The Collaborative International Dictionary of English v.0.48:

Sharpness \Sharp"ness\, n. [AS. scearpness.]
   The quality or condition of being sharp; keenness; acuteness.
   [1913 Webster]

WordNet (r) 3.0 (2006):

sharpness
    n 1: a quick and penetrating intelligence; "he argued with great
         acuteness"; "I admired the keenness of his mind" [syn:
         acuteness, acuity, sharpness, keenness]
    2: the attribute of urgency in tone of voice; "his voice had an
       edge to it" [syn: edge, sharpness]
    3: a strong odor or taste property; "the pungency of mustard";
       "the sulfurous bite of garlic"; "the sharpness of strange
       spices"; "the raciness of the wine" [syn: pungency, bite,
       sharpness, raciness]
    4: the quality of being keenly and painfully felt; "the
       sharpness of her loss"
    5: thinness of edge or fineness of point [syn: sharpness,
       keenness] [ant: bluntness, dullness]
    6: the quality of being sharp and clear [syn: distinctness,
       sharpness] [ant: blurriness, fogginess, fuzziness,
       indistinctness, softness]
    7: harshness of manner [syn: asperity, sharpness] [ant:
       bluntness, dullness]

Moby Thesaurus II by Grady Ward, 1.0:

287 Moby Thesaurus words for "sharpness":
   Italian hand, abruptness, absolute zero, acerbity, acidity,
   acidness, acidulousness, acridity, acridness, acrimony, acuity,
   acuteness, adroitness, aggressiveness, agility, alacrity,
   alertness, algidity, animality, aptitude, aptness, arguteness, art,
   artfulness, artifice, asperity, astringence, astringency,
   astuteness, atonalism, atonality, atrocity, attention,
   attentiveness, barbarity, bearishness, beastliness, bite,
   bitingness, bitter pill, bitterness, bleakness, bloodlust,
   bluntness, boorishness, braininess, brashness, brightness,
   brilliance, briskness, brusqueness, brusquerie, brutality,
   cacophony, cageyness, callidity, canniness, causticity,
   causticness, cheerlessness, chic, chill, chilliness, churlishness,
   clear thinking, cleverness, clinker, clothes-consciousness, cold,
   coldness, comfortlessness, cool, coolness, coolth, corrosiveness,
   coxcombry, craft, craftiness, creakiness, crispness, crustiness,
   cryogenics, cryology, cunning, cunningness, curtness, cuttingness,
   dandyism, decrease in temperature, depression, destructiveness,
   dexterity, discomfort, discord, discordance, discordancy,
   disharmony, dismalness, dispatch, dissonance, dissonancy,
   dissonant chord, distress, distressfulness, dreariness, edge,
   elegance, esprit, expedition, expeditiousness, extremity,
   facetiousness, fierceness, fine Italian hand, finesse, flair,
   flatness, foppery, foppishness, force, foxiness, freezing point,
   freshness, frigidity, frostiness, funniness, furiousness, gall,
   gall and wormwood, gamesmanship, gelidity, genius, giftedness,
   gifts, grief, grievousness, grip, gruffness, guile, harshness,
   highness, humorousness, iciness, impetuosity, incisiveness,
   inclemency, ingeniousness, inharmoniousness, inharmony, inhumanity,
   insidiousness, intense cold, intensity, inventiveness, jauntiness,
   jocoseness, jocularity, joking, joshing, joylessness,
   keen-wittedness, keenness, lamentability, lamentation,
   low temperature, malignity, mental alertness, mercilessness,
   mercurial mind, mindlessness, mordacity, mordancy, mournfulness,
   murderousness, nastiness, native cleverness, nattiness, neatness,
   nimble mind, nimble-wittedness, nimbleness, nip, nippiness, nous,
   off note, one-upmanship, pain, painfulness, pathos, piercingness,
   pipingness, piquancy, pitiability, pitiableness, pitifulness,
   pitilessness, pleasantry, poignancy, point, promptitude,
   promptness, punctuality, pungency, quick parts, quick thinking,
   quick wit, quick-wittedness, quickness, rawness, readiness,
   ready wit, reediness, regrettableness, resourcefulness, rigor,
   roughness, sadness, saltiness, satanic cunning, savagery, savvy,
   screechiness, severity, sharp air, sharp-wittedness, shiftiness,
   shortness, shrewdness, shrillness, sleekness, sleeplessness,
   slipperiness, slyness, smartness, smarts, sneakiness, sophistry,
   sorrowfulness, sour note, sourness, speediness, spiffiness,
   sprightly wit, spryness, stabbingness, stealth, stealthiness,
   sting, stridence, stridency, stridor, stridulousness, stringency,
   subtilty, subtleness, subtlety, suppleness, surliness, swiftness,
   talent, tartness, teeth, terrorism, trenchancy, trickiness,
   trimness, truculence, tunelessness, ungentleness, unharmoniousness,
   unmusicality, untunefulness, vandalism, vehemence, venom,
   viciousness, violence, virulence, wakefulness, wariness, wiles,
   wiliness, wit, wittiness, woebegoneness, woefulness, wolf