What if instead of arguing with one another we deliberately set out to find the source of the disagreement?

I thought of this a long time ago, but have never put it into practice.

Suppose that two people disagree over some issue. One person could write down something to the effect that A is true because of B, C and D. Now the second person might agree with B and C, but disagree with D. So the first person might write down D holds because of E and F.

In this way, things get broken down until the root causes of disagreement are reached. Once the roots have been exposed, it may not be possible to go any further. There may be a difference in values or in the credibility of a particular source.

The net result is that each person gets insight into the thinking of the other and a basis has been set up for each person changing their opinion if something happens to change one of the root causes of the disagreement.

I know this is all very abstract, but I think it would be fun to try to put into practice some time.