I really do believe that the crux of truly being able to understand something, is being proven wrong about your understanding of it. I’m proven wrong all the time when I try to learn something anew and talk about it with a friend, a co-worker, and (un)surprisngly most often, myself.
As a result of being proven wrong about my understanding of something, I need to retract my conclusions, revisit what I thought I knew and try again, but now with knowing what went wrong. I suppose this approach holds true in a general philosophical sense as well:
Reasoners draw conclusions defeasibly when they reserve the right to retract them in the light of further information.
— Non-monotonic Logic, Stanford Encyclopedia of Philosophy1
Monotonicity as a concept is something that I came across back in university, but didn’t really fully grasp until recently. One of the most elegant uses of monotonicity that I recently stumbled upon was in designing coordination free, eventually consistent systems. Specifcially, in the papers describing the CALM Theorem2 and CRDTs3.
if a given argument is deductively valid, it cannot become invalid by the addition of extra premises.
— Monotonicity of entailment4
Conversely, non-monotonicity is when the output does not grow monotonically with the input:
previous “answers” may need to be retracted!
— Keeping CALM: When Distributed Consistency Is Easy2
Having known this, it isn’t too far a stretch to think of the output as how much we’ve understood, and the input as our current understanding + what we got wrong.
We should be proved wrong more often.
If something didn’t make sense, or you’d like to prove me wrong, feel free to reach out!