For this reason, the system proposed in this book is inductive . Generalizations grow from data, not the other way around. There are formal theories and empirical theories. These are the rules by which manipulates symbols of the theory. Empirical theory relates the rules of formal theory to observations.
Formal proofs demonstrate internal consistency among a set of statements.
The student of high school geometry will recall exercises of this kind. Empirical theory must meet additional criteria. We must state the operations with which to measure its symbols. Psychological theory has used such terms as stimulus , cathexis , or vectors . The relation between symbols and that to what they refer is the business of semantics.