In other words, a truth value in a mathematical sense is binary, but human communication is fallible and runs the risk of fallacy, error, and distortion.
The idea of being "close enough" to the truth - even when being sincere - is something I think we can all agree exists so that we do not burden each other with unreasonable expectations of accuracy and precision.
If for example, someone asks me if the glass is full of water and it is 99% full, I will say - with no burden on my conscience - that it is indeed full.
Is it reasonable to conjecture that the human conscience contains a mechanism for assessing truth based on a spectrum of approximations rather than an exact set of criteria that must be met?