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 demonstra

tion, 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.

§7. 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 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 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 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 mens' 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 upon 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 a 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 knowledge where it is thought demonstration has nothing to do, men reason as it were in the lump; and if, upon a summary and confused view, or upon a partial consideration, they can raise the ap