Yeah, but the information erasure didn't happen when you applied double negation. It happened when you accepted a surjective convention where 5 mapped to True (and so did every non-zero value). The erasure wasn't accidental---it was a feature of the axiom set you chose. You can't complain that a system of logic is behaving the way you specified it should behave. If you apply --a, you don't lose any information because now you've applied a different axiom set: one that is algebraic and bijective.