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Titlebook: Reflections on the Foundations of Mathematics; Univalent Foundation Stefania Centrone,Deborah Kant,Deniz Sarikaya Book 2019 Springer Nature

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發(fā)表于 2025-3-21 19:03:36 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Reflections on the Foundations of Mathematics
副標(biāo)題Univalent Foundation
編輯Stefania Centrone,Deborah Kant,Deniz Sarikaya
視頻videohttp://file.papertrans.cn/825/824729/824729.mp4
概述Presents some of the most important scholars in the fields of set theory, univalent foundations and philosophy of mathematics.Considers criteria for a suitable foundation in mathematics, fostering int
叢書名稱Synthese Library
圖書封面Titlebook: Reflections on the Foundations of Mathematics; Univalent Foundation Stefania Centrone,Deborah Kant,Deniz Sarikaya Book 2019 Springer Nature
描述.This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives..The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories..This book shares the work of some of the most import
出版日期Book 2019
關(guān)鍵詞Foundations of Mathematics; Philosophy of Mathematics; Philosophy of Set Theory; Univalent foundations;
版次1
doihttps://doi.org/10.1007/978-3-030-15655-8
isbn_softcover978-3-030-15657-2
isbn_ebook978-3-030-15655-8Series ISSN 0166-6991 Series E-ISSN 2542-8292
issn_series 0166-6991
copyrightSpringer Nature Switzerland AG 2019
The information of publication is updating

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What Do We Want a Foundation to Do?ious what makes it ‘foundational’. This paper begins with a taxonomy of the jobs set theory does that might reasonably be regarded as foundational. It then moves on to category-theoretic and univalent foundations, exploring to what extent they do these same jobs, and to what extent they might do other jobs also reasonably regarded as foundational.
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Book 2019undations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives..The volume i
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Proving Theorems from Reflectionthe axioms of set theory, but are of a less ‘problematic’ nature, as they can be solved by adopting the right axiomatic framework. We contend that any foundations for mathematics should be able to simply formulate such questions as well as to raise at least the theoretical hope for their resolution.
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Univalent Foundations and the UniMath Libraryf formalized mathematics implementing the ideas of the Univalent Foundations (Sect. 8.1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (Sect. 8.2). This leads us to a general discussion about the links between architecture and mathematics where
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