The crucial point in persuasion is the point of agreement from which you start. Your whole argument is reliant on the belief that your opponent will not ‘change his mind’, and end up disagreeing on the starting point. Your persuasion relies on the belief that as long as you both agree, it will end up that you both in fact agree on the matter at hand also. Persuasion, then, is about saying “No, you don’t actually believe that; you only think you do. In actual fact you and I agree completely, let me show you.” I assume the ideal end to persuasion is for you both to laugh about it together, wondering how you could ever have been so foolish as to think there was a disagreement. What usually happens, though, is that neither succeeds in persuading the other, and both go away thinking the other an illogical fool. But who says we can’t try?
This is a rather splendid way of thinking about persuasion, I think. If we went around thinking that actually most people fundamentally agree with us, we all might develop a less confrontational mindset. Such a view of persuasion also gels with the structure of arguments better too: we work from commonly shared premises, using the universal norms of reason and logic, towards a common conclusion. If we find that we disagree on certain premises, we work even further backwards, seeking ever more fundamental points of agreement.
Overall, I think assuming that we already agree but don’t yet know it is basically a more positive way of framing discussion. Kudos to Alex!