Final answer:
The rhetorical appeal most damaged by a fallacy is logos, as a fallacy inherently represents a flaw in logical reasoning and undermines the argument's persuasiveness.
Step-by-step explanation:
The rhetorical appeal most damaged by a fallacy is logos. A fallacy, in its essence, is a flaw in reasoning or logic that undermines the logical appeal of an argument. When a speaker or writer employs a fallacy, the credibility of their logical argument, logos, is compromised, which can diminish the persuasiveness of the overall message. In contrast, ethos relates to the credibility of the speaker, pathos to the emotional connection with the audience, and kairos to the timeliness of the argument. While fallacies can negatively influence ethos to some degree—because the speaker might appear less credible for using flawed reasoning—the specific appeal that is directly concerned with logic and is thus most directly impacted is logos.