經(下)

The Canon, Part 2

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推理與歸謬

Reasoning and Reductio Arguments

止，類以行人。說在同。所存與者，於存與孰存？駟異說。推類之難。說在之大小。五行毋常勝。說在宜。物盡同名：二與斗，愛，食與招，白與視，麗與，夫與履。一，偏棄之，謂而固是也。說在因。

Stopping: by analogy and by bringing in examples. The explanation lies in sameness. Among those who exist and those who are preserved, which truly exists? The analogy of the four horses differs. The difficulty of analogical reasoning: the explanation lies in greater and lesser. The Five Phases do not have a fixed sequence of conquest. The explanation lies in appropriateness. Things that share a name entirely: 'two' and 'fight,' 'love,' 'eat' and 'beckon,' 'white' and 'see,' 'beautiful' and... 'husband' and 'shoe.' When one aspect is removed, if we still call it the same, the explanation lies in the basis.

Notes

1context

The Canon Part 2 presents propositions paired with brief explanations (說在...). These are more advanced logical arguments building on the definitions in Part 1. The text is extremely terse and many passages are corrupt, making definitive interpretation difficult.

光學與幾何

Optics and Geometry

二臨鑒而立，景到。多而若少。說在寡區。鑒位，景一小而易，一大則正。說在中之外內。鑒團景一。景不徙。說在改為。景二。說在重。景到，在午有端與景長。說在端。景迎日。說在摶。景之小、大。說在地正、遠近。

Two people stand before a mirror, and the image is inverted. Many appear as few: the explanation lies in the scarcity of the area. Mirror position: one image is small and reversed, one is large and upright. The explanation lies in being inside or outside the center. A round mirror produces a single image. The image does not move: the explanation lies in changing the arrangement. Two images: the explanation lies in overlap. The inverted image: at the point of intersection there is a point and the image is elongated. The explanation lies in the point. The image faces the sun: the explanation lies in the sphere. The small and large sizes of images: the explanation lies in the angle of the ground and distance.

Notes

1context

These passages on optics describe phenomena of concave and convex mirrors, pinhole cameras, and shadow formation. They represent the earliest known systematic observations of optical phenomena in China and arguably the world. The distinction between images inside and outside the focal point of a concave mirror is particularly notable.

悖論與辯學

Paradoxes and Logic

狗，犬也。而殺狗非殺犬也，可。說在重。牛馬之非牛，與可之同。說在兼。無窮不害兼。說在盈否知。謂辯無勝，必不當。說在辯。不知其所處，不害愛之。說在喪子者。

'Dog' is 'canine.' Yet to say 'killing a dog is not killing a canine' can be acceptable: the explanation lies in different levels of meaning. 'An ox-horse is not an ox' -- this is comparable to the permissible: the explanation lies in combination. The infinite does not prevent universality: the explanation lies in whether fullness can be known. To say that disputation has no winner is necessarily wrong: the explanation lies in the nature of disputation. Not knowing someone's location does not prevent loving them: the explanation lies in the case of one who has lost a child.

Notes

1context

The 'ox-horse is not an ox' paradox (牛馬之非牛) is related to the famous 'white horse is not a horse' (白馬非馬) argument of the logician Gongsun Long. The Mohist response demonstrates a sophisticated understanding of class logic and set theory -- a combined class (ox-horse) is not identical to either component class.

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