Two Theories of a Conspiracy Theorist

A friend of mine, who is quite inquisitive about world affairs, told me about his recent conversation with an acquaintance of his about a deep conspiracy theory that Russia has an intelligence asset in the highest levels of the U.S. government.  Although his acquaintance thought this conspiracy theory was very unlikely, in the end she admitted that she did not know for sure it was false.  My friend’s elaborate description of the thorough discussion he had was not interesting to me, but I was intrigued when he told me he was now more certain of the conspiracy theory.  I asked him for an explanation, and he gave me two. 

There are two kinds of people when it comes to their knowledge of this particular conspiracy, he started by saying.  Some people have no knowledge.  These people may have strong opinion about the conspiracy theory, but like his acquaintance, they do not possess definitive knowledge or proof for one way or the other.  The rest have perfect knowledge.  Some of these people work for the government, and have top secret clearance.  If the conspiracy theory is true, they can prove it; if it is not, they can prove that too.  

At this point, I stopped my friend and told him that meeting a no-knowledge type like his acquaintance should not make him more certain of the conspiracy theory.  He smiled and admitted that the knowledge type of a given person does not change according to whether the conspiracy theory is true or not.  But it does not follow that the knowledge type of the person he may have a conversation with is independent of whether the conspiracy theory holds true or not, he explained.  He asked me if I could imagine that he was more likely to meet someone who has no knowledge when the conspiracy theory holds true than when it does not: If the conspiracy theory is true, wouldn’t the government want to suppress any evidence for it from the public out of self-interest, self-respect or even embarrassment? Conversely, if the conspiracy theory is false, wouldn’t government want to try its best to share the evidence with the public?  I could see where my friend’s argument was going.  If I accept the idea that he was more likely to meet a no-knowledge type when the conspiracy is true than when it is not true, then simply meeting a no-knowledge type became a signal for the conspiracy theory.  But isn’t the idea itself a conspiracy theory?  

Sensing that I was not completely convinced, he offered another explanation for why he became more certain of the conspiracy theory after hearing from his acquaintance that she had no proof for one way or the other.   Imagine that there is a third knowledge type, he said, who cannot prove or disprove the conspiracy theory when it is true but who can disprove the conspiracy theory when it is false.  Then, the possibility of meeting people of this knowledge type in addition to the no-knowledge and perfect-knowledge types makes it more likely for him to meet someone like his acquaintance when the conspiracy theory holds true than when it does not.  I objected: Do people like his acquaintance know their knowledge type?  If she is of the no-knowledge type then whatever she says on this matter is irrelevant; if she is of the third knowledge type then she should already conclude that the conspiracy theory holds true, for otherwise she would have the perfect knowledge.  My friend said he understood my objection, but insisted that there are people who do not make inference as I suggested.  He was right.  I have met people who I believe do not know what they do not know, and I have certainly heard of an insightful claim by someone like that: “… 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.”