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伽利略的数学理性主义导致他对于自然现象解释的根本变革。他从古希腊原子论中异化出了数学实在论,将关于自然现象的解释由亚里士多德式的目的论解释异化为描述性解释。在经验主义方面,早期的伽利略就赞同亚里士多德关于解释性原理必须从感觉经验资料中归纳出来的观点,并且在几何学空间上以量的区别代替了亚里士多德的质的区别,并发展出了“检验自然”意义上的关于实验的观念。在帕多瓦时期的研究中,他对将经验(esperienza)作为科学研究的工具有了更多的信心,他发现诉诸感觉证实往往是很方便的。这使他实现了把自然规律作为可测量的数学关系来表达的目标,从而达到了理性主义与实验主义相结合的科学精神境界。
Galileo’s mathematical rationalism led to his fundamental changes in the interpretation of natural phenomena. He alienated mathematical realism from ancient Greek atomism, alienating the explanation of natural phenomena from Aristotelian teleological interpretation to descriptive explanation. In empiricism, earlier Galileo favored Aristotle’s argument that explanatory principle must be derived from sensory experience and replaced Aristotelian qualitatively with geometric differences in space Difference, and developed the concept of experiment in the sense of “test natural”. In the Padua period, he had more confidence in using esperienza as a tool for scientific research, and found that it was often convenient to resort to sensory proving. This enabled him to achieve the goal of expressing the laws of nature as a measurable mathematical relationship and thus reached the scientific spiritual realm in which rationalism and experimentalism were combined.