Things are either True or False

Strictlly speaking that is not quite correct. Predictions about the future cannot at the time they are made be either true or false, because the future hasn't happened yet. In time it will turn out whether they were correct or false.

However a statement about how someone plans to act in the future is going to be true or false - it's not a statement about the future, but about that person ( or that organisation) intends to act). The same thing applies when it's a matter of predicting events, and basing that on a claim that currently availability evidence indicates that as justifying that prediction.

The complication is that it is possible to change one's mind, so just because someone does not do what they said they would do, that does not necessarily mean that they were lying. But if they actually had no intention of keeping their word, that would have been a lie.

All this provides a certain amount of wriggle room for politicians (or for the rest of us).

But this has nothing to do with "post-truth"