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Wiktionary has the following entry for the etymology of 邏輯:

Phono-semantic matching of English logic.

However, the Chinese Wikipedia entry states the following:

當代中文一般採取音譯方式,將其譯為邏輯。

Which seems to imply there isn't sort of semantic hint in the Chinese translation. Looking at the invidiual characters 邏 (who's meanings revolve around to patrol) and 輯 (to collect, to compile, etc.), I fail to see any semantic hints. Is the Chinese word 邏輯 actually a phono-semantic matching of the English word logic? If so, what is the semantic connection bewteen the two words?

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No, it's a transliteration.

The Chinese term「邏輯」first appeared in a Chinese translation of John Stuart Mill's A System of Logic, Ratiocinative and Inductive. The Chinese translation title is 《穆勒名學》 by 嚴復, and the Chinese word「邏輯」is directly explained there:

案邏輯此翻名學。其名義始於希臘。為邏各斯一根之轉。邏各斯一名兼二義。在心之意。出口之詞。皆以此名。引而申之。則為論為學。故今日泰西諸學。其西名多以羅支結響。羅支即邏輯也。


To add, the only manner of any kind of semantic matching is「輯」(compile), which is the explanation of「邏各斯」turning into「邏輯」. From the same paragraph:

...故邏各斯名義最為奧衍。而本學之所以稱邏輯者。以如貝根言。是學為一切法之法。一切學之學。明其體之尊。為用之廣。則變邏各斯為邏輯以名之。

but this isn't a semantic matching of the Greek root, and more a semantic matching of the rather wide application of the suffix -ology.

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