In 1610, Galileo Galilei discovered Jupiter'smoons with the aid of a new morepowerful telescope of his invention. Analysisof his report reveals that his discoveryinvolved the use of at least three cycles ofhypothetico-deductive reasoning. Galileofirst used hypothetico-deductive reasoning to generateand reject a fixed star hypothesis.He then generated and rejected an ad hocastronomers-made-a-mistake hypothesis.Finally, he generated, tested, and accepted a moonhypothesis. Galileo's reasoningis modeled in terms of Piaget's equilibration theory,Grossberg's theory of neurologicalactivity, a neural network model proposed by Levine &Prueitt, and another proposedby Kosslyn & Koenig. Given that hypothetico-deductivereasoning has played a rolein other important scientific discoveries, thequestion is asked whether it plays a rolein all important scientific discoveries. In otherwords, is hypothetico-deductive reasoningthe essence of the scientific method? Possiblealternative scientific methods, such asBaconian induction and combinatorial analysis,are explored and rejected as viablealternatives. Educational implications of thishypothetico-deductive view of scienceare discussed.