The Collaborative International Dictionary of English v.0.48:

Preposterous \Pre*pos"ter*ous\, a. [L. praeposterus; prae before
   + posterus coming after, latter. See Posterior.]
   [1913 Webster]
   1. Having that first which ought to be last; inverted in
      order. [Obs.]
      [1913 Webster]

            The method I take may be censured as preposterous,
            because I thus treat last of the antediluvian earth,
            which was first in the order of nature. --Woodward.
      [1913 Webster]

   2. Contrary to nature or reason; not adapted to the end;
      utterly and glaringly foolish; unreasonably absurd;
      perverted. "Most preposterous conclusions." --Shak.
      [1913 Webster]

            Preposterous ass, that never read so far! --Shak.
      [1913 Webster]

   Syn: Absurd; perverted; wrong; irrational; foolish;
        monstrous. See Absurd.
        [1913 Webster] -- Pre*pos"ter*ous*ly, adv.
        -Pre*pos"ter*ous*ness, n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

preposterous
    adj 1: incongruous;inviting ridicule; "the absurd excuse that
           the dog ate his homework"; "that's a cockeyed idea"; "ask
           a nonsensical question and get a nonsensical answer"; "a
           contribution so small as to be laughable"; "it is
           ludicrous to call a cottage a mansion"; "a preposterous
           attempt to turn back the pages of history"; "her
           conceited assumption of universal interest in her rather
           dull children was ridiculous" [syn: absurd, cockeyed,
           derisory, idiotic, laughable, ludicrous,
           nonsensical, preposterous, ridiculous]

Moby Thesaurus II by Grady Ward, 1.0:

139 Moby Thesaurus words for "preposterous":
   Gothic, a bit thick, a bit thin, absurd, asinine, balmy, barmy,
   baroque, barred, batty, beyond belief, bizarre, brain-born,
   closed-out, cockamamie, contrary to reason, crazy, cuckoo,
   cutthroat, dotty, doubtable, doubtful, dream-built, dubious,
   dubitable, exacting, excessive, excluded, exorbitant, extortionate,
   extraordinary, extravagant, extreme, fanciful, fancy, fancy-born,
   fancy-built, fancy-woven, fantasque, fantastic, fatuitous, fatuous,
   florid, foolish, gouging, grossly overpriced, grotesque,
   hard of belief, hard to believe, harebrained, high-flown, hopeless,
   idiotic, imbecilic, immoderate, implausible, impossible,
   inconceivable, incredible, inflationary, inordinate, insane,
   irrational, laughable, logically impossible, loony, ludicrous, mad,
   maggoty, mindless, monstrous, moronic, nonmeritorious, nonsensical,
   not coming, not deserving belief, not outstanding, not possible,
   notional, nutty, open to doubt, open to suspicion, out of bounds,
   out of sight, outlandish, outrageous, outre, overpriced,
   oxymoronic, paradoxical, passing belief, poppycockish, potty,
   problematic, prohibited, prohibitive, questionable, ridiculous,
   risible, rococo, ruled-out, screwy, self-contradictory, senseless,
   silly, skyrocketing, spiraling, staggering belief, suspect,
   suspicious, tall, thick, thin, unbelievable, unconscionable,
   unconvincing, undeserved, undeserving, undue, unearned, unearthly,
   unentitled, ungodly, unimaginable, unjustified, unmerited,
   unmeriting, unowed, unowing, unreasonable, unthinkable,
   unwarranted, unworthy, unworthy of belief, usurious, wacky, weird,
   whimsical, wild