Mills says of Inductive Reasoning: "The inductive method of the ancients consisted in ascribing the character of general truths to all propositions which are true in all the instances of which we have knowledge. Bacon exposed the insufficiency of this method, and physical investigation has now far outgrown the Baconian conception.... Induction, then, is that operation 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." Regarding Deductive Reasoning, a writer says: "Deductive Reasoning is that process of reasoning by which we arrive at the necessary consequences, _starting from admitted or established premises_." Brooks says: "The general truths from which we reason to particulars are derived from several distinct sources. Some are intuitive, as the axioms of mathematics or logic. Some of them are derived from induction.... Some of them are merely hypothetical, as in the investigation of the physical sciences. Many of the hypotheses and theories of the physical sciences are used as general truth for deductive reasoning; as the theory of gravitation, the theory of light; etc. Reasoning from the theory of universal gravitation, Leverrier discovered the position of a new planet in the heavens before it had been discovered by human eyes." Halleck points out the interdependence of Inductive and Deductive Reasoning in the following words: "Man has to find out through his own experience, or that of others, the _major premises_ from which he argues or draws his conclusions. By induction we examine what seems to us a sufficient number of individual cases. We then conclude that the rest of these cases, which we have not examined, _will obey the same general laws_.... The premise, 'All cows chew the cud,' was laid down after a certain number of cows had been examined. If we were to see a cow twenty years hence, we should expect that she chewed her cud.... After Induction has classified certain phenomena and _thus given us a major premise_, we proceed deductively to apply the inference to any new specimen that can be shown to belong to that class." The several steps of Deductive Reasoning shall now be considered in turn as we proceed. CHAPTER III. THE CONCEPT