\Cross"-pur`pose\ (-p?r`p?s), n.
1. A counter or opposing purpose; 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.
   --Pepys.
{To be at cross-purposes}, to misunderstand or to act counter
   to one another without intending it; -- said of persons.