-
106A puzzle about naturalismMetaphilosophy 41 (5): 642-648. 2010.Abstract: This article presents and solves a puzzle about methodological naturalism. Trumping naturalism is the thesis that we must accept p if science sanctions p, and biconditional naturalism the apparently stronger thesis that we must accept p if and only if science sanctions p. The puzzle is generated by an apparently cogent argument to the effect that trumping naturalism is equivalent to biconditional naturalism. It turns out that the argument for this equivalence is subtly question-begging…Read more
-
30Should the Logic of Set Theory be Intuitionistic?: Graduate Papers from the Joint Session 2000Proceedings of the Aristotelian Society 101 (3): 369-378. 2001.The paper critically examines whether the open-endedness of the set concepts mandates the use of intuitionistic logic in set theory, as some philosophers think. [The sequel to this paper is ‘The Open-Endedness of the Set Concept and the Semantics of Set Theory' published in Synthese in 2003.]
-
337Proving InductionAustralasian Journal of Logic 10 1-17. 2011.The hard problem of induction is to argue without begging the question that inductive inference, applied properly in the proper circumstances, is conducive to truth. A recent theorem seems to show that the hard problem has a deductive solution. The theorem, provable in ZFC, states that a predictive function M exists with the following property: whatever world we live in, M ncorrectly predicts the world’s present state given its previous states at all times apart from a well-ordered subset. On th…Read more
-
79How to type: Reply to HalbachAnalysis 69 (2): 280-286. 2009.In my paper , I noted that Fitch's argument, which purports to show that if all truths are knowable then all truths are known, can be blocked by typing knowledge. If there is not one knowledge predicate, ‘ K’, but infinitely many, ‘ K 1’, ‘ K 2’, … , then the type rules prevent application of the predicate ‘ K i’ to sentences containing ‘ K i’ such as ‘ p ∧¬ K i⌜ p⌝’. This provides a motivated response to Fitch's argument so long as knowledge typing is itself motivated. It was the burden of my p…Read more
-
319Defining ultimate ontological basis and the fundamental layerPhilosophical Quarterly 60 (238): 169-175. 2010.I explain why Ross Cameron's definition of ultimate ontological basis is incorrect, and propose a different definition in terms of ontological dependence, as well as a definition of reality's fundamental layer. These new definitions cover the conceptual possibility that self-dependent entities exist. They also apply to different conceptions of the relation of ontological dependence.
-
208Resemblance theories of propertiesPhilosophical Studies 157 (3): 361-382. 2012.The paper aims to develop a resemblance theory of properties that technically improves on past versions. The theory is based on a comparative resemblance predicate. In combination with other resources, it solves the various technical problems besetting resemblance nominalism. The paper’s second main aim is to indicate that previously proposed resemblance theories that solve the technical problems, including the comparative theory, are nominalistically unacceptable and have controversial philosop…Read more
-
124Motivating reductionism about setsAustralasian Journal of Philosophy 86 (2). 2008.The paper raises some difficulties for the typical motivations behind set reductionism, the view that sets are reducible to entities identified independently of set theory.
-
78Against the Judgment-Dependence of Mathematics and LogicErkenntnis 76 (1): 23-40. 2012.Although the case for the judgment-dependence of many other domains has been pored over, surprisingly little attention has been paid to mathematics and logic. This paper presents two dilemmas for a judgment-dependent account of these areas. First, the extensionality-substantiality dilemma: in each case, either the judgment-dependent account is extensionally inadequate or it cannot meet the substantiality condition (roughly: non-vacuous specification). Second, the extensionality-extremality dilem…Read more
-
87The subtraction argument(s)Dialectica 60 (2). 2006.The subtraction argument aims to show that there is an empty world, in the sense of a possible world with no concrete objects. The argument has been endorsed by several philosophers. I show that there are currently two versions of the argument around, and that only one of them is valid. I then sketch the main problem for the valid version of the argument
-
225Proofs of the Compactness TheoremHistory and Philosophy of Logic 31 (1): 73-98. 2010.In this study, several proofs of the compactness theorem for propositional logic with countably many atomic sentences are compared. Thereby some steps are taken towards a systematic philosophical study of the compactness theorem. In addition, some related data and morals for the theory of mathematical explanation are presented
-
179Justifying induction mathematically: Strategies and functionsLogique Et Analyse 51 (203): 263. 2008.If the total state of the universe is encodable by a real number, Hardin and Taylor have proved that there is a solution to one version of the problem of induction, or at least a solution to a closely related epistemological problem. Is this philosophical application of the Hardin-Taylor result modest enough? The paper advances grounds for doubt. [A longer and more detailed sequel to this paper, 'Proving Induction', was published in the Australasian Journal of Logic in 2011.]
-
342Naturalism in mathematics and the authority of philosophyBritish Journal for the Philosophy of Science 56 (2): 377-396. 2005.Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I begin by showing that neither form of naturalism …Read more
-
153Naturalism in the Philosophy of MathematicsIn Ed Zalta (ed.), Stanford Encyclopedia of Philosophy, Stanford Encyclopedia of Philosophy. 2012.Contemporary philosophy’s three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion’s share of the attention, so we concentrate on this. Ontological…Read more
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Epistemology |
Metaphysics |
Philosophy of Religion |