The Collaborative International Dictionary of English v.0.48:

Inconceivable \In`con*ceiv"a*ble\, a. [Pref. in- not +
   conceivable: cf. F. inconcevable.]
   Not conceivable; incapable of being conceived by the mind;
   not explicable by the human intellect, or by any known
   principles or agencies; incomprehensible; as, it is
   inconceivable to us how the will acts in producing muscular
   motion.
   [1913 Webster]

         It is inconceivable to me that a spiritual substance
         should represent an extended figure.     --Locke.
   -- In`con*ceiv"a*ble*ness, n. -- In`con*ceiv"a*bly, adv.
   [1913 Webster]

         The inconceivableness of a quality existing without any
         subject to possess it.                   --A. Tucker.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inconceivable
    adj 1: totally unlikely [syn: impossible, inconceivable,
           out of the question, unimaginable]