Part Three: Persuasion (Foundations of Rhetoric)
For classical theorists, persuasion is the specific mechanism through which rhetoric influences the audience. Here, like in arrangement, it's treated as a structured process.
Core Components
From Aristotle:
Logos (reasoning): Structuring of the argument through logic, coherence, and evidence.
Pathos (emotion): "strategic" use of sentiment to garner a response. Perhaps viewed as serving, as an amplifier, Logos.
Ethos (credibility): Trust between speaker and audience. Who is speaking and how they present themselves are important.
(though considered "structured", unlike arrangement, these three function simultaneously, rather than separately).
If an argument isn't persuasive, the Trivium would likely blame too much relying on one of the components above, or disordered reasons, or "over-assertion", where the sense gotten by the audience is coercion.
Correction (becoming rightly guided) involved ordering arguments, "balancing" the above "appeals" (asks), and ensuring clarity/evidence. The "purpose" then aligns to be the effective communication of thought.
Conclusion
For the Trivium, persuasion functions as the applied use-case of rhetoric. Persuasion has effect as the goal, brought about through the above.