How to Make Our Ideas Muddled

You are probably aware of Charles Sanders Peirce’s four ways of forming and holding an opinion, outlined in 'How to Make Our Ideas Clear’. These are:
(1) Tenacity. Sticking to what you happen to believe and ignoring anything that might change your mind.
(2) Authority: Picking someone who knows more than you do and believing what they tell you to.
(3) A Priori Reasoning: Working out a couple of core axioms with like-minded friends and extrapolate everything you need to believe from them.
(4) Experiment: Which as we all know, is the only one that really works.

I think there is another way, which is even more intellectually lazy than (1) and (2), since it saves the person using it from having to commit to anything. I call this despicable intellectual vice the habit of Moderation. If, when confronted with two vociferously argued points of view, you determine the arithmetic mean between the arguments you hear, and decide to hold those opinions, you are following this terminally lazy method. You can say that you are tolerant and wise, and that you can see the valid points in each side's argument, but you will be in the one place you can be sure to be totally useless, smugly suspended over the abyss between two coherent points of view.
I assert that the position that the great Sages and Prophets would recommend; the position that will seem self-evident to posterity; the position that will have the greatest chance, if adopted, of advancing understanding of the point of contention and solving it, will almost always be found in one of two places: (1) On or beyond the extreme fringe of one of the two opposing points of view, or (2) Somewhere completely removed from the continuum between parties A and B, beyond the limits of ‘known idea space’.

Consider the following long-forgotten arguments:
* Radical Abolitionists vs. Gradualists. By the end of the Civil War, the stated policy of the US Government was further to the extreme than all but a very few radical abolitionists had suggested at the War’s beginning.
* Containment vs. Détente. The premises of both fell apart.
* Leninism vs. Trotskyism. Ditto.
* Practically any argument at all from the history of science.
* Bundists vs. Zionists. In hindsight, the best course of action for the Jews of Poland would have been something only the most extreme Zionists of all advocated.
* Chalcedonians vs. Monophysites. For hundreds of years, the Eastern Roman Empire was convulsed by arguments between Chalcedonians and Monophysites. I’ve read hundreds of pages about the argument and am still not entirely sure what it was about. A series of decent and competent Emperors proposed compromise positions between them, all of which came to naught and serve only to complicate the catalogue of heresies. The problem was eventually ‘solved’ only by the conquest of the main Monophysite regions of the Empire by an ideology that rejected the premises of the argument in toto. Today, the page in my atlas where the world is mapped by traditional religious affiliation shows the successors of the two parties mapped in the same colour (pink), and the majority of the world’s Christians- as near as I can follow- belong to groups that are more Chalcedonian than the Chalcedonians.