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.