How to Disagree is an essay written by Paul Graham, explaining eloquently why online conversations turn into (sometimes nasty) debates and breaks down the merits of what typically comprises the arguments.

I'm a big fan of honest debate and Paul explains so well the difference between direct disagreements and the undercurrents. He's stated it well, almost poetically in its conciseness. It's not quite mathematical, but he does present a scale for convincing arguments.

It reminds me of the Monty Python Argument Sketch which demonstrated the finer points of contradiction and other meta-arguments.

I recently got stuck in a baffling exchange on my development blog where I felt under fire not for what I'd actually said, but on tone and derived implications of my intent. I came away from it thinking less of the other person (and least until some time passed) and that's the unfortunate danger of disagreements: That it cements opinion over the exchange rather than the topic.

Regardless of personal example, I do recommend reading the essay. I caught wind of it via Mosh Weitzman's blog and he noted it in more of a political context, which demonstrates how universally it can be applied.