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oapen-20.500.12657-506972022-04-26T11:21:29Z The Many and the One Florio, Salvatore Linnebo, Øystein plurals, plural logic, set theory, mereology, higher-order logic, absolute generality, modality, singularism bic Book Industry Communication::C Language::CF linguistics::CFA Philosophy of language bic Book Industry Communication::H Humanities::HP Philosophy::HPL Philosophy: logic Plural logic has become a well-established subject, especially in philosophical logic. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic’s applications than has been given so far. Questions about the correct logic of plurals play a central role in the last part of the book, where traditional plural logic is rejected in favor of a “critical” alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. 2021-10-05T12:58:52Z 2021-10-05T12:58:52Z 2021 book 9780198791522 https://library.oapen.org/handle/20.500.12657/50697 eng application/pdf Attribution-NonCommercial-NoDerivatives 4.0 International 9780198791522.pdf https://global.oup.com/academic/product/the-many-and-the-one-9780198791522 Oxford University Press 10.1093/oso/9780198791522.001.0001 10.1093/oso/9780198791522.001.0001 b9501915-cdee-4f2a-8030-9c0b187854b2 c273ec27-d2be-4f1d-8917-141b286f1657 9780198791522 336 Oxford University of Oslo open access
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Plural logic has become a well-established subject, especially in philosophical logic. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic’s applications than has been given so far. Questions about the correct logic of plurals play a central role in the last part of the book, where traditional plural logic is rejected in favor of a “critical” alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes.
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