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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Memories of Hilary Putnam,of Putnam’s life, such an essay might have to be rather lengthy!) But we wanted to do something a little different, and at any rate we knew we couldn’t do a better job at biography than what is already in the gripping intellectual autobiography Putnam wrote for his installment in the Library of Living Philosophers series (Auxier et al. 2015).

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Abstraction, Axiomatization and Rigor: Pasch and Hilbertg after Pasch, Hilbert (and others) proposed an alternative standard of rigor. My aim in this paper is to clarify the relationship between Pasch’s and Hilbert’s standards of rigor. There are, I believe, fundamental differences between them.

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Logic, Counterexamples, and TranslationHence, in the face of a counterexample, one can move to a logic that fails to validate the inference seemingly counter-instanced, or one can move to a logic where the best translation of the natural language claims involved in the counterexample are no longer best translated as an instance of the inference in question.

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Hilary Putnam on Logic and Mathematics978-3-319-96274-0Series ISSN 2211-2758 Series E-ISSN 2211-2766