Complex sentence: Another, basic idealized presupposition of argumentation is the presupposition that no relevant argument is suppressed or excluded by the participants; another is the presupposition that no persuasive force except that of the better argument is exerted.
Split into simpler sentences: Another, basic idealized presupposition of argumentation is the presupposition that no relevant argument is suppressed or excluded by the participants. Another is the presupposition that no persuasive force except that of the better argument is exerted.