Historical Variations and Modern Implications of the Concept of Infinity——Centred on Badiou's Study of Dedekind and Cantor
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.
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