Abstract
The modal object calculus is the system of logic which houses the (proper) axiomatic theory of abstract objects.1 This calculus has some rather interesting features in and of itself, independent of the proper theory. The most sophisticated, type-theoretic incarnation of the calculus can be used to analyze the intensional contexts of natural language and so constitutes an intensional logic. However, the simpler second-order version of the calculus couches a theory of fine-grained properties, relations and propositions and serves as a framework for defining situations, possible worlds, stories, and fictional characters, among other things. In the present paper, we focus on the second-order calculus.
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References
G. Bealer. Quality and Concept. Clarendon, Oxford, 1982.
R. Carnap. Meaning and Necessity. University of Chicago Press, Chicago, 1947.
H. Castañeda. Thinking and the structure of the world. Philosophic 4:3–40, 1974.
K. Došen. Second-order logic without variables. In W. Buszkowski, W Marciszewski, and J. van Benthem, editors, Categorial Grammar, John Benjamins, Amsterdam, 1988.
J. Etchemendy. The Concept of Logical Consequence. Harvard University Press, Cambridge, MA, 1990.
G. Frege. On sense and reference. In P. Geach and M. Black, editors, Translations from the Philosophical Writings of Gottlob Frege, pages 56–78, Basil Blackwell, Oxford, 1892.
J. Hintikka. Modality and quantification. Theoria, 27:110–128, 1961.
S. Kripke. A completeness theorem in modal logic. Journal of Symbolic Logic, 24:1–14, 1959.
S. Kripke. Semantical considerations on modal logic. Acta Philosophica Fennica, 16:83–94, 1963.
E. Mally. Gegenstandstheoretische Grundlagen der Logik und Logistik. Barth, Leipzig, 1912.
A. Meinong. Über Gegenstandstheorie. In A. Meinong, editor, Untersuchungen zur Gegenstandstheorie und Psychologie. Barth, Leipzig, 1904. (English translation: On the theory of objects. In R. Chisholm, editor, Realism and the Background of Phenomenology, pages 76–117. The Free Press, Glencoe, 1960.)
C. Menzel. A complete, type-free “second-order” logic and its philosophical foundations. Technical Report No. CSLI-86–40, Center for the Study of Language and Information, Stanford, CA, 1986.
C. Menzel. Actualism, ontological commitment, and possible world semantics. Synthese, 85:355–389, 1990.
R. Montague. Formal Philosophy: Selected Papers of Richard Montague, Richmond Thomason, editor, Yale University Press, New Haven, 1974.
T. Parsons. Nonexistent Objects. Yale University Press, New Haven, 1980.
W. Quine. Variables explained away. In Selected Logical Papers, pages 227–235. Random House, New York, 1960.
W. Rapaport. Meinongian theories and a Russellian paradox. Nous, 12:153–180, 1978.
R. Routley. Exploring Meinong’s Jungle and Beyond, Departmental Monograph #3, Philosophy Program, Research School of the Social Sciences, Australian National University, Canberra, 1979.
A. Tarski. On the concept of logical consequence, 1936. Translated from the Polish and published in Logic, Semantics, and Metamathematics. Clarendon, Oxford, 1956.
A. Tarski. The semantical conception of truth and the foundations of semantics. Philosophy and Phenomenological Research, 4:341–376, 1944.
E. Zalta. Abstract Objects: An Introduction to Axiomatic Metaphysics. D. Reidel, Dordrecht, 1983.
E. Zalta. On the structural similiarities between worlds and times. Philosophical Studies, 51:213–239, 1987.
E. Zalta. Intensional Logic and the Metaphysics of Intentionality. MIT/ Bradford, Cambridge, MA, 1988.
E. Zalta. Twenty-five basic theorems in situation and world theory. Journal of Philosophical Logic, 22:385–428, 1993.
E. Zalta. A philosophical conception of propositional modal logic. Philosophical Topics, 20(2):263–281, 1993.
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Zalta, E.N. (1997). The Modal Object Calculus and its Interpretation. In: de Rijke, M. (eds) Advances in Intensional Logic. Applied Logic Series, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8879-9_9
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DOI: https://doi.org/10.1007/978-94-015-8879-9_9
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