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Titlebook: Epistemology versus Ontology; Essays on the Philos P. Dybjer,Sten Lindstr?m,G. Sundholm Book 2012 Springer Science+Business Media Dordrecht

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發(fā)表于 2025-3-21 18:07:15 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Epistemology versus Ontology
副標(biāo)題Essays on the Philos
編輯P. Dybjer,Sten Lindstr?m,G. Sundholm
視頻videohttp://file.papertrans.cn/314/313350/313350.mp4
概述Comprehensive overview of the philosophical problems of the foundational framework in current mathematics.Demonstrates the impact of the work of the eminent academic: Per Martin-L?f.Contains contribut
叢書名稱Logic, Epistemology, and the Unity of Science
圖書封面Titlebook: Epistemology versus Ontology; Essays on the Philos P. Dybjer,Sten Lindstr?m,G. Sundholm Book 2012 Springer Science+Business Media Dordrecht
描述This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-L?f type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-L?f. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-L?f and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?
出版日期Book 2012
關(guān)鍵詞Constructive Type Theory; Dummett; Gentzen; Intuitionism; Martin-L?f; Martin-L?f‘s type theory; Mathematic
版次1
doihttps://doi.org/10.1007/978-94-007-4435-6
isbn_softcover978-94-017-8238-8
isbn_ebook978-94-007-4435-6Series ISSN 2214-9775 Series E-ISSN 2214-9783
issn_series 2214-9775
copyrightSpringer Science+Business Media Dordrecht. 2012
The information of publication is updating

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,Diphtherie, lobul?re Pneumonie, Scharlach,geometry and, in general, Hilbert’s axiomatic method, but also relativity theory and the so-called method of ideal elements. By drawing upon certain analogies rather than theory-constructions, these ideas affected not only his thinking about mathematics, but also his thinking about language and the nature of philosophy in general.
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Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turingr immediately after mentioning Turing, Wittgenstein frames what he calls a “variant” of Cantor’s diagonal proof. We present and assess Wittgenstein’s variant, contending that it forms a distinctive form of proof, and an elaboration rather than a rejection of Turing or Cantor.
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Ahmed Ghazi,R. Devotini,Domenico Venezianoer logic has categorical characterizations of relevant mathematical structures, while set theory has non-standard models, amounts to no difference at all. Second order logic and set theory permit quite similar categoricity results on one hand, and similar non-standard models on the other hand.
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