appearances to the contrary

:  external show :  semblance

:  outward aspect :  look

:  outward indication

:  a fact or condition incompatible with another :  opposite

:  one of a pair of opposites

:  a proposition (see ¹proposition 2a) so related to another that though both may be false they cannot both be true — compare subcontrary

:  being so different as to be at opposite extremes :  opposite

:  being opposite to or in conflict with each other

:  being not in conformity with what is usual or expected

:  contrariwise, contrarily