
A Proof Of Completeness For Continuous Firstorder LogicJournal of Symbolic Logic 75 (1): 168190. 2010.Continuous firstorder logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures to various natural classes of complete metric structures. With research in continuous firstorder logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result?The primary purpose of this article is to show that a certain, interesting set …Read more

Dilation, Disintegrations, and Delayed DecisionsIn Thomas Augistin, Serena Dora, Enrique Miranda & Erik Quaeghebeur (eds.), Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2015), Aracne Editrice. 2015.Both dilation and nonconglomerability have been alleged to conflict with a fundamental principle of Bayesian methodology that we call \textit{Good's Principle}: one should always delay making a terminal decision between alternative courses of action if given the opportunity to first learn, at zero cost, the outcome of an experiment relevant to the decision. In particular, both dilation and nonconglomerability have been alleged to permit or even mandate choosing to make a terminal decision in …Read more

Fast and frugal heuristics: rationality and the limits of naturalismSynthese 190 (5): 831850. 2013.Gerd Gigerenzer and Thomas Sturm have recently proposed a modest form of what they describe as a normative, ecological and limited naturalism. The basic move in their argument is to infer that certain heuristics we tend to use should be used in the right ecological setting. To address this argument, we first consider the case of a concrete heuristic called Take the Best (TTB). There are at least two variants of the heuristic which we study by making explicit the choice functions they induce, ext…Read more

Continuous firstorder logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous firstorder logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding…Read more

What Language Dependence Problem? A Reply for Joyce to Fitelson on JoycePhilosophy of Science 79 (4): 561574. 2012.In an essay recently published in this journal, Branden Fitelson argues that a variant of Miller’s argument for the language dependence of the accuracy of predictions can be applied to Joyce’s notion of accuracy of credences formulated in terms of scoring rules, resulting in a general potential problem for Joyce’s argument for probabilism. We argue that no relevant problem of the sort Fitelson supposes arises since his main theorem and his supporting arguments presuppose the validity of nonlinea…Read more

This article elaborates on foundational issues in the social sciences and their impact on the contemporary theory of belief revision. Recent work in the foundations of economics has focused on the role external social norms play in choice. Amartya Sen has argued in [Sen93] that the traditional rationalizability approach used in the theory of rational choice has serious problems accommodating the role of social norms. Sen's more recent work [Sen96, Sen97] proposes how one might represent social n…Read more

Comparative ExpectationsStudia Logica 102 (4): 811848. 2014.I introduce a mathematical account of expectation based on a qualitative criterion of coherence for qualitative comparisons between gambles (or random quantities). The qualitative comparisons may be interpreted as an agent’s comparative preference judgments over options or more directly as an agent’s comparative expectation judgments over random quantities. The criterion of coherence is reminiscent of de Finetti’s quantitative criterion of coherence for betting, yet it does not impose an Archime…Read more

A proof of completeness for continuous firstorder logicJournal of Symbolic Logic 75 (1): 168190. 2010.Continuous firstorder logic has found interest among model theorists who wish to extend the classical analysis of "algebraic" structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous firstorder logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding…Read more

Demystifying DilationErkenntnis 79 (6): 13051342. 2014.Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that …Read more

An extension theorem and a numerical representation theorem for qualitative comparative expectationsStudia Logica. forthcoming.