turally, 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 connexion 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 make us so, and we are, indeed, so no farther than industry and application have carried us. And, therefore, in ways of reasoning, which men have not been used to, he that will observe the conclusions. they take up, must be satisfied they are not all rational.

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 to 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 can

not say he is rational, how capable soever he may be, by time and exercise, to become so.

Try in men of low and mean education, who have never elevated their thoughts above the spade and the plough, nor looked beyond the ordinary drudgery of a day-labourer. 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; 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 farther inquiry, and think there is no such thing as certainty. 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 are 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. 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.

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.

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 connexion of two ideas, that, to one whose understanding is more exercised, is as visible as any thing can be. The same would be with a grown man beginning to study mathematics; the understanding, for want of use, often sticks in every plain way, and he himself that is so puzzled, when he comes to see the connexion, wonders what it was he stuck at, in a case so plain.

Mathematics.

§ 7. 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 connexion 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.

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 ba lance 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 schools, leads them quite away from it, by insisting on one topical argument, 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 account, and must come into the reckoning, before a man can form a right judgment. This would enlarge their minds, and give a due freedom to their understandings, that they might not be led into error by presumption, laziness, or precipitancy; for I think nobody can approve such a conduct of the understanding as should mislead it from truth, though it be ever so much in fashion to make use of it.

To this perhaps it will be objected, that to manage the understanding as I propose would require every man to be a scholar, and to be furnished with all the

materials of knowledge, and exercised in all the ways` of reasoning. To which I answer, that it is a shame for those that have time, and the means to attain knowledge, to want any helps or assistance, for the improvement of their understandings, that are to be got; and to such I would be thought here chiefly to speak. Those methinks who, by the industry and parts of their ancestors, have been set free from a constant drudgery to their backs and their bellies, should bestow some of their spare time on their heads, and open their minds, by some trials and essays, in all the sorts and matters of reasoning. I have before mentioned mathematics, wherein algebra gives new helps and views to the understanding. If I propose these, it is not, as I said, to make every man at thorough mathematician, or a deep algebraist; but yet I think the study of them is of infinite use, even to grown men; first, by experimentally convincing them, that to make any one reason well, it is not enough to have parts wherewith he is satisfied, and that serve him well enough in his ordinary course. A man in those studies will see, that however good he may think his understanding, yet in many things, and those very visible, it may fail him. This would take off that presumption that most men have of themselves in this part; and they would not be so apt to think their minds wanted no helps to enlarge them, that there could be nothing added to the acuteness and penetration of their understandings.

Secondly, the study of mathematics would show them the necessity there is in reasoning, to separate all the distinct ideas, and see the habitudes that all those concerned in the present inquiry have to one another, and to lay by those which relate not to the proposition in hand, and wholly to leave them out of the reckoning. This is that which, in other subjects, besides quantity, is what is absolutely requisite to just reasoning, though in them it is not so easily observed, nor so carefully practised. In those parts of know