Crŏss'-pŭr'pose, n.
n. 1. A counter or opposing purpose; hence, that which is inconsistent or contradictory.
Sense 2. (pl.) A game of the nature of conversation, in which questions and answers are made so to concur as to involve ludicrous combinations of ideas.
To be at cross-purposes, to act counter to one another without intending it;—said of persons.