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215On the logic of natural kindsPhilosophy of Science 43 (2): 202-222. 1976.A minimal second order modal logic of natural kinds is formulated. Concepts are distinguished from properties and relations in the conceptual-logistic background of the logic through a distinction between free and bound predicate variables. Not all concepts (as indicated by free predicate variables) need have a property or relation corresponding to them (as values of bound predicate variables). Issues pertaining to identity and existence as impredicative concepts are examined and an analysis of …Read more
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157Logic and OntologyAxiomathes 12 (1-2): 117-150. 2001.A brief review of the historicalrelation between logic and ontologyand of the opposition between the viewsof logic as language and logic as calculusis given. We argue that predication is morefundamental than membership and that differenttheories of predication are based on differenttheories of universals, the three most importantbeing nominalism, conceptualism, and realism.These theories can be formulated as formalontologies, each with its own logic, andcompared with one another in terms of thei…Read more
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151Denoting concepts, reference, and the logic of names, classes as many, groups, and pluralsLinguistics and Philosophy 28 (2). 2005.Bertrand Russell introduced several novel ideas in his 1903 Principles of Mathematics that he later gave up and never went back to in his subsequent work. Two of these are the related notions of denoting concepts and classes as many. In this paper we reconstruct each of these notions in the framework of conceptual realism and connect them through a logic of names that encompasses both proper and common names, and among the latter, complex as well as simple common names. Names, proper or common, …Read more
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144On the logic of classes as manyStudia Logica 70 (3): 303-338. 2002.The notion of a "class as many" was central to Bertrand Russell''s early form of logicism in his 1903 Principles of Mathematics. There is no empty class in this sense, and the singleton of an urelement (or atom in our reconstruction) is identical with that urelement. Also, classes with more than one member are merely pluralities — or what are sometimes called "plural objects" — and cannot as such be themselves members of classes. Russell did not formally develop this notion of a class but used i…Read more
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129Logical atomism, nominalism, and modal logicSynthese 31 (1). 1975.While operators for logical necessity and possibility represent "internal" conditions of propositions (or of their corresponding states of affairs), These conditions will be "formal", As is required by logical atomism, And not "material" in content if from the (pseudo) semantical point of view the modal operators range over "all the possible worlds" of a logical space rather than over arbitrary non-Empty sets of worlds (as is usually done in modal logic). Some of the implications of this require…Read more
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119Predication in Conceptual RealismAxiomathes 23 (2): 301-321. 2013.Conceptual realism begins with a conceptualist theory of the nexus of predication in our speech and mental acts, a theory that explains the unity of those acts in terms of their referential and predicable aspects. This theory also contains as an integral part an intensional realism based on predicate nominalization and a reflexive abstraction in which the intensional contents of our concepts are “object”-ified, and by which an analysis of predication with intensional verbs can be given. Through …Read more
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117Mass Nouns in a Logic of Classes as ManyJournal of Philosophical Logic 38 (3): 343-361. 2009.A semantic analysis of mass nouns is given in terms of a logic of classes as many. In previous work it was shown that plural reference and predication for count nouns can be interpreted within this logic of classes as many in terms of the subclasses of the classes that are the extensions of those count nouns. A brief review of that account of plurals is given here and it is then shown how the same kind of interpretation can also be given for mass nouns
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102Infinity in ontology and mindAxiomathes 18 (1): 1-24. 2008.Two fundamental categories of any ontology are the category of objects and the category of universals. We discuss the question whether either of these categories can be infinite or not. In the category of objects, the subcategory of physical objects is examined within the context of different cosmological theories regarding the different kinds of fundamental objects in the universe. Abstract objects are discussed in terms of sets and the intensional objects of conceptual realism. The category of…Read more
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100Frege's double correlation thesis and Quine's set theories NF and MLJournal of Philosophical Logic 14 (1). 1985.
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90Reference in Conceptual RealismSynthese 114 (2): 169-202. 1998.A conceptual theory of the referential and predicable concepts used in basic speech and mental acts is described in which singular and general, complex and simple, and pronominal and nonpronominal, referential concepts are given a uniform account. The theory includes an intensional realism in which the intensional contents of predicable and referential concepts are represented through nominalized forms of the predicate and quantifier phrases that stand for those concepts. A central part of the t…Read more
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90Conceptual realism versus Quine on classes and higher-order logicSynthese 90 (3). 1992.The problematic features of Quine's set theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intension…Read more
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84Logical atomism and modal logicPhilosophia 4 (1): 41-66. 1974.A propositional logic with modal operators for logical necessity and possibility is formulated as a formal ontology for logical atomism (with negative facts). It is shown that such modal operators represent purely formal, Internal 'properties' of propositions if and only if the notion of 'all possible worlds' has its standard and not the secondary interpretation which it is usually given (as, E.G., In kripke model-Structures). Allowing arbitrary restrictions on the notion of 'all possible worlds…Read more
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82Russell's paradox of the totality of propositionsNordic Journal of Philosophical Logic 5 (1): 25-37. 2000.Russell's "new contradiction" about "the totality of propositions" has been connected with a number of modal paradoxes. M. Oksanen has recently shown how these modal paradoxes are resolved in the set theory NFU. Russell's paradox of the totality of propositions was left unexplained, however. We reconstruct Russell's argument and explain how it is resolved in two intensional logics that are equiconsistent with NFU. We also show how different notions of possible worlds are represented in these int…Read more
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81Russell's involuted path in the development of his theory of logical types from 1903 to 1910-13 is examined and explained in terms of the development in his early philosophy of the notion of a logical subject vis-a-vis the problem of the one and many; i.e., the problem for russell, first, of a class-as-one as a logical subject as opposed to a class as many, and, secondly, of a propositional function as a single and separate logical subject as opposed to existing only in the many propositions tha…Read more
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79On the primary and secondary semantics of logical necessityJournal of Philosophical Logic 4 (1). 1975.
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74Some remarks on second order logic with existence attributesNoûs 2 (2): 165-175. 1968.Some internal and philosophical remarks are made regarding a system of a second order logic of existence axiomatized by the author. Attributes are distinguished in the system according as their possession entails existence or not, The former being called e-Attributes. Some discussion of the special principles assumed for e-Attributes is given as well as of the two notions of identity resulting from such a distinction among attributes. Non-Existing objects are of course indiscernible in terms of …Read more
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66Reply to Gregory Landini’s Review of Formal Ontology and Conceptual RealismAxiomathes 19 (2): 143-153. 2009.
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66Existence entailing attributes, modes of copulation and modes of being in second order logicNoûs 3 (1): 33-48. 1969.
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55A Note on the Definition of Identity in Quine's New FoundationsZeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1): 195-197. 1976.
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51Meinong reconstructed versus early Russell reconstructedJournal of Philosophical Logic 11 (2). 1982.
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50Logical Investigations of Predication Theory and the Problem of UniversalsNoûs 25 (2): 221-230. 1991.
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50Modal logic: an introduction to its syntax and semanticsOxford University Press. 2008.In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight.
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48Two Views of the Logic of Plurals and a Reduction of One to the OtherStudia Logica 103 (4): 757-780. 2015.There are different views of the logic of plurals that are now in circulation, two of which we will compare in this paper. One of these is based on a two-place relation of being among, as in ‘Peter is among the juveniles arrested’. This approach seems to be the one that is discussed the most in philosophical journals today. The other is based on Bertrand Russell’s early notion of a class as many, by which is meant not a class as one, i.e., as a single entity, but merely a plurality of things. It…Read more
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47Nominalism and conceptualism as predicative second-order theories of predicationNotre Dame Journal of Formal Logic 21 (3): 481-500. 1980.
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Indiana University, BloomingtonRetired faculty
Areas of Specialization
Metaphysics |
Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Biology |
Philosophy of Mathematics |