The phrase "on faith" can be substituted with various synonyms that imply trust, belief, and confidence. Some possible alternatives include "without evidence," "based on conviction," "with reliance," "in good faith," "trusting," and "believing without proof." Each of these words signifies a willingness to put faith in someone or something without physical or tangible evidence. It implies that the decision is based on the belief that the person or entity in question can be trusted. These words represent the emotional and psychological mindset behind making a decision or taking an action based on faith and show how faith can be a powerful motivator that goes beyond mere evidence or logic.