Scientific theories should produce statements about the world that are either true or false, but never both. An inconsistent theory is one that is able to simultaneously prove both some specific statement P and the negation of that same statement p. The conjunction of a statement with its own negation, P Λ ¬P, is referred to as logical contradiction. Therefore, the inconsistency of a theory implies the existence of a contradiction. Mathematically proving things from a few axioms is less risky than assuming many experimentally suggested assertions. Thus, collection of new empirical data is always beneficial for science if our old theories are empirically corroborated by the new data; we find out that the old theories actually compress more data than we originally thought. Universal statements have a greater explanatory power compared to singular existential statements because from a universal statement could always be proved a singular existential statement.