completeness theorem

The completeness theorem, in general knowledge contexts, suggests that if a system of rules or beliefs is consistent—meaning it doesn't contradict itself—then every truth that can be expressed within that system can be proven to be true using those rules. In simpler terms, if something is true according to the rules we have, there should be a way to demonstrate it using just those rules. This theorem highlights the relationship between what we know, how we express it, and the structure of logical reasoning that underpins our understanding.