on the contrary

from 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}]
    
from 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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