I think the english language is deficient to describe our differing levels of understanding subjects. Know, believe, etc. all have too many definitions to accurately portray any distinction.
I have noticed this in legal cases, especially when asking lay and expert witness what they know about certain concepts. The audience inevitably has to assume that when the witness says he knows something, it is impossible to demonstrate how well he knows it without entering a 10 minute lecture. This is nonsense. Especially when dealing in abstract areas. Hard science is head over heels ahead of soft sciences in this area. However soft sciences involve empirical data versus propositional knowledge. The attempt to use empirical terms to describe propositional concepts is not working. It would appear to me that it is time for a change.
I would like to attempt to establish at least three new words to describe differentiating levels of knowledge. I haven’t a clue which ones to use, but I am sure someone will have some suggestions.