A common Austrian slogan is that "Neoclassical economists study only cases where people know that they don't know; we study cases where people don't know that they don't know."
All of this sounds plausible until you press the Austrian to do one of two things: 1. Explain his point using standard probability language. What probability does "don't know that you don't know" correspond to? Zero? But if people really assigned p=0 to an event, than the arrival of counter-evidence should make them think that they are delusional, not than a p=0 event has occured. 2. Give a good concrete example.
Let me attempt an answer. I would say that "don't know that you don't know" corresponds to an event for which there is no traded contingent claim. The neoclassical world is one in which there are contingent claims for every meaningful event.
If there is an insurance contract, a security, or a futures market on something, then we know what we don't know. We don't know whether the event will occur, but we know what the market thinks about it.
When there is an event for which there is no traded contingent claim, then we don't know what we don't know. We don't know what we don't know about climate change or a future terrorist attack, and the evidence for that is the lack of any contingent claims market that could be used to draw inferences about climate change.
I think that we will not see contingent claims markets emerge in the case of unknown unknowns, because the bets are too hard to define. If you can define a bet, then you have created a known unknown. If you cannot define a bet, you have an unknown unknown.
There are some bets that one can make about terrorist attacks or climate change. However, I would argue that the set of bets that we could come up with is small relative to the space of possibilities that are potentially interesting.