CHAPTER VII. OF MAXIMS. 1. They are self-evident.-There are a sort of propositions which under the name of "maxims and axioms," have passed for principles of science: and, because they are self-evident, have been supposed innate, although nobody (that I know) ever went about to show the reason and foundation of their clearness or cogency. may, however, be worth while to inquire into the reason of their evidence, and see whether it be peculiar to them alone, and also examine how far they influence and govern our other knowledge. It 2. Wherein that self-evidence consists.-Knowledge, as has been shown, consists in the perception of the agreement or disagreement of ideas: now where that agreement or disagreement is perceived immediately by itself, without the intervention or help of any other, there our knowledge is self-evident. This will appear to be so to any one who will but consider any of those propositions which, without any proof, he assents to at first sight; for in all of them he will find that the reason of his assent is from that agreement or disagreement which the mind, by an immediate comparing them, finds in those ideas, answering the affirmation or negation in the proposition. 3. Self-evidence not peculiar to received axioms. This being so, in the next place let us consider whether this self-evidence be peculiar only to those propositions which commonly pass under the name of "maxims," and have the dignity of axioms allowed them. And here it is plain, that several other truths, not allowed to be axioms, partake equally with them in this self-evidence. This we shall see, if we go over these several sorts of agreement or disagreement of ideas which I have above mentioned, viz. identity, relation, co-existence, and real existence; which will discover to us, that not only those few propositions which have had the credit of maxims are self-evident, but a great many, even almost an infinite number, of other propositions are such. 4. First. As to identity and diversity, all propositions are equally self-evident.-For, First, the immediate perception of the agreement or disagreement of identity being founded in the mind's having distinct ideas, this affords us as many self-evident propositions as we have distinct ideas. Every one that has any knowledge at all has, as the foundation of it, various and distinct ideas: and it is the first act of the mind (without which it can never be capable of any knowledge) to know every one of its ideas by itself, and distinguish it from others. Every one finds in himself, that he knows the ideas he has; that he knows also when any one is in his understanding, and what it is; and that when more than one are there, he knows them distinctly and unconfusedly one from another. Which always being so, (it being impossible but that he should perceive what he perceives,) he can never be in doubt, when any idea is in his mind, that it is there, and is that idea it is; and that two distinct ideas, when they are in his mind, are there, and are not one and the same idea. So that all such affirmations and negations are made without any possibility of doubt, uncertainty, or hesitation, and must necessarily be assented to as soon as understood; that is, as soon as we have in our minds determined ideas which the terms in the proposition stand for. And therefore wherever the mind with attention considers any proposition so as to perceive the two ideas signified by the terms, and affirmed or denied one of the other, to be the same or different, it is presently and infallibly certain of the truth of such a proposition: and this equally whether these propositions be in terms standing for more general ideas, or such as are less so; v. g. whether the general idea of being be affirmed of itself, as in this proposition, "Whatsoever is, is;" or a more particular idea be affirmed of itself, as, "A man is a man," or, 66 Whatsoever is white, is white:" or whether the idea of being in general be denied of not being, which is the only (if I may so call it) idea different from it, as in this other proposition, "It is impossible for the same thing to be, and not to be;" or any idea of any particular being be denied of another different from it, as, "A man is not a horse; red is not blue." The difference of the ideas as soon as the terms are understood makes the truth of the proposition presently visible, and that with an equal certainty and easiness in the less as well as the more general propositions; and all for the same reason, viz. because the mind perceives, in any ideas that it has, the same idea to be the same with itself; and two different ideas to be different, and not the same. And this it is equally certain of, whether these ideas be more or less general, abstract, and comprehensive. It is not therefore alone to these two general propositions,-"Whatsoever is, is ;" and, "It is impossible for the same thing to be, and not to be," that this self-evidence belongs by any peculiar right. The perception of being or not being belongs no more to these vague ideas, signified by the terms "whatsoever" and "thing," than it does to any other ideas. These two general maxims, amounting to no more, in short, but this, that "the same is the same, and " same is not different," are truths known in more particular instances, as well as in these general maxims, and known also in particular instances, before these general maxims are ever thought on, and draw all their force from the discernment of the mind employed about particular ideas. There is nothing more visible than that the mind, without the help of any proof or reflection on either of these general propositions, perceives so clearly, and knows so certainly, that the. idea of white is the idea of white, and not the idea of blue, and that the idea of white, when it is in the mind, is there, and is not absent, that the consideration of these axioms can add nothing to the evidence or certainty of its knowledge. Just so it is (as every one may experiment in himself) in all the ideas a man has in his mind: he knows each to be itself, and not to be another, and to be in his mind, and not away, when it is there, with a certainty that cannot be greater; and therefore the truth of no general proposition can be known with a greater certainty, nor add any thing to this. So that in respect of identity, our intuitive knowledge reaches as far as our ideas. And we are capable of making as many self-evident propositions as we have names for distinct ideas. And I appeal to every one's own mind, whether this proposition, "A circle is a circle," be not as self-evident a proposition as that consisting of more general terms, "Whatsoever is, is:" and again, whether this proposition, "Blue is not red," be not a proposition that the mind can no more doubt of as soon as it understands the words, than it does of that axiom, "It is impossible for the same thing to be, and not to be." And so of all the like. 5. Secondly. In co-existence we have few self-evident propositions.Secondly. As to co-existence, or such necessary connexion between two ideas, that, in the subject where one of them is supposed, there the other must necessarily be also; of such agreement or disagreement as this the mind has an immediate perception but in very few of them; and therefore in this sort we have but very little intuitive knowledge. Nor are there to be found very many propositions that are self-evident, though some there are; v. g. the idea of filling a place equal to the contents of its superficies, being annexed to our idea of body, I think it is a self-evident proposition, that "two bodies cannot be in the same place." 6. Thirdly. In other relations we may have.-Thirdly. As to the relations of modes, mathematicians have framed many axioms concerning that one relation of equality: As, "Equals taken from equals, the remainder will be equals ;" which, with the rest of that kind, however they are received for maxims by the mathematicians, and are unquestionable truths; yet I think that any one who considers them will not find that they have a clearer self-evidence than these, that "one and one are equal to two;" that "if you take from the five fingers of one hand two, and from the five fingers of the other hand two, the remaining numbers will be equal." These and a thousand other such propositions may be found in numbers which, at the very first hearing, force the assent, and carry with them an equal, if not a greater clearness than those mathematical axioms. 7. Fourthly. Concerning real existence we have none.-Fourthly. As to real existence, since that has no connexion with any other of our ideas but that of ourselves and of a first being, we have in that concerning the real existence of all other beings not so much as demonstrative, much less a self-evident, knowledge; and therefore concerning those there are no maxims. 8. These axioms do not much influence our other knowledge.—In the next place let us consider what influence these received maxims have upon the other parts of our knowledge. The rules established in the Schools, that all reasonings are ex præcognitis et præconcessis, seem to lay the foundation of all other knowledge in these maxims, and to suppose them to be præcognita; whereby I think are meant these two things: First, That these axioms are those truths that are first known to the mind; and, Secondly, that upon them the other parts of our knowledge depend. 9. Because they are not the truths we first knew.-First. That they are not the truths first known to the mind, is evident to experience, as we have shown in another place. (Book i. chap. ii.) Who perceives not, that a child certainly knows that a stranger is not its mother, that its sucking-bottle is not the rod, long before he knows that it is impossible for the same thing to be, and not to be? And how many truths are there about numbers which it is obvious to observe that the mind is perfectly acquainted with, and fully convinced of, before it ever thought on these general maxims to which mathematicians in their arguings do sometimes refer them! Whereof the reason is very plain: for, that which makes the mind assent to such propositions being nothing else but the perception it has of the agreement or disagreement of its ideas, according as it finds them affirmed or denied one of another in words it understands, and every idea being known to be what it is, and every two distinct ideas being known not to be the same, it must necessarily follow, that such self-evident truths must be first known which consist of ideas that are first in the mind; and the ideas first in the mind, it is evident, are those of particular things, from whence, by slow degrees, the understanding proceeds to some few general ones; which, being taken from the ordinary and familiar objects of sense, are settled in the mind with general names to them. Thus particular ideas are first received and distinguished, and so knowledge got about them; and next to them the less general or specific, which are next to particular: for, abstract ideas are not so obvious or easy to children or the yet unexercised mind, as particular ones. If they seem so to grown men, it is only because by constant and familiar use they are made so: for when we nicely reflect upon them, we shall find that general ideas are fictions and contrivances of the mind, that carry difficulty with them, and do not so easily offer themselves as we are apt to imagine. For example: Does it not require some pains and skill to form the general idea of a triangle? (which is yet none of the most abstract, comprehensive, 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 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, nor such as its earliest knowledge is conversant about. are 10. Because on them the other parts of our knowledge do not depend.-Secondly. From what has been said, it plainly follows that these magnified maxims are not the principles and foundations of all our other knowledge. For, if there be a great many truths which have as much self-evidence as they, and a great many other 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 together?" 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 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; 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 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 whichever 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 |