• 한국수학사학회지
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• 제30권5호
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• pp.289-304
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• 2017

The interdisciplinary study explores the discussion of actual infinity between Georg Cantor and Roman Catholic Church. Regarding the actual infinity, we first trace the theological background of Cantor by interpreting his correspondence and major works including ${\ddot{U}}ber$ die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche(1885) and Mitteilungen zur Lehre vom Transfiniten (1887), and then investigate his argumentation for two points at issue: (1) pantheism and (2) inconsistency of the necessity with freedom of God. In terms of mathematics and theology, Cantor defined the actual infinity(aphorismenon) as characterized by (1) the transfinite infinity(Transfinitum) and (2) the absolute infinity(Absolutum). Transfinitum is conceptualized here in mathematical terms as a multipliable actual infinity, whereas Absolutum is not as a multipliable actual infinity. The results imply that Cantor's own concept of Transfinitum and Absolutum is adequate for Roman Catholic theology as well as mathematics including the reflection principle.