Sometimes I wonder what the world would be like if it were possible to get everybody to agree on true things.
Suppose that, whenever two people find that they disagree about something, they invoke the Argulator algorithm to resolve the dispute. The Argulator algorithm is trivial for statements which empirically true or false - you just go and do the experiment to find out who is right. For other statements, each side enumerates each argument for their position as a set of statements, then figure out which statements in each of their opponent's arguments they disagree with and recursively invoke the Argulator algorithm on each of those.
The Argulator algorithm isn't guaranteed to terminate, though - you might have two positions which are perfectly internally consistent and consistent with the observable universe, but which still disagree with each other. For example, two people might disagree about the purpose of government - one might argue that its purpose is to provide a safety net or basic minimum standard of living for the least well off members of society. Another might argue that its purpose is to further the cause of human achievement (maximize rate of total long-term economic output) by any means necessary. Without agreement on what the end goal is, the chances of agreeing of a course of action are pretty slim.