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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, as to co-existence, or
2. In co-exsuch necessary connexion between two
istence we ideas, that, in the subject where one of have few them is supposed, there the other must
self-evident necessarily be also : of such agreement or
tions. 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.
$16. Thirdly, as to the relations of 3. In other modes, mathematicians have framed many relations we axioms concerning that one relation of may have.
equality. 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. Concern- § 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 ax
$ 8. In the next place let us consider ioms do not
what influence these received maxims have much influ- upon the other parts of our knowledge.
The rules established in the schools, that other know
all reasonings are ex præcognitis et præledge.
concessis, 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
$ 9. First, that they are not the truths they are not
first known to the mind, is evident to the truths experience, as we have shown in another
place, book i. chap. ii. Who perceives not knew.
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
non; 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 are 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, not such as its earliest knowledge is conversant about.
§ 10. Secondly, from what has been Because on them the said it plainly follows, that these mag
nified maxims are not the principles and of our know- foundations of all our other knowledge. ledge do not
For if there be a great many other depend.
truths, which have as much self-evidence as they, and a great many 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? Manya 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