文章基本信息

标题：Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs
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作者：Stanisław Krajewski
期刊名称：Studia Humana
电子版ISSN：2299-0518
出版年度：2020
卷号：9
期号：3-4
页码：154-164
DOI：10.2478/sh-2020-0034
语种：English
出版社：Sciendo
摘要：The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics. Several points made by its main representatives are mentioned – from the revisability of actual proofs to the stress on real mathematical practice as opposed to its idealized reconstruction. Main features of real proofs are then mentioned; for example, whether they are convincing, understandable, and/or explanatory. Therefore, the new approach questions Hilbert’s Thesis, according to which a correct mathematical proof is in principle reducible to a formal proof, based on explicit axioms and logic.
关键词：mathematical proof;axiomatic proof;formal proof;philosophy of mathematics;foundations of mathematics;mathematical practice;explanatory proof;analytic proof;Hilbert’s thesis