right to feel any confidence in the result of his researches.

It may be added that appropriate conceptions, promising to be fertile in scientific results, are only likely, as a rule, to occur to persons whose minds have been habitually disciplined by the strict observance, conscious or unconscious, of the laws of reasoning. Originality is not a quality, as some seem to think, which admits of no psychological explanation.

CHAPTER IV.

Of Imperfect Inductions.

AN argument from the particular to the general, or from particulars to adjacent particulars, may fall short of absolute proof, or even of moral certainty, while it commends itself as possessing more or less of probability. Arguments of this character may be called Imperfect Inductions. Under this head fall imperfect applications of the experimental or inductive methods, the argument from analogy, and incomplete cases of Inductio per simplicem enumerationem.

The Inductio per simplicem enumerationem is, as already noticed', when complete [Inductio Completa], a deductive, and not an inductive, argument. When incomplete, it is an inductive argument, for it is an inference of the unknown from the known. This form of Induction affords certainty only when, as in the case of the Laws of Universal Causation and of the Uniformity of Nature, or of the Mathematical Axioms, it is grounded.

1 See p. 123, note 2, and Deductive Logic, Part III. chap. i. appended

note 2.

upon universal experience, and we feel assured that, if there had been at any time or were now in any place any instance to the contrary, it would not have escaped our notice. But, in ordinary cases, the incomplete Inductio per simplicem enumerationem affords only a presumption, sometimes very slight, sometimes tolerably strong, in favour of the position which it is adduced to establish. I perceive, say in five, ten, or twenty cases, that the phenomenon a is attended by the phenomenon b, and, knowing of no cases in which the one phenomenon is not attended by the other, I begin to suspect that a and b are connected together in the way of causation. Such a surmise may afterwards be proved by the aid of one or other of the five methods to be correct, and, in that case, it is taken out of the category of inductions per simplicem enumerationem, and becomes an instance of a scientific induction. But, if neither proved nor disproved, it still has a certain amount of probability in its favour, that amount depending on the two following considerations: (1) the number of positive instances which have occurred to us; (2) the likelihood, if there be any negative instances, of our having met with them. The first of these considerations deserves little weight, unless supported by the other. A native of the North of Europe, some centuries ago, might, if the mere accumulation of positive instances were sufficient, have taken it for a certain truth that all men had white complexions. His own personal observation, as well as the reports of travellers and the traditions of his race, would have

furnished numberless instances in favour of the position. But, before drawing the inference, he ought to have reflected that he possessed information about a small portion only of the inhabitants of the earth's surface, that a difference of climate might produce a difference of complexion, and that there was no reason for supposing that the anatomical structure of man, or the various characteristics which we denominate human, are necessarily connected with a skin of one particular colour. But, on the other hand, we may affirm with tolerable certainty that all the varieties of beings possessing the physical structure of man have the capacity of articulate speech; for, if there were any races exhibiting the one set of phenomena without the other, there is every probability, with our present knowledge of the earth's surface, that we should be acquainted with their existence. In this instance the first consideration, which in itself would deserve little weight, is converted into a certainty almost absolute by the support which it derives from the second.

It cannot be too strongly impressed on the mind of the student that a mere simplex enumeratio, that is, a mere assemblage of positive instances, unless we have reason to suppose that, were there any instances to the contrary, they would have become known to us, is simply worthless. 'Inductio quæ procedit per enumerationem simplicem res puerilis est.' But if the enumeratio simplex be accompanied by a well-grounded conviction that there are no instances to the contrary, it may afford a very high

degree of probability, and, if we can assure ourselves that there are no instances to the contrary, to us individually it will afford certainty.

It might seem that an Inductio per Simplicem Enumerationem is always an employment of the Method of Agreement. But there is this essential difference. The Method of Agreement is a method of elimination, selecting some and rejecting other instances, and founding its conclusion not on the quantity but on the character of the instances which it selects. The Inductio per Enumerationem Simplicem, on the other hand, depends for its validity on the number of instances; the instances, indeed, must be gathered from every available field, and hence sometimes we speak of their variety as well as their quantity, but the one essential characteristic of the method is that it does not select, but accumulate instances. A few well-selected instances are often sufficient to satisfy the requirements of the Method of Agreement. The same number, when we abstract the grounds on which they were selected, would be utterly insufficient to justify an Inductio per Enumerationem Simplicem.

It may in fact be remarked of all the Experimental Methods that they are devices for saving labour. The range of our experience is often insufficient to justify an argument founded on an Inductio per Enumerationem Simplicem, but by means of the Experimental or Inductive Methods we so select our instances as to bring the particular case which we are investigating under the