GENERAL FRINCIPLE, OR PROPOSITION.

193

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 some 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.

195

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; heatcold, 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 cause," we might more properly set down the counter-propositions denied; for there are more than one. These are, first,

"Events arise without any cause," and secondly, “The same causes do not produce, in the same circumstances, the same effects." Both these propositions are implicitly denied in the Law of Causation; yet their explicit statement greatly adds to the clearness of the principle.

It has been urged with great force by Ferrier, in his Institutes of Metaphysics, that the statement of the counter-proposition is a means of exposing errors, especially such as are sheltered under vagueness of language.

It is sometimes said "Might is right;" what does this deny? Right has many meanings, and as many opposites. If the opposite meant is wrong, the obverse would be "Might is seldom or never applied in support of wrong,"—a statement that would not be so readily hazarded.

Take again the proposition-" The standard of Art is Nature." What is denied by this? On examining the use made of the maxim, we find the obverse is, "The standard of Art is not Nature badly imitated." In other words, the principle is, when Art imitates Nature, it should imitate well and not ill.

The style of the book of Proverbs abounds in obverse itertion; see chaps. xii., xiii., &c.

59. III. By Examples, or Particular Instances. This must always be the leading method of expounding general principles.

To quote from Physical Science. The statement of the First Law of Motion,-the perseverance of movement once begun,-is followed up by a number of cases or examples of this perseverance. "A large spinning top, with a fine hard point, set in rapid motion in a vacuum, on a hard smooth surface, will continue turning for hours." "A pendulum swinging in a vacuum has to overcome only the slight friction at its point of suspension, and, when once in motion, will vibrate for a day or more." "The earth's rotation maintains itself without diminution," &c. See also Extracts XIII., XVI.

60. When the sole object is to make an abstruse principle intelligible, as in pure scientific exposition, the examples must be chosen on the following grounds:

(1.) They must themselves be intelligible or familiar to the persons addressed.

(2.) Their number is to be regulated by the difficulty and the comprehensiveness of the principle.

(3.) They should be at first simple, and in the end complicated, so as to show the force of the principle in explaining matters of difficulty.

(4.) They are not to contain distracting accompaniments.

This last is the hardest condition to satisfy, and yet the most imperative. To obtain a series of examples bearing directly and evidently upon one principle, yet not suggesting any matter away from the purpose, constitutes the chief labor of the expositor.

61. The particulars are sometimes mentioned first, and the generality last, as in the order of discovery. This gives a stimulus to the learner to find out the principle for himself, and creates a kind of suspense, or plot interest.

See an example in Extract XI.

62. The extreme case is an example showing the principle, as it were, in an exaggerated form. HYPERBOLE.)

(See

Hume, in maintaining that men possess genuinely disinterested impulses, and revolt from inflicting gratuitous pain, puts an extreme instance thus :-" Would any man, in walking along, tread as willingly on the gouty toes of another man that he has no quarrel with, as on the hard flint and pavement?"

Plato puts the question as to pleasure being the sole end of life (unfairly) in this extreme form :-"You are to be without thought, intelligence, reason, sight, memory; you are not to