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than a part; nor be assured of it, till he has learned that maxim? Or cannot a country wench know, that having received a shilling from one that owes her three, and a shilling also from another that owes her three, the remaining debts in each of their hands are equal ? Cannot she know this, I say, unless she fetch
I the certainty of it from this maxim, that if equals from equals, the remainder will be equals, a maxim which possibly she never heard or thought of? I desire any one to consider, from what has been elsewhere said, which is known first and clearest by most people, the particular instance, or the general rule; and which it is that gives life and birth to the other? These general rules are but the comparing our more general and abstract ideas, which are the workmanship of the mind made, and names given to them, for the easier despatch in its reasonings, and drawing into comprehensive terms, and short rules, its various and multiplied observations. But knowledge began in the mind, and was founded on particulars; though afterwards, perhaps, no notice be taken thereof: it being natural for the mind (forward still to enlarge its knowledge) most attentively to lay up those
general notions, and make the proper use of them, which is to disburden the memory of the cumbersome load of particulars. For I desire it may be considered what more certainty there is to a child, or any one, that his body, little finger and all, is bigger than his little finger alone, after you have given to his body the name whole, and to his little finger the name part, than he could have had before; or what new knowledge concerning his body can these two relative terms give him, which he could not have without them ? Could he not know that his body was bigger than his little finger, if his language were yet so imperfect, that he had no such relative terms as whole and part? I ask farther, when he has got these names, how is he more certain that his body is a whole, and his little finger a part, than he was or might be certain, before he learnt those terms, that his body was bigger than his little finger ? Any one may as reasonably doubt or deny that his little finger is a part of his body, as that it is less than his body. And he that can doubt whether it be less, will as certainly doubt whether it be a part. So that the maxim, the whole is bigger than a part, can never be made use of to prove the little finger less than the body, but when it is useless, by being brought to convince one of a truth which he knows already. For he that does not certainly know that any parcel of matter, with another parcel of matter joined to it, is bigger than either of them alone, will never be able to know it by the help of these two relative terms whole and part, make of them what maxim you please. $ 4. But be it in the mathematics as it
Dangerous will, whether it be clearer, that taking an
to build inch from a black line of two inches, and upon prean inch from a red line of two inches, the carious prinremaining parts of the two lines will be ciples. equal, or that if you take equals from equals, the remainder will be equals: which, I say, of these two is the clearer and first known, I leave it to any one to determine, it not being material to my present occasion. That which I have here to do, is to inquire, whether if it be the readiest way to knowledge to begin with general maxims, and build upon them, it be yet a safe way to take the principles which are laid down in any other science as unquestionable truths; and so receive them without examination, and adhere to them, without suffering them to be doubted of, because mathematicians have been so happy, or so fair, to use none but self-evident and undeniable. If this be so, I know not what may not pass for truth in morality, what may not be introduced and proved in natural philosophy:
Let that principle of some of the philosophers, that all is matter, and that there is nothing else, be received for certain and indubitable, and it will be easy to be
seen, by the writings of some that have revived it again in our days, what consequences it will lead us into. Let any one, with Polemo, take the world; or with the stoics, the æther, or the sun; or with Anaximenes, the air, to be God; and what a divinity, religion, and worship must we needs have! Nothing can be so dangerous as principles thus taken up without questioning or examination ; especially if they be such as concern morality, which influence men's lives, and give a bias to all their actions. Who might not justly expect another kind of life in Aristippus, who placed happiness in bodily pleasure; and in Antisthenes, who made virtue sufficient to felicity? And he who, with Plato, shall place beatitude in the knowledge of God, will have his thoughts raised to other contemplations than those who look not beyond this spot of earth, and those perishing things which are to be had in it. He that, with Archelaus, shall lay it down as a principle, that right and wrong, honest and dishonest, are defined only by laws, and not by nature, will have other measures of moral rectitude and pravity than those who take it for granted, that we are under obligations antecedent 'to all human constitutions.
$ 5. If therefore those that pass for This is no
principles are not certain (which we must to truth.
have some way to know, that we may be
able to distinguish them from those that are doubtful) but are only made so to us by our blind assent, we are liable to be misled by them; and instead of being guided into truth, we shall, by principles, be only confirmed in mistake and error.
$ 6. But since the knowledge of the But to com
certainty of principles, as well as of all complete
other truths, depends only upon the perideas under ception we have of the agreement or dissteady agreement of our ideas, the way to improve
our knowledge is not, I am sure, blindly, and with an implicit faith, to receive and swallow principles; but is, I think, to get and fix in our minds clear,
The true method of
distinct, and complete ideas, as far as they are to be had, and annex to them proper and constant names. And thus, perhaps, without any other principles but barely considering those ideas, and by comparing them one with another, finding their agreement and disagreement, and their several relations and habitudes; we shall get more true and clear knowledge, by the conduct of this one rule, than by taking up principles, and thereby putting our minds into the disposal of others.
$ 7. We must, therefore, if we will proceed as reason advises, adapt our methods of inquiry to the nature of the ideas we advancing examine, and the truth we search after. knowledge General and certain truths are only founded is by conin the habitudes and relations of abstract
sidering our ideas. A sagacious and methodical ap- ideas. plication of our thoughts, for the finding out these relations, is the only way to discover all that can be put with truth and certainty concerning them into general propositions. By what steps we are to proceed in these is to be learned in the schools of the mathematicians, who from very plain and easy beginnings, by gentle degrees, and a continued chain of reasonings, proceed to the discovery and demonstration of truths that appear at first sight beyond human capacity. The art of finding proofs, and the admirable methods they have invented for the singling out, and laying in order, those intermediate ideas that demonstratively show the equality or inequality of unapplicable quantities, is that which has carried them so far, and produced such wonderful and unexpected discoveries : but whether something like this, in respect. of other ideas, as well as those of magnitude, may not in time be found out, I will not determine. This, I think, I may say, that if other ideas, that are the real as well as nominal essences of their species, were pursued in the way familiar to mathematicians, they would.carry our thoughts farther, and with greater
evidence and clearness, than' possibly we are apt to imagine.
$ 8. This gave me the confidence to morality advance that conjecture, which I suggest, also may be chap. iii. viz. that morality is capable of made clearer. demonstration, as well as mathematics. For the ideas that ethics are conversant about being all real essences, and such as I imagine have a discoverable connexion and agreement one with another; so far as we can find their habitudes and relations, so far we shall be possessed of certain real and general truths: and I doubt not but, if a right method were taken, a great part of morality might be made out with that clearness, that could leave, to a considering man, no more reason to doubt than he could have to doubt of the truth of propositions in mathematics, which have been demonstrated to him.
$ 9. In our search after the knowledge But knowledge of bo
of substances, our want of ideas, that are dies is to be suitable to such a way of proceeding, improved obliges us to a quite different method. only by
We advance not here, as in the other experience.
(where our abstract ideas are real as well as nominal essences) by contemplating our ideas, and considering their relations and correspondencies; that helps us very little, for the reasons that, in another place, we have at large set down. By which I think it is evident, that substances afford matter of very little general knowledge; and the bare contemplation of their abstract ideas will carry us but a very little way in the search of truth and certainty. What then are we to do for the improvement of our knowledge in substantial beings? Here we are to take a quite contrary course; the want of ideas of their real essences sends us from our own thoughts to the things themselves, as they exist. Experience here must teach me what reason cannot; and it is by trying alone that I can certainly know what other qualities co-exist with those of my complex idea, v.g. whether that yellow,