Our civilization is based on such non-scientific methods.

I'd say that existing folk practices and institutions (what I think you mean by "our civilization") are based on the non-survival of rival practices and institutions. Our civilization has the institutions it has, for the same reason that we have two eyes and not three — not because two eyes are better than three, but because any three-eyed rivals to prototypical two-eyed ancestors happened not to survive.

Folk practices have typically been selected at the speed of generations, with cultures surviving or dying out — the latter sometimes due to war or disease; but sometimes just as the youth choose to convert to a more successful culture. Science aims at improving knowledge at a faster rate than folk practice selection.