•  1
    Structuralism and Conceptual Change in Mathematics
    PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990 (2): 397-401. 1990.
    Professor Grosholz packs a lot into her interesting and suggestive paper “Formal Unities and Real Individuals” (Grosholz 1990b). In the limited space available I can comment briefly on its several parts, or direct more substantive comments at a single issue. I will opt for the latter; specifically, I want to address her critique of mathematical structuralism, as found especially in the writings of Michael Resnik.I begin with a brief, hence necessarily caricatured, summary of Resnik’s influential…Read more
  •  270
    The basic notion of justification
    Philosophical Studies 59 (3): 235-261. 1990.
    Epistemologists often offer theories of justification without paying much attention to the variety and diversity of locutions in which the notion of justification appears. For example, consider the following claims which contain some notion of justification: B is a justified belief, S's belief that p is justified, p is justified for S, S is justified in believing that p, S justifiably believes that p, S's believing p is justified, there is justification for S to believe that p, there is justific…Read more
  •  580
    Pure Logic and Higher-order Metaphysics
    In Peter Fritz & Nicholas K. Jones (eds.), Higher-order Metaphysics, Oxford University Press. 2023.
    W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing b…Read more
  •  88
    The Possibilism-Actualism Debate
    The Stanford Encyclopedia of Philosophy. 2022.
    Actualism is a widely-held view in the metaphysics of modality that arises in response to the thesis of possibilism, the doctrine that, in addition to the things that actually exist — in particular, things that exist alongside us in the causal order — there are merely possible things as well, things that, in fact, fail to be actual but which could have been. The central motivation for possibilism is to explain what it is about reality that grounds such intuitively true propositions as that Wittg…Read more
  •  9
    Proceedings of the KI 2003 Workshop on Reference Ontologies and Application Ontologies (edited book)
    with Pierre Grenon and Barry Smith
    CEUR Workshop Proceedings, Vol. 94. 2004.
    Contains the following contributions: Ingvar Johansson: Ontologies and Concepts. Two Proposals Christopher Menzel: Reference Ontologies - Application Ontologies: Either/Or or Both/And? Luc Schneider: Foundational Ontologies and the Realist Bias Guenther Goerz, Kerstin Buecher, Bernd Ludwig, Frank-Peter Schweinberger, and Iman Thabet: Combining a Lexical Taxonomy with Domain Ontology in the Erlangen Dialogue System Vim Vandenberghe, Burkhard Schafer, John Kingston: Ontology Modelling in the Lega…Read more
  •  1082
    In Defense of the Possibilism–Actualism Distinction
    Philosophical Studies 177 (7): 1971-1997. 2020.
    In Modal Logic as Metaphysics, Timothy Williamson claims that the possibilism-actualism (P-A) distinction is badly muddled. In its place, he introduces a necessitism-contingentism (N-C) distinction that he claims is free of the confusions that purportedly plague the P-A distinction. In this paper I argue first that the P-A distinction, properly understood, is historically well-grounded and entirely coherent. I then look at the two arguments Williamson levels at the P-A distinction and find them …Read more
  •  303
    The IDEF family of languages
    In Peter Bernus, Kai Mertins & Günter J. Schmidt (eds.), Handbook on Architectures of Information Systems, Springer-verlag. pp. 209-241. 1998.
    Summary. The purpose of this article is to serve as a clear introduction to the modeling languages of the three most widely used IDEF methods: IDEF0, IDEF1X, and IDEF3. Each language is presented in turn, beginning with a discussion of the underlying “ontology” the language purports to describe, followed by presentations of the syntax of the language — particularly the notion of a model for the language — and the semantical rules that determine how models are to be interpreted. The level of deta…Read more
  •  64
    Ontology theory
    In Jerome Euzenat, Asuncion Gomez-Perez, Nicola Guarino & Heiner Stuckenschmidt (eds.), CEUR Workshop Proceedings, Vol. 64, . 2002.
    Ontology today is in many ways in a state similar to that of analysis in the late 18th century prior to arithmetization: it lacks the sort rigorous theoretical foundations needed to elevate ontology to the level of a genuine scientific discipline. This paper attempts to make some first steps toward the development of such foundations. Specifically, starting with some basic intuitions about ontologies and their content, I develop an expressively rich framework capable of treating ontologies as th…Read more
  •  70
    Reference ontologies — application ontologies: Either/or or both/and?
    In Pierre Grenon, Christopher Menzel & Barry Smith (eds.), Proceedings of the KI 2003 Workshop on Reference Ontologies and Application Ontologies, Ceur Workshop Proceedings, Vol. 94. 2004.
    The distinction between reference ontologies and application ontologies crept rather unobtrusively into the recent literature on knowledge engineering. A lot of the discourse surrounding this distinction – notably, the one framing the workshop generating this collection of papers – suggests the two types of ontologies are in some sort of opposition to one another. Thus, Borge et al. [3] characterize reference ontologies (more recently, foundational ontologies) as rich, axiomatic theories whose f…Read more
  •  4
    Providing a means of translating RDF, RDF-S, and DAML+OIL descriptions into a first-order predicate calculus logical theory not only specifies the intended meaning of the descriptions, but also produces a representation of the descriptions from which inferences can automatically be made using traditional automatic theorem provers and problem solvers. For example, the DAML+OIL axioms enable a reasoner to infer from the two statements “Class Male and class Female are disjointWith.” and “John is ty…Read more
  • Mathematical Realism and the Theory of Sets
    Dissertation, University of Notre Dame. 1984.
    Set theoretic platonism is the view that there exist objective, mind-independent abstract sets, and that set theory is the science of these entities. For the realist, this view offers the most natural semantical account of set theoretic discourse. Nonetheless, set theoretic platonism is beset by a number of serious difficulties. Chief among these, it turns out, is that it must deny the fundamental set theoretic intuition that any available objects can be collected into a further object. After a …Read more
  •  1590
    Modal set theory
    In Otávio Bueno & Scott A. Shalkowski (eds.), The Routledge Handbook of Modality, Routledge. 2018.
    This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.
  •  1313
    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
  •  5
    Meaning and Argument (review)
    Philosophical Books 44 (1): 69-70. 2003.
    A review of the 1st edition of Lepore's Meaning and Argument, in which the reviewer (me), on the one hand, says that the text contains no proof theory and, on the other, subsequently notes that Lepore makes use of the truth tree method. I guess, at the time, I thought that only axiomatic systems and natural deduction systems fell under the rubric "proof theory". Sorry. Other than that I suppose the review is mildly informative.
  •  213
    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
  •  174
  •  157
    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
  •  641
    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
  •  117
    Haecceities and Mathematical Structuralism
    Philosophia Mathematica 26 (1): 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
  •  46
    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
  •  259
    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
  •  23
    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.
  •  846
    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
  •  473
    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
  •  93
    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.
  •  250
    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
  •  310
    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.