mutualknowledge

A few weeks ago, Terry Tao used Donald Trump’s perceived lack of qualification for the presidency to illustrate the difference between mutual knowledge and common knowledge, in a blog post with the normative title It ought to be common knowledge that Donald Trump is not fit for the presidency of the United States of America.  It’s common knowledge that Terry Tao, in addition to being one of the Mozarts of mathematics, is a very sensible person, and like every sensible person he is appalled by the prospect of Trump’s election as president.  As an attempt to account for this unwelcome prospect, Tao suggested that the correctness of Proposition 1 above is a matter of mutual knowledge  —

information that everyone (or almost everyone) knows

but not (or not yet) common knowledge

something that (almost) everyone knows that everyone else knows (and that everyone knows that everyone else knows that everyone else knows, and so forth).

It seems to me, though, that Tao’s formulation of the question — whether Trump is “fit for the presidency” or, in the words of Proposition 1, is “even remotely qualified” — is ambiguous.  The only axiomatic answer is the one provided by Article II, Section 1 of the U.S. Constitution, which implies unequivocally that Trump, like me but (unfortunately) unlike Tao, is indeed “eligible to the office of President” — though I admit I haven’t seen his birth certificate — and eligible is here the only word that is unambiguous and legally binding.

Now I realize that, even if you are a mathematician and therefore legally or at least professionally bound to respect the axiomatic method, you will object (at least I hope you will) that Tao did not mean to suggest that Trump’s bare eligibility was in question, but rather that Trump did not meet the more stringent criteria of fitness or even remote qualification.  By analogy, no one would deny that  ø (the empty set) is eligible to be a set, according to the usual axioms of set theory, but rather that

  1. ø is hardly anyone’s favorite set;
  2. ø is in no sense a paradigmatic set; and
  3. ø is not the kind of set for which set theory was designed.

Thus, even if it were mutual or even common knowledge that Trump is, so to speak, the empty set of American politics, that would hardly count as a consensus on his fitness or even remote qualification.  I’m naturally sympathetic to this kind of argument, but Tao made it clear that only comments that

directly address the validity or epistemological status of Proposition 1

were eligible for consideration on his blog.  While I’m hardly a strict constructionist, I don’t see how to avoid interpreting the word epistemological in terms of the maximal epistemological framework I share with Tao, which in this case can only be Article II, Section 1 (together with the Zermelo-Fraenkel axioms, but I doubt they are of much help here).

I was already leaning to a different explanation of the Trump phenomenon before fivethirtyeight.com offered this helpful but depressing roster of the worst (and best) presidents in the history of the United States, according to (unspecified) “scholars.”  Running down the list, one sees that, although Barack Obama is undoubtedly one of the most fit of all the presidents, intellectually as well as academically speaking, he only shows up near the middle of the ranking.  Presumably this is because he has been less effective as a politician than the presidents at the top of the list.  Judging by his words, I would like to say that Obama is one of the most morally fit of the presidents on the list; judging by his deeds, on the other hand — these, for example, or these — the record is much less appealing.  Jimmy Carter has proved to be both intellectually and morally admirable since leaving the presidency, but he made two of the biggest foreign policy blunders in recent history while in office (he ranks quite poorly on the list, probably for different reasons).

It is clearly mutual knowledge that the notion of fitness to lead a modern democracy, in particular fitness for the presidency of the USA ,correlates strongly with a shocking disdain for the notion that elections are designed to reflect the popular will.   My sense is that Trump’s supporters, and their counterparts across Europe, would like this to be common knowledge.  Fortunately, they are not the only ones.

This will be the next-to-last post for the summer; the next post will explain why it may be time to put this blog to rest permanently.