[fabianhjr]

Incompletness Theorem states that any system/language with primitive recursive arithmetic is either incomplete (since there is a construction of an undecidable statement via self reference) or unsound (since that same undecidable statement would be in contradiction)

AFAIK but speculating every programming language has primitive recursive arithmetic.

[gizmo686]

You are probably better off going with a computability theorem (such as the halting problem) instead of incompleteness. However, I suspect both will get you to the same place. Namely, there exists a program whose behavior cannot be predicted.

There is no theory that says that there does not exist a program whose behavior can be predicted. We have just criminally underfunded research into formal verification; and somehow decided that even computationally limited, code is law programs handling millions of dollars don't need any type of formal verification

[carnitine]

What does a standard programming language being unsound even imply? It’s not being used for theorem proving, so how is it of consequence?

[fabianhjr]

That it can produce contradictory results, if you have contradictions then at least one must be in error which means that following the language construction rules can produce erroneous results.

[UncleMeat]

You could imagine a semantics that produces different results depending on the order of inference rules.