The Collaborative International Dictionary of English v.0.48:

Incomprehensible \In*com`pre*hen"si*ble\, a. [L.
   incomprehensibilis: cf. F. incompr['e]hensible. See In-
   not, and Comprehensible.]
   [1913 Webster]
   1. Not capable of being contained within limits.
      [1913 Webster]

            An infinite and incomprehensible substance.
                                                  --Hooker.
      [1913 Webster]

   2. Not capable of being comprehended or understood; beyond
      the reach of the human intellect; inconceivable.
      [1913 Webster]

            And all her numbered stars that seem to roll
            Spaces incomprehensible.              --Milton.
      -- In*com`pre*hen"si*ble*ness, n. --
      In*com`pre*hen"si*bly, adv.
      [1913 Webster]

WordNet (r) 3.0 (2006):

incomprehensible
    adj 1: incapable of being explained or accounted for;
           "inexplicable errors"; "left the house at three in the
           morning for inexplicable reasons" [syn: inexplicable,
           incomprehensible] [ant: explicable]
    2: difficult to understand; "the most incomprehensible thing
       about the universe is that it is comprehensible"- A. Einstein
       [syn: incomprehensible, uncomprehensible] [ant:
       comprehendible, comprehensible]

Moby Thesaurus II by Grady Ward, 1.0:

106 Moby Thesaurus words for "incomprehensible":
   Greek to one, abstruse, all-comprehensive, all-inclusive,
   ambiguous, antic, arcane, baffling, beguiling, bewildering,
   beyond understanding, boundless, countless, cryptic, dark, deep,
   endless, enigmatic, eternal, exceptional, exhaustless,
   extending everywhere, extraordinary, fabulous, fanciful, fantastic,
   fascinating, illimitable, illimited, immeasurable, immense,
   impenetrable, impossible, inarticulate, incalculable, incognizable,
   incoherent, inconceivable, incredible, indecipherable,
   inexhaustible, infinite, infinitely continuous, innumerable,
   inscrutable, interminable, interminate, limitless, marvelous,
   measureless, miraculous, mysterious, mystifying, no end of,
   numinous, obscure, occult, opaque, outlandish, passing strange,
   past comprehension, perpetual, perplexing, phenomenal, prodigious,
   puzzling, rambling, rare, recondite, remarkable, sensational,
   shoreless, strange, striking, stupendous, sumless, termless,
   unaccountable, unbelievable, unbounded, uncircumscribed,
   unconnected, undecipherable, unexpected, unfathomable, unheard-of,
   unimaginable, unintelligible, unique, universal, unknowable,
   unlimited, unmeasurable, unmeasured, unnumbered, unplumbed,
   unprecedented, unsearchable, untold, without bound, without end,
   without limit, without measure, without number, wonderful,
   wondrous