For some reason, the human mind balks at iteration. It is the paradigm of the baffling, of egg-headedness, of sophistry.

In philosophy classes, when lecturing on Descartes’ Second Meditation, I introduce the idea, helpful in generalizing Descartes’ cogito argument, of beliefs about beliefs. This always meets with great suspicion and resistance. I almost had a rebellion in another class for which I assigned a reading that discussed a number of different theories about what theories are. “Theories of theories,” they cried. “That’s almost circular”. (Students regularly dismiss any kind of reasoning they find hard to grasp as circular. It’s as if they see reasoning itself as somehow question-begging. But that’s the topic of a future post.) Of course, it isn’t ‘circular’, or in any other way improper, to have a belief about a belief or a theory of theories.

On February 12, 2002, Donald Rumsfeld delivered what has become a classic piece of iteration:

Reports that say that something hasn’t happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don’t know we don’t know.

These remarks brought about howls of derision. awarded them “The Plain English Campaign’s award for most baffling remark by a public figure think”. They were turned into (parodic) poetry at Slate. All this derision, with respect to Rumsfeld’s general point (as opposed to his political use of it in the prosecution of a hateful war), was quite unwarranted. Among the many things we don’t know, it is quite proper, and indeed of great interest, to distinguish between those which we know we do not know, and those which we don’t know that we don’t know. The whole science of epistemic logic is built on such distinctions. But even apart from specialized philosophical theories such as epistemic logic, the value of the distinction is obvious. If you know that you don’t know something, you can, if you want, direct your efforts towards coming to know it; if you don’t even know that you don’t know it, you can’t. If you find the concept of an unknown unknown confusing, just think of a case where someone has a false belief about something, p. That person doesn’t know p, since p is false. But since she mistakenly thinks that she does know p, she obviously doesn’t know that she doesn’t know p. Of course, one cannot give an example of something that oneself does not know that one does not know since, in giving the example, it would become a known unknown. But it is perfectly easy to give example for other people.

Others have also written about why Rumsfeld’s remarks make good sense. For example, John Quiggin, over at Crooked Timber and Geoffrey Pullum at Language Log. What I want to add to these treatments here is the observation that remarks like Rumsfeld’s are so easily derided because of the iteration they contain. It is the “known unknowns” and “unknown unknowns” that offer themselves as the targets of derision, just as “theories of theories” offered itself to my class as an object of amazed ridicule.

Why should that be? No-one would, I assume, balk at “theories of evolution” or “evolution of theories”, or at “known desires” and “unknown desires”. I honestly find this something of a mystery. Suggestions welcome.