or in any of those which we previously all "wrapt up" in a few definitions constructed, is it not evident that the and axioms. Nor does this defence conclusion may, to the person to whom of the syllogism differ much from the syllogism is presented, be actually what its assailants urge against it as and bona fide a new truth? Is it not an accusation, when they charge it matter of daily experience that truths with being of no use except to those previously unthought of, facts which who seek to press the consequences of have not been, and cannot be, directly an admission into which a person has observed, are arrived at by way of been entrapped without having congeneral reasoning? We believe that sidered and understood its full force. the Duke of Wellington is mortal. When you admitted the major preWe do not know this by direct observa- mise, you asserted the conclusion; tion, so long as he is not yet dead. but, says Archbishop Whately, you If we were asked how, this being the asserted it by implication merely : case, we know the Duke to be mortal, this, however, can here only mean we should probably answer, Because that you asserted it unconsciously; all men are so. Here, therefore, we that you did not know you were arrive at the knowledge of a truth not asserting it; but, if so, the difficulty (as yet) susceptible of observation, by revives in this shape-Ought you not a reasoning which admits of being to have known? Were you warranted exhibited in the following syllogism: in asserting the general proposition without having satisfied yourself of the truth of everything which it fairly includes ? And if not, is not the syllogistic art prima facie what its assailants affirm it to be, a contrivance for catching you in a trap, and holding you fast in it? * All men are mortal, The Duke of Wellington is a man, therefore The Duke of Wellington is mortal. And since a large portion of our knowledge is thus acquired, logicians have persisted in representing the syllogism as a process of inference or proof, though none of them has cleared up the difficulty which arises from the inconsistency between that assertion and the principle that if there be anything in the conclusion which was not already asserted in the premises, the argument is vicious. For it is impossible to attach any serious scientific value to such a mere salvo as the distinction drawn between being involved by implication in the premises, and being directly asserted in them. When Archbishop Whately says that the object of reasoning is "merely to expand and unfold the assertions wrapt up, as it were, and implied in those with which we set out, and to bring a person to perceive and acknowledge the full force of that which he has admitted," he does not, I think, meet the real difficulty requiring to be explained, namely, how it happens that a science, like geometry, can be Logic, p. 239 (9th ed.) § 3. From this difficulty there appears to be but one issue. The proposition that the Duke of Wellington is mortal, is evidently an inference; It is hardly necessary to say, that I am not contending for any such absurdity as that we actually "ought to have known" and considered the case of every individual man, past, present, and future, before affirming that all men are mortal: although this interpretation has been, strangely enough, put upon the preceding observations. There is no difference between me and Archbishop Whately, or any other part of the matter; I am only pointing out defender of the syllogism, on the practical an inconsistency in the logical theory of it, as conceived by almost all writers. I before the Duke of Wellington was born, do not say that a person who affirmed, that all men are mortal, knew that the Duke of Wellington was mortal; but I do say that he asserted it and I ask for an of adducing in proof of the Duke of Welexplanation of the apparent logical fallacy lington's mortality a general statement which presupposes it. Finding no sufficient resolution of this difficulty in any of the writers on Logic, I have attempted to supply one. it is got at as a conclusion from some-together with all that we infer from thing else; but do we, in reality, con- our observations, in one concise exclude it from the proposition, All men are mortal? I answer, No. pression; and have thus only one proposition, instead of an endless number, to remember or to communicate. The results of many observations and inferences, and instructions for making innumerable inferences in unforeseen cases, are compressed into one short sentence. The error committed is, I conceive, that of overlooking the distinction between two parts of the process of philosophising, the inferring part, and the registering part, and ascribing to the latter the functions of the former. The mistake is that of referring a person to his own notes for the origin of his knowledge. If a person is asked a question, and is at the moment unable to answer it, he may refresh his memory by turning to a memorandum which he carries about with him. But if he were asked, how the fact came generalisation, All men are mortal, as to his knowledge, he would scarcely answer, because it was set down in his notebook unless the book was written, like the Koran, with a quill from the wing of the angel Gabriel. When, therefore, we conclude from the death of John and Thomas, and every other person we ever heard of in whose case the experiment had been fairly tried, that the Duke of Wellington is mortal like the rest, we may, indeed, pass through the an intermediate stage; but it is not in the latter half of the process, the descent from all men to the Duke of Wellington, that the inference resides. The inference is finished when we have asserted that all men are What remains to be performed afterwards is merely deciphering our own notes. Assuming that the proposition, The Duke of Wellington is mortal, is immortal. mediately an inference from the proposition, All men are mortal; whence do we derive our knowledge of that general truth? Of course from observation. Now, all which man can observe are individual cases. From these all general truths must be drawn, and into these they may be again resolved; for a general truth is but an aggregate of particular truths; a comprehensive expression, by which an indefinite number of individual facts are affirmed or denied at once. But a general proposition is not merely a compendious form for recording and preserving in the memory a number of particular facts, all of which have been observed. Generalisation is not a process of mere naming, it is also a process of inference. From instances which we have observed, we feel warranted in concluding, that what we found true in those instances, holds in all similar ones. past, present, and future, however numerous they may be. We then, by that valuable contrivance of language which enables us to speak of many as if they were one, record all that we have observed, Archbishop Whately has contended that syllogising, or reasoning from generals to particulars, is not, agreeably to the vulgar idea, a peculiar mode of reasoning, but the philosophical analysis of the mode in which all men reason, and must do so if they reason at all. With the deference due to so high an authority, I cannot help thinking that the vulgar notion is, in this case, the more correct. If, from our experience of John, Thomas, &c., who once were living, but are now dead, we are entitled to conclude that all human beings are mortal, we might surely without any logical inconsequence have concluded at once from those instances that the Duke of Wellington is mortal. The mortality of John, Thomas, and others is, after all, the whole evidence we have for the mortality of the Duke of Wellington. Not one iota is added to the proof by interpolating a general proposition. Since the individual cases are all the evidence we can possess, evidence which no logical I believe that, in point of fact, when drawing inferences from our personal experience, and not from maxims form into which we choose to throw | always with the same skill, as a human it can make greater than it is; and creature. Not only the burnt child, since that evidence is either sufficient but the burnt dog, dreads the fire. in itself, or, if insufficient for the one purpose, cannot be sufficient for the other; I am unable to see why we should be forbidden to take the short-handed down to us by books or traest cut from these sufficient premises to the conclusion, and constrained to travel the "high priori road," by the arbitrary fiat of logicians. I cannot perceive why it should be impossible to journey from one place to another unless we 66 march up a hill, and then march down again.' It may be the safest road, and there may be a resting-place at the top of the hill, affording a commanding view of the surrounding country; but for the mere purpose of arriving at our journey's end, our taking that road is perfectly optional; it is a question of time, trouble, and danger. dition, 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 human beings in general, or persons of some particular character, are accustomed to feel Not only may we reason from par- and act; but much oftener from ticulars to particulars without passing merely recollecting the feelings and through generals, but we perpetually conduct of the same person in some do so reason. All our earliest infer- previous instance, or from considering ences are of this nature. From the how we should feel or act ourselves. first dawn of intelligence we draw in- It is not only the village matron, who, ferences, but years elapse before we when called to a consultation upon learn the use of general language. the case of a neighbour's child, proThe child who, having burnt his nounces on the evil and its remedy fingers, avoids to thrust them again simply on the recollection and authointo the fire, has reasoned or inferred, rity of what she accounts the similar though he has never thought of the case of her Lucy. We all, where we general maxim, Fire burns. He have no definite maxims to steer by, knows from memory that he has been guide ourselves in the same way; and burnt, and on this evidence believes, if we have an extensive experience, when he sees a candle, that if he puts and retain its impressions strongly, his finger into the flame of it, he will we may acquire in this manner a very be burnt again. He believes this in considerable power of accurate judgevery case which happens to arise; ment, which we may be utterly incapbut without looking, in each instance, able of justifying or of communicating beyond the present case. He is not to others. Among the higher order generalising; he is inferring a par- of practical intellects there have been ticular from particulars. In the same many of whom it was remarked how way, also, brutes reason. There is admirably they suited their means to no ground for attributing to any of their ends, without being able to give the lower animals the use of signs of any sufficient reasons for what they such a nature as to render general did; and applied, or seemed to apply, propositions possible. But those ani- recondite principles which they were mals profit by experience, and avoid wholly unable to state. This is a what they have found to cause them natural consequence of having a mind pain, in the same manner, though not 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, in 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. The same thing may generally be said of any other 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 the 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 equi valent 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 case, infer the means to be employed, and the effects 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 educa. tion. 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 men of talent performing wonderful things they know not how, are ex amples of the rudest 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, though a help, the most important indeed of all helps, is not an essential. Even the scientifically instructed, who possess, in the form of general propositions, a systematic record of the results of the experience of mankind, need not always revert to those general propositions in order to apply that experience to a new case. It is justly remarked by Dugald Stewart, that though the reasonings in mathematics depend entirely on the axioms, it is by no means necessary to our seeing the conclusiveness of the proof that the axioms should be expressly adverted to. When it is inferred that A B is equal to CD because each of them is equal to E F, the most uncultivated understanding, as soon as the propositions were understood, would assent to the inference, without having ever heard of the general truth that" things which are equal to the same thing are equal to one another." This remark of Stewart, consistently followed out, goes to the root, as I conceive, of the philosophy of ratiocination; and it is to be regretted that he himself stopt short at a much more limited application of it. He saw that the general propositions on which a reasoning is said to depend may, in certain cases, be altogether omitted, without impairing its probative force. But he imagined this to be a peculiarity belonging to axioms; and argued from it, that axioms are not the foundations or first principles of geometry from which all the other truths of the science are synthetically deduced, (as the laws of motion and of the composition of forces in dynamics, the equal mobility of fluids in hydrostatics, the laws of reflection and refraction in optics, are the first principles of those sciences,) but are merely necessary assumptions, self evident indeed, and the denial of which would annihilate all demonstration, but from which, as premises, nothing can be demonstrated. In the present, as in many other instances, this thoughtful and elegant writer has perceived an important truth, but only by halves. Finding, in the case of geometrical axioms, that general names have not any talismanic virtue for conjuring new truths out of the well where they lie hid, and not seeing that this is equally true in every other case of generalisation, he contended that axioms are in their nature barren of consequences, and that the really fruitful truths, the real first principles of geometry, are the definitions; that the definition, for example, of the circle is to the properties of the circle what the laws of equilibrium and of the pressure of the atmosphere are to the rise of the mercury in the Torricellian tube. Yet all that he had asserted respecting the function to which the axioms are confined in the demonstrations of geometry holds equally true of the definitions. Every demonstration in Euclid might be carried on without them. This is apparent from the ordinary process of proving a proposition of geometry by means of a diagram. What assumption, in fact, do we set out from to demonstrate by a diagram any of the properties of the circle? Not that in all circles the radii are equal, but only that they are so in the circle ABC. As our warrant for assuming this, we appeal, it is true, to the definition of a circle in general; but it is only necessary that the assumption be granted in the case of the particular circle supposed. From this, which is not a general but a singular proposition, combined with other propositions of a similar kind, some of which when generalised are called definitions, and others axioms, we prove that a certain conclusion is true, not of all circles, but of the particular circle ABC; or at least would be so, if the facts precisely accorded with our assumptions. The enunciation, as it is called, that is, the |