abstract ideas, and their dependence one on another. Such propositions may be universal and certain. So, having the idea of God and myself, of fear and obedience, I cannot but be sure that God is to be feared and obeyed by me: and this proposition will be certain, concerning man in general, if I have made an abstract idea of such a species, whereof I am one particular. But yet this proposition, how certain soever, that men ought to fear and obey God, proves not to me the existence of men in the world, but will be true of all such creatures whenever they do exist: which certainty of such general propositions, depends on the agreement or disagreement to be discovered in those abstract ideas.

§14. And general propositions concerning abstract ideas. In the former case, our knowledge is the consequence of the existence of things producing ideas in our minds by our senses : in the latter, knowledge is the consequence of the ideas (be they what they will) that are in our minds producing there general certain propositions. Many of these are called aterna veritates, and all of them indeed are so; not from being written all or any of them in the minds of all men, or that they were any of them propositions in any one's mind, till he, having got the abstract ideas, joined or separated them by affirmation or negation. But wheresoever we can suppose such a creature as man is, endowed with such faculties, and thereby furnished with such ideas as we have, we must conclude, he must needs, when he applies his thoughts to the consideration of his ideas, know the truth of certain propositions, that will arise from the agreement or disagreement which he will perceive in his own ideas. Such propositions are therefore called eternal truths, not because they are eternal propositions actually formed, and antecedent to the understanding, that at any time makes them; nor because they are imprinted on the mind from any patterns, that are any where of them out of the mind, and existed before; but because being once made about abstract ideas so as to be true, they will, whenever they can be supposed to be made again at any time past or to come, by a mind having those ideas, always actually be true. For names being supposed to stand perpetually for the same ideas, and the same ideas having immutably the same habitudes one to another: propositions concerning any abstract ideas, that are once true, must needs be eternal verities.

CHAP. XII.

OF THE IMPROVEMENT OF OUR KNOWLEDGE.

§ 1. Knowledge is not from maxims.

IT having been the common received opinion amongst men of Jetters, that maxims were the foundation of all knowledge; and that the sciences were each of them built upon certain præcognita, from whence the understanding was to take its rise, and by which it was to conduct itself, in its inquiries into the matters belonging to that science; the beaten road of the schools has been to lay down in the beginning one or more general propositions, as foundations whereon to build the knowledge that was to be had of that subject.' These doctrines thus laid down for foundations of any science, were called principles, as the beginnings from which we must set -out, and look no farther backwards in our inquiries, as we have already observed.

§ 2. (The occasion of that opinion.)

ONE thing, which might probably give an occasion to this way of proceeding in other sciences, was (as I suppose) the good success it seemed to have in mathematics, wherein men, being observed to attain a great certainty of knowledge, these sciences came by preeminence to be called Matuara and Manors, learning, or things learned, thoroughly learned, as having of all others the greatest certainty, clearness and evidence in them.

§ 3. But from the comparing clear and distinct ideas.

BUT if any one will consider, he will (I guess) find that the great advancement and certainty of real knowledge, which men arrived to in these sciences, was not owing to the influence of these principles, nor derived from any peculiar advantage they received from two or three general maxims, laid down in the beginning; but from the clear, distinct, complete ideas, their thoughts were employed about, and the relation of equality and excess so clear between some of them, that they had an intuitive knowledge, and by that a way to discover it in others, and this without the help of those maxims. For I ask, is it not possible for a young lad to know, that his whole body is bigger than his little finger, but by virtue of this axiom, that the whole is bigger than a part; nor be assured of it, till he has learned that maxim? Or cannot a countrywench know, that having received a shilling from one that owes her three, and a shilling also from another that owes her three, that the remaining debts in each of their hands are equal? Cannot

she know this, I say, without she fetch the certainty of it from this maxim, that if you take 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 learned 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. Dangerous to build upon precarious principics. BUT be it in the mathematics as it will, whether it be clearer, that

\taking an inch from a black line of two inches, and an inch from a red line of two inches, the remaining parts of the two lines will be 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 ether, 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 looked 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. This is no certain way to truth.

IF, therefore, those that pass for principles, are not certain (which we must 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 to compare clear complete ideas under steady names. BUT since the knowledge of the certainty of principles, as well as of all other truths, depends only upon the perception we have of the agreement or disagreement 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, 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. The true method of advancing knowledge is by considering

our abstract ideas.

WE must, therefore, if we will proceed as reason advises, adapt our methods of inquiry to the nature of the ideas we examine, and the truth we search after. General and certain truths are only founded in the habitudes and relations of abstract ideas. A saga⚫ious and methodical application 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,