Creating meaningful dialogue

I read this today in an e-mail from Patricia Digh, author of several books and the thought-provoking, fabulous 37 Days blog, and it occurred to me that if we all did this, the world would be a very different place:

If dialogue is intended to open the doors for understanding how someone arrived at their position, rather than at debating over the "rightness" or "wrongness" of that opinion, and that approach is coupled with assuming positive intent even if that stretches our own world view, perhaps there is hope for holding opposite viewpoints yet living peacefully together.

I can think of any numbers of scenarios where this would be close to impossible to do, but how powerful would it be to try?