contrary (adj.)

mid-14c., from Anglo-French contrarie, from Latin contrarius "opposite, opposed," from contra "against" (see contra).
If we take the statement All men are mortal, its contrary is Not all men are mortal, its converse is All mortal beings are men, & its opposite is No men are mortal. The contrary, however, does not exclude the opposite, but includes it as its most extreme form. Thus This is white has only one opposite, This is black, but many contraries, as This is not white, This is coloured, This is dirty, This is black; & whether the last form is called the contrary, or more emphatically the opposite, is usually indifferent. But to apply the opposite to a mere contrary (e.g. to I did not hit him in relation to I hit him, which has no opposite), or to the converse (e.g. to He hit me in relation to I hit him, to which it is neither contrary nor opposite), is a looseness that may easily result in misunderstanding; the temptation to go wrong is intelligible when it is remembered that with certain types of sentence (A exceeds B) the converse & the opposite are identical (B exceeds A). [Fowler]
As a noun from late 13c. Related: Contrarily; contrariwise.