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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 general, 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; that 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 all known 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.

SECT. 11. What use these general maxims have.-What shall we then say? Are these general maxims of no use? By no means, though perhaps their use is not that which 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 self-evident 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 wranglers, 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 afterward, 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 self-evident, 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.

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 disputes into an endless train of syllogisms, certain general propositions, most of them indeed self-evident, were introduced into the schools;

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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 laid down any other between them) beyond which there was no going, and which must not be receded from by either side. And thus these maxims getting the name of principles, beyond which men in dispute could not retreat, were by mistake taken to be originals and sources, from whence all knowledge began, and the foundation whereon the sciences were built. Because when in their disputes they came to any of these, they stopped there, and went no farther; the matter was determined. But how much this is a mistake hath been already shown.

This method of the schools, which have been thought the fountains of knowledge, introduced, as I suppose, the like use of these maxims into a great part of conversation out of the schools, to stop the mouths of cavillers, whom any one is excused from arguing any longer with, when they deny these general self-evident principles received by all reasonable men, who have once thought of them but yet their use herein is but to put an end to wrangling. They, in truth, when urged in such cases, teach nothing: that is already done by the intermediate ideas made use of in the debate, whose connexion may be seen without the help of those maxims, and so the truth known before the maxim is produced, and the argument brought to a first principle. Men would give off a wrong argument before it came to that, if in their disputes they But the method of the proposed to themselves the finding and embracing of truth, and not a contest for victory. And thus maxims have their use to put a stop to their perverseness, whose ingenuity should have yielded sooner. schools having allowed and encouraged men to oppose and resist evident truth till they are baffled, i. e. till they are reduced to contradict themselves or some established principle; it is no wonder that they should not in civil conversation be ashamed of that, which in the schools is counted a virtue and a glory; obstinately to maintain that side of the question they have chosen, whether true or false, to the last extremity, even after conviction: a strange way to attain truth and knowledge, and that which I think the rational part of mankind, not corrupted by education, could scarce believe should ever be admitted How much such a way among the lovers of truth, and the students of religion or nature, or introduced into the seminaries of those who are to propagate the truths of religion or philosophy among the ignorant and unconvinced. of learning is like to return young men's minds from the sincere search and love of truth, nay, and to make them doubt whether there is any such thing, or at least worth the adhering to, I shall not now inquire. This I think, that bating those places which brought the peripatetic philosophy into their schools, where it continued many ages, without teaching the world any thing but the art of wrangling; these maxims were nowhere thought the foundations on which the sciences were built, nor the great helps to the advancement of knowledge.

As to these general maxims, therefore, they are, as I have said, of great use in disputes, to stop the mouths of wranglers: but not of much use to the discovery of unknown truths, or to help the mind forward in its search after knowledge. For who ever began to build his knowledge on this general proposition, what is, is; or, it is impossible for the same thing to be and not to be: and from either of these, as from a principle of science, deduced a system of useful knowledge? Wrong opinions often involving contradictions, one of these maxims, as a touchstone, may serve well to show whither they lead. But yet, however fit to lay open the absurdity or mistake of a man's reasoning or opinion, they are of very little use for enlightening the understanding: and it will not be found, that the mind receives much help from them in its proIt is true, as I have said, they gress in knowledge; which would be neither less, nor less certain, were these two general propositions never thought on. sometimes serve in argumentation to stop a wrangler's mouth, by showing the absurdity of what he saith, and by exposing him to the shame of contradicting what all the world knows, and he himself cannot but own to be true.

But it is one thing to show a man that he is in an error, and another to put him in possession of truth; and I would fain know what truths these two propositions are able to teach, and by their influence make us know, which we did not know before, or could not know without them. Let us reason from them as well as we can, they are only about identical predications; and influence, if any at all, none but such. Each particular proposition concerning identity or diversity is as clearly and certainly known in itself, if attended to, as either of these general ones: only these general ones, as serving in all cases, are therefore more inculcated and insisted on. As to other less general maxims, many of them are no more than bare verbal propositions, and teach us nothing but the respect and import of names one to another. "The whole is equal to all its parts;" what real truth, I beseech you, does it teach us? What more is contained in that maxim than what the signification of the word totum, or the whole, does of itself import? And he that knows that the word whole stands for what is made up of all its parts, knows very little less than that the whole is equal to all its parts. And upon the same ground, I think that this proposition, a hill is higher than a valley, and several the like, may also pass for maxims. But yet masters of mathematics, when they would, as teachers of what they know, initiate others in that science, do not without reason place this, and some other such maxims, at the entrance of their systems; that their scholars, having in the beginning perfectly acquainted their thoughts with these propositions made in such general terms, may be used to make such reflections, and have these more general propositions, as formed rules and sayings, ready to apply to all particular cases. Not that, if they be equally weighed, they are more clear and evident than the particular instances they are brought to confirm: but that, being more familiar to the mind, the very naming them is enough to satisfy the understanding. But this, I say, is more from our custom of using them, and the establishment they have got in our minds, by our often thinking of them, than from the different evidence of the things. But before custom has settled methods of thinking and reasoning in our minds, I am apt to imagine it is quite otherwise; and that the child, when a part of his apple is taken away, knows it better in that particular instance than by this general proposition, the whole is equal to all its parts; and that if one of these have need to be confirmed to him by the other, the general has more need to be let into his mind by the particular, than the particular by the general. For in particulars our knowledge begins, and so spreads itself by degrees to generals. Though afterward the mind takes the quite contrary course, and having drawn its knowledge into as general propositions as it can, makes those familiar to its thoughts, and accustoms itself to have recourse to them, as to the standards of truth and falsehood. By which familiar use of them, as rules to measure the truth of other propositions, it comes in time to be thought, that more particular propositions have their truth and evidence from their conformity to these more general ones, which in discourse and argumentation are so frequently urged, and constantly admitted. And this I think to be the reason why, among so many self-evident propositions, the most general only have had the title of maxims.

SECT. 12. Maxims, if care be not taken in the use of words, may prove contradictions.-One thing farther, I think, it may not be amiss to observe concerning these general maxims, that they are so far from improving or establishing our minds in true knowledge, that if our notions be wrong, loose, and unsteady, and we resign up our thoughts to the sounds of words, rather than fix them on settled determinate ideas of things; I say, these general maxims will serve to conform us in mistakes; and in such a way of use of words, which is most common, will serve to prove contradictions; v. g. he that, with Des Cartes, shall frame in his mind an idea of what he calls body to be nothing but extension, may easily demonstrate that there is no vacuum, i. e. no space void of body, by this maxim, what is, is. For the idea to which he annexes the name body being bure extension, his knowledge, that space cannot be without body, is certain. For he knows his own idea of extension

clearly and distinctly, and knows that it is what it is, and not another idea, though it be called by these three names, extension, body, space. Which three words, standing for one and the same idea, may no doubt, with the same evidence and certainty, be affirmed one of another, as each of itself: and it is as certain, that whilst I use them all to stand for one and the same idea, this predication is as true and identical in its signification, that space is body, as this predication is true and identical, that body is body, both in signification and sound.

SECT. 13. Instance in vacuum.-But if another should come, and make to himself another idea, different from Des Cartes's, of the thing, which yet, with Des Cartes, he calls by the same name body; and make his idea, which he expresses by the word body, to be of a thing that hath both extension and solidity together; he will as easily demonstrate that there may be a vacuum or space without a body, as Des Cartes demonstrated the contrary. Because the idea to which he gives the name space being barely the simple one of extension; and the idea to which he gives the name body being the complex idea of extension and resistibility, or solidity, together in the same subject; these two ideas are not exactly one and the same, but in the understanding as distinct as the ideas of one and two, white and black, or as of corporiety and humanity, if I may use those barbarous terms: and therefore the predication of them in our minds, or in words standing for them, is not identical, but the negation of them one of another, viz. this proposition, extension or space is not body, is as true and evidently certain, as this maxim, it is impossible for the same thing to be, and not to be, can make any proposition.

SECT. 14. They prove not the existence of things without us.—But yet, though both these propositions (as you see) may be equally demonstrated, viz. that there may be a vacuum, and that there cannot be a vacuum, by these two certain principles, viz. what is, is; and the same thing cannot be, and not be; yet neither of these principles will serve to prove to us, that any, or what bodies do exist; for what we are left to our senses, to discover to us as far as they can. Those universal and self-evident principles, being only our constant, clear, and distinct knowledge of our own ideas, more general or comprehensive, can assure us of nothing that passes without the mind; their certainty is founded only upon the knowledge we have of each idea by itself, and of its distinction from others; about which we cannot be mistaken whilst they are in our minds, though we may be, and often are mistaken when we retain the names without the ideas; or use them confusedly, sometimes for one, and sometimes for another idea. In which cases the force of these axioms reaching only to the sound, and not the signification of the words, serves only to lead us into confusion, mistake, and error. It is to show men that these maxims, however cried up for the great guards of truth, will not secure them from error in a careless loose use of their words, that I have made this remark. In all that is here suggested concerning their little use for the improvement of knowledge, or dangerous use in undetermined ideas, I have been far enough from saying or intending they should be laid aside, as some have been too forward to charge me. I affirm them to be truths, self-evident truths; and so cannot be laid aside. As far as their influence will reach, it is in vain to endeavour, nor will I attempt to abridge it. But yet, without any injury to truth or knowledge, I may have reason to think their use is not answerable to the great stress which seems to be laid on them; and I may warn men not to make an ill use of them, for the confirming themselves in errors.

SECT. 15. Their application dangerous about complex ideas.-But let them be of what use they will in verbal propositions they cannot discover or prove to us the least knowledge of the nature of substances, as they are found and exist without us, any farther than grounded on experience. And though the consequence of these two propositions, called principles, be very clear, and their use not dangerous or hurtful, in the probation of such things where. in there is no need at all of them for proof, but such as are clear by themselves without them, viz. where our ideas are determined, and known by the ЗА

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