| 书目名称 | Founding Mathematics on Semantic Conventions | | 编辑 | Casper Storm Hansen | | 视频video | | | 概述 | Explains how mathematics can be based on the human ability to create and use language.Offers new alternative ways to approach mathematics.Presents a simple solution to the liar paradox and its derivat | | 丛书名称 | Synthese Library | | 图书封面 |  | | 描述 | .This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences..This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory..Semantic conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis..Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, thissolution also applies to Russell’s paradox and the other mathematical paradoxes of self-reference..In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, | | 出版日期 | Book 2021 | | 关键词 | Philosophy of Mathematics; Nominalism; Paradoxes of Self-reference; Intuitionism and choice; Semantic co | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-88534-2 | | isbn_softcover | 978-3-030-88536-6 | | isbn_ebook | 978-3-030-88534-2Series ISSN 0166-6991 Series E-ISSN 2542-8292 | | issn_series | 0166-6991 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 18:00:17
