-

dering our conclusion either more or less general than the premises, as in the following Snowdon is the highest mountain in England or Wales.

Snowdon is not so high as Ben Nevis.

Therefore the highest mountain in England or Wales is not so high as Ben Nevis.

Again :

Lithium is the lightest metal known.

*

Lithium is the metal indicated by one bright red line in the spectrum. Therefore the lightest metal known is the metal indicated by a spectrum of one bright red line.

In these examples all the propositions are singular propositions, and merely assert the identity of singular terms, so that there is no alteration of generality. Each conclusion applies to just such an object as each of the premises applies to. To this kind of reasoning the apt name of Traduction has been given.

Induction is a much more difficult and more important kind of reasoning process than Traduction or even Deduction; for it is engaged in detecting the general laws or uniformities, the relations of cause and effect, or in short all the general truths that may be asserted concerning the numberless and very diverse events that take place in the natural world around us. The greater part, if not, as some philosophers think, the whole of our knowledge, is ultimately due to inductive reasoning. The mind, it is plausibly

* Roscoe's Lessons in Elementary Chemistry, p. 199.

said, is not furnished with knowledge in the form of general propositions ready made and stamped upon it, but is endowed with powers of observation, comparison, and reasoning, which are adequate, when well educated and exercised, to procure knowledge of the world without us and the world within the human mind. Even when we argue synthetically and deductively from simple ideas and truths which seem to be ready in the mind, as in the case of the science of geometry, it may be that we have gathered those simple ideas and truths from previous observation or induction of an almost unconscious kind. This is a debated point upon which I will not here speak positively; but if the truth be as stated, Induction will be the mode by which all the materials of knowledge are brought to the mind and analysed. Deduction will then be the almost equally important process by which the knowledge thus acquired is utilised, and by which new Inductions of a more complicated character, as we shall see, are rendered possible.

An Induction, that is an act of Inductive reasoning, is called Perfect when all the possible cases or instances to which the conclusion can refer, have been examined and enumerated in the premises. If, as usually happens, it is impossible to examine all cases, since they may occur at future times or in distant parts of the earth or other regions of the universe, the Induction is called Imperfect. The assertion that all the months of the year are of less length than thirty

two days is derived from Perfect Induction, and is a certain conclusion because the calendar is a human institution, so that we know beyond doubt how many months there are, and can readily ascertain that each of them is less than thirty-two days in length. But the assertion that all the planets move in one direction round the sun, from West to East, is derived from Imperfect Induction; for it is possible that there exist planets more distant than the most distantknown planet Neptune, and to such a planet of course the assertion would apply.

Hence it is obvious that there is a great difference between Perfect and Imperfect Induction. The latter includes some process by which we are enabled to make assertions concerning things that we have never seen or examined or even known to exist. But it must be carefully remembered also that no Imperfect Induction can give a certain conclusion. It may be highly probable or nearly certain that the cases unexamined will resemble those which have been examined, but it can never be certain. It is quite possible, for instance, that a new planet might go round the sun in an opposite direction to the other planets. In the case of the satellites belonging to the planets more than one exception of this kind has been discovered, and mistakes have constantly occurred in science from expecting that all new cases would exactly resemble old ones. Imperfect Induction thus gives only a certain degree of probability or likelihood that all instances will agree with those

examined. Perfect Induction, on the other hand, gives a necessary and certain conclusion, but it asserts nothing beyond what was asserted in the premises.

Mr. Mill, indeed, differs from almost all other logicians in holding that Perfect Induction is improperly called Induction, because it does not lead to any new knowledge. He defines Induction as inference from the known to the unknown, and considers the unexamined cases which are apparently brought into our knowledge as the only gain from the process of reasoning. Hence Perfect Induction seems to him to be of no scientific value whatever, because the conclusion is a mere reassertion in a briefer form, a mere summing up of the premises. I may point out, however, that if Perfect Induction were no more than a process of abbreviation it is yet of great importance, and requires to be continually used in science and common life. Without it we could never make a comprehensive statement, but should be obliged to enumerate every particnlar. After examining the books in a library and finding them to be all English books we should be unable to sum up our results in the one proposition, "all the books in this library are English books;" but should be required to go over the list of books every time we desired to make any one acquainted with the contents of the library. The fact is, that the power of expressing a great number of particular facts in a very brief space is essential to the progress of science. Just as the whole science of arithmetic

consists in nothing but a series of processes for abbreviating addition and subtraction, and enabling us to deal with a great number of units in a very short time, so Perfect Induction is absolutely necessary to enable us to deal with a great number of particular facts in a very brief space.

It is usual to represent Perfect Induction in the form of an Inductive Syllogism, as in the following instance :—

Mercury, Venus, the Earth, &c., all move round the sun from West to East.

Mercury, Venus, the Earth, &c., are all the known Planets.

Therefore all the known planets move round the sun from West to East.

This argument is a true Perfect Induction because the conclusion only makes an assertion of all known planets, which excludes all reference to possible future discoveries; and we may suppose that all the known planets have been enumerated in the premises.

As another example of a Perfect Induction we may take

January, February,..........December, each contain less than 32 days.

January..

the year.

December are all the months of

Therefore all the months of the year contain less than 32 days.

Although Sir W. Hamilton has entirely rejected the notion, it seems worthy of inquiry whether the Inductive Syllogism be not really of the Disjunctive form of Syllogism. Thus I