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(52.) By the modifications of this system of notation, it is not impossible that acts of Parliament, deeds, and other exact documents may eventually be drawn; for if once the entire words of the English language were arranged in their mutual relations, this mode of writing would probably be the most exact form of language which could be adopted.

CHAPTER IV.

ON INDUCTION.

(53) Induction.-(54) Nature of.-(55) Illustration.-(56) Arrangement. (57) Classes of Induction.-(58) Absolute Inductions.—(59) Induction of Probabilities. -(60) Possible Inductions. (61) Induction of Means.-(62) Induction of Limits. (63) Hypothetical Induction.

(53.) I have now to treat of the method by which the mind classifies a series of facts, so as to represent them by the shortest possible method. It is a faculty of great importance to man, inasmuch as by it he is enabled to communicate a large number of facts in a few words.

(54.) The process of induction consists in finding a definite and constant connection between two or more parts of any images, or sequences of images. When, for instance, we find that every individual person dies, whether male or female, we learn a number of individual facts, or rather, we ascertain that a number of human beings have ceased to live, and taken on the various changes of death.

We then ascertain that that which we call Humanity is common to all the cases, as one part of the fact; and that that which we call Death, is common; and this constitutes the second part of the fact: hence is induced that man is mortal, or in other words, that humanity and death are invariably conjoined at one time or other.

(55.) To illustrate the nature of induction, we may take a number of combinations of nervous elements, and call them by letters. If the combination A represents that part of an idea which is possessed by all men, and W the combination given by a sense of feeling, then, if we find that where A is present W is present, we have acquired a most important information; for if A is present ten thousand times, there will W exist. If B represents that which is common to man, and we find it always conjoined with X, denoting rationality, then we know that all men are rational; so if C represents that which is common to whites, and Y denotes happiness, and D represents the peculiarities of Englishmen, and Z the characteristics of freedom, then by this series of inductions we have acquired most important knowledge.

D C B A

W X Y Z

But we observe, that man partakes of the properties of A B, therefore, he is W X, or is possessed

of feeling and rationality. Whites possess the characteristic of A B C, and, therefore, manifest W X Y, that is to say, they feel, are rational and happy. Lastly, Englishmen being designated by A B C D, manifest the properties of W X Y Z, or evince feeling, rationality, happiness and freedom.

(56.) The above statements may be also arranged as two geometric series, which for many causes are more convenient for study.

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By this arrangement in the first series, A would stand for animal, B for man, D for whites, H for English. In the second series, it is manifest that feeling, rationality, happiness and freedom do not possess any immediate relation to each other, and therefore in the absence of any definite knowledge upon this matter, they may be arbitrarily assigned the symbols of m, n, p, r in the fourth row.

(57.) It may be useful to consider a few speci

man.

mens of inductions arranged in different classes, that we may the more properly estimate their value to For this purpose, we may consider them. under six heads:-Absolute Inductions, Probable Inductions, Possible Inductions, Inductions of Means, Inductions of Limits, Hypothetical Inductions.

(58.) Of absolute inductions we find good illustrations in the properties of numbers: thus, if one be added to one, it makes two; if two be multiplied by two it makes four. These instances are so familiar, that we are apt to forget that they are inductions; but, if I state that the square of any number is equal to the sum of as many consecutive odd numbers beginning with units, as there are units in that number, as thus, 6 × 6 = 1 + 3 + 5 + 7 + 9 + 11, there probably will be but few of my readers who would be aware of the fact, and would only believe it after they had satisfied themselves upon the matter. Other examples of absolute inductions may be observed in our knowledge of the properties of geometric figures.

(59.) The next class of inductions which we have to consider, may be termed Inductions of Probabilities, because we induce a law of probability from a certain number of facts. This induction will not express to us the absolute fact in any one particular case. As an example of a probable

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