_Second Step._ The Making of Hypotheses. _Example_: Upon the basis of the observations and experiments, as above stated, and applying the axiom of Inductive Reasoning, that: "What is true of the many, is true of the whole," we feel justified in forming a hypothesis or inference of a general law or truth, applying the facts of the particulars to the general, whole or universal, thus: "_All_ magnets attract iron." _Third Step._ Deductive Reasoning. _Example_: Picking up a magnet regarding which we have had no experience and upon which we have made no experiments, we reason by the syllogism, as follows: (1) _All_ magnets attract iron; (2) _This thing_ is a magnet; therefore (3) _This thing_ will attract iron. In this we apply the axiom of Deductive Reasoning: "Whatever is true of the whole is true of the parts." _Fourth Step._ Verification. _Example_: We then proceed to test the hypothesis upon the particular magnet, so as to ascertain whether or not it agrees with the particular facts. If the magnet does not attract iron we know that either our hypothesis is wrong and that _some_ magnets do _not_ attract iron; or else that our _judgment_ regarding that particular "thing" being a magnet is at fault and that it is _not_ a magnet. In either case, further examination, observation and experiment is necessary. In case the particular magnet _does_ attract iron, we feel that we have verified our hypothesis and our judgment. CHAPTER XII. REASONING BY INDUCTION The term "Induction," in its logical usage, is defined as follows: "(a) The process of investigating and collecting facts; and (b) the deducing of an inference from these facts; also (c) sometimes loosely used in the sense of an inference from observed facts." Mill says: "_Induction_, then, is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, _Induction_ is the process by which we conclude that what is true of certain individuals of a class, is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times." The _Basis of Induction_ is the axiom that: "_What is true of the many is true of the whole_." Esser, a well known authority, states this axiom in rather more complicated form, as follows: "That which belongs or does not belong to many things of the same kind, belongs or does not belong to all things of the same kind."