recognise in thought the three Primary Laws of Thought considered in Lesson XIV. We have there an à priori knowledge that "matter cannot both have weight and be without weight," or that "every thing must be either selfluminous or not self-luminous." But there is no law of thought which can oblige us to think that matter has weight, and luminous ether has not weight; that Jupiter and Venus are not self-luminous, but that comets are to some extent self-luminous. These are facts which are no doubt necessary consequences of the laws of nature and the general constitution of the world; but as we are not naturally acquainted with all the secrets of creation, we have to learn them by observation, or by the à posteriori method. It is not however usual at the present time to restrict the name à priori to truths obtained altogether without recourse to observation. Knowledge may originally be of an à posteriori origin, and yet having been long in possession, and having acquired the greatest certainty, it may be the ground of deductions, and may then be said to give à priori knowledge. Thus it is now believed by all scientific men that force cannot be created or destroyed by any of the processes of nature. If this be true the force which disappears when a bullet strikes a target must be converted into something else, and on à priori grounds we may assert that heat will be the result. It is true that we might easily learn the same truth à posteriori, by picking up portions of a bullet which has just struck a target and observing that they are warm. But there is a great advantage in à priori knowledge; we can often apply it in cases where experiment or observation would be difficult. If I lift a stone and then drop it, the most delicate instruments could hardly show that the stone was heated by striking the earth; yet on à priori grounds I know that it must have been so, and can easily calcu late the amount of heat produced. Similarly we know, without the trouble of observation, that the Falls of Niagara and all other waterfalls produce heat. This is fairly an instance of à priori knowledge because no one that I have heard of has tried the fact or proved it à posteriori; nevertheless the knowledge is originally founded on the experiments of Mr Joule, who observed in certain well-chosen cases how much force is equivalent to a certain amount of heat. The reader, however, should take care not to confuse the meaning of à priori thus explained with that given to the words by the philosophers who hold the mind to be in the possession of knowledge independently of all observation. It is not difficult to see that the à priori method is equivalent to the synthetic method (see p. 205) considered in intension, the à posteriori method of course being equivalent to the analytic method. But the same difference is really expressed in the words deductive and inductive; and we shall frequently need to consider it in the following lessons. For general remarks upon Method see the Port Royal LESSON XXV. PERFECT INDUCTION AND THE INDUCTIVE SYLLOGISM. WE have in previous lessons considered deductive reasoning, which consists in combining two or more general propositions synthetically, and thus arriving at a conclusion which is a proposition or truth of less generality than the premises, that is to say, it applies to fewer individual instances than the separate premises from which it was inferred. When I combine the general truth that "metals are good conductors of heat," with the truth that "aluminium is a metal," I am enabled by a syllogism in the mood Barbara to infer that "aluminium is a good conductor of heat." As this is a proposition concerning one metal only, it is evidently less general than the premise, which referred to all metals whatsoever. In induction, on the contrary, we proceed from less general, or even from individual facts, to more general propositions, truths, or, as we shall often call them, Laws of Nature. When it is known that Mercury moves in an elliptic orbit round the Sun, as also Venus, the Earth, Mars, Jupiter, &c., we are able to arrive at the simple and general truth that "all the planets move in elliptic orbits round the sun." This is an example of an inductive process of reasoning. It is true that we may reason without rendering 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 spectum of one bright red line. In these examples all the propositions are singular propositions, and merely assert the identity of singular * Roscoe's Lessons in Elementary Chemistry, p. 199. 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 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 Imperfeot. 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. 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 distant-known planet Neptune, and to such a planet of course the assertion would apply. But 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 hard, gives a necessary and |