By all indications, based on external observations, seemingly, apparently, outwardly, from all outward signs, on the face of it, judging from what can be seen, ostensibly, it appears, it seems, as far as one can tell, on the surface, on the face of things, to all appearances, to judge by appearances, from appearances. All of these words and phrases share the idea of presenting a certain image or impression, but with degrees of certainty and subjectivity. While "by all appearances" suggests confidence in a conclusion drawn from observations, synonyms like "seemingly" and "apparently" hint at a greater degree of uncertainty and subjectivity.