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half-a-dozen of the other planets could readily be swallowed up in one of them*. It is plain then that there is little or no analogy between the Sun and the Earth, and we can therefore with difficulty form a conception of anything going on in a sun or star.
Argument from analogy may be defined as direct inductive inference from one instance to any similar instance. It may, as Mr Mill says, be reduced to the following formula :
“Two things resemble each other in one or more respects; a certain proposition is true of the one; therefore it is true of the other.” This is no doubt the type of all reasoning, and the certainty of the process depends entirely upon the degree of resemblance or identity between the cases. In geometry the cases are absolutely identical in all material points by hypothesis, and no doubt attaches to the inference; in physical science the identity is a question of probability, and the conclusion is in a like degree probable. It should be added that Mr Mill considers Geometrical and Mathematical Induction not to be properly called Induction, for reasons of which the force altogether escapes my apprehension ; but the reader will find his opinions in the 2nd chapter of the 3rd book of his System of Logic.
One form of analogical or inductive argument consists in the constant use of examples and instances. The best way to describe the nature of a class of things is to present one of the things itself, and point out the properties which belong to the class as distinguished from those peculiar to the thing. Throughout these Lessons, as throughout every work on Logic, instances of propositions, of compound or complex sentences, of syllogisms, &c., are continually used, and the reader is asked to apply to all
Lockyer's Elementary Lessons in Astronomy, $ 108.
similar cases what he observes in the examples given. It is assumed that the writer selects such examples as truly exhibit the properties in question.
While all inductive and analogical inferences rest upon the same principles there are wide differences between the sources of probability. In analogy we have two cases which resemble each other in a great many properties, and we infer that some additional property in one is probably to be found in the other. The very narrow basis of experience is compensated by the high degree of similarity. In the processes more commonly treated under the name Induction, the things usually resemble each other only in two or three properties, and we require to have more instances to assure us that what is true of of these is probably true of all similar instances. The less, in short, the intension of the resemblance the greater must be the extension of our inquiries.
We proceed to the dinary processes of Induction in the following Lessons. Mr Mill's System of Logic, Book III. Chap. xx, Of
Analogy. Mansel's Aldrich, App. Note H. On
OBSERVATION AND EXPERIMENT.
ALL knowledge, it may be safely said, must be ultimately sounded upon experience, which is but a general name for the various feelings impressed upon the mind at any period of its existence. The mind never creates entirely new knowledge independent of experience, and all that the reasoning powers can do is to arrive at the full meaning
of the facts which are in our possession. In previous centuries men of the highest ability have held that the mind of its own power alone could, by sufficient cogitation, discover what things outside us should be, and would be found to be on examination. They thought that we were able to anticipate Nature by evolving from the human mind an idea of what things would be made by the Creator. The celebrated philosopher Descartes thus held that whatever the mind can clearly conceive may be considered true; but we can conceive the existence of mountains of gold or oceans of fresh water, which do not as a fact exist. Anything that we can clearly conceive must be conformable to the laws of thought, and its existence is then not impossible, so far as our intellect is concerned; but the forms and sizes and manners in which it has pleased the Creator to make things in this or any other part of the universe, cannot possibly be anticipated by the exceedingly limited wisdom of the human mind, and can only be learnt by actual examination of existing things.
In the latter part of the 13th century the great Roger Bacon clearly taught in England the supreme importance of experience as the basis of knowledge; but the same doctrine was also, by a curious coincidence, again upheld in the 17th century by the great Chancellor Francis Bacon, after whom it has been called the Baconian Philosophy. I believe that Roger Bacon was even a greater man than Francis, whose fame is best known; but the words in which Francis Bacon proclaimed the importance of experience and experiment must be ever memorable. In the beginning of his great work, the Novum Organum, or New Instrument, he thus points out our proper position as learners in the world of nature.
“Man, the Servant and Interpreter of Nature, can do and understand as much as he has observed concerning
the order of nature in outward things or in the mind; more, he can neither know nor do."
The above is the first of the aphorisms or paragraphs with which the Novum Organum commences. In the second aphorism he asserts that the unaided mind can effect little and is liable to err; assistance in the form of a definite logical method is requisite, and this it was the purpose of his New Instrument to furnish. The 3rd and 4th aphorisms must be given entire; they are:
“Human science and human power coincide, because ignorance of a cause deprives us of the effect. For nature is not conquered except by obedience; and what we discover as a cause by contemplation becomes a rule in operation.”
“Man can himself do nothing else than move natural bodies to or from each other; nature working within accomplishes the rest.”
It would be impossible more clearly and completely to express the way in which we discover science by interpreting the changes we obserye in nature, and then turn our knowledge to a useful purpose in the promotion of the arts and manufactures. We cannot create and we cannot destroy a particle of matter; it is now known that we cannot even create or destroy force; nor can we really alter the inner nature of any substance that we have to deal with. All that we can do is to observe carefully how one substance by its natural powers acts upon another substance, and then by rioving them together at the right time we can effect our object; as Bacon says, “Nature working within does the rest.” Had it not been the nature of heat when applied to water to develope steam possessing elastic power, it is needless to say that the steam-engine could never have been made, so that the invention of the steam-engine arose from observing the utility of the force of steam, and employing it accordingly,
It is in this sense that Virgil has proclaimed him happy who knows the causes of things
Felix qui potuit rerum cognoscere causas, and that Bacon has said, Knowledge is Power. So far as we have observed how things happen in nature, and on what occasion particular effects are brought to pass, we are enabled to avoid or utilise those effects, as we may desire, not by altering the natures of things, but by allowing them in suitable times and circumstances to manifest their own proper powers. It is thus, as Tennyson has excellently said, that we
“Rule by obeying Nature's Powers.” Inductive logic treats of the methods of reasoning by which we may successfully interpret nature and learn the natural laws which various substances obey in different circumstances. In this lesson we consider the first requisite of induction, namely, the experience or examination of nature which is requisite to furnish us with facts. Such experience is obtained either by observation or experiment. To observe is merely to notice events and changes which are produced in the ordinary course of nature, without being able, or at least attempting, to control or vary those changes. Thus the early astronomers, observed the motions of the sun, moon and planets among the fixed stars, and gradually detected many of the laws or periodical returns of those bodies. Thus it is that the meteorologist observes the ever-changing weather, and notes the height of the barometer, the temperature and moistness of the air, the direction and force of the wind, the height and character of the clouds, without being in the least able to govern any of these facts. The geologist again is genenerally a simple observer when he investigates the nature and position of rocks. The zoologist, the botanist, and