本文選題：普遍數(shù)學(xué) + 萊布尼茨��； 參考：《遼寧大學(xué)》2017年碩士論文

【摘要】：普遍數(shù)學(xué)思想從笛卡爾時代開始就一直貫穿了數(shù)理邏輯體系以及后世哲學(xué)的發(fā)展。笛卡爾在論述幾何學(xué)和代數(shù)學(xué)相結(jié)合從而形成坐標系的同時,發(fā)現(xiàn)了系統(tǒng)的升級可以使得系統(tǒng)內(nèi)本不能被解釋的問題變得不需要解釋,進而引發(fā)了對發(fā)現(xiàn)世間所有真理發(fā)現(xiàn)的探討。萊布尼茨在此基礎(chǔ)之上將表達的意義抽空,只保留純形式的結(jié)構(gòu),論述了普遍數(shù)學(xué)思想的可行性。胡塞爾的現(xiàn)象學(xué)思想從本質(zhì)上講是將普遍數(shù)學(xué)的純形式與事實屬性相交互構(gòu)造而成。哥德爾不完全性定理的論證過程是普遍數(shù)學(xué)思想的應(yīng)用,同時,不完全性定理也直接證明了同時包含有形式與事實的普遍數(shù)學(xué)思想是無法形成一個可以自圓其說的封閉邏輯體系的。當然,不包含事實屬性的空形式下的普遍數(shù)學(xué)思想是可行的,而它最直接的應(yīng)用就是今天無處不在的計算機。它將數(shù)據(jù)與程序進行了統(tǒng)一格式的混合編碼,并且只用邏輯判斷即可完成程序的運行�？梢娖毡閿�(shù)學(xué)思想在哲學(xué)范圍和現(xiàn)實世界范圍內(nèi)都擁有重大的意義。根據(jù)上述寫作思路,本文分為四個主要部分:第一部分重點回顧普遍數(shù)學(xué)思想的歷史淵源及其發(fā)現(xiàn)背景。介紹了亞里士多德三段論系統(tǒng)的公理化與將事實與意義的形式化混合以及笛卡爾借助于系統(tǒng)的升級進而發(fā)現(xiàn)并求證馬特席斯的存在。第二部分的核心內(nèi)容是萊布尼茨的普遍數(shù)學(xué)思想的介紹。同時還介紹了萊布尼茨對亞里士多德三段論系統(tǒng)的進一步闡述和普遍數(shù)學(xué)思想對萊布尼茨后續(xù)思想的影響。第三部分則重點討論了胡塞爾的現(xiàn)象學(xué)數(shù)學(xué)發(fā)源的核心問題就是普遍數(shù)學(xué)思想,并且是直接繼承了萊布尼茨的普遍數(shù)學(xué)思想。后半部分意在將哥德爾的不完全性定理和胡塞爾的現(xiàn)象學(xué)數(shù)理邏輯沖突解決方案在普遍數(shù)學(xué)的視域下進行全面細致的比較,指出兩者在解決數(shù)理邏輯中不可化解的問題中意識上的共同點以及兩者完全不同的解決方案。第四部分是在前三部分討論的基礎(chǔ)之上探求普遍數(shù)學(xué)的意義,包括不同于本體論的由普遍數(shù)學(xué)引出的現(xiàn)象學(xué)之路、普遍數(shù)學(xué)思想在計算機科學(xué)領(lǐng)域產(chǎn)生的影響以及重新審視普遍數(shù)學(xué)思想對未來現(xiàn)象學(xué)發(fā)展產(chǎn)生的深遠影響。
[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.
【學(xué)位授予單位】：遼寧大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O1-0

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