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Kojève had a famous sense of humor and here, as in many of his letters and interviews, it is not entirely clear how serious he is being. But beneath the irony and archness Strauss saw something that, while it earned his intellectual respect, also horrified him.
Could you tell me the meaning of "archness" in the context of the above clause. Does it mean some figure of speech or something similar?
[I'm posting an answer as this sense of arch is relatively uncommon, and may be difficult to suss directly from the dictionary.]
Archness is arch plus the suffix -ness which indicates a noun representing the quality or nature of being something. But this adjective meaning of arch has nothing to do with curves or with superiority.
The Macmillan Dictionary and Cambridge Dicionaries Online definitions of arch are substantially similar to that of the Oxford Advanced Learners Dictionary:
speaking or looking as though you think it is funny that you know something that someone else does not know
This strikes me as somewhat narrow to pair with irony, but the meaning is more explicit in other references. The American Heritage Dictionary definition is
a. Mischievous; roguish; b. Teasing, ironic, or sardonic
The Merriam-Webster definition definition is
a. mischievous, saucy; b. marked by a deliberate and often forced playfulness, irony, or impudence
Perhaps, then archness is more than cleverness — it is a writer's cleverness plus a self-satisfaction with the cleverness; Kojève was perhaps too pleased with his own way with words. The writer of the passage says that despite this literary equivalent of a smirk, Strauss perceived a serious side to Kojève's writing.
