
14The Fundamental Theorem of World TheoryJournal of Philosophical Logic 43 (23): 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

4Worlds 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

60Edward 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

451In 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

50Ontology 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

56Reference 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

114The 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

(Pretty much complete)

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

582Modal 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.

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

257The 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

101The 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

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

167Cantor 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

204The Fundamental Theorem of World TheoryJournal of Philosophical Logic (23): 131. 2013.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

136Possible 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).

58Logic and Reality: Essays on the Legacy of Arthur PriorPhilosophical 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

318Actualism, ontological commitment, and possible world semanticsSynthese 85 (3). 1990.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

897Wide Sets, ZFCU, and the Iterative ConceptionJournal of Philosophy 111 (2): 5783. 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

136The true modal logicJournal 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

148Sets and worlds againAnalysis 72 (2): 304309. 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

112On Set Theoretic Possible WorldsAnalysis 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.

56Frege Numbers and the Relativity ArgumentCanadian Journal of Philosophy 18 (1): 8798. 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

169ActualismStanford 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 lifeform 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

140The objective conception of context and its logicMinds and Machines 9 (1): 2956. 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 firstorder language for this account is developed. The language contains complex terms for propositions, …Read more
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19th Century Logic 
20th Century Logic 
Philosophy of Religion 
PhilPapers Editorships
Actualism and Possibilism 