David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Axiomathes 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 universals is discussed in terms of the three major theories of universals: nominalism, realism, and conceptualism. The finitude of mind pertains only to conceptualism. We consider the question of whether or not this finitude precludes impredicative concept formation. An explication of potential infinity, especially as applied to concepts and expressions, is given. We also briefly discuss a logic of plural objects, or groups of single objects (individuals), which is based on Bertrand Russell’s (1903, The principles of mathematics, 2nd edn. (1938). Norton & Co, NY) notion of a class as many. The universal class as many does not exist in this logic if there are two or more single objects; but the issue is undecided if there is just one individual. We note that adding plural objects (groups) to an ontology with a countable infinity of individuals (single objects) does not generate an uncountable infinity of classes as many.
|Keywords||Formal ontology Ontology Universals Conceptual realism Conceptualism Nominalism Logical realism Natural realism Plural objects Infinity Potential infinity|
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References found in this work BETA
W. V. Quine (1953/1980). From a Logical Point of View. Harvard University Press.
Claude E. Shannon & Warren Weaver (1949). The Mathematical Theory of Communication. University of Illinois Press.
Storrs McCall (1994). A Model of the Universe. Clarendon Press.
Donald Cary Williams (1953). The Elements of Being. Review of Metaphysics 7 (2):3-18, 171-92.
Keith Campbell (1981). The Metaphysic of Abstract Particulars. Midwest Studies in Philosophy 6 (1):477-488.
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