无穷概念的历史变奏与现代意涵——以巴迪欧对戴德金和康托尔的研究为中心
Historical Variations and Modern Implications of the Concept of Infinity——Centred on Badiou's Study of Dedekind and Cantor
邢冰1
作者信息
摘要
无穷或日无限是数学和哲学的重要概念,也是巴迪欧数学本体论中集合的核心特征.在巴迪欧看来,经由戴德金和康托尔所阐发的数学上的实无穷的哲学意义在于,它宣告了一个现代时代的到来.实无穷突破了哲学史和宗教史上将无限视为唯一的、人类无法理解的本原的路径,而使无穷成为人类知性可以把握的事物,辞别上帝与国王,敞开了多元与能动的主体性空间.然而,现代性中存在的一系列悲剧揭示了抽象的普遍理性的内在问题,以及资本主义如何通过垄断理性解释权完成对无限性的复魅,使无产阶级重新臣服于一元的体系之下.而康托尔多元异质的无穷观以及连续统假设(Continuum hypothesis)的不可判定性则为突破这种现状提供了启发.
Abstract
Infinity is an important concept in mathematics and philosophy and a central feature of sets in Badiou's mathematical ontology.In Badiou's view,the philosophical significance of actual infinity,as elucidated through Dedekind and Cantor,is that it is a modern manifesto.Actual infinity would break with the path of treating the infinite as the unique origin which is incomprehensible to human understanding in the history of philosophy and religion,and make the infinite something graspable by human knowledges,resigning God and the king,and opening up the space of pluralistic and active subjectivity.However,a series of tragedy in modernity show the internal problems of abstract universal reason,and capitalism completes the reenchantment of the infinity through the monopoly of the interpretation of the reason,subjugating the proletariat to the monistic system.However,Cantor's pluralistic and heterogeneous view of infinity and the undecidability of the continuum hypothesis provide inspiration for a break from this status quo.
关键词
无穷/巴迪欧/戴德金/康托尔/现代性Key words
Infinity/Badiou/Dedekind/Cantor/Modernity引用本文复制引用
出版年
2024
NETL
NSTL
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