Abstract:
Although the logical problems of 'changeology' (Yi xue 易學) represent an important issue inChinese cultural history, history of thought, and history of Chinese logic, they have usually been ignored in the research of changeology and logic. Nevertheless, it is important to know that the logical thought in changeology occurred prior to the theories of naming and disputes (mingbianxue 名辯學), thus it should be looked upon as the starting point of Chinese logic. The logic of changeology was the logic of type-deduction (tuilei 推纇). In the present text, the author tries to prove, explain and discuss the logical system of changeology in the light of modem logical methods. He points out that the logic of changeology is a special form of a logical system, which is determined by the characteristics of Chinese culture and thought. It was formed upon the basis of the common ancient language and formed an autochthonous semantic system. In this sense, it is comparable to western logic that also provided the most suitable cognition method and offered a cognitive tool for ancient European science.
Keywords: type deduction, type symbol, cognitive method, scientific tools, common language
The Zhou Book of Change (Zhou yi 周易) is one of the most important and earliest books in ancient China; its contents reflect the earliest thoughts of Chinese culture and civilisation. As the classic of the earliest Chinese periods, it includes many elements that prevailed in the further development of ancient thought. Thus, it profoundly influenced the ancient Chinese culture, and formed a basis for the grandiose and impressive discipline, named changeology (yi xue易學). In changeological research, there is a problem that deserves attention, namely the problem of its logical system. At first, The Zhou Book of Change was only a text of divination, and the influence of its soothsaying function remained strong throughout the entire historical development of changeology that was to follow. Consequently, the soothsaying function would later be connected to the logical 'deduction', and this kind of logical deduction would assure the accuracy of the conclusions. This means, that by using a series of rules, it was possibleto deduce the right conclusion from the right premise. This is the basic cognitive presumption of changeology and simultaneously one of the most important tools of ancient Chinese logic.
In addition, some parts of The Zhou Book of Change were earlier than the theories of naming and disputes (mingbian xue 名辯學). The first piece of evidence of this fact is to be found in Stories of the Words of Hexagrams in The Zhou Book of Change (The story of Zhou yi guayao ci 周易卦爻辭中的故事), written by Gu Xiegang in 1929.According to his detailed textual research, the words of hexagrams (guayao ci 卦爻辭)expounded the relation between the Yin and Zhou Dynasties by means of events, which proved the fact that the name 'hexagrams' (gua 卦) were founded by King Wen's divination when he planed to marry the princess of the Yin state. This event was recorded as a posthumous work of the King Wen.(p.401-403)[1] This historical example appeared before Confucius. The second piece of evidence was provided by 22 quotations that can be found in the work Zuo zhuan - Guo yu （左傳·國語） in The Zhou Book of Change.(p.109)[2] For example, there was a record, which described that the official recorder of the Zhou Dynasty was called to pay a visit to king Chen. King Chen asked him to tell his fortune from The Zhou Book of Change. This was the first time that The Zhou Book of Change was mentioned in a historical work, which dated back to the year 672 BC, which also proves that it appeared long before Confucius. The third piece of evidence that Confucius not only read The Zhou Book of Change, but also referred to it several times can be found in his Analects (Lunyu 論語). Due to all of this proof that The Zhou Book of Change appeared before Confucius, it is clear, that it also appeared before Mozi 墨子.The fourth piece of evidence can be found in Xiao Jiefu's introduction to Zhang Dainian's 張岱年 work Some Important Historical Data in the History of Chinese philosophy ( Zhongguo zhexueshi shiliao yuanliu jiuyao 中國哲學史史料源流舉要) Zhang Dainian proved that some parts from The Zhou Book of Change appeared not only before Zhuang Zhou 莊周 and Hui Shi 惠施, but even earlier.
In the chapter Tian xia 天下篇 found in the book Zhuangzi 荘子, we can find the following quotation of Hui Shi, who was one of the main representatives of the Nomenalist school (ming Jia 名家):
“天與地卑，山與澤平。”
“The sky and the ground are of the same height,' mountains and waters are
on the same level.”(p.227)[3].
This quotation was merely a contrary proposition to the famous sentence:
“天尊地卑。”
“The sky is exalted but the ground is ornery.”(p.118)[4]
Which can be found in the Xi ci 繫辭 chapter within The Zhou Book of Change. According to the logical order of development, a correct proposition always appears before the contrary proposition, which means that The Zhou Book of Change appeared before the theory of naming (ming xue 名學), and also before the Nomenalist school (mingjia 名家), including Hui Shi and other representatives of this philosophical current. Therefore, it is clear that The Zhou Book of Change appeared not only before the theories of naming (ming xue 名學), but also before the theories of disputes (bian xue 辯學). By the time these currents appeared, The Zhou Book of Change was already extensively quoted in several ancient works. Therefore it is clear, that it has had a certain influence upon the theories of naming and the theories of disputes. This is important, because most of the scholars, who deal with research in the history of classical Chinese logic, still regard the theories of naming and the theories of disputes as the origin of the entire ancient logic in China. In this respect, most of them have
completely ignored the importance and the crucial position of The Zhou Book of Change in the history of Chinese logic. Recently, this opinion has been rectified, for example in The Textbook of the History of Chinese Logic (Zhongguo luojishi jiaocheng 中國邏輯史教程), written by Wen Gongyi and edited by Cui Qingtian. In this work, The Zhou Book of Change was regarded as the origin of classical Chinese logic.(p.10)[5]
1. The logical character of type deduction in changeology
The logical system of ancient China is based upon the type deduction method (tui lei推類). What is type deduction? It is a method of deduction, which functions according to the relation between equal or unequal types of statements.(p.110)[6] In the classical work of ancient Chinese logic, i.e. The Book of the Moist School (Mojing 墨經) it was defined as
“以類取，以類予。”
“getting results in accordance to the type.”(p.78)[7]
This method is based upon the general characteristics of different kinds of types, which serve as a deduction criterion. Therefore, it is called type-deduction. There are
numerous examples of this kind of deduction in The Zhou Book of Change. For example, the sixth symbol from the first line of the Kun hexagram (Kungua 坤卦) describes the natural phenomena of
“履霜，堅冰至。”
"treading on the frost to know the thickness of ice.”(p.113)[4]
From this it can be deducted that the truth about the good or bad results
“並非一朝一夕之故，其所由來者漸矣。”
“can not be obtained in a single night, but gradually."
Another example can be found in the ninth symbol of the fourth line of the Lǚ
hexagram (Lǚgua 履卦), which states that
“履虎尾，愬愬，終吉。”
"treading on the tiger 's tail, while being chary and careful, brings good
fortune.”
While a person,who
“眇能視，跛能履，履虎尾咥人，凶。”
"has poor eyesight, but forces himself to look, or who is lame on one leg but
forces himself to walk, will be bitten by the tiger and will have bad luck.”
This means, that a person who is chasing a tiger will be lucky if he is very careful and a person who does not pay attention and who over estimates his abilities will have bad luck and will be defeated by the tiger he is chasing. From this situation, a similar general result can be concluded： a gentleman, who is careful and decent although the situation is dangerous, can eventually still come across good fortune, while blindness in action inevitably leads to defeat.
A similar conclusion can be found in The Bi·Yuan Explanation (Bi·Yuanzhuan 賁·彖傅)：
“觀乎天文，以察時變。觀乎人文，以化成天下。”
"Research the law of the sky to know the change of the seasons, research the
law of society to know the laws of educating people.”
This example shows a type deduction, which concludes the laws of social regulation
from the laws of nature.
In another comment to The Zhou Book of Change, which is called Explaining the
Tradition of Hexagrams (Shuogua zhuan 說卦傅) the following is stated:
“是以立天之道，曰陰與陽；立地之道，曰剛與柔：立人之道，曰仁與義。”
"Yin and yang constitute the Way of Heaven; hardness and softness constitute
the Way of heaven and earth; humanity and righteousness constitute the way of men."
In this comment, again, we can find a type deduction, in which the laws of society are
concluded the laws of nature:
In the chapter Xi ci from The Zhou Book of Change (Zhou yi.xici 周易·繫辭) it is
said:
“易者,象也。”
“The change is (based upon) exact symbolic resemblance (xiang 象)."
The character xiang 象 represents a crucial factor of changeology. (p.93)[2] In the Xi ci chapter of The Zhou Book of Change it is explained as exact resemblance.
The eight main hexagrams (bajinggua 八經卦), i.e. Qian 乾, Dui 兌, Li離, Zhen 震,Xun 巽, Kan坎, Gen 艮, and Kun 坤in The Zhou Book of Change symbolise the eight types of universe, i.e. sky, pool, fire, thunder, wind, water, mountains, and earth. Thus,the hexagrams also represent the symbols (xiang 象) of these types. As we can observe in the same chapter, the foundation of this classification was formed by the following statement
“方以類聚,物以群分。”
“The method of type deduction (is based upon) selecting things by type and
their separation into groups.”(p114)[4]
Thus, the eight hexagrams (八卦)) are signs (symbols) of eight kinds or types of things.
We could say that the xiang in The Zhou Book of Change has been set up according to the type. Analogously, the deductions in The Zhou Book of Change have been carried out according to type.
In the context of Changeology the historical research of The Zhou Book of Change showed that the rules of the central cosmic powers (yin, yang and the five elements 陰陽五行 were also based upon type deduction. These powers were abstracted from the seven types (two + five respectively) of things that exist in the universe. Each of these types was represented by a symbol, which stands for a certain type of an existing structure. This was the basis for type deductions. For example, the semantic intention of the statement
“木克土”
“wood restrains soil”
Indicates that all things belonging to the 'wood type' (for instance the east, the jiao - tone, or the liver, etc.) restrain all things that belong to the 'soil type' (for instance the centre, the gong - tone and the spleen), and can therefore be treated symbolically by the simple form 'wood restrains soil (muketu 木克土)'. This is very important, because the preliminary logical system of Changeology was built upon the basis of such simple type signs that served as assumptions for the rules of logical deduction. In this respect, we can point out the following quotation from the Xi ci chapter in The Zhou Book of Change:
“易則易知，簡則易從 易簡而天下之理得矣。”
“It is quite easy to understand the change… because the change is simple, but
it contains the principles of the world.''
This statement expresses the logical character of deduction, which concludes the result from a basic premise. Hu Shi commented this as follows:
“有了極易極簡的，才有極繁賾的……萬物變化，既然都是從極簡易
的原起漸漸變出來，若能知道那簡易的原因，便可以推知後來那些複雜
的後果，因為如此，所以能“彰往而察來”，所以能“溫故而知新”，萬物變化都是由簡而繁，成一條前後不斷的直線，所以能由前段推知後段，由前因推到後果。”
“The precondition to understand the most complex phenomena is the
comprehension of the simplest ones. Everything that exists gradually develops from the simplest into increasingly complex forms. If we understand the simple ones, we can conclude their more complex consequences ... Because of this we can conclude the unknown from the known. All that exists is the linear development from simple to more complex forms. Thus, we can conclude consequences from the premises.”(p.60)[8]
However, the logical system in ancient Chinese changeology was not only used to explain society, but also - which was even more important - offered a basic cognitive tool for ancient science.
As an example we can mention the most famous sciences of ancient China, i.e. astronomy and traditional Chinese medicine.
2. Social implications in medicine and astronomy
In ancient Chinese astronomy, the 'twelve branches' (shier dizhi 十二地支) symbolised the twelve months of a year. Each month was assigned one hexagram (gua 卦). The Pi hexagram, which stood for all twelve months (shier yue pigua十二月辟卦), expressed the changing regulation (rising or falling of the yin and yang poles) during the twelve months. This cycle was developed as follows:
The Fu hexagram ( fugua 復卦), which was called Zi 子 stood for November and expressed that the first yang was on the rise.
The Lin hexagram ( lingua 臨卦)', which was called Chou 丑, stood for December and expressed that the second yang was on the rise.
The Tai hexagram ( taigua 泰卦), which was called yin寅, stood for the Spring Festival (January) and expressed that the third yang was on the rise.
The Dazhuan hexagram ( dazhuangua大壯卦), which was called Mao卯 ,stood for February and expressed that the fourth yang was on the rise
The Jue hexagram ( guaigua 夬卦), which was called Chen 辰, stood for March and expressed that the fifth yang was on the rise.
The Qian hexagram ( qiangua乾卦, which was called Si 巳 stood for April and expressed that the sixth yang was on the rise.
The Gou hexagram ( gougua 姤卦), which was called Wu 午, stood for May and expressed that the first yin was on the decline.
The Dun hexagram ( dungua遯卦)', which was called Wei 未, stood for June and expressed that the second yin was on the decline.
The Pi hexagram ( pigua否卦), which was called Shen申, stood for July and expressed that the third yin was on the decline.
The Guan hexagram ( guangua 觀卦), which was called You 酉 stood for August and expressed that the fourth yin was on the decline.
The Bo hexagram ( bogua 剝卦), which was called Xu 戌, stood for September and expressed that the fifth yin was on the decline.
The Kun hexagram ( kungua 坤卦), which was called Hai 亥, stood for October and expressed that the sixth yin was on the decline.
The transformation from the Fu hexagram ( fugua復卦) to the Qian hexagram ( qiangua 乾卦) represented ,the process of 'the rising yang spirit' (vangying陽盈) and was therefore called 'The rising hexagram' (Xigua ,息卦). The transformation from the Guo hexagram ( gougua姤卦) to the Kun hexagram ( kungua 坤卦) represented the process of 'the falling yin spirit' (yinxu陰虛) and was thus called 'the falling hexagram' (xiaogua 消卦). Hereby, yin and yang represent complementary poles that rise, fall and integrate with each other mutually. They represent a reflection of the philosophical thought, as can be found in the famous statement
“一陰一陽之謂道。”
"Together, yin and yang form the way (Dao).”
This is the basic logical axiom of changeology and the Pi hexagram as a symbol for the twelve months (shier yue pi gua 十二月辟卦) is a result of type deduction according to this axiom. It did not take long for the ancient Chinese scholars to discover that there was a relation between the Big Dipper's handle and the weather on the ground. In the classical astronomy work from the Han Dynasty, i.e. The Han Shu Theory of Astronomy 漢書·天文志 we can find the following statement:
“斗為帝車，運於中央，臨制四海，分陰陽，建四時，均五行，移節
度，定諸季，皆系於門。”
“The Big Dipper is a divine vehicle: it circulates at the centre of the day and
controls all directions. It divides yin and yang and creates the four seasons. It equilibrates the five elements and determines the climate according to its
own motion.”(p.467)[9]
Thus we can conclude that the Big Dipper was an important part within the system of traditional Chinese astronomy. The ancient scholars were of the opinion that the visible form of the Big Dipper was merely that part of this cosmic constellation that belonged to the yang - pole. Thus, they called it 'the yang Big Dipper' (yangdou 陽斗斗), so according to the above mentioned axiom 'Together, yin and yang form the way (Dao)' (一陽一陽之謂道) there had to be an equal constellation on the opposite side of the sky. This invisible constellation was therefore called 'the yin Big Dipper' (yindou 陰斗). The Astronomic Theory chapter in the book Huai Nanzi (淮南子·天文訓) contains the following statement:
“北斗之神有雌雄，十一月始建於子，雄左行，雌右行。”
"The Big Dipper's spirit has the female and the male aspect; in November,
when it points to the position of Zi the male aspect moves to the left while
the female one moves to the right.”(p.124)[10]
Another example of type deduction in ancient astronomy can be found in the descriptions of the planet Jupiter, which was called Sui 歳in ancient Chinese. It was assumed that the years could be counted by the laws of movement on this planet:
“歲星紀年”
“The planet Sui is counting years.”（p.3）[11]
Ancient Chinese scholars predicted that the solar circular movement of the planet Jupiter took 12 years. This unity was described as one Zhoutian 周天. Hence, this unit of Jupiter's ecliptic movement was divided into 12 equal parts. Because the 12 sequences (branches zhi支) on earth, i.e. zi :子, chou 丑, yin 寅, mou 卯, chen 辰，si巳, wu 午, wei 未, shen申, you酉, xu戌and hai亥, were widely known to people at that time, they conceived that there had to be a planet, the speed of which was also one Zhoutian (i.e. 12 years), and which had to be circulating in the direction, that followed the 12 heavenly sequences (chen 辰), which corresponded to the 12 above mentioned earthly branches and assigned certain regions in the sky.
Besides, the ancient astronomers thought that Jupiter was moving towards the right, as can be seen from the following statement:
“歲星右行於天。”
"During daytime, the planet Sui (Jupiter) moves rightwards.”
According to the above mentioned axiom 'Together, yin and yang form the way (Dao)', the ancient astronomers applied type deduction in order to ascertain that there had to be a planet moving in the opposite direction, i.e. leftwards and from east to west. The
invented planet was called Tai Sui (太歲). Since the starting points of both planets were defined according to type deduction, the ancient scholars could calculate the position of this invented planet at any time from the position of Jupiter. As a result they could count years according to the sequences of the 12 above-mentioned heavenly regions (12 chen辰). From this example it is clear that the axiom 'Together, yin and yang form the way’ profoundly influenced the methodology of ancient sciences.
The theory of yin and yang and the five elements (yin yang wu xing 陰陽五行) also had a great impact upon traditional Chinese medicine. This theory defined its basic rules since antiquity up to the very present. In the context of the so-called eight dialectic rules (ba gang bianzheng 八綱辯證) of Chinese medicine, which is composed of four pairs of mutually opposite concepts, the complementary and correlative relation between yin and yang formed the first or general law, which summed up the laws of the remaining three relations between the other bipolar concepts. Traditional Chinese medicine is based upon the presumption that the main reason for diseases, produced by the body, is to be found in the loss of harmony between these two poles.
“陰陽反作，病之逆從也。”
“If yin and yang lose their harmony, a disease follows.”(p.63)[12]
Therefore, the adjustment of both poles is the key of curing the illness.
“陰陽者，天地之道也，萬物之綱紀，變化之父母，生殺之本始，神
明之府也，治病必求於本。”
“yin and yang are the way of Heaven and Earth. They form the order of all
beings, and they are parents to all changes. They represent the origin of life
and death and the source of spirit. If we want to cure an illness, we have to
follow their rules.”(p.62)[12]
This kind of type deductions, that were established as early as in The Zhou Book of Change, are still a valid tool for guiding traditional Chinese medicine in diagnostics and revealing the variety and regulation of diseases.
The relations between the five elements (wood 木, fire 火, earth土, metal 金, water 水) were also defined by basic logical rules: wood produces fire, fire produces earth, earth produces metal, metal produces water, and water produces wood. Analogously, wood restrains earth, earth restrains water, water restrains fire, fire restrains metal and metal restrains wood. Since each of the five elements corresponded to a certain combination of the 12 heavenly sequences and the 12 branches of the earth, the application of type deduction led to the following conclusions: the phrase 'metal restrains wood', for instance, could be changed into the phrase 'the combination of the
sequences Geng and Xin (庚辛) restrains the liver', which meant that 'at the time of Geng or Xin the liver dies.' This conclusion was derived from a series of type deductions: since the sequences Geng and Xin correspond to metal, and since metal restrains wood, and since wood corresponds to the liver, the conclusion is, that sections Geng and Xin restrain the liver (so the patient has to die).
Feng Qi 馮契, one of the most famous modem Chinese philosophers, explained the logical thought of the yin and yang theory, the eight triangles and the five elements in the following way:
“中國古代哲學開端於原始的陰陽學說……《易傳》講八卦，《呂
氏春秋》與《黃帝內經》講通常所謂陰陽五行學說。但從邏輯看，這
兩個系統已彼此溝通……而陰陽五行學說更明顯的作為一種自然哲學，
與天文、曆法、音律、醫學、農學等有密切聯繫，因此它所講的邏輯
更明顯的具有方法論的意義，也不妨說，在《呂氏春秋》、《黃帝內經》
等著作中，辯證邏輯的比較法已被運用於具體科學領域，而成為卓有
成效的方法。”
“Ancient Chinese philosophy started with the primitive theory of yin and yang. The classical book Commentaries on the Book of Change contains triangles, while other classical sources such as Lu shi chunqiu or Huangdi nei ring contain theories about yin and yang and the five elements. From the viewpoint of logic, both theories are mutually compatible. They clearly represent a kind of natural philosophy, which has been tightly connected to traditional Chinese astronomy, calendar science, metrics, medicine, agronomy, etc. Hence, its logic is of great methodological importance. We can say that the comparative method of dialectical logic, as can be found in these classical sources, has already been applied in different fields of concrete sciences, and therefore represented a crucial and efficient method.”(p.21)[13]
Although he was mainly discussing dialectical logic in this statement, we do not need to focus on the problems of dialectical logic. Instead, we should look upon the thought of yin and yang and the five elements as a kind of complete method and a valid tool for seeking the genuine guidelines of ancient Chinese science.
In ancient Greece, Aristotle regarded logic as a tool used to recognise the scientific truth. In his logical research, Aristotle's main purpose was to find an exact method and an exact form of thought that could be applied to scientific research(p.66)[14] Similar to Aristotle's role in ancient Europe, The Zhou Book of Change had a great impact upon the further development of ancient Chinese science, since it provided exact forms and methods. This formalised logical structure is based upon type deductions.
3. The logical system of type deduction in changeology
According to Zhou Liquan, logic is mainly a scientific discipline that deals with research in different forms of deduction.(CD1.1.,No.1)[6] Forming the original, specific form of classical Chinese logic, the logic of changeology is a kind of general logic, since it possesses a common logical character, which revealed ancient Chinese thought and provided it with general forms of deduction. The method of type deduction found in this work represented the most basic and common formal structure in ancient Chinese culture. Its rules can be seen as similar to the axioms of the ancient Greek system of deduction. Therefore, it is not surprising that it became the starting point of the entire humanities and natural sciences in ancient China. The method of type deduction, as applied in The Zhou Book of Change was based upon the most elementary logical premises, such as yin, yang, the five elements and the sequences and branches (ganzhi 干支); from these premises, it proceeded through several limited steps in order to reach the inevitable conclusion. This method represented the main tool for exploring the truth in ancient Chinese science. It played an important part in scientific research, and had a great impact upon its development, which could be seen in the brilliant achievements of ancient Chinese astronomy, traditional Chinese medicine, agriculture, hydraulics, constructional engineering, etc. In addition, it represents one of the possible explanations for 'N. Joseph's puzzle' and 'Einstein's puzzle'.
Let us indicate a formal description of the type deduction method as found in changeology.
3.1 A brief list of semantic categories, applied in the type deduction method in changeology (M)
(1)Dao or the Way (taiji 太極)
(2)Two poles(liangyi 兩儀):M(yin陰),S(yang 陽)
(3)Four images(si xiang 四象) :spring,summer,autumn,winter
(4)Eight triangles(ba gua八卦)
(5)sixty-four hexgrams:(liushi si gua 六十四卦)
(6)five elements(wu xing 五行)：wood (mu 木)，fire (huo 火)，earth(tu 土)，metal(jin 金)，water (shui 水)
(7)Five directions(wu fang 五方)：east,south,centre,west,north
(8)Five tones(wu yin五音)：jiao角，zhi 徵，gong 宮,shang 商,yu 羽
(9)Five seasons(五季)：spring,summer,long summer(chang xia 長夏),autumn,winter
(10)The heavenly sequences(tian gan 天干):jia 甲,yi 乙,bing 丙,ding 丁,wu戊，ji己,geng庚，xin 辛，ren 壬,gui 癸
(11)The earthly branches(di zhi 地支)：zi子，chou 丑,yin 寅,mao 卯,chen 辰,si巳,wu 午,wei 未,shen 申,you 酉,xu 戌,hai 亥.
(12)Odd numbers(ji shu yang 奇數陽)
(13)Even numbers (ou shu yin 偶數陰)
In the changeological system of logical type deduction there is a corresponding relation between the basic concepts and attributes on one side, and the brief list of semantic categories, listed above on the other. They form a basis for further formulae that can be stated in a matrix table of tree and false values.
3.2 A description of the logical system of type deduction in changeology
The grammatical structure of type deductions:
I. The original symbols:
a) Elementary notions: yin and yang, four images, eight triangles, five elements, five directions, five seasons, five tones, heavenly sequences, earthly branches, odd and even numbers
b)Conjunctions:Λ,V,→， ⏛,«,< >,=,∈,·
c)The left and right parentheses:( ),[ ],{ }
Ⅱ.Definition
a) The symbol in type (class)A is a well-formed formula (‘ ’is a grammatical variable,representing any symbol in class A)
b) If the symbol series X and Y are well formed formulae,then XΛY , X V Y , X→Y , X⏛⏛ Y , X«Y, <X,Y> , X·Ｙ，X=Y, X∈Y are also well-formed formulae.
c) Only those consistent with(a)and (b)are well-formed formulae
Ⅲ.The rule of transformation:
X,Y,Z,Q,……are grammatical variables,represented by any well-formed formula.
Ⅳ.The rule of substitution
Xa(x«y)b├X’(X/Y)b
(x∈X)
In the changeological system of type deductions,the formal structure of inferences has been carried out as follows:If x is a sentence that corresponds to type(class)a in the list of semantic categories and if it is a well formed formula and x is a constant in X,that corresponds to type (class)b in the semantic category table ,x«y,then the sentenceX(’),which is substituted by Y from a is a well formed formula.a and b are grammatical variables representing arbitrary categories in the category list,‘ ’is a symbol,which represents formal inference.
From X«Y,we can deduce X→Y,Y→X
From XΛY,we can deduce X V Y
From X·Y«Z,we can deduce X«Z，Y←→Z
From XΛY,we can deduce X·Y
From X«Z,X«Y,we can deduce X«ZΛY, X«Z(Y)
From XΛY«Z,we can deduce X« Z , Y« Z
From X«Y,we can deduce X(Y)
From {X,Y,Q……}∈Z,we can deduce XΛYΛQ→Z
From X<Y,Z,……>«Q,we can deduce X«Q, or<Y, Z …> «Q
Ⅴ.The axiom
In the changeological system of type deduction,the axioms are self-evident and have been recognised as a part of the Chinese cultural system,e.g.‘Together, yin and yang form the way (Dao)(一陰一陽之謂道)’，or ‘The five elements mutually produce and restrain each other’,etc. For a better understanding we shall produce only a few of them:
(1)The law of the yin and yang identity (yinyang tongyilǜ 陰陽同一律)：M·S«1
(2)The law of the yin and yang numbers (yin yang gui shu lǜ 陰陽歸數律)
X is the law of yin and yang numbers,if and only if ,X is sufficient to one of the formulae,stated below
①{1,3,5,7,9……}∈ S
②{2,4,6,8,10……}∈ M
③The law of the river diagram (hetulǜ 河圖律)
Xa is the law of the river diagram,if and only if ,Xa is sufficient to one of the formulae,stated below:
① <1,6> « water
② <2,7> « fire
③ <3,8> « wood
④ <4,9> « gold
⑤ <5,10> « soil
Xb (The law of the five elements and directions)(wuxingfangweilǜ 五行方位律)：Xb is the law of the river diagram b),,if and only if ,,Xb is sufficient to one of the formulae,stated below:
① water <1,6> « north
② fire <2,7> « south
③ wood <3,8> « east
④ metal <4,9> « west
⑤ earth <5,10> « centre
The law of heavenly sequences and the five elements (tianganwuxinglǜ天干五行律):X is the law of heavenly sequences and the five elements ,if and only if ,X is sufficient to one of the formulas stated below:
① jiaΛyi « wood
②bingΛding « fire
③gengΛxin « mental
④wuΛji « earth
⑤renΛgui « water
The law of the numbers of heavenly sequences (tiangan guishulǜ天干歸數律):(jia«1) Λ(yi«2)Λ(bing«3)Λ(ding«4)Λ(wu«5)Λ(ji«6)Λ(geng«7)Λ(xin«8)Λ(ren«9)Λ(gui«10).
Ⅵ.The theorem
The theorems in the changeological system of type deduction have been deduced according to the axioms and the rule of transformation.We give two examples to elucidate this process.
The law of the directions of the heavenly branches (tiangan fangweilǜ 天干方位律):X is the law of the directions of the heavenly branches,if and only if ,X is sufficient to one of the formulae stated below :
(1) (jiaΛyi) « east
(2) (bingΛding) « south
(3) (wuΛji) « centre
(4) (gengΛxin) « east
(5) (renΛgui) « north
Proof:
(1)wood<3,8>«east……The law of the five elements and directions
(2)wood«east……The rule of transformation
(3)east«wood……The rule of transformation
(4)jiaΛyi«wood……The law of heavenly branches and the five elements
(5)jiaΛyi«east……The rule of substitution
(6)(bingΛding) « south,(wuΛji) « centre,(gengΛxin) « west,(renΛgui) « north
(the proof of 6 is the as ‘jiaΛyi«east’(omitted))
(7)Proof over.
The law of yin or yang of the heavenly sequences (tianganyinyang guishulǜ 天干陰陽歸屬律)：X is the law of yin or yang of the heavenly sequences, if and only if ,X is sufficient to one of the formulae stated below:
(1){jia,bing,wu,geng,ren}∈S
(2){yi,ding,ji,xin,gui}∈M
Proof :
(1)(jia«1)Λ(yi«2)Λ(bing«3)Λ(ding«4)Λ(wu«5)Λ(ji«6)Λ(geng«7) Λ(xin«8)Λ(ren«9)Λ(gui«10)
……The law of numbers of the heavenly sequences
(2){1,3,5,7,9……}∈S
{2,4,6,8,10……}∈M
……The law of yin and yang numbers
(3){jia,bing,wu,geng,ren}∈S
{yi,ding,ji,xin,gui}∈M
……The rule of substitution
(4)Proof over.
3.3 The explanation of the conjunction in the logical system of type deduction in changeology
Explanation1:
(1) Λ (read as ‘conjunction’)
(2) V (read as ‘disjunction’)
(3) → (read as‘affiliation to characteristics(xingzhi shuyu性質屬於’),‘to bring into (na 納)’，‘mutual production (xiangsheng 相生)’,or‘to deduce(tuichu推出)’)
(4) (read as ‘restrain(ke克)’)
(5) « (read as ‘belong to each other(hushu互屬)’,’equal to and belong to (dengshuyu等屬於))
(6) < >(read as‘order’)
(7) · (read as ‘and’:can be omitted)
(8) = (read as‘equal’)
(9)∈(read sa ‘belong to’)
Explanation2:
(1)pΛq,read as the conjunctive form of p and q,if and only if ,p and q belong to the same categorical character in the semantic list of categories.
(2)p∨q,can be omitted.
(3)p→q,read as the form of deduction from p and q.It expresses the deduction from p to q ,with the meaning that there are a few relations among p and q：
(a)‘affiliation to characteristics(xingzhi shuyu 性質屬於)’,if and only if ,q includes some characteristics of p in some categories in the semantic list of categories .
(b)produce each other (xinagsheng相生),if and only if ,the character p can change into q in some categories in the semantic list , as the substitution object.
(4) p q,read as a restraining form of p and q, if and only if , p can restrain the development of q to some kinds of characteristics in the semantic list ,as the substitution object.
(5)p«q, read as ,‘equal and belonging to the form of p and q’ ,if and only if ,p has some of the same characteristics as q in the semantic list .
(6)<p,q,r……>, read as an order form of p,q,r…,if and only if, the order of p,q,r ……is fixed and can not change.
(7)p·q, read as ‘and form of p and q’, if and only if ,p and q form the nature arrangement of the changeological type deduction, the ‘and’sign can be omitted,and p·q can be written as pq.
(8)p=q, read as the ‘equal’form of p and q; if and only if ,p and q belong to the same categorical character in some categories in the semantic list
(9)p∈q, read as ‘affiliation of p and q’: if and only if ,p is a member of q, and p includes the characteristics of q.
4.The semantic explanation of the logical system of The Zhou Book of Change
In order to explain the logical character of changeological type deduction,which formed the basic methodology of ancient science,we shall firstly try to explain the semantic meaning of the axiom,and then illustrate it by a concrete example.
The law of the river diagram (hetulǜ 河圖律): in the classical Chinese encyclopaedia the Complete works from the four Archives (siku quanshu 四庫全書) we can find the following statement：
“河圖，一、六為水，居北；二、七為火，居南；三、八為木，居東；
四、九為金，居西；五、十為土，居中。北方水生東方木，東方木生南方
火，南方火生中央土，中央土生西方金，西方金生北方水，此五行相生之
序也。”
“The river diagram: the numbers one and six stand for water; their position is in the north . The numbers two and seven stand for fire and their position is in the south. The numbers three and eight stand for wood and their position is in the east . The numbers four and nine stand for metal and their position is in the west. The numbers five and ten stand for soil and their position is in the centre. North and water produce east and wood ,east and wood produce south and fire ,south and five produce centre and earth ,centre and earth produce west and metal ,west and metal produce north and water ,this is the order, in which the five elements produce each other.”（p.135）[15]
The River Diagram and the Book of the Luo River (Luo shu 洛書), contain the earliest ideas of yin and yang, odd and even numbers and the five elements (wuxing 五行), as well as their mutual production and restraint. Ancient Chinese scholars believed that the spirit was the essence of the universe. This spirit manifested itself in the five elements, namely in wood, fire, earth, metal and water. The spirit was continually moving and changing. Each period was predominated by a certain element of this spirit. The element that predominated at a certain period was called 'the spirit on duty (zhiqi 值氣)' in this period. When one kind (or element) of the spirit is on duty, it can produce (sheng 生) or restrain (ke 克) the other elements.
,
5. Conclusions
First, the symbols applied in the type deduction process within The Zhou Book of Change are self-sufficient in respect to grammar and semantics. Each of them has a parallel symbol that can be found in the list of semantic categories. They are self referential and self-sufficient. The propositions in type deduction of The Zhou Book of Change can also be explained according to their position within the semantic list. They are also sufficient and this is important, since we know that the sufficiency of a proposition forms the basic condition for any logical system. These facts provide us with the foundation to expound and prove the validity of propositions in the logic of type deductions in changeology.
Second, the changeological system of type deductions was based upon a common language. In Europe, concerns as regards the calculable common language can be traced back to the 17th Century, when Gottfried Wilhelm Leibniz stated that it formed the basic precondition for mathematical logic.(CD1.1.,No1) [6] In fact, the idea of 'the common language' has been one of the basic thoughts in Western logic? However, the logical language of the type deductions from The Zhou Book of Change (yixue luoji 易學邏輯) differed from the formal traditional common language in the West. Jin Yuelin called it 'the empty shelf (kongjiazi 空架子)' and claimed that it was found in the thought of numerous ideologists from the pre-Qin era. Although it was expressed through a natural language, it stood outside of it, and provided the basis for the common language in ancient China. Within the framework of classical Chinese culture, this language was only used to express the meaning of the most abstract and simplest signs; it provided a form of inferential processes, which became the mechanical limit for deductions of the relations between individual signs. If we try to describe it with the methods of modem logic, its construction becomes more intelligible, but we also have to work hard to realise it within the frame of the modem logical system.
Third, the changeological logic of type deductions is a special form of logic, which has been formed under the cultural background of ancient China and expressed in Chinese characters; thus, the logical variables in deductions are symbolised by Chinese characters, and the constant terms generalise the logical relations between them. This fact provides us with a new method for researching the logical relations between Chinese characters, as well as a new insight into the different types of their structure, which enables us to analyse them in a new way.
Heinrich Scholz, a famous expert in the history of logic once said that logic was an outcome of certain ages; if mathematical logic came into existence in ancient Greece, it would be seen as a monster. We can not presume that the ancient Chinese logic was
automatically on par to the logic that sprung from the Western cultural background, but nevertheless we can also notice amazing similarities in both kinds of thought. If we temporary put aside the political and ethical thought of changeology and focus upon its logical system, we can rest assured, that it established a kind of common cognitive method, which functioned as a tool for ancient Chinese science in its exploration of truth. The fact that ancient Chinese science developed to a rather high level was without a doubt connected to the application of this cognitive tool. Therefore, both systems of thought, the Chinese as well as the Western logic, can be seen as similar in respect to their basic character, which provided humans with methods of thought and with criteria for defining truth as an invaluable tool for scientific research.
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原载ASIA AND AFRICA STUDY Vol.Ⅸ,No.2, was printed on the 15th of November 2005 in Ljubljana, p.161-186页。
