The Collaborative International Dictionary of English v.0.48:

Contrary \Con"tra*ry\, n.; pl. Contraries.
   1. A thing that is of contrary or opposite qualities.
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            No contraries hold more antipathy
            Than I and such a knave.              --Shak.
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   2. An opponent; an enemy. [Obs.] --Chaucer.
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   3. the opposite; a proposition, fact, or condition
      incompatible with another; as, slender proofs which rather
      show the contrary. See Converse, n., 1. --Locke.
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   4. (Logic) See Contraries.
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   On the contrary, in opposition; on the other hand. --Swift.

   To the contrary, to an opposite purpose or intent; on the
      other side. "They did it, not for want of instruction to
      the contrary." --Bp. Stillingfleet.
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WordNet (r) 3.0 (2006):

on the contrary
    adv 1: contrary to expectations; "he didn't stay home; on the
           contrary, he went out with his friends" [syn:
           contrarily, to the contrary, contrariwise, on the
           contrary]