伽利略《关于两门新科学的对话》中的无限观念

探讨了在《关于两门新科学的对话》中伽利略对无限量及其与有限量之间关系的论述,认为伽利略的无限观念由4种见解构成:(1)物质是由无限多的不可分的原素构成的;(2)由连续可分量到无限不可分量的转换不是通过分割,而是通过数学技巧去把握;(3)单独的不可分量亦等于无限多的不可分量;(4)通常对有限量适用的性质不能用于无限量.这些讨论体现和代表了伽利略关于"新科学"的研究思路和方法,更是后来一些数学思想的早期萌芽和雏形.伽利略对于无限问题的关注也和他的科学研究目的有关,即追求对自然本质的真理性描述.

Views on Infinity in Galileo's Discourses and Mathematical Demonstrations Concerning to Two New Science

In his Discourses and Mathematical Demonstrations Concerning to Two New Science(1638),Galileo states his view point about the infinity.We find it consists of four notions: 1) the substance was made up by infinitely non-quanta.2) the transition of quanta to non-quanta cannot be realized step by step by continued divisions but by the mathematical artifice.3) a non-quanta was equal to the infinitely non-quanta.4) the rules of finity differed from the infinity.These notions can show the method how Galileo explo...