In Aristotle's proofs, which one refers to rational appeals based on logic and factual analysis?

The correct choice is logos, which refers to the use of rational appeals in argumentation that rely on logic and factual analysis. When a speaker employs logos, they focus on constructing a solid argument through reasoning, using evidence, statistics, and logical reasoning to persuade the audience. This method emphasizes clarity of thought and the coherence of the argument, allowing listeners to follow and understand the speaker's points effectively.

Logos is fundamental in public speaking because it appeals to the audience's intellect and reason, encouraging them to engage critically with the topic. For example, a speaker might present data from research studies to support their claims, helping the audience draw logical conclusions.

In contrast, ethos relates to the credibility and ethical appeal of the speaker, influencing how trustworthy or authoritative they seem to the audience. Pathos appeals to the emotions of the audience, aiming to evoke feelings that align with the speaker's message. Telos, which refers to the purpose or end goal behind a speaker's message, is essential in understanding the intention behind the argument but does not specifically pertain to rational appeals. Each of these elements plays a distinct role in persuasion, yet logos stands out for its emphasis on logical reasoning and factual support.