1. Maxims or axioms are self-evident propositions. 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, without that anybody (that I know) ever went about to show the
reason and foundation of their clearness or cogency. It may, however, be worth while to inquire into
the reason of their evidence, and see whether it be peculiar to them alone; and also to examine how
far they influence and govern our other knowledge.
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 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, coexistence, 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. I. 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 al 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 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 the 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 anything 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. II. In co-existence we have few self-evident propositions. Secondly, as to co-existence, or such a
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. III. In other relations we may have many. 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 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.
7. IV. 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 praeognitis et praeconcessis, seem to lay the foundation of
all other knowledge in these maxims, and to suppose them to be praecognita. 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 maxims or axioms 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. (Bk. I. chap. i.)
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 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, nor such as its earliest knowledge is
conversant about.
10. Because on perception of 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 other 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?" 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 praecognita 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 infallibly true, as soon as it understands the terms, without
hesitation or need of proof, or regarding those made in more general terms and called maxims.
11. What use these general maxims or axioms have. What shall we then say? Are these general
maxims of no use? By no means; though perhaps their use is not that which it is commonly taken to
be. But, since doubting in the least of what hath been by some men ascribed to these maxims may
be apt to be cried out against, as overturning the foundations of al the sciences; it may be worth
while to consider them with respect to other parts of our knowledge, and examine more particularly
to what purposes they serve, and to what not.
(1) It is evident from what has been already said, that they are of no use to prove or confirm less
general self-evident propositions.
(2) It is as plain that they are not, nor have been the foundations whereon any science hath been
built. There is, I know, a great deal of talk, propagated from scholastic men, of sciences and the
maxims on which they are built: but it has been my ill-luck never to meet with any such sciences;
much less any one built upon these two maxims, what is, is; and it is impossible for the same thing
to be and not to be. And I would be glad to be shown where any such science, erected upon these
or any other general axioms is to be found: and should be obliged to any one who would lay before
me the frame and system of any science so built on these or any such like maxims, that could not
be shown to stand as firm without any consideration of them. I ask, Whether these general maxims
have not the same use in the study of divinity, and in theological questions, that they have in other
sciences? They serve here, too, to silence wranglers, and put an end to dispute. But I think that
nobody will therefore say, that the Christian religion is built upon these maxims, or that the
knowledge we have of it is derived from these principals. It is from revelation we have received it,
and without revelation these maxims had never been able to help us to it. When we find out an idea
by whose intervention we discover the connexion of two others, this is a revelation from God to us
by the voice of reason: for we then come to know a truth that we did not know before. When God
declares any truth to us, this is a revelation to us by the voice of his Spirit, and we are advanced in
our knowledge. But in neither of these do we receive our light or knowledge from maxims. But in the
one, the things themselves afford it: and we see the truth in them by perceiving their agreement or
disagreement. In the other, God himself affords it immediately to us: and we see the truth of what he
says in his unerring veracity.
(3) They are not of use to help men forward in the advancement of sciences, or new discoveries of
yet unknown truths. Mr. Newton, in his never enough to be admired book, has demonstrated several
propositions, which are so many new truths, before unknown to the world, and are further advances
in mathematical knowledge: but, for the discovery of these, it was not the general maxims, "what is,
is;" or, "the whole is bigger than a part," or the like, that helped him. These were not the clues that
led him into the discovery of the truth and certainty of those propositions. Nor was it by them that he
got the knowledge of those demonstrations, but by finding out intermediate ideas that showed the
agreement or disagreement of the ideas, as expressed in the propositions he demonstrated. This is
the greatest exercise and improvement of human understanding in the enlarging of knowledge, and
advancing the sciences; wherein they are far enough from receiving any help from the
contemplation of these or the like magnified maxims. Would those who have this traditional
admiration of these propositions, that they think no step can be made in knowledge without the
support of an axiom, no stone laid in the building of the sciences without a general maxim, but
distinguish between the method of acquiring knowledge, and of communicating it; between the
method of raising any science, and that of teaching it to others, as far as it is advanced--they would
see that those general maxims were not the foundations on which the first discoverers raised their
admirable structures, not the keys that unlocked and opened those secrets of knowledge. Though
afterwards, when schools were erected, and sciences had their professors to teach what others had
found out, they often made use of maxims, i.e., laid down certain propositions which were self-
evident, or to be received for true; which being settled in the minds of their scholars as
unquestionable verities they on occasion made use of, to convince them of truths in particular
instances, that were not so familiar to their minds as those general axioms which had before been
inculcated to them, and carefully settled in their minds. Though these particular instances, when well
reflected on, are no less self-evident to the understanding than the general maxims brought to
confirm them: and it was in those particular instances that the first discoverer found the truth, without
the help of the general maxims: and so may any one else do, who with attention considers them.
Maxims of use in the exposition of what has been discovered, and in silencing obstinate wranglers.
To come, therefore, to the use that is made of maxims.
(1) They are of use, as has been observed, in the ordinary methods of teaching sciences as far as
they are advanced: but of little or none in advancing them further.
(2) They are of use in disputes, for the silencing of obstinate wranglers, and bringing those contests
to some conclusion. Whether a need of them to that end came not in the manner following, I crave
leave to inquire. The Schools having made disputation the touchstone of men's abilities, and the
criterion of knowledge, adjudged victory to him that kept the field: and he that had the last word was
concluded to have the better of the argument, if not of the cause. But because by this means there
was like to be no decision between skilful combatants, whilst one never failed of a medius terminus
to prove any proposition; and the other could as constantly, without or with a distinction, deny the
major or minor; to prevent, as much as could be, running out of disputes into an endless train of
syllogisms, certain general propositions--most of them, indeed, self-evident--were introduced into
the Schools: which being such as all men allowed and agreed in, were looked on as general
measures of truth, and served instead of principles (where the disputants had not lain down any
other between them) beyond which there was no going, and which must not be receded from by
either side. And thus these maxims, getting the name of principles, beyond which men in dispute
could not retreat, were by mistake taken to be the originals and sources from whence all knowledge
began, and the foundations whereon the sciences were built. Because when in their disputes they
came to any of these, they stopped there, and went no further; the matter was determined. But how
much this is a mistake, hath been already shown.
How maxims came to be so much in vogue. This method of the Schools, which have been thought
the fountains of knowledge, introduced, as I suppose, the like use of these maxims into a great part
of conversation out of the Schools, to stop the mouths of cavillers, whom any one is excused from
arguing any longer with, when they deny these general self-evident principles received by all
reasonable men who have once thought of them: but yet their use herein is but to put an end to
wrangling. They in truth, when urged in such cases, teach nothing: that is already done by the
intermediate ideas made use of in the debate, whose connexion may be seen without the help of
those maxims, and so the truth known before the maxim is produced, and the argument brought to a
first principle. Men would give off a wrong argument before it came to that, if in their disputes they
proposed to themselves the finding and embracing of truth, and not a contest for victory. And thus
maxims have their use to put a stop to their perverseness, whose ingenuity should have yielded
sooner. But the method of the Schools having allowed and encouraged men to oppose and resist
evident truth till they are baffled, i.e., till they are reduced to contradict themselves, or some
established principles: it is no wonder that they should not in civil conversation be ashamed of that
which in the Schools is counted a virtue and a glory, viz., obstinately to maintain that side of the
question they have chosen, whether true or false, to the last extremity; even after conviction. A
strange way to attain truth and knowledge: and that which I think the rational part of mankind, not
corrupted by education, could scarce believe should ever be admitted amongst the lovers of truth,
and students of religion or nature, or introduced into the seminaries of those who are to propagate
the truths of religion or philosophy amongst the ignorant and unconvinced. How much such a way of
learning is like to turn young men's minds from the sincere search and love of truth; nay, and to
make them doubt whether there is any such thing, or, at least, worth the adhering to, I shall not now
inquire. This I think, that, bating those places, which brought the Peripatetick Philosophy into their
schools, w