[undead_knight]

Mathematics
Mathematical and logical statements are typically regarded as unfalsifiable, since they are tautologies, not existential or universal statements. For example, "all bachelors are male" and "all green things are green" are necessarily true (or given) without any knowledge of the world.

Proving mathematical theorems involves reducing them to tautologies, which can be mechanically proven as true given the axioms of the system or reducing the negative to a contradiction. Theorems are unfalsifiable, since this process, coupled with the notion of consistency, eliminates the possibility of counterexamples - a process that the philosophy of mathematics studies in depth as a separate matter. How a mathematical formula might apply to the physical world, however, is a physical question, and thus testable, within certain limits.

Ethics
Many philosophers have held that claims about morality (such as "murder is evil" and "John was wrong to steal that money") are not part of scientific inquiry; their function in language is not even to state facts, but simply to express certain moral sentiments. Hence they are not falsifiable.

Falsifiability Articles and Information