often happens in the atmosphere. It is thus discovered that whenever moist air is allowed to expand cloud is produced, and it may be drops of rain. Dr Hutton, too, found that whenever cold moist air is mixed with warm moist air cloud is again produced. We can safely argue from such small experiments to what takes place in the atmosphere. Putting together synthetically, from the sciences of chemistry, mechanics, and electricity, all that we know of air, wind, cloud and lightning, we are able to explain what takes place in a thunder-storm far more completely than we could do by merely observing directly what happens in the storm. We are here however anticipating the methods of inductive investigation, which we must consider in the following lessons. It will appear that Induction is equivalent to analysis, and that the deductive kinds of reasoning which we have treated in prior lessons are of a synthetic character. It has been said that the synthetic method usually corresponds to the method of instruction and the analytic method to that of discovery. But it may be possible to discover new truths by synthesis and to teach old ones by analysis. Sir John Herschel in his well-known Outlines of Astronomy partially adopts the analytic method; he supposes a spectator in the first place to survey the appearances of the heavenly bodies and the surface of the earth, and to seek an explanation; he then leads him through a course of arguments to show that these appearances really indicate the rotundity of the earth, its revolution about its own axis and round the sun, and its subordinate position as one of the smaller planets of the solar system. Mr Norman Lockyer's Elementary Lessons in Astronomy is a clear example of the synthetic method of instruction; for he commences by describing the sun, the centre of the system, and successively adds the planets and other members of the system, until at last we have the complete picture; and the reader who has temporarily received everything on the writer's authority, sees that the description corresponds with the truth. Each method, it must be allowed, has its own advantages. It must be carefully observed that the meaning of analysis, and therefore that of synthesis, varies according as we look to the intension or extension of terms. To divide or analyse a class of things in extension I must add a quality or difference. Thus I divide the class organism when I add the quality vegetable, and separate vegetable organism from what is not vegetable. Analysis in extension is therefore the same process as synthesis in intension; and vice versa, whenever I separate or analyse a group of qualities each part belongs to a larger class of things in extension. When I analyse the notion vegetable organism, and regard the notion organism apart from vegetable, it is apparent that I really add the whole class of animal organisms to the class I am considering—so that analysis in intension is synthesis in extension. The reader who has well considered the contents of Lessons V. and XII. will probably see that this connection of the two processes is only a re-statement of the law, (p. 40), that "as the intension of a term is increased the extension is decreased." To express the difference between knowledge derived deductively and that obtained inductively the Latin phrases à priori and à posteriori are often used. By A priori reasoning we mean argument based on truths previously known; A posteriori reasoning, on the contrary, proceeds to infer from the consequences of a general truth what that general truth is. Many philosophers consider that the mind is naturally in possession of certain laws or truths which it must recognise in every act of thought; all such, if they exist, would be à priori truths. It cannot be doubted, for instance, that we must always 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. |