I also dispute that the theorem says what Aumann claimed it says, for two reasons.

First, it requires agents to know each others’ partition functions. This is laughably impossible in the real world.

Second, I believe that Aumann’s attempt to justify saying that “The meet at w of the partitions of X and Y is a subset of event E” means the same as the English phrase “X knows that Y knows event E” means, is incorrect.

I was stymied at the time, but have searched for a satisfactory explanation ever since. I hadn’t come across Aumann at the time, but am satisfied to learn that this is a well-explored problem at a formal level.

Suffice to say, the best explanation I’ve since come across was characterised by George Lakoff — a sometime student of Chomsky’s — in his book ‘Moral Politics’ (and more accessibly in his recent short political book, ‘Don’t Think of an Elephant’). He shares with Chomsky a journey from linguistics to politics. Loosely, his analysis is that someone’s ‘political persuasion’ is not just a set of postulates and logical inferences, but a Weltanschauung; Lakoff uses the term ‘deep metaphor’, though I don’t know if that is originally his coinage.

His case is fairly persuasive, and can also be expressed in cost/benefit evolutionary psychology terms: where the brain is held to be a complex adaptive system thoroughly remodelling a worldview in the light of each new piece of evidence is, however ‘rational’, only possible if it is not unreasonably expensive. A radical re-evaluation would typically be unacceptably costly, involving as it would a period of tumultuous dissonance, with the potential for dangerous even chaotic disequilibrium states in the ensuing ‘logic cascades’ that would lead to a period of serious cognitive impairment. Sanity might be at risk, perhaps permanently. The brain, being resilient, avoids this danger, and so applies limits to its receptiveness for even the most compelling controverting evidence. We tolerate some degree of discrepancy where the cost of accommodation exceeds the cost of dissonance.

Instead, picture the brain in a condition of constant unresolved inconsistency. Much like a lived-in house, where the latest interior design whimsy may affect one or two rooms, but the whole is never quite aligned. It’s just too expensive to whip out the Victorian fireplace just because minimalism is ‘in’ this season — and besides, we might miss it.

(How else, incidentally, can you begin to explain the tenacity of latent religious beliefs in otherwise committed Dawkins-readers?)

The underlying error, here, if there is one, is in applying the word ‘rational’ to humans (implied by the term ‘debaters’ in your first paragraph, Hal). Rationality — viz. the pursuit of consistency and deductive inference — might be said to be a process, or even a goal, but it can’t ever be an equilibrium state of a living brain. Brains as systems are just far too complex for that, the selection pressures on their operations too dynamic, the tumult perpetual.

Tremendous blog, by the way.

Propositions are, like Paul Feyerabend argued, ultimately a confluence of myriad sources hardly amenable to pure logic. So we must choose to weight supporting and confounding data subjectively, there is no totally objective way. Humans have a finite life, and must act before sufficient data is available, and in any case there’s the logical issue with induction in a complex non-linear adaptive systems such as societies. As Richard Feynman noted, we develop theories, see how the implications of these theories fit the data, looking for prediction, generality and parsimony (even beauty), all judged relative to existing theory–quite different than a search for Truth.

Humans are not merely discovering the truth, they are competing for it via different policy platforms, academic papers, and business models. At some level most arguments become based on assumptions that are hardly provable, such as whether or not people will work more efficiently with lower marginal tax rates, or whether the costs of crime prevention in terms of civil liberties is worth the costs of crime prevented. A worldview, or theory, is both a lens and a filter: it amplifies and excludes various observations. But because the alternative is to have no theory, in which the world is random, that’s the best we can do. Evolution makes us predisposed to develop theories and act on them, which makes us treat data points differently.

http://ideas.repec.org/a/aea/aecrev/v95y2005i5p1355-1368.html