cross-purpose

• cross purpose

Attested (in the plural form) since the 1660s, originally meaning ‘contradictory intentions.’[1]

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cross-purpose (plural cross-purposes)

1. (idiomatic) A contrary or conflicting purpose or understanding, especially an unintentional or misconceived one.

   We are working at cross-purposes here, if you're trying to reduce the count and I'm trying to increase it.

2. (dated) A conversational game, in which questions and answers are made so as to involve ludicrous combinations of ideas.

   (Can we find and add a quotation of Samuel Pepys to this entry?)

• at cross-purposes