The thesis that entities exist in, at, or in relation to logically possible worlds is criticized. The suggestion that actually nonexistent fictional characters might nevertheless exist in nonactual merely logically possible worlds runs afoul of the most general transworld identity requirements. An influential philosophical argument for the concept of world-relativized existence is examined in Alvin Plantinga’s formal development and explanation of modal semantic relations. Despite proposing an attractive unified semantics of alethic modality, Plantinga’s argument is rejected on formal grounds as supporting materially false actual existence assertions in the case of actually nonexistent objects in the framework of Plantinga’s own underlying classical predicate-quantificational logic.
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I do not further define the concept, but the idea of relevant predicational completeness or incompleteness is suggested in a negative way by the example that it is not a relevant predicational incompleteness on the part of Sherlock Holmes, who is supposed to be a human being, to be neither prime nor non-prime, neither even nor odd, just as it is not a relevant predicational incompleteness for the abstract number π to be neither blue-eyed nor non-blue-eyed.
My conclusions are largely in accord with and some my terminology and concepts are freely adopted from Kripke (1980, especially pp. 15–20, 42–53, 76–7). I am critical of Kripke’s actualism in modal semantics, but interested in tracking similar conclusions from very different assumptions.
David Hume, An Enquiry Concerning Human Understanding in Hume (1975, 47): “[Imagination] can feign a train of events, with all the appearance of reality, ascribe to them a particular time and place, conceive them as existent, and paint them out to itself with every circumstance, that belongs to any historical fact, which it believes with the greatest certainty. Wherein, therefore, consists the difference between such a fiction and belief?” See also Hume’s remarks, pp. 48–50.
Plantinga (1974, 46). Plantinga’s world-relativized existence-at-a-world modal semantics is the polar opposite of Kripke’s modal actualism.
I further discuss the metaphysics of possible worlds semantics in Jacquette (2005), special issue on “Aperçus philosophiques en logique et en mathématiques”, edited by Gerhard Heinzmann and Manuel Rebuschi, pp. 239-58. Jacquette (2006, 49–63). Jacquette, “Propositions, Sets, and Worlds”, Studia Logica: An International Journal for Symbolic Logic, special double issue “Ways of Worlds” on 40 Years of Possible Worlds Semantics, Vol. 1: On Possible Worlds and Related Notions, edited by Vincent F. Hendricks and Stig Andur Pedersen, 82, 2006, pp. 337–343. See also Jacquette and Imaguire (2010); especially, “Introduction: Logical Possibilities and the Concept of a Logically Possible World”, pp. 15–22.
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