Titlebook: Hilary Putnam on Logic and Mathematics; Geoffrey Hellman,Roy T. Cook Book 2018 Springer Nature Switzerland AG 2018 Diophantine Equations.M

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https://doi.org/10.1007/978-3-319-96274-0Diophantine Equations; Mathematical Logic; Quantum Logic; Decidability; Number Theory; Modal Logic; Model

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Putnam on Foundations: Models, Modals, MuddlesPutnam has famously offered a sketch of a mathematics without foundations, existing in two equivalent descriptions, set-theoretic and modal-logical. Here his proposal is critically examined, with attention to difficulties surrounding both the modal-logical description itself and especially the notion of equivalence of descriptions.

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Pragmatic PlatonismIt is argued that to a greater or lesser extent, all mathematical knowledge is empirical.

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Putnam on Mathematics as Modal LogicTwo uses of modal logic to explicate mathematics—due primarily to Hilary Putnam and Charles Parsons—are compared and contrasted. The approaches differ both technically and concerning ontology. Some reasons to push the former approach in the direction of the latter are articulated and discussed.

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Outstanding Contributions to Logichttp://image.papertrans.cn/h/image/427061.jpg

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