Second Order Ignorance (2OI)—Lack of Awareness:
I do not know that I do not know something.
With Second Order Ignorance, I am in a much more difficult place [1].
By definition, I don’t have the answer, but I also don’t even have the question, or at least a sufficiently detailed question that can elicit a sufficiently detailed answer that can add to my knowledge.
Essentially, I am lacking any detailed context where the knowledge resides. More specifically, whatever context I do have is so high-level and abstract that it doesn’t help me locate my ignorance. Giving clear examples of 2OI is difficult because being “clear” means that there is a specific characterization and 2OI, by definition, exists where specific characterization is impossible.
As a test: try to list all the things you don’t know that you don’t know [2].
FOOTNOTES
[1] While I can give reasonable examples of 0OI and 1OI, I cannot give a specific example of 2OI. I can give a non-specific example such as: there are lots of things I don't know about science. But this awareness does not aid me much in resolving this ignorance. One could argue that, simply locating my ignorance (in the field of "science") I am demonstrating some level of awareness and, indeed, I am. But it is a very high contextual level and an associated question ("What do I need to know about science?") could have many different answers.
[2] If you were to to try to obey this directive, you might list contexts and domains, but you cannot list the specific knowledge elements in those domains. Were you able to do that, you would have 1OI, not 2OI.