In context, the word “preposterously” serves two functions. It modifies the adjective “exaggerated” to indicate that the claims are greatly rather than slightly exaggerated. It also conveys the author’s perspective toward these claims. The word “preposterous” means “contrary to nature, reason or common sense.” By describing “the claims of the science fiends” as “preposterously exaggerated,” the author emphasizes his skeptical attitude toward these claims.
