In fact, the structure of the fallacious argument in deductive logic, the Fallacy of Affirming the Consequent, is at the heart of scientific method. In this step of scientific method we have carefully observed the fact of objects falling to the earth. Very often, the scientist will attempt to give a mathematical description of the observed facts. He will measure and tabulate. Inductively we argue with probability from the specific facts we have observed to a generalization that all unsupported bodies heavier than air will fall to the earth.
Logic can examine some of the guidelines for making good inductive generalizations.
Given the inductive generalization of Newton that bodies attract each other directly proportionally to their masses and inversely proportionally to the square of the distance between them, in the second step of scientific method we now try to develop a hypothesis about the nature of bodies that would explain why bodies behave the way we have observed them. If the proposed hypothesis is true, then the already observed facts would be predicted to occur and certain new facts not yet observed would also be predicted to occur. The predictions must follow deductively or mathematically from the proposed hypothesis. However, it is obvious that we do not have an hypothesis which explains why the law of gravitation is as Newton has mathematically described it. If we could come up with such an hypothesis, we must be able to deduce, strictly logically, strictly mathematically, why the bodies would attract each other directly proportionally to their masses and inversely proportionally to the square of the distance between them.