•  642
    Problems with the Bootstrapping Objection to Theistic Activism
    American Philosophical Quarterly 53 (1): 55-68. 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
  • LEPORE, E.-Meaning and Argument
    Philosophical Books 44 (1): 69-69. 2003.
  •  141
    Worlds and Propositions Set Free
    Erkenntnis 79 (4). 2014.
    The authors provide an object-theoretic 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 object-theoretic 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
  •  123
  •  134
    Singular Propositions and Modal Logic
    Philosophical Topics 21 (2): 113-148. 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
  •  621
    On the iterative explanation of the paradoxes
    Philosophical 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 so-called 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
  •  70
    Haecceities and Mathematical Structuralism
    Philosophia Mathematica 84-111. 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 non-structural. I will argue to the contrary that haecceities can be viewed as structural …Read more
  •  42
    In this report I motivate and develop a type-free 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
  •  226
    Theism, Platonism, and the Metaphysics of Mathematics
    Faith and Philosophy 4 (4): 365-382. 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
  •  20
    Structuralism and Conceptual Change in Mathematics
    PSA: 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.
  •  561
    Logic, Essence, and Modality — Review of Bob Hale's Necessary Beings (review)
    Philosophia Mathematica 23 (3): 407-428. 2015.
    Bob Hale’s distinguished record of research places him among the most important and influential contemporary analytic metaphysicians. In his deep, wide ranging, yet highly readable book Necessary Beings, Hale draws upon, but substantially integrates and extends, a good deal his past research to produce a sustained and richly textured essay on — as promised in the subtitle — ontology, modality, and the relations between them. I’ve set myself two tasks in this review: first, to provide a reasonabl…Read more
  •  278
    Basic semantic integration
    Semantic Interoperability and Integration, Proceedings of Dagstuhl Seminar 04391. 2004.
    The use of highly abstract mathematical frameworks is essential for building the sort of theoretical foundation for semantic integration needed to bring it to the level of a genuine engineering discipline. At the same time, much of the work that has been done by means of these frameworks assumes a certain amount of background knowledge in mathematics that a lot of people working in ontology, even at a fairly high theoretical level, lack. The major purpose of this short paper is provide a (compar…Read more
  •  71
    On an unsound proof of the existence of possible worlds
    Notre Dame Journal of Formal Logic 30 (4): 598-603. 1989.
    In this paper, an argument of Alvin Plantinga's for the existence of abstract possible worlds is shown to be unsound. The argument is based on a principle Plantinga calls "Quasicompactness", due to its structural similarity to the notion of compactness in first-order logic. The principle is shown to be false.
  •  231
    Temporal actualism and singular foreknowledge
    Philosophical Perspectives 5 475-507. 1991.
    Suppose we believe that God created the world. Then surely we want it to be the case that he intended, in some sense at least, to create THIS world. Moreover, most theists want to hold that God didn't just guess or hope that the world would take one course or another; rather, he KNEW precisely what was going to take place in the world he planned to create. In particular, of each person P, God knew that P was to exist. Call this the "standard" conception. Most theists find the standard conception…Read more
  •  297
    Possibilism and object theory
    Philosophical Studies 69 (2-3). 1993.
    A central stream running through the history of philosophy has been the attempt to gather a wide range of ostensibly disparate intuitive phenomena under a small, integrated set of concepts. Edward Zalta’s work is a sustained celebration of this tradition. This paper — part of a symposium on Zalta's work — is a friendly, but critical examination of Zalta's commitment to possibilism and the roles they play in his theory.
  •  196
    It is almost universally acknowledged that first-order logic (FOL), with its clean, well-understood syntax and semantics, allows for the clear expression of philosophical arguments and ideas. Indeed, an argument or philosophical theory rendered in FOL is perhaps the cleanest example there is of “representing philosophy”. A number of prominent syntactic and semantic properties of FOL reflect metaphysical presuppositions that stem from its Fregean origins, particularly the idea of an inviolable di…Read more