Having seen that the first step in Inductive Reasoning is Preliminary Observation, let us now consider the next steps in which we may see what we do with the facts and ideas which we have acquired by this Observation and Experiment. CHAPTER XIII. THEORY AND HYPOTHESES Following Jevons' classification, we find that the Second Step in Inductive Reasoning is that called "The Making of Hypotheses." A _Hypothesis_ is: "A supposition, proposition or principle _assumed or taken for granted_ in order to draw a conclusion or inference in proof of the point or question; a proposition assumed or taken for granted, though not proved, for the purpose of deducing proof of a point in question." It will be seen that a Hypothesis is merely held to be _possibly or probably true_, and _not certainly true_; it is in the nature of a _working assumption_, whose truth must be tested by observed facts. The assumption may apply either to the _cause_ of things, or to the _laws_ which govern things. Akin to a hypothesis, and by many people confused in meaning with the latter, is what is called a Theory. A _Theory_ is: "A verified hypothesis; a hypothesis which has been established as, apparently, the true one." An authority says "_Theory_ is a stronger word than _hypothesis_. A _theory_ is founded on principles which have been established on independent evidence. A _hypothesis_ merely assumes the operation of a cause which would account for the phenomena, but has not evidence that such cause was actually at work. Metaphysically, a theory is nothing but a hypothesis supported by a large amount of probable evidence." Brooks says: "When a hypothesis is shown to explain all the facts that are known, these facts being varied and extensive, it is said to be verified, and becomes a theory. Thus we have the theory of universal gravitation, the Copernican theory of the solar system, the undulatory theory of light, etc., all of which were originally mere hypotheses. This is the manner in which the term is usually employed in the inductive philosophy; though it must be admitted that it is not always used in this strict sense. Discarded hypotheses are often referred to as theories; and that which is actually a theory is sometimes called a hypothesis." The steps by which we build up a hypothesis are numerous and varied. In the first place we may erect a hypothesis by the methods of what we have described as Perfect Induction, or Logical Induction. In this case we proceed by simple generalization or simple enumeration. The example of the freckled, red-haired children of Brown, mentioned in a previous chapter, explains this method. It requires the examination and knowledge of every object or fact of which the statement or hypothesis is made. Hamilton states that it is the only induction which is absolutely necessitated by the laws of thought. It does not extend further than the plane of experience. It is akin to mathematical reasoning.