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- W2903764808 abstract "In this essay we examine the revengeRevenge problem as it arises with respect to accounts of both the set-theoretic and theSemantic paradox semantic paradoxesParadox. First we review revenge as it arises in the set-theoretic setting – the Burali-Forti paradoxBurali-Forti paradox – and outline its modal-structural resolution, highlighting the roles played by the logicLogic of plurals, modal principles, and especially the extendability of modelsModel of set theorySet theory on this account. We then we turn to theSemantic paradox semantic paradoxesParadox, especially the Liar, and develop an analogy between the problems of expressive incompletenessIncompleteness and revengeRevenge affecting proposals to resolve the semantic paradoxesSemantic paradox, on the one hand, and, on the other, the always incomplete and extendable nature of domains of sets on the modal structural approach to set theorySet theory. We then argue for a corresponding parallelism in resolutions of the set-theoretic and theSemantic paradox semantic paradoxesParadox. Focusing on recent accounts stemming from the work of MartinMartin, Robert and WoodruffWoodruff, Peter (Philosophia, 5(3):213–217, 1975) and KripkeKripke, Saul (Journal of Philosophy, 72:690–716, 1975), we formulate a modal account of the extendability of languages on the EmbracingRevenge RevengeEmbracing Revenge account of the semanticSemantic paradox paradoxesCook, Roy (see, e.g. Cook, Embracing RevengeEmbracing Revenge: On the Indefinite Extendability of Language, 2007; SchlenkerSchlenker, Philippe, Review of Symbolic Logic, 3(3):374–414, 2010) analogous to the formulation of extendability principlesExtendability principle for set theoretic universes on the modal structural approach. Finally, however, we examine an interesting dis-analogy via a meta-revengeMeta-revenge version of theParadox Liar paradoxLiar paradox that seems to have no analogue in the set-theoretic context, and we show how the solution to this puzzle also highlights even deeper connections between the modal-structural account of set theorySet theory and the EmbracingRevenge RevengeEmbracing Revenge account of truth and semantics." @default.
- W2903764808 created "2018-12-22" @default.
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- W2903764808 date "2018-01-01" @default.
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- W2903764808 title "Extendability and Paradox" @default.
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- W2903764808 doi "https://doi.org/10.1007/978-3-319-96274-0_5" @default.
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