pp. 90-101. 2015.
    Savage's framework of subjective preference among acts provides a paradigmatic derivation of rational subjective probabilities within a more general theory of rational decisions. The system is based on a set of possible states of the world, and on acts, which are functions that assign to each state a consequence€. The representation theorem states that the given preference between acts is determined by their expected utilities, based on uniquely determined probabilities (assigned to sets of sta…Read more