What convinces is conviction. Believe in the argument you're advancing. If you don't you're as good as dead. The other person will sense that something isn't there, and no chain of reasoning, no matter how logical or elegant or brilliant, will win your case for you.
“If you were a medieval scholar reading a book, you knew that there was a reasonable likelihood you'd never see that particular text again, and so a high premium was placed on remembering what you read. You couldn't just pull a book off the shelf to consult it for a quote or an idea.”