希腊几何学的社会文化根源

The Social and Cultural Roots of Greek Geometry

本文从古希腊独特的社会文化形态作为切入点 ,探索求解了数学思想史上著名的“克莱因问题” ,从而破解了希腊证明几何学的成因之谜。古希腊社会在从氏族社会向民族社会转轨变形的过程中 ,爆发了一场绵延数世纪的思想启蒙运动。希腊人从宗教神学中解放了出来 ,开始了对世界的理性思考 ,他们为了解决社会秩序的重组问题 ,提出了以法治国的政治主张。从此希腊社会走上了法制的轨道。在古典的民主政治和商品经济形成的同时 ,古希腊民族也孕育出了一种独特的文化形态———古典的理性文化或科学文化。希腊几何学正是在这种以法律文化为核心、以语言文化为生长点的理性文化中诞生、形成和发展起来的。希腊哲学文化则是使公理几何学最终定型的关键因素。

The origin of the Greek deductive geometry or axiomatic geometry has long been an important problem in the research of the history of mathematical thoughts.In his book Mathematical Thought From Ancient to Modem Times,M.Kline,a famous American historian of mathematics,points out that this is'one of the major problems in the history of civilization,a problem in probing the cause for the ancient Greeks'talents and creativity'.This paper,starting from the unique social and cultural formation of ancient Greece,provides a solution to the famous'Kline Problem',and thus decodes the puzzle for the origin of the Greek deductive geometry in the history of mathematics. Ancient Greece was the cradle for the science of law and its legal culture then enjoyed a full development.From the 8 th to 3 rd century before Christ,the ancient Greek society underwent an unprecedented social revolution and Greece as a whole completed its transformation from its former clan social to the national society.This enlightenment in its real sense emancipated the Greek people from religion and theology and they began to think,with a cooled mind,about the life and the problem of the restructuring of the social order.Greek,from this time,stepped on to the road to the system of law.In this emancipation of thought,the Greek's intelligence and competence,especially their creative thinking ability,were brought to the full play.In the meantime when the classic commodity economy and democratic politics were taking shape,an unique cultural formation was brought forward in the ancient Greek national-the classic rational culture or science culture.It was in this rational culture,with the legal culture in its center,that the Greek geometry was born,formed and developed.