
7Worlds and Propositions Set FreeErkenntnis 79 (4): 797820. 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

62Edward N. Zalta. Intensional logic and the metaphysics of intentionality. Bradford books. The MIT Press, Cambridge, Mass., and London, 1988, xiii + 256 pp (review)Journal of Symbolic Logic 57 (3): 11461150. 1992.

2Proceedings of the KI 2003 Workshop on Reference Ontologies and Application Ontologies (edited book)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, FrankPeter 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

523In defense of the possibilism–actualism distinctionPhilosophical Studies 177 (7): 19711997. 2020.In Modal Logic as Metaphysics, Timothy Williamson claims that the possibilismactualism (PA) distinction is badly muddled. In its place, he introduces a necessitismcontingentism (NC) distinction that he claims is free of the confusions that purportedly plague the PA distinction. In this paper I argue first that the PA distinction, properly understood, is historically wellgrounded and entirely coherent. I then look at the two arguments Williamson levels at the PA distinction and find them …Read more

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51Ontology theoryIn Jerome Euzenat, Asuncion GomezPerez, 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

57Reference 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

4Providing a means of translating RDF, RDFS, and DAML+OIL descriptions into a firstorder 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

150The IDEF family of languagesIn Peter Bernus, Kai Mertins & Günter J. Schmidt (eds.), Handbook on Architectures of Information Systems, Springerverlag. pp. 209241. 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

Mathematical Realism and the Theory of SetsDissertation, University of Notre Dame. 1984.Set theoretic platonism is the view that there exist objective, mindindependent 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

668Modal Set TheoryIn Otávio Bueno & Scott Shalkowski (eds.), The Routledge Handbook of Modality, Routledge. forthcoming.This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.

79Haecceities and Mathematical StructuralismPhilosophia Mathematica 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

234Theism, 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

20Structuralism 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.

618Logic, Essence, and Modality — Review of Bob Hale's Necessary Beings (review)Philosophia Mathematica 23 (3): 407428. 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

313Basic semantic integrationSemantic 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

76On an unsound proof of the existence of possible worldsNotre Dame Journal of Formal Logic 30 (4): 598603. 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 firstorder logic. The principle is shown to be false.

236Temporal actualism and singular foreknowledgePhilosophical Perspectives 5 475507. 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

298Possibilism and object theoryPhilosophical Studies 69 (23). 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.

200Knowledge representation, the World Wide Web, and the evolution of logicSynthese 182 (2): 269295. 2011.It is almost universally acknowledged that firstorder logic (FOL), with its clean, wellunderstood 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

46A Formal Foundation for Process ModelingIn 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

104The proper treatment of predication in finegrained intensional logicPhilosophical Perspectives 7 6187. 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

310The Argument from CollectionsIn J. Walls & T. Dougherty (eds.), Two Dozen (or so) Arguments for God: The Plantinga Project, Oxford University Press. pp. 2958. 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

42SCL: A Logic Standard for Semantic IntegrationSemantic 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 logicbased frameworks being used for knowl…Read more

123Logical formIn 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

173Cantor and the BuraliForti ParadoxThe Monist 67 (1): 92107. 1984.In studying the early history of mathematical logic and set theory one typically reads that Georg Cantor discovered the socalled BuraliForti (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

66The Process Specification Language: Theory and ApplicationsAI Magazine 24 (3): 6374. 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

227The Fundamental Theorem of World TheoryJournal of Philosophical Logic 43 333363. 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

150Possible WorldsStanford 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).
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Areas of Interest
19th Century Logic 
20th Century Logic 
Philosophy of Religion 
PhilPapers Editorships
Actualism and Possibilism 