Abstract
In this paper we give an example of intertranslatability between an ontology of individuals (nominalism), an ontology of properties (realism), and an ontology of facts (factualism). We demonstrate that these three ontologies are dual to each other, meaning that each ontology can be translated into, and recaptured from, each of the others. The aim of the enterprise is to raise the possibility that, at least in some settings, there may be no need for considerations of ontological primacy. Whether the world is made up of things, or properties, or facts, may be no more than a matter of how we look at it.
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REFERENCES
Abramsky, S. and Jung, A.: 1994, Domain theory, in S. Abramsky, D. Gabbay and T. Maibaum (eds.), Handbook of Logic in Computer Science, Vol. III, Clarendon Press, Oxford, pp. 1-168.
Armstrong, D.: 1978, Universals and Scientific Realism. Vol 1: Nominalism and Realism, Cambridge Univ. Press, Cambridge.
Armstrong, D.: 1995, Universals and Scientific Realism. Vol 2: A Theory of Universals, Cambridge Univ. Press, Cambridge.
Armstrong, D.: 1997, A World of States of Affairs, Cambridge Univ. Press, Cambridge.
Boole, G.: 1847, The Mathematical Analysis of Logic, Being an Essay Toward a Calculus of Deductive Reasoning, Macmillan, Cambridge.
Brink, C. and Rewitzky, I.: 2001, A Paradigm for Program Semantics: Power Stuctures and Duality, Studies in Logic, Language and Information, CSLI Publications, Stanford.
Burris, S. and Sankappanavar, H.: 1981, A Course in Universal Algebra, Springer-Verlag, Berlin.
Chagrov, A. and Zakharyaschev, M.: 1997, Modal Logic, Oxford Logic Guides 35, Clarendon Press, Oxford.
Cleave, J.: 1994, A Study of Logics, Oxford Logic Guides 18, Clarendon Press, Oxford.
Davey, B. and Priestley, H.: 1990, Introduction to Lattices and Order, Cambridge Univ. Press, Cambridge.
Droste, M. and Göbel, R.: 1990, Nondeterministic information systems and their domains, Theoret. Comput. Sci. 75, 289-309.
Edalaat, A. and Smyth, M.: 1993, I-Categories as a framework for solving domain equations, Theoret. Comput. Sci. 115, 77-106.
Gabbay, D. M., Hogger, C. J. and Robinson, J. A. (eds.): 1994, Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 1-4, Clarendon Press, Oxford.
Abramsky, S., Gabbay, D. M. and Maibaum, T. S. E. (eds.): 1992-2000, Handbook of Logic in Computer Science, Oxford Science Publications, Vol. 1-5, Clarendon Press, Oxford.
Gabbay, D. and Guenthner, F. (eds.): 1983-1989, Handbook of Philosophical Logic, Synthese Library, Vol. I-IV, Kluwer Academic Publishers, Dordrecht.
van Leeuwen, J. (ed.): 1990, Handbook of Theoretical Computer Science, Vol. A-B, Elsevier, Amsterdam.
Hamilton, P.: 1988, Logic for Mathematicians, Cambridge Univ. Press, Cambridge, revised edition.
Honderich, T. (ed.): 1995, The Oxford Companion to Philosophy, Oxford Univ. Press, Oxford.
Hughes, G. and Cresswell, M.: 1996, A New Introduction to Modal Logic, Routledge and Kegan Paul, London.
Jónsson, B. and Tarski, A.: 1951, Boolean algebras with operators I, Amer. J. Math. 73, 891-939.
Jónsson, B. and Tarski, A.: 1952, Boolean algebras with operators II, Amer. J. Math. 74, 127-167.
Kripke, S.: 1959, A completeness theorem in modal logic, J. Symbolic Logic 24, 1-14.
Priestley, H.: 1970, Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2, 186-190.
Priestley, H.: 1972, Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. 24(3), 507-530.
Priestley, H.: 1984, Ordered sets and duality for distributive lattices, Ann. Discrete Math. (Orders, Descriptions and Rules) 23, 39-60.
Quine, W.: 1953, 1961, 1980, On what there is, in From a Logical Point of View, Harvard Univ. Press.
Scott, D.: 1970, Outline of a mathematical theory of computations, in Proceedings of the Fourth Annual Princeton Conference on Information Sciences and Systems, pp. 169-176.
Scott, D.: 1982, Domains for denotational semantics, in M. Nielson and E. Schmidt (eds.), Proceedings of ICALP 9, Lecture Notes in Comput. Sci. 140, pp. 577-613.
Smyth, M.: 1983, Power domains and predicate transformers: A topological view, in J. Diaz (ed.), Proceedings of ICALP 10, Lecture Notes in Comput. Sci. 154, Springer-Verlag, Berlin, pp. 662-675.
Stone, M.: 1936, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40, 37-111.
Stone,M.: 1937, Topological representations of distributive lattices and Brouwerian logics, Casopis Pro Potování Mathematiky 67, 1-25.
Wittgenstein, L.: 1922, Tractatus Logico-Philosophicus, Routledge and Kegan Paul, London.
Zhang, G.-Q.: 1994, A representation of SFP, Inform. and Comput. 110, 233-263.
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Brink, C., Rewitzky, I. Three Dual Ontologies. Journal of Philosophical Logic 31, 543–568 (2002). https://doi.org/10.1023/A:1021204628219
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DOI: https://doi.org/10.1023/A:1021204628219