Here is a possible set of criteria for understanding something:
- You know the concepts and facts, and how they link together
- You know the underlying assumptions
- You know the implications of the thing you understand
- You know the conditions under which your current understanding would be false
These may be either too stringent or too loose, and might be a possibly incomplete list. The term 'understanding' is fairly vague - and as will be clear from what follows, important in clarifying the question.
It is important to note: Whether you judge yourself to have understood something is logically independent of whether you have actually understood it. Consider the following four cases:
- You have not understood something, but judge yourself to have.
An example: You believe yourself to have understood why 13 is a prime number, even though you don't know the reasoning behind it, or have a mistaken notion of the reasoning behind it.
- You have not understood something, and judge yourself not to have.
You don't get what implicit differentiation is. And you judge yourself not to have gotten it. No problems here
- You have understood something, but judge yourself not to have.
This case is probably most problematic. One path I could posit here is that you have met the criteria that others would reasonably expect you to have met - e.g. being able to teach it to someone else, replicate the steps in a proof, but you intuitively believe that there is more that you need to know in order for it to count as understanding, according to your self-imposed definition.
- You have understood something, and judge yourself to have.
You understand the principle of addition - 2+3 = 5. And you know that you understand it.
This means you could be wrong about having judged yourself to have understood a thing. You are probably right that there is some complacency involved after we have judged that we have understood something. Maybe we should be more hesitant with our judgments of our own understanding.
On the issue of falsification, it is true that most of what we believe ourselves to understand could be falsified under some imaginable circumstance. And you are right that insisting on complete unfalsifiability is unrealistic. This suggests that in order for the concept of 'understanding' to have any practical import, we have to set a lower benchmark than "complete, unfalsifiable knowledge". Otherwise it would follow that we do not understand anything, in which case 'understanding' would be a useless notion. I think this stems from an unreasonably high benchmark for 'understanding', and that we could moderate it.
I think that criterion 4: "You know the conditions under which your current understanding would be false." - introduces a notion of defeasibility which could be useful in fine-tuning your understanding.
Hope this helps!