a most binding and solemn nature. That the acts in question impair this contract, has been sufficiently shown. They repeal and abrogate its most essential parts.

The deductive method is a very important and useful method of reasoning, but it has its limitations. Its great defect is that, of itself, it is powerless to aid us in the discovery of new truth. Every conclusion we arrive at by this method is but the rendering clear, or the making application of, some particular truth involved in a more general one, and therefore by implication already known. When we wish to find out new truth, to make new generalizations or establish new laws, we must proceed by the inductive method. In inductive reasoning, we start with particular facts or truths known to us from our observation and seek to find some general truth or principle underlying them and giving them meaning or unity.

A conclusion arrived at by the inductive method, once it is established, may be used, of course, as a starting point for a deductive argumentation. Thus a writer, in endeavoring to establish a given truth, may use both the inductive and deductive methods in one and the same discourse. He may proceed now by means of the one and again by means of the other, using them in succession and each as an aid and support to the other. As a matter of fact, reasoning in this way is much more common than reasoning by the purely inductive, or the purely deductive method. It is the method the mind naturally employs in unstudied and informal reasoning. "Our thought," says Professor Creighton, uses every means which

will help it to its desired end. It is often able, after pushing its inquiries a little way, to discover some general principle, or to guess what the law of connection must be. When this is possible, it is found profitable to proceed deductively, and to show what results necessarily follow from the truth of such a general law. Of course, it is always essential to verify results obtained in this deductive way, by comparing them with the actual facts. But in general, the best results are obtained when induction and deduction go hand in hand."1

Inductive reasoning is essentially the endeavor to establish causes for the phenomena which have engaged our attention. When we note facts and seek an explanation of those facts, we reason inductively. In this search for the explanation we desire, our ordinary procedure is first to make a guess as to what that explanation is and then to try to find out whether our guess is correct or not. Thus, in the whole process of inductive reasoning, three distinct steps are distinguishable:

(1) Observation, or the gathering of the particular facts to be used as the basis of the induction.

(2) The making of an hypothesis, or the provisional explanation of the facts.

(3) Verification, or the comparison of deductions from the hypothesis with known facts or principles. The gathering of the facts is, of course, preliminary work. Ordinarily, the writer begins his argumentation with some reference to his hypothesis, which may 1J. E. Creighton, Introductory Logic, pp. 174, 175.

be stated explicitly at the beginning or left as a matter of inference for the reader. The one decisive test of a good hypothesis is its complete accordance with facts. If it is not in agreement with known facts, or is inadequate to the explanation of all the facts it is required to explain, it must be discarded and some more probable hypothesis adopted. That this test may be applied, however, the hypothesis must be of such a nature as to admit of deductions being made from it. "An hypothesis from which nothing can be deduced, . is of no value whatever. It always remains at the stage of mere possibility, and without any real connection with fact. It is a mere guess which has no significance whatever, for it is entirely incapable either of proof or of disproof.'

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Such a useless hypothesis is that, for example, stated first in the following passage:

The adaptation of the external coloring of animals to their condition of life has long been recognized, and has been imputed either to an originally created specific peculiarity, or to the direct action of climate, soil, or food. Where the former explanation has been accepted, it has completely checked inquiry, since we coull never get any further than the fact of the adaptation. There was nothing more to be known about the matter. The second explanation was soon found to be quite inadequate to deal with all the varied phenomena, and to be contradicted by many well-known facts. For example, wild rabbits are always of gray or brown tints well suited for concealment among grass and fern. But when these rabbits are domesticated, without any change of climate or food, they 1 Ibid., p. 242.

vary into white or black, and these varieties may be multiplied to any extent, forming white or black races. Exactly the same thing has occurred with pigeons; and in the case of rats and mice, the white variety has not been shown to be at all dependent on alteration of climate, food, or other external conditions. In many cases, the wings of an insect not only assume the exact tint of the bark or leaf it is accustomed to rest on, but the form and veining of the leaf or the exact rugosity of the bark is imitated; and these detailed modifications cannot be reasonably imputed to climate or food, since in many cases the species does not feed on the substance it resembles, and when it does, no reasonable connection can be shown to exist between the supposed cause and the effect produced.1

The verification or proof of an hypothesis is essentially a deductive process. In verifying an hypothesis, we reason in some such fashion as this: If this hypothesis is true, then such and such consequences should follow; these consequences do follow-that is, they are in accord with all the known facts bearing on the matter; therefore the hypothesis is true.

The familiar story of how Torricelli proved that the air has weight, and incidentally invented the barometer, illustrates the method perfectly. It had been noticed by his master, Galileo, that water would not rise in a suction pump beyond thirty-two or thirtythree feet. Torricelli, in trying to explain why it should rise at all, hit upon the idea that it was because of the pressure of the atmosphere, the weight of the air balancing the column of water. If this were so,

1 From Alfred Russel Wallace's Natural Selection.

he reasoned, then a liquid heavier than water would rise to a less height. Mercury, for instance, which is a little more than thirteen times heavier than water, would rise less than one thirteenth as far. On inverting, in a basin of mercury, a glass tube about four feet long, and hermetically sealed at one end, he found that the result was as he had conjectured. The mercury in the tube sank to about thirty inches above the level of that in the basin. His hypothesis was thus verified, and the world was benefited by the invention of a very useful instrument.

The verification of the hypothesis should, of course, be conducted with the utmost care possible. Accurate observations and rigid scrutiny of the facts used are indispensable as a preliminary, since no induction based on doubtful facts can have much validity. But even if the writer is sure of his facts, he needs to be cautioned against generalizing on too narrow a basis. He needs to be cautioned also against the assumption that a single test satisfactorily passed necessarily establishes an hypothesis. In some cases, such as the one just cited, a single test may be sufficient; but in most cases it is not. It often happens that a phenomenon results from a complexity of causes, in which case a number of tests made under varying conditions will be necessary to reveal all the causes. For example, at a given altitude the application of a certain degree of heat to water in an open vessel will cause it to boil; but we cannot therefore infer that water will always boil when brought to this same temperature. At a lower altitude, it will not boil until a higher temperature is reached. In other words, pressure as well as heat