古希腊人没有掌握无理数的认识论根源研究

Why Ancient Greeks didn't Master Irrational Numbers from the Perspective of Epistemology

古希腊人没有真正的掌握无理数是历史的必然.从认识论研究对象的角度来讲,无理数不符合古希腊数学“数”的标准,或者说古希腊人畏惧无限的观念阻碍了希腊人认识无理数.第一次数学危机之后,古希腊数学研究重心的转移,对“数”的研究遭到冷落和把“无理数”拉到了几何学的队伍这些都阻碍了古希腊人对无理数的认识;古希腊数学在第一次数学危机之后拒绝了数学是经验的科学,极端的强调了数学的演绎性的同时,强调数学是发现的科学,而客观上也没有形成数学是发明的科学的观点.从后来无理数被人类认识的整个历程来讲,无理数不仅是人类演绎的之物,也是经验之物,不仅是人类的发现之物,而且还是人类的发明之物,人类认识无理数是一个复杂的、艰辛的、漫长的、曲折的历程.

The ancient Greeks did not fully grasp irrational numbers.Their mathematical standards and fear of infinity prevented recognition of irrational numbers as legitimate“numbers.”After the first mathematical crisis,Greek focus shifted from numbers to geometry,hindering further understanding.Greek mathematics emphasized deduction and discovery,rejecting the notion of mathematics as empirical or inventive.Over time,the recognition of irrational numbers evolved,showing they are both objects of deduction and experience,discovery and invention.Understanding irrational numbers has been a complex and lengthy journey.