some one point; for otherwise they could not be referable to any one class, and there would consequently be no basis to the subsequent inference drawn in the conclusion. 2. That the conclusion must be modified by a reference to the circumstances of the particular to which we argue. For herein consists the essential distinction between an analogical and an inductive argument." (Fleming, Vocab Phil.) 198. "I hate set dissertations; and, above all things in the world, 'tis one of the silliest things in one of them, to darken your hypothesis by placing a number of tall, opake words, one before another, in a right line, betwixt your own and your reader's conception,—when, in all likelihood, if you had looked about, you might have seen something standing, or hanging up, which would have cleared the point at once ;— 'for what hindrance, hurt, or harm doth the laudable desire of knowledge bring to any man, if even from a sot, a pot, a fool, a stool, a winter-mitten, a truckle for a pulley, the lid of a goldsmith's crucible, an oil-bottle, an old slipper, or a cane-chair?' I am this moment sitting upon one. Will you give me leave to illustrate this affair of wit and judgment, by the two knobs on the top of the back of it ?—they are fastened on, you see, with two pegs stuck slightly into two gimlet-holes, and will place what I have to say in so clear a light, as to let you see through the drift and meaning of my whole preface, as plainly as if every point and particle of it was made up of sunbeams. I enter now directly upon the point. Here stands wit,-and there stands judgment, close beside it, just like the two knobs I'm speaking of, upon the back of this self-same chair on which I am sitting. You see, they are the highest and most ornamental parts of its frame,—as wit and judgment are of ours,and, like them too, indubitably both made and fitted to go together, in order, as we may say in all such cases of duplicated embellishment, to answer one another. Now, for the sake of an experiment, and for the clearer illustrating this matter,let us for a moment take off one of these two curious ornaments (I care not which) from the point or pinnacle of the chair it now stands on;-nay, don't laugh at it, but did you ever see, in the whole course of your lives, such a ridiculous business as this has made of it? -Why, 'tis as miserable a sight as a sow with one ear; and there is just as much sense and symmetry in the one as in the other.-Do,—pray, get off your seats, only to take a view of it.-Now, would any man who valued his character a straw, have turned a piece of work out of his hand in such a condition ?-Nay, lay your hands upon your hearts, and answer this plain question, Whether this one single knob, which now stands here like a block-head by itself, can serve any purpose upon earth, but to put one in mind of the want of the other?-and let me farther ask, in case the chair was your own, if you would not in your consciences think, rather than be as it is, that it would be ten times better without any knobs at all? - "Now these two knobs, or top-ornaments of the mind of man, which crown the whole entablature,-being, as I said, wit and judgment, which, of all others, as I have proved it, are the most needful, the most prized,—the most calamitous to be without, and consequently the hardest to come at ;-for all these reasons put together, there is not a mortal among us so destitute of a love of good fame or feeding,-or so ignorant of what will do him good therein,-who does not wish and steadfastly resolve in his own mind, to be, or to be thought at least, master of the one or the other, and indeed of both of them, if the thing seems any way feasible, or likely to be brought to pass. " (Sterne, Tristram Shandy, pp. 88-9, ed. 1844, Philadelphia.) 199. Illustrative Teaching is seeking something that bears a resemblance in form, nature, or kind to the point to be learned, or taught, presenting it instead of the point, and thus enabling the powers of comparison possessed by the pupil to act by inference from the analogy. This is a process of extending the meaning of words, called sometimes "the process of analogous or metaphorical extension of the meaning of words. This change may be said, no doubt, to consist in generalization, since there must always be a resemblance between the new and old applications of the term. But the resemblance is often one of a most distant and obscure kind, such as we should call analogy rather than identity." (Jevons, El. Lessons in Logic, p. 50, ed. 1878.) 200. Example would be something akin to analogy, excepting that example may be of the kind of thing itself, as well as an example illustrating the case at issue. 201. Illustrative Teaching is often called, unfortunately in conception, Objective Teaching. An object can be used for but two possible purposes in teaching: (1) To be learned, in and for itself; (2) Or to be an aid in learning something else. The first is Object Teaching, the second is Illustrative Teaching. 202. The distinction between the province of Object Teaching and that of Illustrative Teaching has been indistinctly apprehended by teachers. This misapprehension has led to serious obscurity of conceptions of teaching, for the expression Object Teaching has been applied without discrimination to all kinds of teaching where objects were used, whatever their purpose, whether as objects to be learned, or as objects to use in illustrating other points. "The science which enlightens, and the physick that cures, are doubtless very useful but the pretended science that misleads, and the physick that kills, are as certainly destructive. Teach us, therefore, to distinguish between them. It may be replied, as it constantly is, the fault is in the physician, and not in the science of medicine, which is otherwise infallible. Well, well, be it so take care, however, the physick be never accompanied by the doctor: for, as sure as ever they come together, there will be an hundred times more to fear from the blunders of the artist, than to hope for from the efficacy of the art." (Rousseau, Emilius, Vol. I., pp. 45-6.) 203. It has already been remarked that Object Teaching can be resorted to only with those subjects where facts obtained by perception and discrimination are desired. There are branches to be taught where it is impossible, from the nature of the subject-matter, to teach in this way. The subject of mathematics is one that has grown from a basis of definitions. The axioms follow definitions, but they are phases of conclusive reasoning, and assume things which are the creations of definitions. Definitions are the bases of mathematic science in its matter. Axioms are the bases in its logical processes of reasoning. Definitions are things which are products growing out of relations. Relations are objects only as they are products of the activities of the faculty of Thought. Hence all mathematical subjects are, from their nature, incapable of being taught objectively. All lines, mathematical blocks, charts, astronomical apparatus, and calculating machines, are but objects which illustrate mathematical truths, its definitions, and results, as intellectual products-they are not the things which are learned in themselves. What are called Applied Mathematics are only hypothetical illustrations of mental creations. It is. also true that this science is one in whose reasonings both matter and form can be furnished by the mind itself," and not one where the form alone is from the mind, the matter being |