and difficult), for it must be neither oblique, nor rectangle, neither equilateral, equicrural, nor scalenon ; but all and none of these at once. In effect, it is something imperfect, that cannot exist; an idea wherein some parts of several different and inconsistent ideas are put together. It is true, the mind, in this imperfect state, has need of such ideas, and makes all the haste to them it can, for the conveniency of communication and enlargement of knowledge; to both which it is naturally very much inclined. But yet one has reason to suspect such ideas are marks of our imperfection; at least this is enough to show, that the most abstract and general ideas are not those that the mind is first and most easily acquainted with, not such as its earliest knowledge is conversant about.

them the

depend.

Because on §. 10. Secondly, from what has been said it plainly follows, that these magnified maxother parts ims are not the principles and foundations of our know of all our other knowledge. For if there ledge do not be a great many other truths, which have as much self-evidence as they, and a great many that we know before them, it is impossible they should be the principles, from which we deduce all other truths. Is it impossible to know that one and two are equal to three, but by virtue of this, or some such axiom, viz. the whole is equal to all its parts taken to gether? Many a one knows that one and two are equal to three, without having heard, or thought on that, or any other axiom, by which it might be proved: and knows it as certainly, as any other man knows, that the whole is equal to all its parts, or any other maxim, and all from the same reason of self-evidence; the equality of those ideas being as visible and certain to him without that, or any other axiom, as with it, it needing no proof to make it perceived. Nor after the knowledge that the whole is equal to all its parts, does he know that one and two are equal to three, better or more certainly than he did before. For if there be any odds in those ideas, the whole and parts are more obscure, or at least more difficult to be settled in the mind, than those of one, two, and three. And indeed, I think, I may ask

these men, who will needs have all knowledge, besides those general principles themselves, to depend on ge neral, innate, and self-evident principles: what principle is requisite to prove, that one and one are two, that two and two are four, that three times two are six? Which being known without any proof, do evince that either all knowledge does not depend on certain præcognita or general maxims, called principles, or else that these are principles; and if these are to be counted principles, a great part of numeration will be so. To which if we add all the self-evident propositions, which may be made about all our distinct ideas, principles will be almost infinite, at least innumerable, which men arrive to the knowledge of, at different ages; and a great many of these innate principles they never come to know all their lives. But whether they come in view of the mind, earlier or later, this is true of them, that they are allknown by their native evidence, are wholly independent, receive no light, nor are capable of any proof one from another; much less the more particular, from the more general; or the more simple, from the more compounded: the more simple, and less abstract, being the most familiar, and the easier and earlier apprehended. But which ever be the clearest ideas, the evidence and certainty of all such propositions is in this, that a man sees the same idea to be the same idea, and infallibly perceives two different ideas to be different ideas. For when a man has in his understanding the ideas of one and of two, the idea of yellow, and the idea of blue, he cannot but certainly know, that the idea of one is the idea of one, and not the idea of two; and that the idea of yellow is the idea of yellow, and not the idea of blue. For a man cannot confound the ideas in his mind, which he has distinct: that would be to have them confused and distinct at the same time, which is a contradiction: and to have none distinct is to have no use of our faculties, to have no knowledge at all. And therefore what idea soever is affirmed of itself, or whatsoever two entire distinct ideas are denied one of another, the mind cannot but assent to such a proposition as infallibly true, as soon as it understands the terms, without hesitation or

need of proof, or regarding those made in more general terms, and called maxims,

What use §. 11. What shall we then say? Are these these gene- general maxims of no use? By no means; ral maxims though perhaps their use is not that, which have. it is commonly taken to be. But since

doubting in the least of what hath been by some men ascribed to these maxims may be apt to be cried out against, as overturning the foundations of all the sciences; it may be worth while to consider them, with respect to other parts of our knowledge, and examine more particularly to what purposes they serve, and to what not.

1. It is evident from what has been already said, that they are of no use to prove or confirm less general selfevident propositions.

2. It is as plain that they are not, nor have been the foundations whereon any science hath been built. There is, I know, a great deal of talk, propagated from scholastic men, of sciences and the maxims on which they are built but it has been my ill luck never to meet with any such sciences; much less any one built upon these two maxims, what is, is; and it is impossible for the same thing to be, and not to be. And I would be glad to be shown where any such science, erected upon these, or any other general axioms, is to be found: and should be obliged to any one who would lay before me the frame and system of any science so built on these or any such-like maxims, that could not be shown to stand as firm without any consideration of them. I ask, whether these general maxims have not the same use in the study of divinity, and in theological questions, that they have in other sciences? They serve here too to silence wran glers, and put an end to dispute. But I think that nobody will therefore say, that the christian religion is built upon these maxims, or that the knowledge we have of it is derived from these principles. It is from revelation we have received it, and without revelation these maxims had never been able to help us to it. When we find out an idea, by whose intervention we discover the connexion of two others, this is a revelation from

God to us, by the voice of reason. For we then come to know a truth that we did not know before. When God declares any truth to us, this is a revelation to us by the voice of his spirit, and we are advanced in our knowledge. But in neither of these do we receive our light or knowledge from maxims. But in the one the things themselves afford it, and we see the truth in them by perceiving their agreement or disagreement. In the other, God himself affords it immediately to us, and we see the truth of what he says in his unerring veracity.

3. They are not of use to help men forward in the advancement of sciences, or new discoveries of yet unknown truths. Mr. Newton, in his never enough to be admired book, has demonstrated several propositions, which are so many new truths, before unknown to the world, and are farther advances in mathematical knowledge but, for the discovery of these, it was not the general maxims, what is, is; or, the whole is bigger than a part; or the like; that helped him. These were not the clues that led him into the discovery of the truth. and certainty of those propositions. Nor was it by them that he got the knowledge of those demonstrations; but by finding out' intermediate ideas, that showed the agreement or disagreement of the ideas, as expressed in the propositions he demonstrated. This is the greatest exercise and improvement of human understanding in the enlarging of knowledge, and advancing the sciences; wherein they are far enough from receiving any help from the contemplation of these, or the like magnified maxims. Would those who have this traditional admiration of these propositions, that they think no step' can' be made in knowledge without the support of an axiom, no stone laid in the building of the sciences without a general maxim, but distinguish between the method of acquiring knowledge, and of communicating; between the method of raising any science and that of teaching it to others as far as it is advanced; they would see that those general maxims were not the foundations on which the first discoverers raised their admirable structures, nor the keys that unlocked and opened those secrets of knowledge. Though afterwards, when schools were

erected, and sciences had their professors to teach what others had found out, they often made use of maxims, i. e. laid down certain propositions which were selfevident, or to be received for true; which being settled in the minds of their scholars, as unquestionable verities, they on occasion made use of, to convince them of truths in particular instances that were not so familiar to their minds as those general axioms which had before been inculcated to them, and carefully settled in their minds. Though these particular instances, when well reflected on, are no less self-evident to the understanding than the general maxims brought to confirm them and it was in those particular instances that the first discoverer found the truth, without the help of the general maxims and so may any one else do, who with attention considers them.

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To come therefore to the use that is made of maxims, 1. They are of use, as has been observed, in the ordinary methods of teaching sciences as far as they are advanced; but of little or none in advancing them farther.

2. They are of use in disputes, for the silencing of obstinate wranglers, and bringing those contests to some conclusion. Whether a need of them to that end came not in, in the manner following, I crave leave to inquire. The schools having made disputation the touchstone of men's abilities, and the criterion of knowledge, adjudged victory to him that kept the field: and he that had the last word, was concluded to have the better of the argument, if not of the cause. But because by this means there was like to be no decision between skilful combatants, whilst one never failed of a medius terminus to prove any proposition; and the other could as constantly without, or with a distinction, deny the major or minor; to prevent, as much as could be, running out of dis putes into an endless train of syllogisms, certain general Portain propositions, most of them indeed self-evident, were introduced into the schools; which being such as all men allowed and agreed in, were looked on as general measures of truth, and served instead of principles (where the disputants had not lain down any other between them) beyond which there was no going, and which

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