"The antecedent in a Reasoning may consist of a single Judgment, or of a plurality of Judgments. If it consist of but one Judgment, the Reasoning is called an Immediate Reasoning; as, Man is a rational animal; therefore, Man is rational. If the antecedent consists of more than one Judgment, the Reasoning is called a Mediate Reasoning, or, more technically, a Syllogism." (Day, "Elements of Logic," ed. 1868, pp. 91-94.)

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186. Reason, on the other hand, has no relation to the body, except as the soul's lodging and instrument; it belongs to the soul, purely and abidingly, and may be exercised without giving the slightest external token. Instead of framing bodily organs, it spans the sciences, sails deliciously through the heavenly realms of poetic analogy, penetrates the significance of things, and looks into the very mind of God himself. (Grindon, Life, p. 365, third ed., London.)

187. "Thinking, as Plato has observed, is but the conversation of the soul with herself; and the instrument employed is the echo of that which forms the medium of communication with others. To this it may be added that the notion, as represented in language, is but the substitute for the notion embodied in intuition, and derives all the conditions of its validity from the possibility of the latter; for language, though indispensable as an instrument of thought, lends itself with equal facility to every combination, and thus furnishes no criterion by which we can

judge between sense and nonsense-between the conceivable and the inconceivable." (Mansel, Metaphysics, pp. 1671-68, ed. 1871.)

(B) ON THE NATURE OF SUBJECT-MATTER.

188. In addition to a knowledge of mind and of knowing, the teacher, engaged in the discovery of Methods of Teaching, must diligently investigate the nature of the subject-matter that he is to teach.

189. By nature of subject-matter is meant that subtle, original, and permanent property of the subject-matter, at the presence of which the faculties of the mind are intuitively incited to their specific activities.

190. Some of this matter lies in the world that is external to the mind of man, and is called material.

191. Other matter rests exclusively within the ego. The mind creates it both as to its matter and form. In the case of material subject-matter, the mind determines only the form under which it exists as knowledge. In the other case, the immaterial, the matter and form would never exist as knowledge, or as matter for knowledge, were it not for the mind. The investigation of this whole subject is too vast to attempt to do more, at this time, than touch upon two or three subjects, except in the most cursory manner. The inquiry is directed towards the nature of Object Teaching, a familiar expression, and the nature of the subject-matter of

mathematics, one branch of which, arithmetic, forms so important an element in the lower schools.

192. Object Teaching is that teaching in which a knowledge of objects, or object-matter,

or where the subject-matters are objects-is the real end and purpose of the instruction. Object Teaching regards a knowledge of objects as an end-it does not consider anything beyond the objects themselves-it is served fully when this knowledge of facts is secured-its province is with the actual, which exists as individual facts -its subject-matter is that which addresses itself exclusively to the perceptive and discriminative faculties of the mind, as matter to be learned for its own sake. The powers of the mind that are mainly instrumental in acquisitions by the learner, who is taught by Object Teaching, are the perceptive, which cognize intuitively and immediately; the discriminative, which outline one object from another; and memory, which retains. Whatever is purely distinctive of Object Teaching is found within the above limitations. It relates to the region of individual facts.

193. Wherever an abundance of facts is wanted as materials for the other faculties of the mind to use subsequently in constructing science, Object Teaching is the way by which the necessities can be met.

194. But Object Teaching is only possible where a knowledge of facts, as such, is to be obtained, and where the materials, the matters,

of knowledge, exist as objects of perception and discrimination.

195. All those ways of teaching where objects, as charts, maps, apparatus, pictures, are used, by the teacher and pupil, not as ends of knowledge unto themselves, but as helps, by analogy, to acquiring knowledge of other things as ends all these ways of teaching are not Objective, they are Illustrative.

196. Ideas in the memory are joined together by the nexus of their nature, termed the Laws of Association. When, by any chance, one idea is brought into consciousness from unconsciousness -one modification reproduced-the whole group of ideas, related by sameness of time, space, or circumstances, come flitting as flocks through consciousness. Connected with this association of ideas is the power of imagination, which creates new mental beings, and which seizes upon analogies. These states or modes of the activities make Illustrative Teaching possible.

197. Illustrations are lights set by the wayside in parabolic mirrors, to illuminate obscure passages-they are voices which call out a welcome to him who is bewildered in the midst of a mazy mass of half-obscured and obscuring numbers they are guides that accompany the student to reveal to him on a sudden the secret labyrinths through which he may arise into the upper levels of light-they are the Aladdin Lamp and Ring, by whose mystic power their possessor may be instantaneously transported into

the palaces of the Beautiful and the True. The value of an illustration consists in its brevity, its brilliancy, its pointedness, its unexpected and unforeseen applicability, and its convincing force of plain analogy.

"Illustration is vivid elucidation ( to make more fully intelligible) by certain specific and effective means, as similitudes, comparisons, appropriate incidents or anecdotes, and the like, graphic representations, and even artistic drawings." (Smith, Syn. Discr.)

"Analogy is often used familiarly, as if it meant mere moral resemblance or similarity. Strictly speaking, however, analogy implies a third term, or four terms, as follows:-As A is to B, so is C; or as A is to B, so is C to D. Analogy, therefore, is similarity of relations. When we argue from example, we argue from the likeness of things; when from analogy, we argue from the likeness of their relations. If I argue that, because the seed dies in the earth before it springs up anew, therefore it is probable that the human body will rise again after death; this is, as to the character of the idea, a resemblance, as to the argument, an analogy; the principle being that, as the same God is the author of a natural and a spiritual world, He may be expected to act toward each upon similar and common laws." (Ibid.)

Analogy and Induction.-There are two requisites in order to every analogical argument : 1. That the two or several particulars concerned in the argument should be known to agree in