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《皇极经世》数学之理研究

The Theoretical Study of Mathematics in Huangji Jingshi

【作者】 徐亮

【导师】 李尚信;

【作者基本信息】 山东大学 , 中国哲学, 2020, 硕士

【摘要】 邵雍的易学通过《皇极经世》进行表达,并于“观物”之中体现出来。其易学的核心内容为“物理之学”与“性命之学”,“物理之学”的表现形式为“数学”。由此,只有系统地了解“皇极经世”、“观物”、“物理之学”、“性命之学”以及“数学”这几者之间的关系,才能真正进入邵雍易学之门;只有系统分析“数学”背后之理,才能明晰“物理之学”的最终归路与“性命之学”是殊途同归的。第一章,研究邵雍其人,主要从以下几个方面展开:第一节,研究道德何以接续,这部分内容属于“道统”之学,通过说明邵雍之学根于三皇、接续孔子,以此确证邵雍之学的历史合理性;第二节与第三节,分别研究“道体论”与“性命之学”,通过研究“太极”、“太极不动,性也”以及“命之在人谓之性”这些内容,说明邵雍是如何解决“道德何以可能”以及“道德如何实现”之问题第二章,研究邵雍其书,主要解决以下几个问题。第一节,探讨“皇极经世”之编排,由史料可知邵雍其书之编排经过多人之手。然而,其书之内容并无多大变动;第二节,探讨“皇极经世”之内涵,由史料可知,“皇极经世”即以三皇所传的“大中至正,应变无方之道”经纶万世之事业。“皇极经世”是“体用”之学,亦是“内圣外王”之学;第三节探讨《皇极经世》之内容,其内容至少包括以下几个方面:一,其学源于道家,归宗儒家;其书是物理之学,以数学作为主要的表达形式,蕴含穷通造化之理;第三,其书推步靠的是卦象,以此鉴照历史,继往开来;第四,其书做的整齐,包括得尽;第五,其书是“内圣外王”之学,书的目的是本天道责成人事,其最终归向是期待世道大治;其六,《皇极经世》的具体内容,包括以元经会、以会经运、以运经世、声音律吕,这几个部分统称《观物篇》;除此之外还包括《观物内篇》与《观物外篇》。《观物内篇》主要研究宇宙造化内在的原理,阐述“皇帝王霸”之道以及如何以“数学”呈现万物变化内在的原理;而外篇则注重对于内篇的阐释。总而言之,这几个部分皆是以不同的形式叙述“皇极”之理;第四节,探讨“皇极经世”与“观物”之关系,由于“皇极之理”无所不包,故“经世”无所不经,“观物”无所不观。以“皇极”而“经世”故谓“皇极经世”,观“皇极”之“经世”即“观物”,而所以观者即“皇极之理”。舍“皇极”无“经世”之实,无“观物”之理;舍“经世”则“皇极之理”无以显现,“观物”则无物可观;舍“观物”,则“皇极之理”不晰,“经世”无从谈起。故“皇极”“经世”“观物”一以贯之,前后呼应,要在人心悟神契。第五节,探讨“皇极经世”与“皇极经世学”,研究者研究“皇极经世”之学,应以《皇极经世》为主,“皇极经世学”为辅。然而,舍“皇极经世学”于《皇极经世》难得其门而入,亦难以对邵雍之“数学”有深入之了解。但是,一味偏执“皇极经世学”亦难免出现与《皇极经世》原本不相符之处。第三章至第六章主要系统研究邵雍“数学”之理,表明邵雍如何通过“数学”的形式表达万物变易之理。第三章主要分成四部分论述,第一节探讨“物理之学”与“性命之学”以及“物理之学”与“数学”之关系。在邵雍之学中,物理之学研究的内容是万物消长之理,其最终来源是性,核心指向是人,根本目标是以为后世鉴。万物之理根于万物之性,故物理之学与性命通贯为一,二者统一于太极之理。物理之学指向的是外王之学,性命之学指向的是内圣之学,二者是二而一的关系,不可截然分判为二。邵雍物理之学核心的表达方式是“数学”,只有系统研究“数学”,以及“数学”背后之理,才能真正审视邵雍的“物理之学”;第二节主要研究“数”之来源、性质。从来源层面而言,“数”源于太极之动静;从性质层面而言,万物皆有“数”,“数”是大道运行开显之机,是理呈现自身的方式,是阴阳运化的分度;同时说明象与数、理与数之间的关系。从宇宙生成论而言,象数关系为有数而后有象;从器世界而言,数与象是互相通贯的;理为“数”之根,是“数”之所以然,是“数”之最终的归向;第三节主要探讨一至十这十个数,十数之中,“一”为数之原,“五”与“十”为太极之数;“一”与“二”为数之本,由一二之数可以衍至无穷之数;一与十不可变,二与九之数皆用其变数。而所言之数皆有理存焉,以此说明邵雍言数旨在说明其理。第四章分成五个部分进行研究,第一节研究“体四用三”之理,在“一”与“二”的基础上研究“三”与“四”。笔者从天文、卦象、阴阳等不同之角度分别研究,说明“体四用三”之理本于天道而以数说之;第二节研究“方圆之数”内在的原理,旨在说明方圆之数根于“一”与“二”;二者性质各有不同,圆数主运行,方数主生物;圆数主用,方数主体;二者之数体不离用,用不离体;并说明如何从“一”与“二”推衍至于“三”与“六”、“四”与“八”、“九”与“十二”等数。第三节研究“天六地四”之理,旨在说明天运之数其内在根源在于“神”与“气”,二者是“数”得以运行之内在依据,并说明“生物必四”乃根于自然之理;第四节主要从卦变、蓍法、体用之数的角度研究“体者八变,用者六变”之理,旨在说明“八”、“六”之数显现宇宙造化亦根于阴阳之理。第五节研究阴阳刚柔之数,说明如何通过“一”与“二”之数以推衍万物之数,以证明邵雍数学总归不离乾坤之道;第五章分成四个部分对“数”之“理”进行研究,第一节研究策数与大衍之数,旨在说明邵雍如何从蓍法的角度探究数之源,以尽阴阳之道;第二节研究昼数夜数,以此说明如何通过先天图卦爻之数说明一年以及一元阴阳流行之理;第三节研究闰数,主要研究邵雍卦气说内在之原理,说明置闰之产生在于太阳、太阴之行速不同所致,并说明置闰之目的在于使得卦气之学更加精密;第四节研究余分,通过研究“余分之数”说明任何事物发挥其作用,必须有其根本,没有根本之用,必然无法长久。第六章分成三个部分进行研究,第一节说明元会运世之本意来源于天文学,讨论一二三四如何推衍为元会运世之数,以及十二与三十之由来亦根于自然之理,通篇旨在说明元会运世之学亦根于阴阳之理;第二节从四分法的角度研究元会运世之数,讨论其配卦之法与卦象对应之数;第三节研究大数分为小数以及小数分为大数之理,最终仍归宗于阴阳之理。总论统论全篇,通论邵雍“数学”根于万物之理,“数学”形式的多样性体现了宇宙变化之理的丰富性,“数学”之本质其实是阴阳变易之理的展现形式。而所谓阴阳变易之理,也即“物理”。故而,“数学”乃诠释“物理之学”的工具。而“物理之学”又与“性命之学”既各有侧重又互相贯通,其中,“物理之学”偏向“外王”之学,“性命之学”偏向“内圣”之学,二者的核心立足点皆在人道,二者于“太极”处得以通贯。而“太极”之理的本质即以大中至正应变无方之道经纶万世之事业。由此,邵雍之学得以首尾相通,一以贯之。

【Abstract】 Shao Yong’(1012-1077)s Yi study is expressed in huangji jingshi(Supreme Principles That Rule the World)and embodied in "observing things".Its core contents are "the study of physics" and "the study of nature and fate",and "the study of physics" is manifested by mathematics.Therefore,only by systematically understanding the relationship of huangji jingshi,observing things,the study of physics,the study of mature and fate and "mathematics" can we begin to understand Shao Yongs Yi study and only by systematically analyzing the theory behind mathematics can we make it clear that the final path of his study of physics and nature and life are the same.In the first chapter,the study of Shao Yong is mainly carried out from the following aspects:the first section studies the theory of "daotong",and confirms the historical rationality of Shao Yongs study by explaining that Shao Yongs learning originated from the three sovereigns and succeeded Confucius.The second and third sections respectively study "the body of Dao" and "nature and life learning".By studying the contents of "taiji","immovability is taiji’s nature" and "life depends on human being",they explain how Shao Yong solved the problem of "how morality is possible" and how Shao Yong solved the problem of "how to realize morality" by studying "removing dregs" and "honesty"..The second chapter focuses on the book of Shaoyong and mainly solves the several following problems.In the first section,the author discusses the arrangement of the book and finds out that it was arranged by many people while the contents,however,have not changed much.The second section discusses the connotation of huangji jingshi.It can be seen from the historical data that huangji jingshi means to rule the world by supreme rules passed by the three sovereigns.huangji jingshi is a body-using study and also about cultivating sageliness within and then manifesting it in service to society.The third section discusses the content of the book huangji jingshi,which has the following aspects at least:1.His studies originated from Taoism and returned to Confucianism.2.His book is the study of physics,with mathematics as the main form of expression,containing the theory of universal change.3.The book is based on the image of the hexagrams,which reflects the history and open up the future.4.The book is well organized,including all its achievements.5.The book is about cultivating sageliness and then manifesting it in service to society.The purpose of the book is to bring the people under the responsibility of heaven and the ultimate return is to look forward to the great governance of the world.6.The specific contents of the book including yiyuan jinghui,yihui jingyun,yiyun jingshi,and something about sound,which are collectively referred to the chapter view of things.In addition,it also includes the and the external part of the observation of things.Internal part of the observation of things mainly studies the inner principle of the creation of the universe,expounding the way of the emperor and the king and how to explore the number of all things by mathematics.These parts describe supreme principles in different forms.The fourth section discusses the relationship between "Supreme Principles That Rule the World" and "observing things".Since"Supreme Principles" covers everything,there is nothing that can’t be ruled or observed.Using the supreme principles to rule the world is called huangji jingshi and observing how the supreme principles rule the world is called observing things,so the viewer is "the supreme rules".Give up the huangji without the reality of the world,there is no reason to view things;Give up "the world" the huangji can not appear,"the view of things" is nothing appreciable.Therefore,"huangji","rule the world","the view of things" a consistent,echoing back and forth,we must realize it in the heart.In the fifth section,the author discusses the study of "huangji jingshi" and "huangji jingshi".In the study of "huangji jingshi" the author should give priority to "huangji jingshi" and the study of "huangji jingshi" as a supplement.However,it is difficult to enter the "huangji jingshi" and have a deep understanding of Shao Yong’s mathematics without the study of "huangji jingshi".But,blindly paranoid the study of "huangji jingshi" also unavoidably appears with "huangji jingshi" originally inconsistent place.Chapter three to chapter six is a systematic study of Shao Yongs theory of"mathematics",showing how Shao Yong expressed the theory of the change of things in the form of mathematics.The third chapter is mainly divided into four parts.The first section discusses the relationship between "the study of physics" and "the study of life" and "the study of physics" and "mathematics".In Shao Yongs study,the study of physics is the theory of the rise and fall of all things and the ultimate source is nature,its core is human,and its ultimate goal is to give advice to the future.The principle of all things is rooted in the nature of all things,so the study of physics and the study of nature and life are one and the two are united in the principle of taiji.The study of physics points to the study of outer Kings,and the study of life to the study of inner saints.The core expression of Shao Yong’s physics is "mathematics".Only by systematically studying "mathematics" and the theory behind"mathematics" can we truly examine Shao Yong’s "physics".Section two focuses on the origin and nature of "number".From the source level,"number" comes from the movement of taiji and from the nature level,all things have "number","number" is the internal invisible scale of Dao operation,is the internal standard of principle to realize itself,is the internal division of yin and yang.Meanwhile,this section also studies the relationship between image and number,principles and number.From the relation level,the a priori number gives birth to the image and is mutually consistent with the posteriori number.The principles are the reason of "number" and the final return of "number";The third section mainly discusses the ten numbers from one to ten.Among the ten Numbers,"one" is the origin of number,and "five" and "ten" are the numbers of taiji.The infinite numbers are derived from the number one and two.The one and ten are immutable,and two and nine are variable.And all the Numbers are reasonable which explains Shao Yong’s number is intended to explain the reason.Chapter four is divided into five parts.Section one studies the principle of "four represents body and three represents use".On the basis of "one" and "two",it studies"three" and "four".By studying from different perspectives such as astronomy,hexagram,yin and yang,it is explained that the principle of "four represents body and three represents use" is based on heaven;the second section studies the internal principle of "the number of squares",which aims to explain the square numbers are rooted in one and two.The nature of the two is different:the circle number is the main operation,the square number is the main creature;the circle number is mainly used,the square number is the main body.It also explains one and two can derive to three and six,four and eight,nine and twelve.The third section studies the theory of "six represents heaven and four represents earth",and aims to explain that the inherent roots of the number of heavens are "god" and "qi".The fourth section mainly studies the theory of "the body changes eight times and the the user changes six times" from the perspectives of hexagram change,sacred method,and the number of uses.The number shows that the creation of the universe is also rooted in the theory of yin and yang.Derive the number of all things to prove that Shao Yong’s mathematics is inseparable from the way of qian and kun.The fifth chapter is divided into four parts to study the "number" theory.The first section studies the strategy and the number of great expansion.The purpose is to explain how Shao Yong explores the source of the number from the perspective of method of divination,in order to make the most of the yin and yang;Section 2 studies the number of days and nights in order to explain how to explain a year and the principle of the epidemic of yin and yang through the number of congenital diagrams;Section 3 explains that the creation of Zhirun is caused by the different speeds of the sun and the taiyin,and that the purpose of Zhirun is to make the study of hexagrams more precise;Section studies the remaining points.By studying "the number of remaining points",it shows that everything plays its role.It must have its roots.Without its roots,it must not last.The sixth chapter is divided into three parts for research.The first section explains that the original meaning of yuanhui yunshi comes from astronomy,discusses how one,two,three,and four can be derived into yuanhui yunshi number,and the origin of the twelve and thirty is also the root.Based on the theory of nature,the whole article aims to explain that the theory of yuanhui yunshi is also rooted in the theory of yin and yang;the second section studies the yuanhui yunshi from the perspective of quartiles,and discusses the corresponding method of hexagrams and the correspondence of hexagrams;the third section studies the theory of the division of large numbers into small numbers and the division of small numbers into large numbers.In the end,it is still attributed to the theory that the change of numbers to small numbers is rooted in yin and yang.The diversity of the forms of "mathematics" reflects the richness of the theory of cosmic change,and the essence of "mathematics" is actually the manifestation of the theory of yin and yang.The so-called yin and yang theory of change,that is,the "physical".Therefore,"mathematics" is a tool for interpreting the "science of physics".The "science of physics" and the "science of life" both focus on and are consistent with each other,with the "science of physics" leaning towards the "king of the outside" and the "science of life"leaning towards the "saint of the inside",both of which are based on humanity at their core,and both are consistent in the "Taiji".The essence of the "Tai Chi" philosophy is that it is the cause of the whole world by strain and strain without any prescription.As a result,Shaoyongs learning has been consistent and consistent.

【关键词】 皇极经世物理性命数学
【Key words】 huangji jingshiphysicsnature and lifemathematics
  • 【网络出版投稿人】 山东大学
  • 【网络出版年期】2020年 12期
  • 【分类号】B244.3
  • 【下载频次】306
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