When searching for synonyms for the phrase "unsupported by evidence," some suitable options include baseless, unfounded, groundless, and unsubstantiated. The term "baseless" carries the meaning of lacking a foundation of supporting evidence, while "unfounded" denotes an absence of substantiation or proof. Similarly, "groundless" and "unsubstantiated" describe assertions without valid evidence or support. These synonyms can help to express skepticism towards spurious claims or arguments that lack solid backing. By utilizing alternatives such as these, one can communicate more effectively and accurately convey ideas of doubt or disbelief in unsupported statements or positions.