Deductive and Inductive Reasoning
When you are sure at the outset of your general proposition, and need only to see its application to special cases, your reasoning is said to be "deductive". Such reasoning is specially used in mathematics. But in natural science you are said to employ "inductive reasoning". The process has already been described. You start with particular facts demanding explanation or generalization, and try to find some accepted law that explains them. Failing in that, you are driven to guess at a general law, i.e., to formulate a hypothesis that will fit the known facts. Then, having found such a conjectural general law, you proceed to deduce its consequences; you see that, if the hypothesis is true, such and such facts must be true. Next you go out and see whether these facts are true, and if they are, your hypothesis [{475}] is verified to that extent, though it may be upset later. If the deduced facts are not true, the hypothesis is false, and you have to begin all over again.
The would-be natural scientist may fail at any one of several points. First, he may see no question that calls for investigation. Everything seems a matter-of-course, and he concludes that science is complete, with nothing left for him to discover. Second, seeing something that still requires explanation, he may lack fertility in guessing, or may be a poor guesser and set off on a wild-goose chase. Helmholtz, an extremely fertile inventor of high-grade hypotheses, describes how he went about it. He would load up in the morning with all the knowledge he could assemble on the given question, and go out in the afternoon for a leisurely ramble; when, without any strenuous effort on his part, the various facts would get together in new combinations and suggest explanations that neither he nor any one else had ever thought of before. Third, our would-be scientific investigator may lack the clear, steady vision to see the consequences of his hypothesis; and, fourth, he may lack the enterprise to go out and look for the facts that his hypothesis tells him should be found.