The Collaborative International Dictionary of English v.0.48:

Paradoxical \Par`a*dox"ic*al\ (p[a^]r`[.a]*d[o^]ks"[i^]*kal), a.
   1. Of the nature of a paradox.
      [1913 Webster]

   2. Inclined to paradoxes, or to tenets or notions contrary to
      received opinions. --Southey.
      [1913 Webster] -- Par`a*dox"ic*al*ly, adv. --
      Par`a*dox"ic*al*ness, n.
      [1913 Webster]

WordNet (r) 3.0 (2006):

paradoxical
    adj 1: seemingly contradictory but nonetheless possibly true;
           "it is paradoxical that standing is more tiring than
           walking" [syn: paradoxical, self-contradictory]

Moby Thesaurus II by Grady Ward, 1.0:

49 Moby Thesaurus words for "paradoxical":
   abnormal, absurd, ambiguous, ambivalent, anomalous, antinomic,
   baffling, barred, bewildering, closed-out, conflicting, confusing,
   contradictory, contrary to reason, disproportionate, enigmatic,
   equivocal, excluded, hopeless, illogical, impossible, improbable,
   incoherent, incommensurable, incommensurate, incompatible,
   incomprehensible, inconceivable, incongruous, inconsequent,
   inconsistent, inconsonant, ironic, irreconcilable,
   logically impossible, mysterious, not possible, out of proportion,
   oxymoronic, perplexing, preposterous, problematic, prohibited,
   puzzling, ridiculous, ruled-out, self-contradictory, unimaginable,
   unthinkable