The quality of being callid; cunning, craftiness, or skillful deception; cleverness in dishonest dealings.
From callid + -ity (quality of). Forms a noun from the Latin-derived adjective, creating a word for the state or characteristic of being cunning and shrewd.
Callidity is what happens when you try to sound admiring of someone's intelligence while also acknowledging they're probably lying to you—it's an honest word about dishonesty.
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