In logic, there is a subtle but important distinction between the concept of mutual knowledge – information that everyone (or almost everyone) knows – and common knowledge, which is not only knowledge that (almost) everyone knows, but something that (almost) everyone knows that everyone else knows (and that everyone knows that everyone else knows that everyone else knows, and so forth). A classic example arises from Hans Christian Andersens’ fable of the Emperor’s New Clothes: the fact that the emperor in fact has no clothes is mutual knowledge, but not common knowledge, because everyone (save, eventually, for a small child) is refusing to acknowledge the emperor’s nakedness, thus perpetuating the charade that the emperor is actually wearing some incredibly expensive and special clothing that is only visible to a select few. My own personal favourite example of the distinction comes from the blue-eyed islander puzzle, discussed previously here, here and here on the blog. (By the way, I would ask that any commentary about that puzzle be directed to those blog posts, rather than to the current one.)

I believe that there is now a real-life instance of this situation in the US presidential election, regarding the following

Proposition 1. The presumptive nominee of the Republican Party, Donald Trump, is not even remotely qualified to carry out the duties of the presidency of the United States of America.

Proposition 1 is a statement which I think is approaching the level of mutual knowledge amongst the US population (and probably a large proportion of people following US politics overseas): even many of Trump’s nominal supporters secretly suspect that this proposition is true, even if they are hesitant to say it out loud. And there have been many prominent people, from both major parties, that have made the case for Proposition 1: for instance Mitt Romney, the Republican presidential nominee in 2012, did so back in March, and just a few days ago Hillary Clinton, the likely Democratic presidential nominee this year, did so in this speech:



I highly recommend watching the entirety of the (35 mins or so) speech, followed by the entirety of Trump’s rebuttal.

However, even if Proposition 1 is approaching the status of “mutual knowledge”, it does not yet seem to be close to the status of “common knowledge”: one may secretly believe that Trump cannot be considered as a serious candidate for the US presidency, but must continue to entertain this possibility, because they feel that others around them, or in politics or the media, appear to be doing so. To reconcile these views can require taking on some implausible hypotheses that are not otherwise supported by any evidence, such as the hypothesis that Trump’s displays of policy ignorance, pettiness, and other clearly unpresidential behaviour are merely “for show”, and that behind this facade there is actually a competent and qualified presidential candidate; much like the emperor’s new clothes, this alleged competence is supposedly only visible to a select few. And so the charade continues.

I feel that it is time for the charade to end: Trump is unfit to be president, and everybody knows it. But more people need to say so, openly.

Important note: I anticipate there will be any number of “tu quoque” responses, asserting for instance that Hillary Clinton is also unfit to be the US president. I personally do not believe that to be the case (and certainly not to the extent that Trump exhibits), but in any event such an assertion has no logical bearing on the qualification of Trump for the presidency. As such, any comments that are purely of this “tu quoque” nature, and which do not directly address the validity or epistemological status of Proposition 1, will be deleted as off-topic. However, there is a legitimate case to be made that there is a fundamental weakness in the current mechanics of the US presidential election, particularly with the “first-past-the-post” voting system, in that (once the presidential primaries are concluded) a voter in the presidential election is effectively limited to choosing between just two viable choices, one from each of the two major parties, or else refusing to vote or making a largely symbolic protest vote. This weakness is particularly evident when at least one of these two major choices is demonstrably unfit for office, as per Proposition 1. I think there is a serious case for debating the possibility of major electoral reform in the US (I am particularly partial to the Instant Runoff Voting system, used for instance in my home country of Australia, which allows for meaningful votes to third parties), and I would consider such a debate to be on-topic for this post. But this is very much a longer term issue, as there is absolutely no chance that any such reform would be implemented by the time of the US elections in November (particularly given that any significant reform would almost certainly require, at minimum, a constitutional amendment).