•  21
    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 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 Wittgenstein (who was childless) could ha…Read more
  •  18
    Worlds and Propositions Set Free
    with Edward N. Zalta and Otávio Bueno
    Erkenntnis 79 (4): 797-820. 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
  •  6
    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
  •  785
    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
  •  64
    Reference ontologies — application ontologies: Either/or or both/and?
    In Pierre M. Pierre, Christopher Menzel & Barry Smith (eds.), 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
  •  210
    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
  •  57
    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
  • 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
  •  1029
    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.
  •  247
    The Fundamental Theorem of World Theory
    Journal of Philosophical Logic 43 333-363. 2014.
    The fundamental principle of the theory of possible worlds is that a proposition p is possible if and only if there is a possible world at which p is true. In this paper we present a valid derivation of this principle from a more general theory in which possible worlds are defined rather than taken as primitive. The general theory uses a primitive modality and axiomatizes abstract objects, properties, and propositions. We then show that this general theory has very small models and hence that it…Read more
  •  179
    Possible Worlds
    Stanford Encyclopedia of Philosophy. 2013.
    This article includes a basic overview of possible world semantics and a relatively comprehensive overview of three central philosophical conceptions of possible worlds: Concretism (represented chiefly by Lewis), Abstractionism (represented chiefly by Plantinga), and Combinatorialism (represented chiefly by Armstrong).
  •  59
    Logic and Reality: Essays on the Legacy of Arthur Prior
    Philosophical Review 109 (2): 281. 2000.
    Arthur Prior was a truly philosophical logician. Though he believed formal logic to be worthy of study in its own right, of course, the source of Prior’s great passion for logic was his faith in its capacity for clarifying philosophical issues, untangling philosophical puzzles, and solving philosophical problems. Despite the fact that he has received far less attention than he deserves, Prior has had a profound influence on the development of philosophical and formal logic over the past forty ye…Read more
  •  346
    Actualism is the doctrine that the only things there are, that have being in any sense, are the things that actually exist. In particular, actualism eschews possibilism, the doctrine that there are merely possible objects. It is widely held that one cannot both be an actualist and at the same time take possible world semantics seriously — that is, take it as the basis for a genuine theory of truth for modal languages, or look to it for insight into the modal structure of reality. For possible wo…Read more
  •  1114
    Wide Sets, ZFCU, and the Iterative Conception
    Journal of Philosophy 111 (2): 57-83. 2014.
    The iterative conception of set is typically considered to provide the intuitive underpinnings for ZFCU (ZFC+Urelements). It is an easy theorem of ZFCU that all sets have a definite cardinality. But the iterative conception seems to be entirely consistent with the existence of “wide” sets, sets (of, in particular, urelements) that are larger than any cardinal. This paper diagnoses the source of the apparent disconnect here and proposes modifications of the Replacement and Powerset axioms so as t…Read more
  •  162
    The true modal logic
    Journal of Philosophical Logic 20 (4). 1991.
    This paper traces the course of Prior’s struggles with the concepts and phenomena of modality, and the reasoning that led him to his own rather peculiar modal logic Q. I find myself in almost complete agreement with Prior’s intuitions and the arguments that rest upon them. However, I argue that those intuitions do not of themselves lead to Q, but that one must also accept a certain picture of what it is for a proposition to be possible. That picture. though, is not inevitable. Rather, implicit i…Read more
  •  167
    Sets and worlds again
    Analysis 72 (2): 304-309. 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
  •  121
    On Set Theoretic Possible Worlds
    Analysis 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.
  •  61
    Frege Numbers and the Relativity Argument
    Canadian Journal of Philosophy 18 (1): 87-98. 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
  •  196
    Actualism
    Stanford 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 life-form 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
  •  147
    The objective conception of context and its logic
    Minds and Machines 9 (1): 29-56. 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 first-order language for this account is developed. The language contains complex terms for propositions, …Read more
  •  1109
    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
  •  1
    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 of truth trees as a semantic method, which of course, the name notwithstanding, it is not (although it is of course much more semantically inspired than natural deduction). Sorry. Other than that I suppose the review is mildly inform…Read more
  •  165
    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
  •  158
  •  151
    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
  •  632
    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