Induction is an inference from many facts. Induction is verification. Just as in a syllogism we show that a part is contained in the whole, so in induction we show that a part is illustrated by the whole. It seems that every single fact contains many truths, but induction establishes their universality. A single brain contains all the truths of phrenology, a single stone includes the phenomena of gravitation, the temperance of a single individual exhibits the whole law of moderation, but we learn the universality of these truths by induction. Every legal statute, says Dr. Johnson, is founded on induction. 'Law is the science in which the greatest powers of understanding are applied to the greatest number of facts.' The basis of all science is such an extensive induction of particulars as leads to general definitions and fundamental axioms, and furnishes the premises from which inferences may be deduced.
Inductive observation is the great instrument of discovering important truths. 'What are called the principles of human nature are learned from individual instances. It is the only possible way of learning them. * * When we reason from a general law or principle, we are in truth reasoning from a number of instances represented by It.'*
     * Rationale of Political Representation, p. 34.
A general election is an induction of the intelligence of the country represented by the members of Parliament. The difference between democracy and monarchy is in one sense an affair of logic. Where electors are limited in franchise, and candidates restricted by property qualification, the induction is partial, but where all can vote and many can be chosen from, the premises are more capacious and the inference sounder.
Dr. Whately says, that 'in Natural Philosophy a single instance is often accounted a sufficient induction; e.g., having once ascertained that an individual magnet will attract iron, we are authorised to conclude that this property is universal.'
'The Edinburgh Reviewer of Whewell's "History of the Inductive Sciences," observes that, "by the accidental placing of a rhomb of calcareous spar, upon a book or line, Bartholinus discovered the property of the double refraction of light. By accidentally combining two rhombs in different positions, Huygens discovered the polarisation of light. By accidentally looking through a prism of the same substance, and turning it round, Mains discovered the polarisation of light by reflection; and by placing thin chrystalline films between two similar prisms or rhombs, M. Arago discovered the phenomena of polarised tints."
'To this Mr. Whewell, in his "Philosophy of the Inductive Sciences," makes the following reply:—"But Bartholinus could have seen no such consequence in the accident, if he had not previously had a clear conception of single refraction. A lady, in describing an optical experiment which had been shown her, said of her teacher, 'he told me to increase and diminish the angle of refraction: and, at last, I found that he only meant me to move my head up and down.' At any rate, till the lady had acquired a knowledge of the meaning which the technical terms convey, she could not have made Bartholinus's discovery by means of this accident. Suppose that Huygens made the experiment alluded to, without design, what he really observed was that the images appeared and disappeared alternately as he turned the rhomb round. His success depended on his clearness of thought, which enabled him to perform the intellectual analysis which would never have occurred to most men, however often they had combined two rhombs in different positions. Malus saw that in some positions the light reflected from the windows of the Louvre became dim. Another person would have attributed this to accident; he, however, considered the position of the prism, and the window; repeated the experiment often; and by virtue of the eminently distinct conceptions of space which he possessed, resolved the phenomenon into its geometrical conditions."* "If it were true, that the fall of an apple was the occasion of Newton's pursuing that train of thought which led to the doctrine of universal gravitation, the habits and constitution of Newton's intellect were the real source of this great event in the progress of knowledge."** "In whatever manner facts may be presented to the notice of a discoverer, they can never become the materials of exact knowledge, except they find his mind already provided with precise and suitable conceptions, by which they may be analysed and connected."'***
     * Whewell:  Phil. Induct. Sciences, vol. 2. pp. 199-1.
 
     ** Ibid, vol. 2, p. 189.
 
     *** See J. N. Bailey's Essays pp. 87-8-9.
These admissions seem to me to prove that whenever a casual fact proves to us a new truth, it does so by its coincidence with previously known facts, and that the novelty of the occasion attracts all credit to itself, and we lose sight of the generalisation below—the fruitful soil of experience on which the new fact, like a seed, falls. We only recognise difference by comparison, and the comparison is an induction, however slender.
Monsieur de Montmorine was recaptured and brought to the scaffold, through the trifling circumstance of some chicken bones being found near the door of his landlady—a woman too poor to indulge in such dainties.* The discovery of de Montmorine was not, as at first sight appears, an inference from a single fact, but from an adjacent induction. It was a general truth, (known to the party who observed the bones) a truth inducted from a number of facts that poor people could not afford to luxuriate on chickens. It was, therefore, from this induction, inferred that some one of superior fortune must be living in that particular place.
     * Chambers' Miscellany of Useful and Entertaining Tracts,
     No. 61: the Story of Lavaiette, p. 27
The judicious care which the great fathers of science have exhibited in making their inferences, incontestably establishes their conviction of the danger of any other reasoning than that from inductions. Lord Brougham informs us, that what Newton's Principia is to science, Locke's essay to metaphysics, Demosthenes in oratory, and Homer in poetry, Cuvier's researches to our fossil osteology. But Cuvier never attempted to draw any inferences until he had examined the whole osteology of the living species.
Lord Brougham remarks, that 'from examining a single fragment of bone we infer that, in the wilds where we found it, there lived and ranged, some thousands of years ago, an animal of a peculiar kind.' This is a case in which the inference spoken of is arrived at in a way different from that apparently stated. We recognise in the 'fragment of bone' a link in a chain of facts constituting the basis of a well-known induction, which comparative anatomy has many times verified. It is important to distinguish well the grounds from which accurate inferences, such as these in the cases before us, have really been adduced, in order to ascertain the grounds from which we should reason generally. It will be found that solid reasoning can only proceed from general rules—i.e., inductions from facts. It will be found that the prime source of fallacy lies in reasoning from isolated facts. It is not to be denied that such reasoning is sometimes right, but it is to be remembered that it is right by accident, not by design. There is no science or certainty in it. It is hazard, not logic.
This habit however, is very common. Mr. Mill says, that 'Not only may we reason from particulars to particulars, without passing through generals, but we perpetually do so reason. All our earliest inferences are of this nature. From the first dawn of intelligence we draw inferences, but years elapse before we learn the use of general language. The child, who, having burnt his fingers, avoids to thrust them again into the fire, has reasoned or inferred, though he has never thought of the general maxim—fire burns. He knows from memory that he has been burnt, and on this evidence believes, when he sees a candle, that if he puts his fingers into the flame of it, he will be burnt again. He believes this in every case which happens to arise; but without looking, in each instance, beyond the present case. He is not generalising; he is inferring a particular from particulars. In the same way, also, brutes reason. There is little or no ground, for attributing to any of the lower animals the use of conventional signs, without which general propositions are impossible. But those animals profit by experience, and avoid what they have found to cause them pain, in the same manner, though not always with the same skill, as a human creature. Not only the burnt child, but the burnt dog, dreads the fire.
'I believe that, in point of fact, when drawing inferences from our personal experience, and not from maxims handed down to us by books or tradition, we much oftener conclude from particulars to particulars directly, than through the intermediate agency of any general proposition. We are constantly reasoning from ourselves to other people, or from one person to another, without giving ourselves the trouble to erect our observations into general maxims of human or external nature. When we conclude that some person will, on some given occasion, feel or act so and so, we sometimes judge from an enlarged consideration of the manner in which men in general, or men of some particular character, are accustomed to feel and act; but much oftener from having known the feelings and conduct of the same man in some previous instance, or from considering how we should feel or act ourselves. It is not only the village matron who, when called to a consultation upon the case of a neighbour's child, pronounces on the evil and its remedy simply on the recollection and authority of what she accounts the similar case of her Lucy. We all, where we have no definite maxims to steer by, guide ourselves in the same way; and if we have an extensive experience, and retain its impressions strongly, we may acquire, in this manner, a very considerable power of accurate judgment, which we may be utterly incapable of justifying or of communicating to others. Among the higher order of practical intellects, there have been many of whom it was remarked how admirably they suited their means to their ends, without being able to give any sufficient reasons for what they did and applied, or seemed to apply, recondite principles which they were wholly unable to state. This is a natural consequence of having a mind stored with appropriate particulars, and having been long accustomed to reason at once from these to fresh particulars, without practising the habit of stating to oneself or to others the corresponding general propositions. An old warrior, on a rapid glance at the outlines of the ground, is able at once to give the necessary orders for a skilful arrangement of his troops; though if he has received little theoretical instruction, and has seldom been called upon to answer to other people for his conduct, he may never have had in his mind a single general theorem respecting the relation between ground and array. But his experience of encampments, under circumstances more or less similar, has left a number of vivid, unexpressed, ungeneralised analogies in his mind, the most appropriate of which, instantly suggesting itself, determines him to a judicious arrangement.
'The skill of an uneducated person in the use of weapons, or of tools, is of a precisely similar nature. The savage who executes unerringly the exact throw which brings down his game, or his enemy, in the manner most suited to his purpose, under the operation of all the conditions necessarily involved, the weight and form of the weapon, the direction and distance of the object, the action of the wind, &c., owes this power to a long series of previous experiments, the results of which he certainly never framed into any verbal theorems or rules. It is the same in all extraordinary manual dexterity. Not long ago a Scotch manufacturer procured from England, at a high rate of wages, a working dyer, famous for producing very fine colours, with a view of teaching to his other workmen the same skill. The workman came; but his mode of proportioning the ingredients, in which lay the secret of the effects he produced, was by taking them up in handfuls while the common method was to weigh them. The manufacturer sought to make him turn his handling system into an equivalent weighing system, that the general principle of his peculiar mode of proceeding might be ascertained. This, however, the man found himself quite unable to do, and therefore could impart his skill to nobody. He had, from the individual cases of his own experience, established a connection in his mind between fine effects of colour, and tactual perceptions in handling his dyeing materials; and from these perceptions he could, in any particular cases, infer the means to be employed, and the effect which would be produced, but could not put others in possession of the grounds on which he proceeded, from having never generalised them in his own mind, or expressed them in language.
'Almost every one knows Lord Mansfield's advice to a man of practical good sense, who, being appointed governor of a colony, had to preside in its court of justice, without previous judicial practice or legal education. The advice was to give his decision boldly, for it would probably be right; but never to venture on assigning reasons, for they would almost infallibly be wrong. In cases like this, which are of no uncommon occurrence, it would be absurd to suppose that the bad reason was the source of the good decision. Lord Mansfield knew that if any reason were assigned it would be necessarily an afterthought, the judge being in fact guided by impressions from past experience, without the circuitous process of framing general principles from them, and that if he attempted to frame any such he would assuredly fail. Lord Mansfield, however, would not have doubted that a man of equal experience, who had also a mind stored with general propositions derived by legitimate induction from that experience, would have been greatly preferable as a judge, to one, however sagacious, who could not be trusted with the explanation and justification of his own judgments. The cases of able men performing wonderful things they know not how, are examples of the less civilised and most spontaneous form of the operations of superior minds It is a defect in them, and often a source of errors, not to have generalised as they went on; but generalisation is a help, the most important indeed of all helps, yet not an essential.'*
     * Mill's Logic, pp. 251-5.
In illustration of generalising from single instances, Miss Martineau gives this example:—'A raw Chinese traveller in England was landed by a Thames waterman who had a wooden leg. The stranger saw that the wooden leg was used to stand in the water with, while the other was high and dry. The apparent economy of the fact struck the Chinese; he saw in it strong evidence of design, and wrote home that in England one-legged men are kept for watermen, to the saving of all injury to health, shoe, and stocking, from standing in the river.'*
Reasoning on insufficient data—
     Falls like an inverted cone,
     Wanting its proper base to stand upon.
Samuel Bailey has furnished, in one passage, both a clear illustration of the process, and the validity of an induction:—'Whoever had witnessed the acts of a landlord to his tenants, of a schoolmaster to his pupils, of artizans towards their apprentices, of husbands towards their wives, on points where the power of the superior could not be contested, and where his personal gratification was incompatible with just conduct to the subordinate, would necessarily have formed in his own mind a species of general rule; and from this rule he might safely draw an inference as to what would be the conduct of a despot, seated on a throne, in the possession of unchecked authority; assisted too, as the inquirer would be, by that indispensable and inestimable guide to the knowledge of mankind, an appeal to his own feelings, in a variety of analogous instances.
'We conclude, that a ruler with uncontrolled power will act the tyrant, not merely from the fact that Caligula, or Nero, or Bonaparte did, but from a thousand facts attesting that men, in, every situation, use uncontrolled power in this way—just as we infer that all bodies tend to the centre of the earth, not merely from the circumstance of an apple dropping from a tree, but from seeing the tendency in stones, water, animals, and all things within our observation. The use of uncontrolled power, for the gratification of the possessor, without an equitable respect to others, is no more peculiar to monarchs, than a tendency to the earth is peculiar to apples. It may be useful to know that monarchs act in this way, as it may be useful to know that apples drop to the ground; but it is much more useful to know that men act in this manner. An inference is safer when gathered from the widest induction.'
     *  How to Observe, p. 6.
 
     ** Rationale of Political Representation. Introduction, pp.
     85-6. The last sentence of this extract is abridged—but, as
     the reader will find upon reference, the sense of the author
     is faithfully rendered.
It may be useful to observe that, though a few instances are insufficient to establish a theory, one may be sufficient to overturn a theory, fancifully or hypothetically supported, Gibbon overturns the entertaining theory of Rudbeck, an antiquarian of Upsal, of profound learning and easy faith, who, by the dim light of legends and traditions, of conjectures and etymologies, sought to establish the antiquity of Sweden over half the earth. Gibbon annihilated this well laboured system of German antiquities, by a single fact too well attested to admit of any doubt, and of too decisive a nature to leave room for any reply—the fact that the Germans, of the age of Tacitus, were unacquainted with the use of letters. A circumstance fatal to their literary claims, urged by Olaus Rudbeck.
In the chapter on 'Facts' I have cautioned the reader against unquestioned data. This seems the place to remark that the unsuspected sources of error and unfriendliness have their rise in the criminal implicitness with which we listen to reports, and infer from rumours as from facts. These are the very little handles which move men and women to strange performances.'* All the plots of dramas and romances are founded on misunderstandings, which a little sagacity of action (such as a wise resolution not to be imposed upon would lead to) would commonly suffice to arrest the error at its birth. With regard to character we constantly infer from data, partial, limited, and doubtful. If most quarrelers were called into a court of Inquiry to confess the real grounds from which they have arrived at certain conclusions with regard to their neighbours, and often with regard to their friends, they would be at once overwhelmed with a conviction of the weakness of which they have been guilty. Upon analysing the miserable sources of opinions of which scandal and calumny are born, I have found it impossible to restrain astonishment at the imbecility of logical power men will sometimes be content to exhibit, where meanness prevails, malice incites, and passion governs. Well might Bacon exclaim—'Doth any man doubt, that if there were taken out of men's minds, vain opinions, flattering hopes, false valuations, imaginations, and the like, but it would leave the minds of a number of men poor shrunken things?'** The wise rule is, never judge from appearances when facts can be had—never receive a report without challenging its foundation, nor adopt it without permission to give the authority.
     * Cricket on the Hearth.
 
     ** Essay on Truth.
In all cases, in which you must judge from appearances and reason from conjectures, adopt the fairest interpretation possible. On this principle, credit will sometimes be given where none is due—but in nine cases out of ten, justice will be done, for I am satisfied that there is more worth among men than ............