DEFINING BY ANALYSIS.

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made up of such simple elements as the foregoing. Now, on the supposition of our perfect mastery of all the elementary conceptions, we ought to be capable of understanding all compounds, when their component parts are mentioned. Very often we are able to do so. And hence it is part of the business of an expositor, to define or explain by Analysis, or enumeration of parts.

Thus a Circle is defined as 66 a plane figure contained by one line everywhere equidistant from a point called the centre." Here an appeal is made to our knowledge of certain constituent notions, as plane figure, line, equality of distance, point: these we are supposed previously to know; and by putting them together as prescribed, we attain the notion of the circle.

This is the method of mathematical definition throughout. Indeed, mathematicians have incautiously applied it to the simplest notions of the science, as "point," "line," in defining which they perform the inverted operation of explaining the simple by the complex; point being a simpler idea than position, or magnitude; and line, the concrete, than length, the abstract.

So in Physical Science:-"Elasticity" is "the power of bodies to recover their form after compression; " we are supposed to understand the more elementary notions of power, bodies, recovery, compression.

Again, in the Mental and Moral Sciences. While, in them, there are certain ultimate notions, as Feeling, Discrimination, &c., by far the greater number are complex, and may be defined by analysis, or verbally. For example, "Memory is the power of recalling to the present view of the mind past impressions without the renewal of their original cause, or by mental forces alone." "Veneration is a feeling drawn out towards beings of superior power, wisdom, and goodness, and constituted by the feelings of manifested power, wonder, fear, and love."

To refer to Political Science:-"Law is a general command by one intelligent being to another, followed by the infliction of pain in case of disobedience." "Property is the recognition in each person of a right to the exclusive disposal of what he

has produced by his own exertions, or received by free gift or by fair agreement from such as have produced it."

52. The scholastic mode of defining by "the genus and the difference" (per genus et differentiam) is only a mode of expressing the definition by Analysis.

When we define Mathematics as “the science of quantity," we assign the two simpler notions, supposed to be already understood, science and quantity; in other words, we define by Analysis. But the old logicians remarked that in such definitions there are (1) some one term more general than the thing defined, and (2) one or more other terms of specification applying exactly to the difference between the thing and the genus. Thus "science" is more comprehensive than "Mathematics," including as it does other subjects also-Chemistry, Natural History, &c. Hence, after assigning the class or genus, science, we must say wherein Mathematics differs from all other members of the class, or all other sciences, namely, in having for its subject-matter Quantity: this is the "difference" and completes the definition.

All the foregoing examples could be resolved according to this method:-A circle is "a plane figure contained by one line" (genus), which line differs from other lines in being everywhere equidistant from a certain point" (difference).

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53. Although the method of Analysis, for complex notions, may be all that is demanded in strict rigor, yet we often require to superadd an explanation by the other methods.

Being made up of purely abstract elements, the definition by analysis is not always readily comprehended; whence it has to be aided by particulars and by contrast. Thus, "Elasticity," besides being scientifically defined by analysis, is rendered easier of understanding by a series of examples of elastic bodies-a piece of India rubber, a spring, an ivory ball, a bladder of air, &c.—and by counter reference to non-elastic substances, as clay.

GENERAL PRINCIPLE, OR PROPOSITION.

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The concrete method is not entirely excluded even from Mathematics, the science of abstraction by pre-eminence. In Arithmetic, the formation of numbers is illustrated, on the Pestalozzian system, by pebbles arranged in rows.

So Property, or Law, or Justice, may be defined by analysis (or by genus and difference), and explained by particulars and by contrast.

54. The second, and the chief, scientific element is the PROPOSITION, Principle, or General Affirmation; as, "Heat expands bodies," "All matter gravitates," "Exercise strengthens the body and the mind."

Even the Notion is commonly expounded as it appears in Home Proposition, that is, as coupled with some second notion; for example, "Gravity varies inversely as the square of the distance." It is rare, although it might be advantageous, to separate the defining of the notion from the truth or falsehood of the affirmations respecting it. The notion, in fact, is of value as preparatory to the proposition, which alone amounts to knowledge.

55. We have now to consider the methods of expounding the General Principle, or Proposition.

I. By Iteration, or by repeating the statement of the principle in the same or in different words.

It being the nature of a principle to give information respecting a wide range of particulars in a few words, a single enunciation of those words is not enough to impress the meaning adequately. The oral expounder repeats the exact words of a proposition several times; he may vary the statement besides. The writer confines himself to the last method.

The following is an example of iteration :—

"Bias is not a direct source of wrong conclusions; the intellect must first be corrupted" [short statement of the principle, followed by a series of varied expressions of it]. "We cannot believe a

proposition only by wishing, or only by dreading, to believe it (1). The most violent inclination to find a set of propositions true, will not enable the weakest of mankind to believe them without a ves

tige of intellectual grounds, without any even apparent evidence (2). Though the opinions of the generality of mankind, when not dependent on mere habit and inculcation, have their root much more in the inclinations than in the intellect, it is a necessary condition to the triumph of a moral bias that it should first pervert the understanding (3). If the sophistry of the intellect could be rendered impossible, that of the feelings, having no instrument to work with, would be powerless (4)."

56. There should always be one chief statement of the principle, for which the natural place is the commencement, although it may not improperly be given at the end.

Whately remarks that of two expressions of a principle differing in length, we understand the diffuse, and remember the concise.

The iterations should all harmonize with the main statement, according to the Second law of the Paragraph.

Iteration might be applied to the Definition likewise, when very abstruse or highly concentrated.

In some writers, and in some subjects, iteration is the prevailing form of exposition. Much of Adam Smith's Theory of Moral Sentiments is of this character. Without actually quoting examples in the concrete, the mere variation of the language is calculated to suggest them.

57. II. By Obverse Iteration, or the Counter-proposition denied.

As, from the nature of knowledge, every notion has some other notion (or notions) opposed to it (light-darkness, straight -crooked), so to every proposition affirmed there corresponds some other proposition (or propositions) denied. "This room is light; ""This room is not dark." "Socrates was wise; "Socrates was the reverse of foolish." "All our knowledge is obtained from experience;" "We have no intuitive knowledge." The affirmation and the denial in these cases are not different meanings, but the same meaning differently viewed and expressed. To the statement denied when anything is affirmed, Ferrier has given the name "Counter-proposition ;" and the

BY OBVERSE ITERATION.

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denial of this, which is equivalent to the original affirmation, may be called Obverse Iteration.

As examples of Obverse Iteration we may give the following:-"Heat expands bodies;" "Cold contracts bodies." "Heat relaxes the frame;" "Cold braces it." "Exercise improves the powers of body and of mind;" "Inaction or neglect deteriorates the same powers." These double statements are, strictly speaking, the complements of each other; the first implies the second; and therefore the mention of the second is the repetition of the first from another side, or from the obverse aspect.

"Socrates declares justice to be good, or a cause of happiness, to the just agent, most of all in itself-but also, additionally, in its consequences; and injustice to be bad, or a cause of misery to the unjust agent, both in itself and also in its consequences."

58. All that has been advanced respecting the power of antithesis, or contrast, in making things definite and clear, applies to the Counter-proposition and the Obverse

statement.

In the counter-proposition, the contrast or opposite of the predicate is given. "This man is a Briton ; "This man is an alien." In the obverse affirmation, the counter-proposition is denied, which gives an equivalent of the original proposition; “This man is not an alien;" Briton and not alien being the two obverse expressions for the same attribute.

In cases such as "Heat expands bodies," ""Cold contracts them," both the subject and the predicate are obverted; heat— cold, expansion-contraction.

When it is said, "The poet is born, the orator is made," the obversion is essential to the meaning of the statement; we should not know in what senses the words poet and born were intended, but for the statement of what they are put in contrast with.

Instead of merely iterating the principle, "Every effect has a cause," we might more properly set down the counter-propositions denied; for there are more than one. These are, first,