Consider that even murder isn't universally considered bad. Examples include wars, self defense, proponents of the death penalty, the sentinelese, etc. Debates can get particularly heated when one gets into things like abortion and ethical dilemmas.
As for the dichotomy of logical verification given our meat-based fallible physical medium, I'm reminded of Godel's incompleteness theory, i.e. that it is possible for a set of axioms to be internally consistent (e.g. basic algebra), yet we can construct a meta set of axioms to demonstrate that it is impossible to mathematically prove every truth therein.
As for the dichotomy of logical verification given our meat-based fallible physical medium, I'm reminded of Godel's incompleteness theory, i.e. that it is possible for a set of axioms to be internally consistent (e.g. basic algebra), yet we can construct a meta set of axioms to demonstrate that it is impossible to mathematically prove every truth therein.