The leading concept, epistemic superiority (discussed in 11.0), refers to relatively greater capacity to distinguish relevant truth from falsity, as demonstrated by objective evidence. Epistemic justification refers to evidence proving an adherent's epistemic superiority. Credentialing means according epistemic superiority. The agreement theorem (according to my parsing) requires epistemic justification to claim epistemic superiority rationally. Rational adherents modify their beliefs upon learning that an epistemic equal disagrees.
Proving the agreement theorem is mathematically trivial, and the previous post was supposed to demonstrate, almost intuitive. Yet, because the theorem conflicts with prevailing norms, which reinforce adherents' untoward opinionation, mathematically sophisticated students commonly reject the proof initially. Contentious beliefs—their adherents regarding themselves epistemically superior—indeed complicate matters, but self-description isn't epistemic justification: a claim to epistemic superiority is just another justification-requiring belief. Self-credentialing is rational only if adherents first prove their epistemic superiority with respect to their claim to epistemic superiority!
Circular reasoning is obvious when adherents contend adherence to the belief itself proves their epistemic qualifications, but some dodges are subtler. As an example of the evasions, consider "birthers" (Americans who believe Obama's "real" birthplace is presidentially disqualifying), called upon to justify their ideological self-confidence enough to survive their beliefs' overwhelming rejection. Birthers may believe that, as such, antibirther beliefs epistemically discredit their adherents, but this argument is circular because the same ideological isolation discredits both belief and credential. Sophisticated birthers might invoke a subtler form of question begging, claiming vindication by other equally contentious positions—perhaps, adherents' "discernment" that Obama is Muslim—but these adherents' struggles against the stigma of intellectual isolation unwittingly prove their epistemic inferiority, despite the lesser absurdity of Muslim baiting compared to citizenship paranoia.
Leveraging credible beliefs to demonstrate adherents' expertise occasionally succeeds, but credentialing is more commonly based on direct grounds, as when experts' training vouchsafes their expertise against masses of disagreeing nonprofessionals. Also, experts reasonably disregard lesser experts, as Albert Einstein did Niels Bohr, who insisted Einstein was mistaken to reject quantum mechanics. Einstein replied he had earned the right to be mistaken. His demonstrated powers of physical intuition justified self-credentialing his opinion. Analogizing the credentialing process to averaging measurements of duration—with equally accurate clocks, the readings should be averaged, but a reading from an ancient 0-jewel wind-up clock should be overridden by one from an atomic clock.
Claiming superiority in method—in the manner of the Catholic Church—is a systematic way to bolster epistemic credentials and save an opinion from its fate as one of many. If the Church's claim that the Pope speaks for God were demonstrable, then taking your cue from priests would be more rational than relying on your cogitations.
Another bootstrapping method is Marxist sociological justification, which can be treated as an answer to demands for epistemic justification: under the agreement theorem, what justifies accepting Marxism when most intellectuals disagree? The Marxist answers that these opponents, however erudite, belong to (or identify with) an exploitative social class, blinding them to subversive truths. If the workers accept Marxist socialism, while the bourgeoisie espouses liberalism, conservatism, or reaction, the line-up reveals politics' class dependence, and the argument avoids circularity if independent historical evidence supports the bourgeoisie's epistemic inferiority. Thus, Marxism contains theoretical machinery adequate, in principle, to justify Marxists' intellectually isolated iconoclasm. No doubt this contributes to its endurance.
Granting the Marxist claim that the main political divisions represent social classes differing in epistemic endowment, most political and religious disputes still would be between approximate epistemic equals. Republicans and Democrats vituperate with language proven lethal, without there being a rational basis justifying either's epistemic superiority. Marxist ideologues, too, disagree vehemently, although none occupy superior epistemic positions. The disputants' epistemic equality doesn't temper these disagreements, whereas it should among rational adherents.
Under-weighting others' beliefs in effect equates belief (all-things-considered position) with individual opinion (others' beliefs factored out) despite the rationality of differentiating them. Confusion about the distinct societal roles of belief and opinion explains this irrationality.
Next essay: The distinct societal functions of belief and opinion.