1. Truth itself is an invention of the human mind to try and sort physical observations / claims about the external world into two neat buckets.

2. Time as a linear description is the same, a way of sorting the physical world into a series of events.

Both have generalizations. Topos Theory generalizes Set Theory with different notions of what is "true." There are several variations on temporal logic with Linear Temporal Logic being only one such idea.

With all that in mind, your thought experiment does not cause any issues because you can say that the framework for reasoning about the example is _itself_ the problem. Hence, it fails as a counterexample for our inability to potentially understand reality without flaw.