Question: What is a (or the) scientific theory V based on a set B of syntactical L -formulas, interpreted according to the intended interpretations of the language L? What probably corresponds to the traditional candidate for V is found to be inadequate for use in deductively explaining experimental facts of a certain form. A second candidate for V, called a strong scientific theory (SST), does not suffer such an inadequacy because it is existentially strong, i.e., it has considerable existential import. It even satisfies the particle physicist's dictum: WHAT IS NOT FORBIDDEN WILL HAPPEN.