Mathematics and the Rise of Scientific Disciplines

17世纪的“科学革命”是世界文明发展的分水岭。当时我们看待世界的方式发生转变的一个主要组成部分是安德烈·科伊尔所说的自然几何化。为了理解科学以及它是如何发展的，我们必须理解西方自然哲学家是如何以及为什么把数学作为解开自然秘密的钥匙。伽利略为这场革命吹响了战斗的号角，但为什么他如此感动地把数学放在这个特殊的位置呢？利弗西博士正在调查这个问题，并从一个最不可能的方向发现了一个可能的来源，至少根据我们目前的预期。尽管人们认为数学是对科学的反感，利弗西博士还是假设自然数学化的源头来自神学，具体来说，他在14、15和16世纪对神学论文彼得·隆巴德（Peter Lombard）的《句子》（Sentences）的评论中发现，科学本质的讨论允许在自然研究中使用数学。亚里士多德在他的《后验分析》中禁止在科学中使用数学，除非在非常有限的情况下。有了这笔资金，李甫西博士将试图确定这些神学评论所产生的运动的规模，以创建数学物理学。该项目将分两个阶段进行。第一阶段将考察雷丁的约翰（John of Reading）的早期评论，他与奥卡姆的威廉（William of Ockham）同时代。研究的第二阶段将是对伽利略的后期发展进行更全面的考察。这项研究很有希望从根本上改变我们对现代科学发展过程和科学与宗教关系的看法。＊＊＊

The "Scientific Revolution" of the 17th century stands as a watershed in the development of world civilization. A major component of the transformation which took place at that time in the way we look at the world is what Andre Koyre called the geometrization of nature. In order to understand science and how it has developed, it is essential that we should understand how and why Western natural philosophers turned to mathematics as the key to unlock the secrets of nature. Galileo sounded the battle cry for this revolution, but why was he so moved to put mathematics in this special place? Dr. Livesey is investigating this issue and has found a possible source coming from a most unlikely direction, at least given our current expectations. Despite its supposed antipathy to science, Dr. Livesey hypothesizes that the source of the mathematization of nature came from theology| Specifically, he has found in the commentaries in the 14th, 15th and 16th centuries to a theological treatise, Peter Lombard's "Sentences," discussions of the nature of science which allowed for the use of mathematics in the study of nature. Aristotle, except in very limited circumstances, proscribed in his "Posterior Analytics" the use of mathematics in science. With this grant, Dr. Livesey will seek to determine the dimensions of the movement stemming from these theological commentaries to create a mathematical physics. The project will be carried out in two stages. The first stage will examine an early commentary by John of Reading, a contemporary of William of Ockham. The second phase of the study will be a more comprehensive examination of the later developments leading up to Galileo. This study holds great promise to radically change our view of the processes of development of modern science and of the relationship of science and religion. ***