The language pattern the author refers to is called litotes (https://en.wikipedia.org/wiki/Litotes), but to say that English doesn’t use them is… not quite right.
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If I'm understanding the author's account of Chinese assertion-by-negation correctly, doesn't it sound like assertion-by-negation is the ordinary case in that linguistic tradition, and it's the assertive case that jars the ear? Same pattern, different effect?