In my recent conference talk I mentioned the “ladder of inference” as a thinking tool, and described how it can help us understand the views of those who disagree with us. The end result may be that, having understood the basis for their views better, we find those views more persuasive that they first appeared. Another possible outcome is that both parties find those views less persuasive, once their underlying facts are highlighted. Or perhaps, together, both parties might come up with an even better idea.
Benjamin Mitchell points out an important thing which I omitted from my talk: the ladder of inference applies equally to us understanding our own thoughts. I recommend you take a look at his post on the subject, here.