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we can from particular experiments; fince we cannot, from a discovery of their real effences, grasp at a time whole fheaves, and in bundles comprehend the nature and properties of whole fpecies together. Where our inquiry is concerning co-existence, or repugnancy to co-exift, which by contemplation of our ideas we cannot difcover, there experience, obfervation and natural history must give us by our fenfes, and by retail, an infight into corporeal fubftances. The knowledge of bodies we must get by our fenfes, warily employed in taking notice of their qualities and operations on one another; and what we hope to know of separate spirits in this world, we must, I think, expect only from revelation. He that fhall confider bow little general maxims, precarious principles, and bypothefes laid down at pleasure, have promoted true knowledge, or helped to fatisfy the inquiries of rational men after real improvements; how little, I fay, the fetting out at that end has, for many ages together, advanced mens progress towards the knowledge of natural philosophy, will think we have reafon to thank thofe, who in this latter age have taken another course, and have trod out to us, though not an easier way to learned ignorance, yet a furer way to profitable knowledge.

§ 13. The true ufe of Hypotheses.

Nor that we may not, to explain any phenomena of nature, make use of any probable bypothefis whatfoever: Hypothefes, if they are well made, are at least great helps to the memory, and often direct us to new discoveries; but my meaning is, that we should not take up any one too baftily (which the mind, that would always penetrate into the caufes of things, and have principles to reft on, is very apt to do), till we have very well examined particulars, and made feveral experiments in that thing which we would explain by our hypothefis, and fee whether it will agree to them all; whether our principles will carry us quite through, and not be as inconfiftent with one phenomenon of nature, as they seem to accommodate and explain ano

ther; and at least that we take care that the name of principles deceive us not, nor impofe on us, by making us receive that for an unquestionable truth, which is really at beft but a very doubtful conjecture, fuch as are most (I had almost said all) of the bypothefes in natural philofophy.

$14. Clear and diftinct Ideas with fettled Names, and the finding of those which show their Agreement or Difagreement, are the ways to enlarge our Knowl.dge.

BUT whether natural philofophy be capable of certainty or no, the ways to enlarge our knowledge, as far as we are capable, feem to me in fhort to be these two :

First, The first is to get and fettle in our minds determined ideas of thofe things whereof we have general or specific names, at least of fo many of them as we would confider and improve our knowledge in, or reafon about; and if they be fpecific ideas of fubftances, we should endeavour alfo to make them as complete as we can, whereby I mean that we should put together as many fimple ideas, as being conftantly obferved to co-exist, may perfectly determine the fpecies; and each of thofe fimple ideas, which are the ingredients of our complex ones, fhould be clear and diftinét in our minds; for it being evident that our knowledge cannot exceed our ideas, as far as they are either imperfect, confufed, or obfcure, we cannot expect to have certain, perfect or clear knowledge.

Secondly, The other is the art of finding out those intermediate ideas, which may show us the agreement or repugnancy of other ideas which cannot be immediately compared.

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15. Mathematics, an Inftance of it. THAT thefe two (and not the relying on maxims, and drawing confequences from fome general propofitions) are the right method of improving our knowledge in the ideas of other modes befides those of quantity, the confideration of mathematical knowledge will eafily inform us; where first we shall find, that he that has not a perfect and clear idea of

thofe angles or figures of which he defires to know any thing, is utterly thereby incapable of any knowledge about them. Suppofe but a man not to have a perfect exact idea of a right angle, a scalenum, or trapezium, and there is nothing more certain than that he will in vain feek any demonftration about them. Farther, it is evident that it was not the influence of those maxims, which are taken for principles in mathematics, that hath led the masters of that fcience into thofe wonderful difcoveries they have made. Let a man of good parts know all the maxims generally made use of in mathematics never so perfectly, and contemplate their extent and confequences as much as he pleafes, he will by their affiftance, I fuppofe, fcarce ever come to know that the fquare of the hypotenuse in a right angled triangle, is equal to the fquares of the two other fides; the knowledge that the whole is equal to all its parts, and if you take equals from equals, the remainder will be equals, &c. helped him not, I prefume, to this demonftration; and a man may, I think, pore long enough on thofe axioms, without ever feeing one jot the more of mathematical truths: They have been discovered by the thoughts otherwife applied; the mind had other objects, other views before it, far different from those maxims, when it first got the knowledge of fuch kind of truths in mathematics, which men well enough acquainted with thofe received axioms, but ignorant of their method, who first made thefe demonftrations, can never fufficiently admire; and who knows what methods, to enlarge our knowledge in other parts of fcience, may hereafter be invented, anfwering that of algebra in mathematics, which fo readily finds out ideas of quantities to measure others by, whofe equality or proportion we could otherwife very hardly, or perhaps never come to know?

CHAP. XIII.

SOME FARTHER CONSIDERATIONS CONCERNING OUR KNOWLEDGE.

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§ 1. Our Knowledge partly necessary, partly voluntary. OUR UR knowledge, as in other things, fo in this, has a great conformity with our fight, that it is neither wholly neceffary, nor wholly voluntary. If our knowledge were altogether neceffary, all mens knowledge would not only be alike, but every man would know all that is knowable and if it were wholly voluntary, fome men fo little regard or value it, that they would have extreme little, or none at all. Men that have fenfes cannot choose but receive fome ideas by them; and if they have memory, they cannot but retain some of them; and if they have any distinguishing faculty, cannot but perceive the agreement or difagreement of fome of them one with another; as he that has eyes, if he will open them by day, cannot but fee fome objects, and perceive a difference in them. But though a man, with his eyes open in the light, cannot but fee, yet there be certain objects, which he may choose whether he will turn his eyes to; there may be in his reach a book containing pictures and difcourfes, capable to delight or instruct him, which yet he may never have the will to open, never take the pains to look into.

§ 2. The Application voluntary; but we know as things are, not as we pleafe.

THERE is also another thing in a man's power, and that is, though he turns his eyes fometimes towards an object, yet he may choose whether he will curiously survey it, and with an intent application, endeavour to obferve accurately all that is visible in it. But yet what he does fee, he cannot fee otherwife than he does. It depends not on his will to fee that black which appears yellow; nor to perfuade himself, that what actually fcalds him, feels cold.. The earth will not appear painted with flowers, nor the fields covered with verdure, whenever he has a mind to it in the cold winter, he cannot help feeing it white

146 Confiderations concerning our Knowledge. Book IV. and hoary, if he will look abroad. Juft thus is it with our understanding; all that is voluntary in our knowledge, is the employing or with-holding any of our faculties from this or that fort of objects, and a more or less accurate survey of them: but they being employed, cur will hath no power to determine the knowledge of the mind one way or others that is done only by the objects themfelves, as far as they are clearly difcovered. And therefore, as far as mens fenfes are conversant about external objects, the mind cannot but receive thofe ideas which are prefented by them, and be informed of the existence of things without: and fo far as mens thoughts converfe with their own determined ideas, they cannot but in fome measure obferve the agreement and difagreement that is to be found amongft fome of them, which is fo far knowledge: and if they have names for those ideas which they have thus confidered, they must needs be affured of the truth of thofe propofitions which exprefs that agreement or difagreement they perceive in them, and be undoubtedly convinced of thofe truths. For what a man fees, he cannot but fee; and what he perceives, he cannot but know that he perceives.

$3. Infiance-In Numbers.

THUS he that has got the ideas of numbers, and hath taken the pains to compare one, tavo and three, to fix, cannot choose but know that they are equal: he that hath got the idea of a triangle, and found the ways to measure its angles, and their magnitudes, is certain that its three angles are equal to two right ones, and can as little doubt of that, as of this truth, that it is impossible for the fame thing to be, and not to be.

In Natural Religion.

He also that hath the idea of an intelligent, but frail and weak being, made by and depending on another, who is eternal, omnipotent, perfectly wife and good, will as certainly know that man is to honour, fear and obey GOD, as that the fun fhines when he fees it. For if he hath but the ideas of two fuch beings in his mind, and will turn his thoughts that way, and confider them, he will as certainly find that the inferior, finite and de

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