论普遍数学思想—从对现象学发展意义角度看

发布时间：2018-06-15 18:48

本文选题：普遍数学 + 莱布尼茨　；参考：《辽宁大学》2017年硕士论文

【摘要】：普遍数学思想从笛卡尔时代开始就一直贯穿了数理逻辑体系以及后世哲学的发展。笛卡尔在论述几何学和代数学相结合从而形成坐标系的同时,发现了系统的升级可以使得系统内本不能被解释的问题变得不需要解释,进而引发了对发现世间所有真理发现的探讨。莱布尼茨在此基础之上将表达的意义抽空,只保留纯形式的结构,论述了普遍数学思想的可行性。胡塞尔的现象学思想从本质上讲是将普遍数学的纯形式与事实属性相交互构造而成。哥德尔不完全性定理的论证过程是普遍数学思想的应用,同时,不完全性定理也直接证明了同时包含有形式与事实的普遍数学思想是无法形成一个可以自圆其说的封闭逻辑体系的。当然,不包含事实属性的空形式下的普遍数学思想是可行的,而它最直接的应用就是今天无处不在的计算机。它将数据与程序进行了统一格式的混合编码,并且只用逻辑判断即可完成程序的运行。可见普遍数学思想在哲学范围和现实世界范围内都拥有重大的意义。根据上述写作思路,本文分为四个主要部分:第一部分重点回顾普遍数学思想的历史渊源及其发现背景。介绍了亚里士多德三段论系统的公理化与将事实与意义的形式化混合以及笛卡尔借助于系统的升级进而发现并求证马特席斯的存在。第二部分的核心内容是莱布尼茨的普遍数学思想的介绍。同时还介绍了莱布尼茨对亚里士多德三段论系统的进一步阐述和普遍数学思想对莱布尼茨后续思想的影响。第三部分则重点讨论了胡塞尔的现象学数学发源的核心问题就是普遍数学思想,并且是直接继承了莱布尼茨的普遍数学思想。后半部分意在将哥德尔的不完全性定理和胡塞尔的现象学数理逻辑冲突解决方案在普遍数学的视域下进行全面细致的比较,指出两者在解决数理逻辑中不可化解的问题中意识上的共同点以及两者完全不同的解决方案。第四部分是在前三部分讨论的基础之上探求普遍数学的意义,包括不同于本体论的由普遍数学引出的现象学之路、普遍数学思想在计算机科学领域产生的影响以及重新审视普遍数学思想对未来现象学发展产生的深远影响。
[Abstract]:The thought of universal mathematics has been running through the development of mathematical logic system and later philosophy since Descartes era. Descartes, while discussing the combination of geometry and algebra to form a coordinate system, found that the upgrading of the system could make it unnecessary to explain the problems in the system that could not be explained. In turn, the discovery of all the truth of the world to explore the discovery. On the basis of this, Leibniz empties the meaning of the expression, only retains the pure form of structure, and discusses the feasibility of the universal mathematical thought. Husserl's phenomenological thought is essentially an interaction between the pure form of universal mathematics and the attribute of fact. The process of proving Godel's incompleteness theorem is the application of universal mathematical thought, and at the same time, The incompleteness theorem also directly proves that a closed logic system can not be formed by the universal mathematical thought which contains both form and fact. Of course, a general mathematical idea without factual attributes is feasible, and its most direct application is today's ubiquitous computer. It encodes the data and the program in a unified format, and the program can be run only by logical judgment. It can be seen that the universal mathematical thought has great significance in the scope of philosophy and the real world. According to the above ideas, this paper is divided into four main parts: the first part focuses on reviewing the historical origin and the background of the general mathematical thought. This paper introduces the axiom of Aristotelian syllogism system and the formal mixing of facts and meanings, and Descartes discovers and proves the existence of Matt Schirth by means of the upgrade of the system. The second part is the introduction of Leibniz's general mathematics thought. It also introduces Leibniz's further elaboration of Aristotle syllogism system and the influence of general mathematical thought on Leibniz's subsequent thought. In the third part, the core problem of Husserl's origin of phenomenological mathematics is that of universal mathematics, and it inherits Leibniz's thought of universal mathematics directly. The latter part is intended to compare Godel's incomplete theorem with Husserl's phenomenological mathematical logic conflict solution in a comprehensive and meticulous way from the perspective of universal mathematics. It is pointed out that they have common consciousness in solving the insoluble problems in mathematical logic and their solutions are completely different. The fourth part explores the significance of universal mathematics on the basis of the discussion in the first three parts, including the phenomenological road derived from universal mathematics, which is different from ontology. The influence of general mathematics thought on computer science and the profound influence of general mathematics thought on the development of phenomenology in the future.
【学位授予单位】：辽宁大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O1-0

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