笛卡尔的“普遍数学”思想阐释

发布时间：2018-05-29 19:05

本文选题：普遍数学 + 笛卡尔　；参考：《上海师范大学》2017年硕士论文

【摘要】：笛卡尔作为近代哲学的创始人,他创立了一套理性主义的方法,形成了较完整的科学方法论,并运用这套方法来建立自己的哲学体系。在笛卡尔的早期思想中,笛卡尔选择了结合“量”、“秩序”与“理性”的数学方法作为其方法的模式,建立了一套以“普遍数学”为指导原则,以精神直观和理性演绎为核心,以分析和综合为步骤的独特数学方法论体系。并将这种方法运用到具体数学中,创立了解析几何学,打开了数学史上新纪元。“普遍数学”思想的思维方式、数学的论证方法、数学的本质特征都在很大程度上影响了笛卡尔哲学思想及其哲学体系的建构。“普遍数学”对西方近代的其他理性主义哲学家斯宾诺莎、莱布尼茨、帕斯卡尔等人的哲学观也产生了深远的影响。“普遍数学”的思想让数学推动了西方近代哲学家对于世界本原的思考,这种影响是基于人类的理性追求秩序、确定、永恒、统一的内在的自然倾向和数学证明所彰显的确定、有序、自明的形式的内在同一性。对于“普遍数学”思想的研究,国内一部分学者把重点放在“普遍数学”的翻译上,以探求“普遍数学”和“普遍方法”的区别问题;也有学者把笛卡尔的数学思想放在整个西方近代哲学史上进行综合性考量。国外研究主要集中在笛卡尔数学思想中的具体数学问题;还有学者关注出现“普遍数学”思想的《探求真理的指导原则》的文本的重要性和完整性。根据国内外相关文献,笔者发现并没有对于笛卡尔“普遍数学”的系统性研究,所以这就是本文的构思初衷。首先本文第一章就笛卡尔所处的时代背景进行考察,特殊的生长环境、教育背景,为笛卡尔的“普遍数学”思想提供了前期准备。宗教思想的碰撞、教会学校对数学教育的重视、生长环境的自由与开放,都让笛卡尔对于数学的确定性、简明性开始着迷。第二章对“普遍数学”的思想渊源进行探讨,柏拉图的可知世界、奥古斯丁的“自然之光”,从一定程度上都影响着笛卡尔“普遍数学”思想的形成,再加上伽利略的定量方法造成了科学革命的爆发,并导致科学主义的兴起,哲学开始往科学化和数学化的方向发展,这一切都是“普遍数学”思想产生所需要的时代背景。第三章就“普遍数学”的思想涵义展开讨论,最初“普遍数学”一词在何文本中出现,笛卡尔对其的解释又是什么,笛卡尔早期从事的分析数学和后来的物理数学等相关领域如何体现了“普遍数学”的思想。第四章重点讨论现在争议最多的,出现“普遍数学”一词的文本《探求真理的指导原则》中第四原则异构性的问题,这直接表明了笛卡尔在书写文本时处在了不同的两个时期,而这关键的两个时期恰好很好的说明了笛卡尔关于”普遍数学”思想从早期雏形到后来在实践应用的整个过程。这对整体把握“普遍数学”思想有着很大的作用。本文对笛卡尔的“普遍数学”思想的阐释,希望能够系统性理解“普遍数学”的思想涵义。“普遍数学”思想在近代哲学史、数学史上都产生了深远影响,这个方面本文没有进行详细讨论,相关内容有待进一步研究。
[Abstract]:As the founder of modern philosophy, Descartes created a set of rationalist methods, formed a more complete scientific methodology and used this set of methods to establish his own philosophical system. In the early thoughts of Descartes, Descartes chose the mathematical method of combining "quantity", "order" and "rational" as the model of his method. A set of unique mathematical methodology system is set up with the principle of "universal mathematics" as the guiding principle, the core of the spiritual intuition and the rational deduction, and the analysis and synthesis of the mathematical methodology. And this method is applied to the concrete mathematics, and the analytic geometry is founded, the new era of mathematical history has been opened. The thinking mode of "universal mathematics" thought and mathematics have been opened. The method of argumentation and the essential characteristics of mathematics have greatly influenced the construction of Descartes's philosophy and its philosophical system. "Universal mathematics" has a profound influence on the philosophy of other western modern rationalist philosophers, Spinoza, Leibniz, Pascale and others. It has promoted the thinking of the modern western philosophers on the original world. This effect is based on the intrinsic identity of the definite, orderly and self-evident form based on the rational pursuit of order, determination, eternity, unity and mathematical proof, based on the rational pursuit of order, determination, eternity, and mathematical proof. For the study of "universal mathematics", some scholars in China focus on the research. In the translation of "universal mathematics", the difference between "universal mathematics" and "universal method" was explored, and some scholars put Descartes's mathematical thought in the history of modern western philosophy to make a comprehensive consideration. Foreign studies mainly focused on the specific mathematical problems in Descartes's mathematical thought; and some scholars paid attention to the emergence of "universal mathematics". According to the relevant literature at home and abroad, the author finds that there is no systematic study of Cartesian "universal mathematics", so this is the original intention of this article. First of all, the first chapter of this article is to investigate the background of the times of the flute Carle. The growth environment and educational background provide the early preparation for Descartes's "universal mathematics" thought. The collision of religious thought, the attention of the church school to mathematics education, the freedom and opening of the growing environment all let Descartes be fascinated by the certainty and simplicity of mathematics. The second chapter discusses the ideological origin of "universal mathematics". Platon's knowable world and Augustin's "light of nature", to a certain extent, influenced the formation of Cartesian "universal mathematics", and the quantitative method of Galileo caused the outbreak of the scientific revolution, which led to the rise of scientism and the development of Philosophy in the direction of science and mathematics, all of which were " The third chapter discusses the ideological meaning of "universal mathematics". The first "universal mathematics" is discussed in the third chapter. The first word "universal mathematics" appears in the text, what is the explanation of the "general mathematics", and how the relevant fields such as the analytical mathematics and the later physics and mathematics that Descartes engaged in earlier are "universal." The fourth chapter focuses on the most controversial, the text of the word "universal mathematics", "the guiding principle of seeking truth", the problem of the isomerism of the fourth principles, which directly indicates that Descartes was in a different two period when writing the text, and the two period of the key was just a good explanation of the Cartesian card. The whole process of the idea of "universal mathematics" from early embryonic form to practical application. This has a great effect on the overall grasp of "universal mathematics". This article explains Descartes's "universal mathematics" thought, hoping to systematically understand the ideological meaning of "universal mathematics". "Universal mathematics" is in the near future. The history of philosophy and the history of mathematics have had a profound impact. This aspect has not been discussed in detail, and the relevant contents need further study.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O1-0

【参考文献】