Axiom of Consistency

The Axiom of Consistency in logic and mathematics states that if a system or set of rules is reliable, it shouldn't lead to contradictions. In other words, you can't prove both a statement and its opposite within the same system. This ensures that the system's conclusions are dependable and that no logical conflicts arise. It's fundamental for maintaining trustworthiness in reasoning, mathematics, and formal systems, meaning that the rules used to derive truths are coherent and do not produce paradoxes or falsehoods.