
157Sets and worlds againAnalysis 72 (2): 304309. 2012.Bringsjord (1985) argues that the definition W of possible worlds as maximal possible sets of propositions is incoherent. Menzel (1986a) notes that Bringsjord’s argument depends on the Powerset axiom and that the axiom can be reasonably denied. Grim (1986) counters that W can be proved to be incoherent without Powerset. Grim was right. However, the argument he provided is deeply flawed. The purpose of this note is to detail the problems with Grim’s argument and to present a sound alternative arg…Read more

117On Set Theoretic Possible WorldsAnalysis 46 (2). 1986.In his paper "Are There Set Theoretic Possible Worlds?", Selmer Bringsjord argued that the set theoretic definition of possible worlds proffered by, among others, Robert Adams and Alvin Plantinga is incoherent. It is the purpose of this note to evaluate that argument. The upshot: these set theoretic accounts can be preserved, but only by abandoning the power set axiom.

60Frege Numbers and the Relativity ArgumentCanadian Journal of Philosophy 18 (1): 8798. 1988.Textual and historical subtleties aside, let's call the idea that numbers are properties of equinumerous sets ‘the Fregean thesis.’ In a recent paper, Palle Yourgrau claims to have found a decisive refutation of this thesis. More surprising still, he claims in addition that the essence of this refutation is found in the Grundlagen itself – the very masterpiece in which Frege first proffered his thesis. My intention in this note is to evaluate these claims, and along the way to shed some light on…Read more

182ActualismStanford Encyclopedia of Philosophy. 2008.To understand the thesis of actualism, consider the following example. Imagine a race of beings — call them ‘Aliens’ — that is very different from any lifeform that exists anywhere in the universe; different enough, in fact, that no actually existing thing could have been an Alien, any more than a given gorilla could have been a fruitfly. Now, even though there are no Aliens, it seems intuitively the case that there could have been such things. After all, life might have evolved very differentl…Read more

145The objective conception of context and its logicMinds and Machines 9 (1): 2956. 1999.In this paper, an objective conception of contexts based loosely upon situation theory is developed and formalized. Unlike subjective conceptions, which take contexts to be something like sets of beliefs, contexts on the objective conception are taken to be complex, structured pieces of the world that (in general) contain individuals, other contexts, and propositions about them. An extended firstorder language for this account is developed. The language contains complex terms for propositions, …Read more

922Problems with the Bootstrapping Objection to Theistic ActivismAmerican Philosophical Quarterly 53 (1): 5568. 2016.According to traditional theism, God alone exists a se, independent of all other things, and all other things exist ab alio, i.e., God both creates them and sustains them in existence. On the face of it, divine "aseity" is inconsistent with classical Platonism, i.e., the view that there are objectively existing, abstract objects. For according to the classical Platonist, at least some abstract entities are wholly uncreated, necessary beings and, hence, as such, they also exist a se. The thesis o…Read more

152Worlds and Propositions Set FreeErkenntnis 79 (4). 2014.The authors provide an objecttheoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent objecttheoretic versions of the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory in the definition of worl…Read more

143Singular Propositions and Modal LogicPhilosophical Topics 21 (2): 113148. 1993.According to many actualists, propositions, singular propositions in particular, are structurally complex, that is, roughly, (i) they have, in some sense, an internal structure that corresponds rather directly to the syntactic structure of the sentences that express them, and (ii) the metaphysical components, or constituents, of that structure are the semantic values — the meanings — of the corresponding syntactic components of those sentences. Given that reference is "direct", i.e., that the me…Read more

629On the iterative explanation of the paradoxesPhilosophical Studies 49 (1). 1986.As the story goes, the source of the paradoxes of naive set theory lies in a conflation of two distinct conceptions of set: the socalled iterative, or mathematical, conception, and the Fregean, or logical, conception. While the latter conception is provably inconsistent, the former, as Godel notes, "has never led to any antinomy whatsoever". More important, the iterative conception explains the paradoxes by showing precisely where the Fregean conception goes wrong by enabling us to distinguish …Read more

86Haecceities and Mathematical StructuralismPhilosophia Mathematica 26 (1): 84111. 2018.Recent work in the philosophy of mathematics has suggested that mathematical structuralism is not committed to a strong form of the Identity of Indiscernibles (II). José Bermúdez demurs, and argues that a strong form of II can be warranted on structuralist grounds by countenancing identity properties, or haecceities, as legitimately structural. Typically, structuralists dismiss such properties as obviously nonstructural. I will argue to the contrary that haecceities can be viewed as structural …Read more

45A Complete, TypeFree "SecondOrder" Logic and its Philosophical FoundationsCSLI Publications. 1986.In this report I motivate and develop a typefree logic with predicate quantifiers within the general ontological framework of properties, relations, and propositions. In Part I, I present the major ideas of the system informally and discuss its philosophical significance, especially with regard to Russell's paradox. In Part II, I prove the soundness, consistency, and completeness of the logic

242Theism, Platonism, and the Metaphysics of MathematicsFaith and Philosophy 4 (4): 365382. 1987.In a previous paper, Thomas V. Morris and I sketched a view on which abstract objects, in particular, properties, relations, and propositions , are created by God no less than contingent, concrete objects. In this paper r suggest a way of extending this account to cover mathematical objects as well. Drawing on some recent work in logic and metaphysics, I also develop a more detailed account of the structure of PRPs in answer to the paradoxes that arise on a naive understanding of the structure o…Read more

21Structuralism and Conceptual Change in MathematicsPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990. 1990.I address Grosholz's critique of Resnik's mathematical structuralism and suggest that although Resnik's structuralism is not without its difficulties it survives Grosholz's attacks.
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Actualism and Possibilism 