Analogical Reasoning in Ancient China : some examples

Volkov, Alexei

doi:10.3406/oroc.1992.962

Cited by 14 publications

(7 citation statements)

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“…We have here a striking example of "analogical reasoning," 3 described by Alexei Volkov in his article "Analogical Reasoning in Ancient China" (Volkov 1992). It can be defined in a simple way as "a is to A what b is to B."…”

Section: How Liu Discovered a Planet Through Analogical Reasoningmentioning

confidence: 98%

The Fortunes of a Scholar: When the Yijing Challenged Modern Astronomy

Homola¹

2014

J of Asian Stud

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Liu Zihua arrived in France in 1919 as part of the Sino-French Work-Study Movement. In 1940, he completed a PhD thesis in which he combined modern astronomy and the Yijing through “analogical reasoning” to discover a planet. After Liu went back to China in 1945, his efforts to win recognition came up against nationalist and communist anti-traditionalism but were eventually integrated into the intellectual revival of the 1980s. This study relies on historical sources and anthropological fieldwork to show that Liu is an emblematic figure of the cultural upheaval caused by the introduction of modern Western categories of science, religion, and superstition at the beginning of the twentieth century. Liu's example reveals the changing status of the Yijing in Chinese society, the cross-cultural understanding of science and sacred literature as embodied in this classic, and the role of analogy in cultural assimilation. It also sheds light on the shaping of academic standards in China and on the connection between traditional literary scholars and contemporary “amateur scientists.”

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Section: How Liu Discovered a Planet Through Analogical Reasoningmentioning

confidence: 98%

The Fortunes of a Scholar: When the Yijing Challenged Modern Astronomy

Homola¹

2014

J of Asian Stud

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“…On the latter: "with what is in excess, one fills up the void," see Volkov 1992 andChemla 1992, where a bibliography is given. 33 32 This clause is quite important.…”

Section: The Opening Passage Of the Gnomon Of The Zhoumentioning

confidence: 99%

Geometrical Figures and Generality in Ancient China and Beyond: Liu Hui and Zhao Shuang, Plato and Thabit ibn Qurra

Chemla

2005

Science in Context

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ArgumentThis paper argues that there was a shift in China in the nature, and use, of geometrical figures between around the beginning of the Common Era and the third century. Moreover, I suggest that the emphasis mathematicians in ancient China placed on generality as a guiding theoretical value may account for this shift. To make this point, I first give a new interpretation of a text often discussed, which is part of the opening section of The Gnomon of the Zhou (first century B.C.E. or C.E.). This interpretation suggests that the argument presented in this text for establishing the so-called “Pythagorean theorem” is based upon a certain kind of drawing. Secondly, I contrast this passage with Chinese texts from the third century on the same topic, but relying on a completely different type of drawing. What commands the difference in the kinds of drawing is that the latter drawings are “more general” than the former, in a sense to be made explicit. This paper hence aims at making a contribution to the study of geometrical figures in ancient China.Commenting on one of the latter figures, one of the authors of the third century, Liu Hui, describes how various algorithms emerge out of the same transformation of one particular figure. His remarks provide grounds for commenting on the link between the general and the particular, in relation to figures and how algorithms rely on them, as the issue was perceived by the practitioners themselves.The particular figure in question and its transformation are exactly what we find in the Meno, though in relation to a different mathematical issue. The link of that very figure to the one that is perceived as its “generalization” for several algorithms, including the so-called “Pythagorean theorem,” is made not only in Liu Hui, but also by Thabit ibn Qurra (ninth century C.E.), in a letter where he explicitly addresses the purpose of generalizing the reasoning of the Meno. This parallel offers an appropriate basis to highlight differences in terms of conception and use of figures.

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“…We shall develop aspects of this practice of proof that are related to the theme of the present paper. For other aspects, the reader is referred to Wagner 1979;Wu Wenjun 1982;Volkov 1992Volkov , 1994Chemla 1991Chemla , 1992Chemla , 1997a. A more exhaustive bibliography can be found in Chemla, Guo forthcoming.…”

Section: Generality Without Abstractionmentioning

confidence: 99%

Generality above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China

Chemla

2003

SIC

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Argument Abstraction is commonly valued as being essential to mathematics or even consubstantial with it. In relation to this belief, mathematical texts from Antiquity-be they from Babylon, Egypt, or China-, which are composed of seemingly concrete problems and algorithms solving them, have been considered to be practice-oriented and deprived of theory. This paper offers an alternative view on both issues. Relying on evidence given by third-century commentaries on The Nine Chapters on Mathematical Procedures, a Chinese treatise composed around the beginning of the Common Era, this paper argues that, in the scholarly mathematical tradition of ancient China, generality was more valued than abstraction. In this respect, problems must be interpreted as paradigms, in the sense grammarians use the term. One of the goals of theoretical endeavor was to exhibit the most general operations possible, and this purpose can be read in quite a few specific features of mathematical practice and concepts. Moreover, it is shown that abstraction is not absent from The Nine Chapters, but that it entertains with generality a relationship that requires analysis and can by no means be taken for granted. These ancient sources hence constitute an invitation to develop a critical approach toward the relation of mathematics to abstraction and generality taken separately, as well as the relation of these two values with each other.

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Analogical Reasoning in Ancient China : some examples

Cited by 14 publications

References 1 publication

The Fortunes of a Scholar: When the Yijing Challenged Modern Astronomy

The Fortunes of a Scholar: When the Yijing Challenged Modern Astronomy

Geometrical Figures and Generality in Ancient China and Beyond: Liu Hui and Zhao Shuang, Plato and Thabit ibn Qurra

Generality above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China

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