I think the OP used 'logical fallacy' ironically.

But maybe not: Consider this. Many, many formal systems describe behavior and not some underlying truth. The question of whether reality can even be reduced to a formal system is still open.

From the above axioms, we can reasonably conclude that what formal systems prove is provably true only insofar as the axioms reflect underlying reality exactly.

In 'social' formal systems like the one that describes logical fallacies, it is clear that context is inherently lacking, that the axioms are approximations, and that the system cannot be expected to accurately describe reality.

Thus, we can formally conclude that logical fallacies are, well, approximations.