分割不可分割的一——雅各布·克莱因论希腊数学中的单元

The Division of the Indivisible One:Jacob Klein on Monad in Greek Mathematics

雅各布·克莱因将胡塞尔晚期的历史现象学充分运用于科学史研究。他发现,希腊人对数的理解浸透着当时人们对存在的领悟。以计数与计算技艺为基础,柏拉图区分出依次奠基的四种数学知识,并将计数单元与数的统一性建立在与可感世界分离的理念间的属种关系中。亚里士多德则以实体理论为基础,激烈地批评了柏拉图的分离理论,将数学对象的存在归于灵魂的抽象,从而淡化了柏拉图对计数单元“不可分割性”的排斥,为一种涉及分数使用的计算科学提供了存在论上的可能性。

Jacob Klein made full development of Husserl’s late work on phenomenology of history in the study of the history of science,and found that the Greeks’understanding of numbers was saturated with the understanding of being at that time.On the basis of counting and calculating skills,Plato distinguished four kinds of knowledge of numbers that were founded in turn,and established the unity of counting units and numbers in the relationship between Species and Genus that are separated from the sensible world.Aristotle,on the basis of the theory of Ousia,fiercely criticized his teacher’s theory of separation,and attributed the being of mathematical objects to the abstraction of the soul,thereby downplaying Plato’s rejection of the“indivisibility”of counting units,and provided ontological possibility for a calculating science involving the use of fractions.