scientiil a singe on. Fa measure he mind thing 1 to one unts f ced pro Taw seen which ould be ccepted nces d equal are Sus made f e time the one eralised al and ce. We equal hat the cussion h each ball exerts is exactly met and counteracted by that CHAP. V. SECT. X. § 208. Thus we see that all general laws are the Different kinds of result of induction, as well as those general proposi-induction. tions which express the characteristics of classes of objects. But there are inductions and inductions. Some inductions-as those regarding the relations of mathematical magnitudes, and the laws of forces-are founded upon particular inferences, these inferences being unavoidable in the present condition of things. Other inductions are founded upon the perceived relations of certain qualities which we have determined, by observation and comparison, to be essential to the constitution of particular classes. Thus, in all cases of induction there must be recognised the existence of a certain established objective order of things, and our inductions are only an expression in language of what we believe to be essential relations of this objective order. If our inductions accurately correspond to the objective order, we say that they are true; if not, not. § 209. We are now brought to the study of the last Deduction. CHAP. V. Certainty of infer ence depends upon major premise. form of inference-the deductive. Here the mind passes in reasoning from the general or universal to the particular. Having already known something to be true of a whole class of things, we are able to affirm it to be true of every individual of the class. Familiar illustrations of the deductive process are seen in the application of the general laws of natural forces to particular cases, and in inferences regarding the qualities of particular individuals of a class from our knowledge of the essential constituents of the class. The astronomer, having determined the laws of the motion of some particular planet, is able to infer with precision the particular point in the heavens which it will occupy at any particular moment. The chemist, having determined the laws of the combination of particular elements, is able to predict the result in any special case. The naturalist, having discovered the universal characteristics of some species of animals or plants, expects with certainty to find these characteristics in every new specimen. The natural form in which inference of this kind is thrown is, no doubt, the syllogism. And the principal value of the syllogism is to state, in an explicit, methodical form, those deductive inferences at which the mind arrives, frequently without any conscious reference to the major premise at all. § 210. In order that the deductive inference may be thoroughly trustworthy, the major premise must be an expression of some essential objective order or law of things. If, for example, the major premise of a syllogism be "All swans are white," an inference from that, with reference to the colour of any particular swans hitherto unseen, could not be made with perfect certainty. We could never feel certain but that birds might be found possessing all the essential characteristics of swans, but which were of some other colour. Whereas, if we have for our major premise, "All cows ruminate," the inference with reference to particular animals of the species is certain, because the predication of the major premise expresses an essential condition of the class. Deductive inferences which have for their object some accidental quality or state of things can never amount to more than a probability. The probability of the inference is the consequence of the want of certainty which characterises the major premise. And that want of certainty arises either from the accidental nature of the relation which is predicated in the premise, or from our partial ignorance regarding it. CHAP. V. SECT. XI. SECTION XI. CONCLUSION. thetical § 211. By way of summing up the conclusions at Hypowhich we have arrived in the preceding sections, we Inference. may first point out the different kinds of inferences which we draw. One of the most important of these is the Hypothetical Inference,* by the object of which we account for the existence of known phenomena. The existence of any particular sensation is accounted * This, of course, is altogether different from the hypothetical form of the syllogism. CHAP. V. SECT. XI. Particular inference. for by inferring some objective hypothetical power. The existence of a foot-print upon the sand is accounted for by the supposition that a man walked along the sand some time previous. The statements of a historical writer are accounted for by the inference that the events which he describes actually occurred. Any particular phenomenon or complex series of phenomena being given, we account for its existence and character by inferring hypothetically some antecedent cause sufficient to account for it. In many cases, we may never be able to verify the inference by direct knowledge; but it matters not; the inference must be made, nevertheless, to satisfy that insatiable craving after a knowledge of the causes of things which is our birthright as rational beings. In many other cases, the hypothetical inference may be verified, as in the discovery of the planet Neptune, and in the discovery of certain new metals which had been inferred to account for peculiar phenomena in the spectroscope. In cases where the hypothetical inference cannot be verified by direct observation, various degrees of probability, or even a practical certainty, may be obtained by considering the degree of completeness with which the particular inference accounts for the phenomena, and the absence of a foundation for any other inference. § 212. The Particular Inference founded upon subjective association is very familiar. Two or more objects of knowledge having occurred together a few or several times, there is formed an expectation that, where one of them appears, the others may be looked for. The occurrence of these objects together leads the mind to suppose that there is some objective connection between them, and this supposition forms the ground of the inference. When this supposition is converted into actual knowledge, and the connection between the two associated phenomena is ascertained, the inference is no longer problematical, but acquires the character of a certainty. The Particular Inference founded upon a comparison of simple Intuitions is also characterised by certainty from the very first. When we infer that the lines A and B, being each equal to C, are equal to one another, there is no other inference which we could possibly draw. CHAP. V. SECT. XI. § 213. The Inductive Inference, founded upon uni- Inductive inference. formity of experience, never amounts to more than a high degree of probability. But it is not, therefore, to be despised, because in many cases nothing but a certain degree of probability is attainable. And in the practical concerns of life probability is our usual guide. The Inductive Inference, founded upon a knowledge of the essential relations of the things concerned, partakes of the same amount of certainty as the knowledge on which it is founded. Illustrations of this are seen in the axioms of mathematics and of natural forces, and in the inductive generalisations regarding natural orders and species. The Deductive Inference is based upon some general Deductive inference. principle, and rests for its conformity to truth upon the assumed truth of the principle from which it |