Nay, the most of men are so wholly strangers to this, that they do not so much as perceive their want of it. They despatch the ordinary business of their callings by rote, as we say, as they have learnt it, and, if at any time they miss success, they impute it to anything rather than want of thought or skill; that they conclude (because they know no better) they have in perfection. Or if there be any subject that interest or fancy has recommended to their thoughts, their reasoning about it is still after their own fashion; be it better or worse, it serves their turns, and is the best they are acquainted with: and therefore when they are led by it into mistakes, and their business succeeds accordingly, they impute it to any cross accident, or default of others, rather than to their own want of understanding; that is what nobody discovers or complains of in himself. Whatsoever made his business to miscarry, it was not want of right thought and judgment in himself: he sees no such defect in himself, but is satisfied that he carries on his designs well enough by his own reasoning, or at least should have done, had it not been for unlucky traverses not in his power. Thus being content with this short and very imperfect use of his understanding, he never troubles himself to seek out methods of improving his mind, and lives all his life without any notion of close reasoning in a continued connection of a long train of consequences from sure foundations, such as is requisite for the making out and clearing most of the speculative truths most men own to believe and are most concerned in. Not to mention here what I shall have occasion to insist on by and by [Section VII.] more fully, namely, that in many cases it is not one series of consequences will serve the turn, but many different and opposite deductions must be examined and laid together, before a man can come to make a right judgment of the point in question. What then can be expected from men that neither see the want of any such kind of reasoning as this, nor, if they do, know they how to set about it, or could perform it? You may as well set a countryman who scarce knows the figures, and never cast up a sum of three particulars, to state a merchant's long account, and find the true balance of it.

What then should be done in the case? I answer, we should always remember what I said above, that the faculties of our souls are improved and made useful to us just after the same manner as our bodies are. Would you have a man write or paint, dance or fence well, or perform any other manual operation dexterously and with ease, let him have ever so much vigor and activity, suppleness

and address naturally, yet nobody expects this from him unless he has been used to it, and has employed time and pains in fashioning and forming his hand or outward parts to these motions. Just so it is in the mind; would you have a man reason well, you must use him to it betimes, exercise his mind in observing the connection of ideas and following them in train. Nothing does this better than mathematics, which therefore I think should be taught all those who have the time and opportunity, not so much to make them mathematicians as to make them reasonable creatures; for though we all call ourselves so, because we are born to it if we please, yet we may truly say, nature gives us but the seeds of it; we are born to be, if we please, rational creatures, but it is use and exercise only that makes us so, and we are indeed so no farther than industry and application has carried us.

This has been the less taken notice of, because every one, in his private affairs, uses some sort of reasoning or other, enough to denominate him reasonable. But the mistake is, that he that is found reasonable in one thing is concluded to be so in all, and to think or say otherwise is thought so unjust an affront, and so senseless a censure, that nobody ventures to do it. It looks like the degradation of a man below the dignity of his nature. It is true that he that reasons well in any one thing has a mind naturally capable of reasoning well in others, and to the same degree of strength and clearness, and possibly much greater, had his understanding been so employed. But it is as true that he who can reason well to-day about one sort of matters cannot at all reason to-day about others, though perhaps a year hence he may. But wherever a man's rational faculty fails him, and will not serve him to reason, there we cannot say he is rational, how capable soever he may be by time and exercise to become so.

2

Try in men of low and mean education, who have never elevated their thoughts above the spade and the plough, nor looked beyond

1 To cultivate habits of precise reasoning, and to train the mind to deal with abstract ideas and principles, no discipline can be better adapted than that of mathematics. But a mind trained exclusively on mathematics would be very ill equipped to deal with the various and complicated problems of life and science. An early training in mathematical reasoning should always be supplemented, as education proceeds, by forming a habit of analyzing and estimating the value of evidence in subjects which admit, not only of certain, but of more or less probable conclusions, such as language, law, the moral and physical sciences, history, and the affairs of ordinary life.

'Natural incapacity'

This remark is not only true, but eminently useful and instructive. for particular branches of study, say mathematics or language, rarely exists, except in imagination; unless indeed the subject of it is deficient in mental power generally.

the ordinary drudgery of a day-laborer. Take the thoughts of such an one, used for many years to one track, out of that narrow compass he has been all his life confined to, you will find him no more capable of reasoning than almost a perfect natural. Some one or two rules, on which their conclusions immediately depend, you will find in most men have governed all their thoughts;1 these, true or false, have been the maxims they have been guided by: take these from them, and they are perfectly at a loss, their compass and pole star then are gone, and their understanding is perfectly at a nonplus, and therefore they either immediately return to their old maxims again as the foundations of all truth to them, notwithstanding all that can be said to show their weakness, or, if they give them up to their reasons, they with them give up all truth and further inquiry, and think there is no such thing as certainty.2 For if you would enlarge their thoughts, and settle them upon more remote and surer principles, they either cannot easily apprehend them, or, if they can, know not what use to make of them; for long deductions from remote principles is what they have not been used to, and cannot manage.

What then, can grown men never be improved or enlarged in their understandings? I say not so, but this I think I may say, that it will not be done without industry and application, which will require more time and pains than grown men, settled in their course of life, will allow to it, and therefore very seldom is done.3 And this very capacity of attaining it by use and exercise only brings us back to that which I laid down before, that it is only practice that improves our minds as well as bodies, and we must expect nothing from our understandings any farther than they are perfected by habits.

1 Men should be peculiarly on their guard against constantly repeating, to themselves or others, compact and neatly worded maxims. Principles of this kind come after a time to exercise a tyranny over the mind, recur on every occasion, and, being taken without any qualification, often have a wonderful effect in perverting the judgment. The tendency to be constantly enunciating and acting on maxims of this kind is often particularly observable in old men, or persons whose experience has been mainly confined to some one sphere of activity, such as seafaring men or lawyers.

2 Bacon, in his Essay on Atheism: A little philosophy inclineth man's mind to Atheism; but depth in philosophy bringeth men's minds about to religion; for while the mind of man looketh upon second causes scattered, it may rest in them, and go no further; but when it beholdeth the chain of them confederate and linked together, it must needs fly to Providence and Deity.'

3 Bishop Butler, in his Analogy of Religion, Part I. ch. v., remarks: The former part of life. . . . is a state of education, in which we are much assisted by the example, instruction, and care of others, and in which a great deal is left for ourselves to do. This opportunity, when lost, is not to be recovered.'

The Americans are not all born with worse understandings than the Europeans, though we see none of them have such reaches in the arts and sciences. And among the children of a poor countryman, the lucky chance of education and getting into the world gives one infinitely the superiority in parts over the rest, who, continuing at home, had continued also just of the same size with his brethren.

1

He that has to do with young scholars, especially in mathematics, may perceive how their minds open by degrees, and how it is exercise alone that opens them. Sometimes they will stick a long time at a part of a demonstration, not for want of will and application, but really for want of perceiving the connection of two ideas, that, to one whose understanding is more exercised, is as visible as anything can be. The same would be with a grown man beginning to study mathematics; the understanding, for want of use, often sticks in very plain way, and he himself that is so puzzled, when he comes to see the connection, wonders what it was he stuck at in a case so plain.

VII. MATHEMATICS.

I have mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that having got the way of reasoning, which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge as they shall have occasion. For, in all sorts of reasoning, every single argument should be managed as a mathematical demonstration, the connection and dependence of ideas should be followed till the mind is brought to the source on which it bottoms and observes the coherence all along, though, in proofs of probability, one such train is not enough to settle the judgment as in demonstrative knowledge.2

1 Locke speaks from experience. Not only had he given much advice with respect to the education of children and young men, but he had spent a great part of his time in the practical work of instruction. In early life he acted as Tutor and Censor of Christ Church. Afterwards, he was instructor to the second, and supervised the studies of the third, Earl of Shaftesbury. Moreover, while in France during the years 1677 and 1678, he travelled with a pupil, the son of a rich merchant named Sir John Banks. It is curious, when we remember Locke's attacks on the logic of the Schools, to learn the nature of his objections to entering young Banks in the study of mathematics. 'To engage one in mathematics who is not yet acquainted with the very rudiments of logic is a method of study I have not known practised, and seems to me not very reasonable.'

2 What Locke means by demonstrative knowledge is, that the mode of proof, that is, the analysis of the reasoning, is the same in all cases, though in some cases the conclusions may

Where a truth is made out by one demonstration, there needs no farther inquiry, but in probabilities where there wants demonstration to establish the truth beyond doubt, there it is not enough to trace one argument to its source, and observe its strength and weakness, but all the arguments, after having been so examined on both sides, must be laid in balance one against another, and upon the whole the understanding determine its assent.

This is a way of reasoning the understanding should be accustomed to, which, is so different from what the illiterate are used to, that even learned men oftentimes seem to have very little or no notion of it. Nor is it to be wondered, since the way of disputing in the schools1 leads them quite away from it, by insisting on one topical argument,2 by the success of which the truth or falsehood of the question is to be determined, and victory adjudged to the opponent or defendant; which is all one as if one should balance an account by one sum charged and discharged, when there are an hundred others to be taken into consideration.

This therefore it would be well if men's minds were accustomed to, and that early, that they might not erect their opinions upon one single view, when so many other are requisite to make up the

be demonstrative, in others only probable. The only differences which he recognizes between demonstrative and probable reasoning are, that, in the one, a single proof is sufficient to establish the conclusion, which may then be taken for certain, whereas, in the other, several arguments of varying degrees of probability, some tending one way and some another, have to be taken into account, the conclusion expressing the preponderance of the evidence. For his remarks on Probability, see Essay, Bk. IV. chs. 15, 16, and ch. 17, § 5.

It is by no means correct to say that in all sorts of reasoning every single argument should be managed as a mathematical demonstration.' It is indeed true that, in all cases, a belief should be traced to the source on which it bottoms,' or that the propositions on which our assent is based should be so put together that we may see their connection with the conclusion. But this connection may be exhibited in various ways. Thus, the best and most natural mode of representing an inductive argument (see the first chapter of my Elements of Inductive Logic) is entirely different from that of representing a deductive argument, though, by a certain amount of manipulation, the one form may be brought under the other. Again, even in deductive ratiocination, there are rules, quite distinct from those of the ordinary syllogism, for estimating the precise value to be attached to probable arguments, whether in single syllogisms or in combinations of syllogisms, or on a balance of rival probabilities. The student will find a statement and discussion of such rules in almost any recent work on Logic. Mr. Venn's Logic of Chance is specially appropriated to the discussion of these and kindred subjects.

1 What Locke thought of the 'disputations,' which were then in common use throughout the universities of Europe, may be gathered from Thoughts concerning Education,' § 189.

2 Cp. Essay, Bk. IV. ch. 17, § 5. The expression topical argument' applies to an argument derived from certain general heads of probability, which, in the language of Aristotle and his followers, were called Tónоt, commonplaces, or common forms. They were the main subject of the art entitled Tomiký or diadektiký, and of the eight (or, including the Sophistici Elenchi, the nine) books called the Topics. This work deals with logic when applied to disputation on disputable (probable) matter, as opposed to the logic of demonstration in science, which is treated in the Posterior Analytics.