Truth, relevance, and topology

The set of all arguments, consisting of both "truth" and "not truth" consists of boundless Fiction and a circumscribed subset, Truth. A further subset of true arguments are those which are relevant. This is illustrated below as concentric rings outside which fiction exists.

The arguments favored by the three groups from last post (and there may well be more, for it is also artificial to consider every question as having two sides between which we must choose) may be placed into that framework, giving rise, as I count them, to twenty-four possible regions (The sketch below may not accurately depict them all - it was tougher than I thought, and I'm tired of messing with it. Apparently, topography is not for the meek).

• Non overlapping Pro fiction, truth, relevant truth
• Non overlapping Con fiction, truth, relevant truth
• Non overlapping 3rd party fiction, truth, relevant truth
• Overlapping pro and con fiction, truth, relevant truth
• Overlapping pro and 3rd party fiction, truth, relevant truth
• Overlapping con and 3rd party fiction, truth, relevant truth
• Overlapping pro, con, and 3rd party fiction, truth, relevant truth
• Fiction, truth, and relevant truth that nobody has yet laid claim to

Of those, we should reject all but the relevant, true arguments. We should especially concentrate on those areas in which two or more groups have overlapping true and relevant points of view in order to build a common framework for working through difficult problems. Unfortunately, that is far easier said than done.