經說(上) (Canon Explanation, Part 1) — Chinese ink painting

墨子 Mozi · Chapter 42

經說(上)

Canon Explanation, Part 1

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因果與知識之說

Explanations of Cause and Knowledge

故:小故,有之不必然,無之必不然。體也,若有端。大故,有之必無然,若見之成見也。體:若二之一、尺之端也。知材:知也者,所以知也,而必知,若明。慮:慮也者,以其知有求也,而不必得之,若睨。知:知也者,以其知過物而能貌之,若見。

Cause: A minor cause is one whose presence does not necessarily produce the effect, but whose absence necessarily prevents it -- like having a point as part of a body. A major cause is one whose presence necessarily produces the effect, as seeing necessarily constitutes perception. Part: like one of two, or the point of a ruler. The capacity to know: that by which one knows, and necessarily knows -- like sight. Deliberation: using one's knowledge to seek something, but not necessarily obtaining it -- like glancing sideways. Knowledge: using one's knowledge to encounter things and being able to describe their appearance -- like seeing.

Notes

1context

The distinction between 'minor cause' (小故, necessary condition) and 'major cause' (大故, sufficient condition) is a remarkable anticipation of the necessary/sufficient condition distinction in modern logic, formulated over two millennia before John Stuart Mill's systematic treatment.

倫理概念之說

Explanations of Ethical Concepts

仁:愛己者,非為用己也,不若愛馬,著若明。義:志以天下為芬,而能能利之,不必用。禮:貴者公,賤者名,而俱有敬僈焉。等,異論也。孝:以親為芬,而能能利親,不必得。信:不以其言之當也,使人視城得金。

Benevolence: loving oneself not for the sake of using oneself -- unlike loving a horse. This is as clear as sight. Righteousness: having the aspiration to consider the world as one's charge, and being able to benefit it, though not necessarily being employed. Ritual propriety: the honored have official titles, the lowly have personal names, yet both have reverence and neglect; the ranks involve different assessments. Filial devotion: considering one's parents as one's charge and being able to benefit them, though not necessarily succeeding. Trustworthiness: it lies not in whether one's words are correct, but in making someone look at a city wall and find gold.

時空與數學之說

Explanations of Space, Time, and Mathematics

久:古今旦莫。宇:東西家南北。窮:或不容尺,有窮;莫不容尺,無窮也。盡:但止動。始:時或有久,或無久。始當無久。化:若蛙為鶉。端:是無同也。圜:規寫支也。方:矩見支也。倍:二尺與尺,但去一。

Duration: past and present, morning and evening. Space: east and west, home, south and north. Limit: if somewhere a foot cannot fit, there is a limit; if nowhere is a foot unable to fit, there is no limit -- that is infinity. Completeness: simply stopping movement. Beginning: time either has duration or has no duration; the beginning is when there is no prior duration. Transformation: like a frog becoming a quail. Point: that which has no equal part. Circle: drawn by a compass from a support point. Square: shown by a set-square from a support point. Double: two feet from one foot -- simply removing one.

Notes

1context

The definition of infinity (無窮) as the condition where 'nowhere is a foot unable to fit' is a spatial definition remarkably close to modern mathematical concepts. The definition of a point (端) as 'having no equal part' (i.e., indivisible) parallels Euclid's definition: 'a point is that which has no part.'

Edition & Source

Text
《墨子》 Mozi
Edition
中華古詩文古書籍網 transcription, 《四部叢刊》本
Commentary
Mo Di (墨翟) et al., Warring States period