1. a contrary aim
; - Example: "at cross-purposes"
The Collaborative International Dictionary of English v.0.48:
cross-purpose \cross"-pur`pose\ (-p?r`p?s), n.
1. A counter or opposing purpose; a contrary aim; hence, that
which is inconsistent or contradictory. --Shaftesbury.
2. pl. A conversational game, in which questions and answers
are made so as to involve ludicrous combinations of ideas.
To be at cross-purposes, to misunderstand or to act counter
to one another without intending it; -- said of persons.
WordNet (r) 3.0 (2006):
n 1: a contrary aim; "at cross-purposes"