The document discusses various argumentation methods including: 1) Plato's Socratic method which uses questioning to analyze arguments between interlocutors, though it is difficult to translate to writing. 2) Thrasymachus who represents sophists asserting the most convincing argument is more important than an accurate one. 3) Classical Aristotelian appeals to logos, pathos, and ethos. 4) Rogerian argument which avoids confrontation through civil discourse and cooperation. 5) Common fallacies used in arguments such as red herrings, spin doctoring, equivocation, appeals to doubtful authority, personal attacks, and sweeping generalizations.