•  246
    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
  •  22
    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.
  •  702
    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
  •  348
    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
  •  82
    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.
  •  240
    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
  •  306
    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.
  •  209
    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
  •  46
    A Formal Foundation for Process Modeling
    with Michael Grüninger
    In C. Welty B. Smith (ed.), Formal Ontology in Information Systems (FOIS), Acm Press. 2001.
    Process modeling is ubiquitous in business and industry. While a great deal of effort has been devoted to the formal and philosophical investigation of processes, surprisingly little research connects this work to real world process modeling. The purpose of this paper is to begin making such a connection. To do so, we first develop a simple mathematical model of activities and their instances based upon the model theory for the NIST Process Specification Language (PSL), a simple language for descr…Read more
  •  108
    The proper treatment of predication in fine-grained intensional logic
    Philosophical Perspectives 7 61-87. 1993.
    In this paper I rehearse two central failings of traditional possible world semantics. I then present a much more robust framework for intensional logic and semantics based liberally on the work of George Bealer in his book Quality and Concept. Certain expressive limitations of Bealer's approach, however, lead me to extend the framework in a particularly natural and useful way. This extension, in turn, brings to light associated limitations of Bealer's account of predication. In response, I deve…Read more
  •  478
    The Argument from Collections
    In J. Walls & T. Dougherty (eds.), Two Dozen (or so) Arguments for God: The Plantinga Project, Oxford University Press. pp. 29-58. 2018.
    Very broadly, an argument from collections is an argument that purports to show that our beliefs about sets imply — in some sense — the existence of God. Plantinga (2007) first sketched such an argument in “Two Dozen” and filled it out somewhat in his 2011 monograph Where the Conflict Really Lies: Religion, Science, and Naturalism. In this paper I reconstruct what strikes me as the most plausible version of Plantinga’s argument. While it is a good argument in at least a fairly weak sense, it doe…Read more
  •  44
    SCL: A Logic Standard for Semantic Integration
    with Patrick Hayes
    Semantic Integration, CEUR Workshop Proceedings, Vol. 82 (2003). 2003.
    The Knowledge Interchange Format (KIF) [2] is an ASCII- based framework for use in exchanging of declarative knowledge among disparate computer systems. KIF has been widely used in the fields of knowledge engineering and artificial intelligence. Due to its growing importance, there arose a renewed push to make KIF an offi- cial international standard. A central motivation behind KIF standardization is the wide variation in quality, style, and content — of logic-based frameworks being used for knowl…Read more
  •  124
    Logical form
    In Edward Craig (ed.), Routledge Encyclopedia of Philosophy, Routledge. 1998.
    Consider the following argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Intuitively, what makes this a valid argument has nothing to do with Socrates, men, or mortality. Rather, each sentence in the argument exhibits a certain logical form, which, together with the forms of the other two, constitute a pattern that, of itself, guarantees the truth of the conclusion given the truth of the premises. More generally, then, the logical form of a sentence of natural langu…Read more
  •  186
    Cantor and the Burali-Forti Paradox
    The Monist 67 (1): 92-107. 1984.
    In studying the early history of mathematical logic and set theory one typically reads that Georg Cantor discovered the so-called Burali-Forti (BF) paradox sometime in 1895, and that he offered his solution to it in his famous 1899 letter to Dedekind. This account, however, leaves it something of a mystery why Cantor never discussed the paradox in his writings. Far from regarding the foundations of set theory to be shaken, he showed no apparent concern over the paradox and its implications whate…Read more
  •  66
    The Process Specification Language: Theory and Applications
    with Michael Grüninger
    AI Magazine 24 (3): 63-74. 2003.
    The Process Specification Language (PSL) has been designed to facilitate correct and complete exchange of process information among manufacturing systems, such as scheduling, process modeling, process planning, production planning, simulation, project management, work flow, and business process reengineering. We given an overview of the theories with the PSL ontology, discuss some of the design principles for the ontology, and finish with examples of process specifications that are based on the …Read more
  •  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).