The common phrase outward appearances is a redundancy. The concept of outward is implied in the meaning appearance (there’s no such thing as inward appearances), so there’s no justification for the extra adjective.
Each of these examples would benefit from the removal of outward:
He had all the outward appearances [had the appearance?] of cool sophistication . . . [World Net Daily]
Contrary to outward appearances, many guys have fragile egos . . . [JS Online]
The focus of this week was simple, despite outward appearances or suggestions to the contrary. [Seattle Times]
If appearance alone doesn’t seem right, try synonyms such as aspect, bearing, manner, or look.
