idea of observed resemblances, is the province of Classification. (See Appendix H, § 232.)

52. (e) When generalization or classification is complete in extension at any point in the ascending degrees, and the scholar, by his powers of thought, extends the generalization by inference so as to include objects which the preceding generalization does not cover in his experience or observation-thus making a new creation, known as a universal, sometimes as a generalthe product is called an Induction. (See Appendix I, § 233.)

53. Induction should not be confounded with pure explanation, or what is known as Mathematical Interpretation. Induction creates a new inferential product, the elements of which are discovered only by the examination of many objects, and the inference extends over unexamined and unexplored territory. Interpretation places itself at the point of completion of a single observation, operation, or process, and retraces the steps over the way followed, and explains fully the meaning, extensive and intensive, of what is observed, predicting simply that all similar examples will be traced along the same way, and the same ends reached. Sciences founded upon general definitions instead of observation and experiment, are not inductive. The Pure Mathematical sciences are not properly inductive, and from their nature cannot be. What is usually called Mathematical Induction is Interpretation. The so-called Perfect Induction is hardly Induction in its nature, because no product is created

beyond a generalization, or classification, and nothing is gained by using two terms for the same thing, when there are two notions to be distinguished from each other. (See Appendix I, § 233, Nos. 4, 5, and 7. Also Appendix J, 234.)

54. Another point should be clearly outlined: The mere Repetition of examples, substantially identical, does not increase the force and certitude, nor extend the range, of an inference. One example covers the whole territory, and it, together with all others of the kind, does no more than illustrate the original principle established directly or indirectly by definition. In arithmetic, for example, repetition of examples adds nothing to the elements of which the "rule" is made it simply serves to impress the way, the procedure, upon the mind of a learner, similarly to the repetition in the finger exercises upon the piano. (See §§ 204-7.)

It should be observed that there is a great variety of opinions among authors concerning the nature of Induction. The citations in the Appendix exhibit some of the views.

55. (f) If a scholar assume the possession of generals or universals, furnished either by Induction, by Definition, or by Intuition, and then use them with which to compare individual facts or truths, and by this means establish individual truths of like kind as an end of the process, the way of proceeding is known as Deduction. (See Appendix K, § 235.)

56. III. Consider the way in which the

individual student addresses himself to his tasks. He may be proceeding by any of the abovenamed modes, or ways, usually called Methods, and his own characteristics of disposition, habits, eccentricities, may be prominent. These may or may not be aids in securing valuable results of his labors. In any case, these are simply and solely individualities-they belong exclusively to the investigator-they are no necessary part of the mode or Method he is following-they are his Manner.

Critical discrimination should be made between what is necessary to a way, and what is purely incidental to the individual who is proceeding over that way. Indifference to this discrimination is followed by the pedantic assertion that each man can have a method of his own. Methods are ways which are independent of this or that man, and which are determined by the nature of the mind of man, or by the nature of the object-matter to be investigated. But Manner is his individuality when proceeding in a Method. (See § 123.)

57. When one's Manner is well ordered in its System, it is designated by the term Mode. (See 123.)