Theories

In some contemporary circles, 'Logic' is the 'Theory of Theories'. For example, 'Mathematical Logic' organizes Mathematics structurally in a manner reminiscent of Euclid's systematizing of Geometry. The structure involved is nowadays formally characterized as a 'Theory'. A 'Theory', in general, is any set of statements pertaining to some associated phenomena. Typically, those statements are either Axioms or Theorems, Axioms being statements that are self-evidentally True, and Theorems being statements that are derived from Axioms by an inference rule or rules. The two criteria for the evaluation of a Theory is Consistency and Completeness. Consistency is presumably guaranteed by strict adherence to inferential procedure, i. e. any properly derived Theorem cannot contradict any other statement in the Theory. Completeness can also be guaranteed if a Theory concerns a finite range of phenomena, such as in Mathematics, when 'Infinity' is treated as a Cardinal Number. Usually, though, the range is indefinite, and ever-increasing, so there is no guarantee that the description of some previously undiscovered phenomenon will not emerge as inconsistent with the established statements of a Theory. Such an inconsistency, at minimum, challenge the Theory, and if it is compelling enough, can force the formulation of a new Theory. So, while Completeness for at least empirical Theories cannot be guaranteed, a Theory can be more or less Comprehensive, and evaluated on the basis of explanatory power, e. g. Einsteinian Physics explains better high-velocity phenomena than does Newtonian. In Formaterial terms, Comprehensiveness is Complexity, so Theories can be evaluated as more or less Evolved.