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A classically-based theory of impossible worlds. (English) Zbl 0914.03001
In the author’s metaphysics a situation is an abstract object which encodes a set of propositions, where a proposition is a $$0$$-ary property. A possible world encodes a maximal consistent set of propositions and an impossible world encodes a maximal set of propositions which is not consistent.

##### MSC:
 03A05 Philosophical and critical aspects of logic and foundations
##### Keywords:
abstract object; possible world; impossible world
Full Text:
##### References:
 [1] Cresswell, M., “The interpretation of some Lewis systems of modal logic,” Australasian Journal of Philosophy , vol. 45 (1967), pp. 198–206. [2] Cresswell, M., “Intensional logics and logical truth,” Journal of Philosophical Logic , vol. 1 (1972), pp. 2–15. · Zbl 0239.02012 [3] Kripke, S., “Semantic analysis of modal logic II: Non-normal modal propositional calculi,” pp. 206–20 in The Theory of Models , edited by J. Addison et al., North-Holland, Amsterdam, 1965. · Zbl 0163.00502 [4] Linsky, B., and E. Zalta, “Naturalized Platonism vs. platonized naturalism,” The Journal of Philosophy , vol. 92, (1995), pp. 525–55. JSTOR: [5] Mares, E., “Who’s afraid of impossible worlds?,” Notre Dame Journal of Formal Logic , vol. 38 (1997), pp. 516–26. · Zbl 0916.03014 [6] Morgan, C., “Systems of modal logic for impossible worlds,” Inquiry , vol. 16 (1973), pp. 280–9. [7] Paśniczek, J., “Non-standard possible worlds, generalised quantifiers, and modal logic,” pp. 187–98 in Philosophical Logic in Poland , edited by J. Wolenski, Kluwer, Dordrecht, 1994. [8] Perszyk, K., “Against extended modal realism,” Journal of Philosophical Logic , vol. 22 (1993), pp. 205–14. · Zbl 0780.03002 [9] Priest, G., “What is a non-normal world?,” Logique et Analyse , vol. 35 (1992), pp. 291–302. · Zbl 0834.03002 [10] Priest, G., In Contradiction , Martinus Nijhoff, The Hague, 1987. · Zbl 0682.03002 [11] Priest, G., and R. Sylvan, “Simplified semantics for basic relevant logics,” Journal of Philosophical Logic , vol. 21 (1992), pp. 217–32. · Zbl 0782.03008 [12] Rantala, V., “Impossible world semantics and logical omniscience,” Acta Philosophica Fennica , vol. 35 (1982), pp. 106–15. · Zbl 0519.03002 [13] Rescher, N., and R. Brandom, The Logic of Inconsistency : A Study in Non-Standard Possible World Semantics and Ontology, Basil Blackwell, Oxford, 1980. · Zbl 0598.03001 [14] Restall, G., “Ways things can’t be,” Notre Dame Journal of Formal Logic , vol. 38 (1997), pp. 583–96. · Zbl 0916.03015 [15] Routley, R., Exploring Meinong ’s Jungle and Beyond, Departmental Monograph #3, Philosophy Department, Research School of Social Sciences, Australian National University, Canberra, 1980. [16] Yagisawa, T., “Beyond possible worlds,” Philosophical Studies , vol. 53 (1988), pp. 175–204. [17] Zalta, E., “The modal object calculus and its interpretation,” pp. 249–79 in Advances in Intensional Logic , edited by M. de Rijke, Kluwer, Dordrecht, 1997. · Zbl 0908.03025 [18] Zalta, E., “Twenty-five basic theorems in situation and world theory,” Journal of Philosophical Logic , vol. 22 (1993), pp. 385–428. · Zbl 0775.03003 [19] Zalta, E., Intensional Logic and the Metaphysics of Intentionality , Bradford Books, The MIT Press, Cambridge, 1988. [20] Zalta, E., “A comparison of two intensional logics,” Linguistics and Philosophy , vol. 11 (1988), pp. 59–89. [21] Zalta, E., Abstract Objects : An Introduction to Axiomatic Metaphysics, D. Reidel, Dordrecht, 1983. · Zbl 0976.03007 [22] Zalta, E., “Meinongian type theory and its applications,” Studia Logica , vol. 41 (1982), pp. 297–307. · Zbl 0531.03003
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