1. As to

identity and diversity, all propositions are equally

self-evident.

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. 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 selfevident 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 whenever 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, 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 sort of selfevidence 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 those 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.

2. In co-existence we

have few self-evident proposi

tions.

§ 5. 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, as to the relations of modes, mathematicians have framed many axioms concerning that one relation of

3. In other relations we may have.

équality. As, equals taken from equals, the remainder will be equal; 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 greater clearness, than those mathematical axioms. 4. Concerning real

existence we have

none.

§ 7. 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.

These axioms do not much influ

ence our

other knowledge.

§ 8. 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.

Because they are not the truths we first

knew.

$ 9. 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 be the same; it must necessarily follow, that such selfevident 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 scale