contrariety(n = noun.linkdef) - the relation between contraries;
is a kind of oppositeness, opposition

1.  The state or quality of being contrary; opposition; repugnance; disagreement; antagonism. [1913 Webster]
"There is a contrariety between those things that conscience inclines to, and those that entertain the senses." [1913 Webster]

2.  Something which is contrary to, or inconsistent with, something else; an inconsistency. [1913 Webster]
"How can these contrarieties agree?"

contrariety, n.
1 opposition in nature, quality, or action.
2 disagreement, inconsistency.

Etymology:
ME f. OF contrariet{eacute} f. LL contrarietas -tatis (as CONTRARY)

N  contrariety, contrast, foil, antithesis, oppositeness, contradiction, antagonism, clashing, repugnance, inversion, the opposite, the reverse, the inverse, the converse, the antipodes, the antithesis, the other extreme, contrary, contrarious, contrariant, opposite, counter, dead against, converse, reverse, opposed, antithetical, contrasted, antipodean, antagonistic, opposing, conflicting, inconsistent, contradictory, at cross purposes, negative, hostile, differing toto coelo, diametrically opposite, diametrically opposed, as opposite as black and white, as opposite as light and darkness, as opposite as fire and water, as opposite as the poles, as different as night and day, Hyperion to a satyr, quite the contrary, quite the reverse, no such thing, just the other way, tout au contraire, contrarily, contra, contrariwise, per contra, on the contrary, nay rather, vice versa, on the other hand, all concord's born of contraries, Thesis, antithesis, synthesis.

N  opposition, antagonism, oppugnancy, oppugnation, impugnation, contrariety, contravention, counteraction, counterplot, cross fire, undercurrent, head wind, clashing, collision, conflict, competition, two of a trade, rivalry, emulation, race, absence of aid, resistance, restraint, hindrance, opposing, opposed, adverse, antagonistic, contrary, at variance, at issue, at war with, unfavorable, unfriendly, hostile, inimical, cross, unpropitious, in hostile array, front to front, with crossed bayonets, at daggers drawn, up in arms, resistant, competitive, emulous, against, versus, counter to, in conflict with, at cross purposes, against the grain, against the current, against the stream, against the wind, against the tide, with a headwind, with the wind ahead, with the wind in one's teeth, in spite, in despite, in defiance, in the way, in the teeth of, in the face of, across, athwart, overthwart, where the shoe pinches, in spite of one's teeth, though, even, quand meme, per contra, nitor in adversum.

N  counteraction, opposition, contrariety, antagonism, polarity, clashing, collision, interference, inhibition, resistance, renitency, friction, reaction, retroaction, counterblast, neutralization, vis inertiae, check, voluntary opposition &c, voluntary resistance, repression, opposites, action and reaction, yang and yin, yang-yin (contrariety), counteracting, antagonistic, conflicting, retroactive, renitent, reactionary, contrary, although, in spite of, against, for every action there is a reaction, equal in force and opposite in direction.

N  inversion, eversion, subversion, reversion, retroversion, introversion, contraposition, contrariety, reversal, turn of the tide, overturn, somersault, somerset, summerset, culbute, revulsion, pirouette, transposition, transposal, anastrophy, metastasis, hyperbaton, anastrophe, hysteron proteron, hypallage, synchysis, tmesis, parenthesis, metathesis, palindrome, pronation and supination, inverted, wrong side out, wrong side up, inside out, upside down, bottom upwards, keel upwards, supine, on one's head, topsy-turvy, sens dessus dessous, inverse, reverse, opposite, top heavy, inversely, hirdy-girdy, heels over head, head over heels.