Is there an English word whose definition is the ability to tell truth from a lie?

Solution 1:

How about the word wisdom?

Def: The ability to discern what is true, right, etc. if you can discern truth then you automatically negate lies.

The use of the word discern in the definition also, in my opinion, doesn't pose a problem since it is defined as follows: if you discern something, you are aware of it and know it. ie the truth

Collins dictionary.