Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts
暫譯: 數學基礎的反思：單值基礎、集合論與一般思考
Centrone, Stefania, Kant, Deborah, Sarikaya, Deniz
- 出版商: Springer
- 出版日期: 2019-11-20
- 售價: $6,780
- 貴賓價: 9.5 折 $6,441
- 語言: 英文
- 頁數: 535
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3030156540
- ISBN-13: 9783030156541
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商品描述
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 important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.
商品描述(中文翻譯)
這本編輯作品展示了當代數學實踐在基礎數學理論中的應用，特別是集合論和單值基礎。它分享了數學、哲學和計算機科學領域中重要學者的研究成果。讀者將發現有關數學適當基礎的標準的系統性思考，以及圍繞數學觀點的哲學反思。
本書分為三個部分，前兩部分專注於數學基礎的兩個最重要的候選理論。讀者可以追溯集合論的當前研究，這被廣泛認為是解決基礎問題的框架，以及有關單值基礎的新材料，考慮基於同倫類型理論（HoTT）的方法。第三部分則在此基礎上，集中於與數學基礎相關的哲學問題。在這裡，作者對基礎標準的討論提供了更一般的思考，這些思考並不與特定理論相關。
本書分享了一些在集合論（S. Friedman）、非古典邏輯（G. Priest）和數學哲學（P. Maddy）領域中最重要學者的研究成果。讀者將意識到每個理論的優勢及其作為基礎的反對意見，並跟隨各領域最新和最佳的研究成果，因此對於任何從事數學基礎或數學哲學研究的人來說，這本書都是一個有價值的讀物。
作者簡介
Deborah Kant studied mathematics at Free University and Humboldt University in Berlin, and specialized in set theory and logic. At the DMV Students' Conference 2015 in Hamburg, her talk about her master's thesis "Cardinal Sequences in ZFC" was being awarded. Since 2015, she is a PhD student at the Humboldt University Berlin under the supervision of Karl-Georg Niebergall with a project on naturalness in set theory.
Deniz Sarikaya is PhD-Student of Philosophy (BA: 2012, MA: 2016) and studies Mathematics (BA: 2015) at the University of Hamburg with experience abroad at the Universiteit van Amsterdam and Universidad de Barcelona. He stayed a term as a Visiting Student Researcher at the University of California, Berkeley developing a project on the Philosophy of Mathematical Practice concerning the Philosophical impact of the usage of automatic theorem prover and as a RISE research intern at the University of British Columbia. He is mainly focusing on philosophy of mathematics and logic.
作者簡介(中文翻譯)
Stefania Centrone 目前是漢堡大學的 Privatdozentin，曾擔任喬治-奧古斯特大學的理論哲學副教授。她於2012年獲得DFG-Eigene Stelle，專案為「Bolzanos 與 Husserl 對 Leibniz 數學普遍性思想的進一步發展」，該專案在卡爾-馮-奧西茨基大學進行。她是多部著作的作者/編輯，包括《Logic and philosophy of Mathematics in the Early Husserl》（Springer 2010）和《Studien zu Bolzano》（Academia Verlag 2015）。
Deborah Kant 在柏林的自由大學和洪堡大學學習數學，專攻集合論和邏輯。在2015年於漢堡舉行的DMV學生會議上，她的演講主題為碩士論文「ZFC中的基數序列」獲得獎項。自2015年以來，她在洪堡大學柏林攻讀博士學位，指導教授為Karl-Georg Niebergall，研究專案為集合論中的自然性。
Deniz Sarikaya 是哲學博士生（學士：2012，碩士：2016），並在漢堡大學學習數學（學士：2015），曾在阿姆斯特丹大學和巴塞隆納大學有海外經驗。他曾在加州大學伯克利分校擔任訪問學生研究員，開展有關數學實踐哲學的專案，探討自動定理證明器使用的哲學影響，並在不列顛哥倫比亞大學擔任RISE研究實習生。他主要專注於數學哲學和邏輯。
