1. Of the degrees, or differences in clearness, of our knowledge: 1. Intuitive. All our knowledge
consisting, as I have said, in the view the mind has of its own ideas, which is the utmost light and
greatest certainty we, with our faculties, and in our way of knowledge, are capable of, it may not be
amiss to consider a little the degrees of its evidence. The different clearness of our knowledge
seems to me to lie in the different way of perception the mind has of the agreement or disagreement
of any of its ideas. For if we will reflect on our own ways of thinking, we will find, that sometimes the
mind perceives the agreement or disagreement of two ideas immediately by themselves, without the
intervention of any other: and this I think we may call intuitive knowledge. For in this the mind is at
no pains of proving or examining, but perceives the truth as the eye doth light, only by being
directed towards it. Thus the mind perceives that white is not black, that a circle is not a triangle, that
three are more than two and equal to one and two. Such kinds of truths the mind perceives at the
first sight of the ideas together, by bare intuition; without the intervention of any other idea: and this
kind of knowledge is the clearest and most certain that human frailty is capable of. This part of
knowledge is irresistible, and, like bright sunshine, forces itself immediately to be perceived, as
soon as ever the mind turns its view that way; and leaves no room for hesitation, doubt, or
examination, but the mind is presently filled with the clear light of it. It is on this intuition that
depends all the certainty and evidence of all our knowledge; Which certainty every one finds to be
so great, that he cannot imagine, and therefore not require a greater: for a man cannot conceive
himself capable of a greater certainty than to know that any idea in his mind is such as he perceives
it to be; and that two ideas, wherein he perceives a difference, are different and not precisely the
same. He that demands a greater certainty than this, demands he knows not what, and shows only
that he has a mind to be a sceptic, without being able to be so. Certainty depends so wholly on this
intuition, that, in the next degree of knowledge which I call demonstrative, this intuition is necessary
in all the connexions of the intermediate ideas, without which we cannot attain knowledge and
certainty.
2. II. Demonstrative. The next degree of knowledge is, where the mind perceives the agreement or
disagreement of any ideas, but not immediately. Though wherever the mind perceives the
agreement or disagreement of any of its ideas, there be certain knowledge; yet it does not always
happen, that the mind sees that agreement or disagreement, which there is between them, even
where it is discoverable; and in that case remains in ignorance, and at most gets no further than a
probable conjecture. The reason why the mind cannot always perceive presently the agreement or
disagreement of two ideas, is, because those ideas, concerning whose agreement or disagreement
the inquiry is made, cannot by the mind be so put together as to show it. In this case then, when the
mind cannot so bring its ideas together as by their immediate comparison, and as it were juxta-
position or application one to another, to perceive their agreement or disagreement, it is fain, by the
intervention of other ideas (one or more, as it happens) to discover the agreement or disagreement
which it searches; and this is that which we call reasoning. Thus, the mind being willing to know the
agreement or disagreement in bigness between the three angles of a triangle and two right ones,
cannot by an immediate view and comparing them do it: because the three angles of a triangle
cannot be brought at once, and be compared with any other one, or two, angles; and so of this the
mind has no immediate, no intuitive knowledge. In this case the mind is fain to find out some other
angles, to which the three angles of a triangle have an equality; and, finding those equal to two right
ones. comes to know their equality to two right ones.
3. Demonstration depends on clearly perceived proofs. Those intervening ideas, which serve to
show the agreement of any two others, are called proofs; and where the agreement and
disagreement is by this means plainly and clearly perceived, it is called demonstration; it being
shown to the understanding, and the mind made to see that it is so. A quickness in the mind to find
out these intermediate ideas, (that shall discover the agreement or disagreement of any other,) and
to apply them right, is, I suppose, that which is called sagacity.
4. As certain, but not so easy and ready as intuitive knowledge. This knowledge, by intervening
proofs, though it be certain, yet the evidence of it is not altogether so clear and bright, nor the assent
so ready, as in intuitive knowledge. For, though in demonstration the mind does at last perceive the
agreement or disagreement of the ideas it considers; yet it is not without pains and attention: there
must be more than one transient view to find it. A steady application and pursuit are required to this
discovery: and there must be a progression by steps and degrees, before the mind can in this way
arrive at certainty, and come to perceive the agreement or repugnancy between two ideas that need
proofs and the use of reason to show it.
5. The demonstrated conclusion not without doubt, precedent to the demonstration. Another
difference between intuitive and demonstrative knowledge is, that, though in the latter all doubt be
removed when, by the intervention of the intermediate ideas, the agreement or disagreement is
perceived, yet before the demonstration there was a doubt; which in intuitive knowledge cannot
happen to the mind that has its faculty of perception left to a degree capable of distinct ideas; no
more than it can be a doubt to the eye (that can distinctly see white and black), Whether this ink and
this paper be all of a colour. If there be sight in the eyes, it will, at first glimpse, without hesitation,
perceive the words printed on this paper different from the colour of the paper: and so if the mind
have the faculty of distinct perception, it will perceive the agreement or disagreement of those ideas
that produce intuitive knowledge. If the eyes have lost the faculty of seeing, or the mind of
perceiving, we in vain inquire after the quickness of sight in one, or clearness of perception in the
other.
6. Not so clear as intuitive knowledge. It is true, the perception produced by demonstration is also
very clear; yet it is often with a great abatement of that evident lustre and full assurance that always
accompany that which I call intuitive: like a face reflected by several mirrors one to another, where,
as long as it retains the similitude and agreement with the object, it produces a knowledge; but it is
still, in every successive reflection, with a lessening of that perfect clearness and distinctness which
is in the first; till at last, after many removes, it has a great mixture of dimness, and is not at first
sight so knowable, especially to weak eyes. Thus it is with knowledge made out by a long train of
proof.
7. Each step in demonstrated knowledge must have intuitive evidence. Now, in every step reason
makes in demonstrative knowledge, there is an intuitive knowledge of that agreement or
disagreement it seeks with the next intermediate idea which it uses as a proof: for if it were not so,
that yet would need a proof; since without the perception of such agreement or disagreement, there
is no knowledge produced: if it be perceived by itself, it is intuitive knowledge: if it cannot be
perceived by itself, there is need of some intervening idea, as a common measure, to show their
agreement or disagreement. By which it is plain that every step in reasoning that produces
knowledge, has intuitive certainty; which when the mind perceives, there is no more required but to
remember it, to make the agreement or disagreement of the ideas concerning which we inquire
visible and certain. So that to make anything a demonstration, it is necessary to perceive the
immediate agreement of the intervening ideas, whereby the agreement or disagreement of the two
ideas under examination (whereof the one is always the first, and the other the last in the account) is
found. This intuitive perception of the agreement or disagreement of the intermediate ideas, in each
step and progression of the demonstration, must also be carried exactly in the mind, and a man
must be sure that no part is left out: which, because in long deductions, and the use of many proofs,
the memory does not always so readily and exactly retain; therefore it comes to pass, that this is
more imperfect than intuitive knowledge, and men embrace often falsehood for demonstrations.
8. Hence the mistake, ex praecognitis, et praeconcessis. The necessity of this intuitive knowledge,
in each step of scientifical or demonstrative reasoning, gave occasion, I imagine, to that mistaken
axiom, That all reasoning was ex pracognitis et praeconcessis: which, how far it is a mistake, I shall
have occasion to show more at large, when I come to consider propositions, and particularly those
propositions which are called maxims, and to show that it is by a mistake that they are supposed to
be the foundations of all our knowledge and reasonings.
9. Demonstration not limited to ideas of mathematical quantity. It has been generally taken for
granted, that mathematics alone are capable of demonstrative certainty: but to have such an
agreement or disagreement as may intuitively be perceived, being, as I imagine, not the privilege of
the ideas of number, extension, and figure alone, it may possibly be the want of due method and
application in us, and not of sufficient evidence in things, that demonstration has been thought to
have so little to do in other parts of knowledge, and been scarce so much as aimed at by any but
mathematicians. For whatever ideas we have wherein the mind can perceive the immediate
agreement or disagreement that is between them, there the mind is capable of intuitive knowledge;
and where it can perceive the agreement or disagreement of any two ideas, by an intuitive
perception of the agreement or disagreement they have with any intermediate ideas, there the mind
is capable of demonstration: which is not limited to ideas of extension, figure, number, and their
modes.
10. Why it has been thought to be so limited. The reason why it has been generally sought for, and
supposed to be only in those, I imagine has been, not only the general usefulness of those
sciences: but because, in comparing their equality or excess, the modes of numbers have every the
least difference very clear and perceivable: and though in extension every the least excess is not so
perceptible, yet the mind has found out ways to examine, and discover demonstratively, the just
equality of two angles, or extensions, or figures: and both these, i.e., numbers and figures, can be
set down by visible and lasting marks, wherein the ideas under consideration are perfectly
determined; which for the most part they are not, where they are marked only by names and words.
11. Modes of qualities not demonstrable like modes of quantity. But in other simple ideas, whose
modes and differences are made and counted by degrees, and not quantity, we have not so nice
and accurate a distinction of their differences as to perceive, or find ways to measure, their just
equality, or the least differences. For those other simple ideas, being appearances of sensations
produced in us, by the size, figure, number, and motion of minute corpuscles singly insensible; their
different degrees also depend upon the variation of some or of all those causes: which, since it
cannot be observed by us, in particles of matter whereof each is too subtile to be perceived, it is
impossible for us to have any exact measures of the different degrees of these simple ideas. For,
supposing the sensation or idea we name whiteness be produced in us by a certain number of
globules, which, having a verticity about their own centres, strike upon the retina of the eye, with a
certain degree of rotation, as well as progressive swiftness; it will hence easily follow, that the more
the superficial parts of any body are so ordered as to reflect the greater number of globules of light,
and to give them the proper rotation, which is fit to produce this sensation of white in us, the more
white will that body appear, that from an equal space sends to the retina the greater number of such
corpuscles, with that peculiar sort of motion. I do not say that the nature of light consists in very
small round globules; nor of whiteness in such a texture of parts as gives a certain rotation to these
globules when it reflects them: for I am not now treating physically of light or colours. But this I think
I may say, that I cannot (and I would be glad any one would make intelligible that he did), conceive
how bodies without us can any ways affect our senses, but by the immediate contact of the sensible
bodies themselves, as in tasting and feeling, or the impulse of some sensible particles coming from
them, as in seeing, hearing, and smelling; by the different impulse of which parts, caused by their
different size, figure, and motion, the variety of sensations is produced in us.
12. Particles of light and simple ideas of colour. Whether then they be globules or no; or whether
they have a verticity about their own centres that produces the idea of whiteness in us; this is
certain, that the more particles of light are reflected from a body, fitted to give them that peculiar
motion which produces the sensation of whiteness in us; and possibly too, the quicker that peculiar
motion is,--the whiter does the body appear from which the greatest number are reflected, as is
evident in the same piece of paper put in the sunbeams, in the shade, and in a dark hole; in each of
which it will produce in us the idea of whiteness in far different degrees.
13. The secondary qualities of things not discovered by demonstration. Not knowing, therefore, what
number of particles, nor what motion of them, is fit to produce any precise degree of whiteness, we
cannot demonstrate the certain equality of any two degrees of whiteness; because we have no
certain standard to measure them by, nor means to distinguish every the least real difference, the
only help we have being from our senses, which in this point fail us. But where the difference is so
great as to produce in the mind clearly distinct ideas, whose differences can be perfectly retained,
there these ideas or colours, as we see in different kinds, as blue and red, are as capable of
demonstration as ideas of number and extension. What I have here said of whiteness and colours, I
think holds true in al secondary qualities and their modes.
14. Sensitive knowledge of the particular existence of finite beings without us. These two, viz.,
intuition and demonstration, are the degrees of our knowledge; whatever comes short of one of
these, with what assurance soever embraced, is but faith or opinion, but not knowledge, at least in
all general truths. There is, indeed, another perception of the mind, employed about the particular
existence of finite beings without us, which, going beyond bare probability, and yet not reaching
perfectly to either of the foregoing degrees of certainty, passes under the name of knowledge. There
can be nothing more certain than that the idea we receive from an external object is in our minds:
this is intuitive knowledge. But whether there be anything more than barely that idea in our minds;
whether we can thence certainly infer the existence of anything without us, which corresponds to
that idea, is that whereof some men think there may be a question made; because men may have
such ideas in their minds, when no such thing exists, no such object affects their senses. But yet
here I think we are provided with an evidence that puts us past doubting. For I ask any one,
Whether he be not invincibly conscious to himself of a different perception, when he looks on the
sun by day, and thinks on it by night; when he actually tastes wormwood, or smells a rose, or only
thinks on that savour or odour? We as plainly find the difference there is between any idea revived
in our minds by our own memory, and actually coming into our minds by our senses, as we do
between any two distinct ideas. If any one say, a dream may do the same thing, and all these ideas
may be produced in us without any external objects; he may please to dream that I make him this
answer:--1. That it is no great matter, whether I remove his scruple or no: where all is but dream,
reasoning and arguments are of no use, truth and knowledge nothing. 2. That I believe he will allow
a very manifest difference between dreaming of being in the fire, and being actually in it. But yet if
he be resolved to appear so sceptical as to maintain, that what I call being actually in the fire is
nothing but a dream; and that we cannot thereby certainly know, that any such thing as fire actually
exists without us: I answer, That we certainly finding that pleasure or pain follows upon the
application of certain objects to us, whose existence we perceive, or dream that we perceive, by our
senses; this certainty is as great as our happiness or misery, beyond which we have no
concernment to know or to be. So that, I think, we may add to the two former sorts of knowledge this
also, of the existence of particular external objects, by that perception and consciousness we have
of the actual entrance of ideas from them, and allow these three degrees of knowledge, viz.,
intuitive, demonstrative, and sensitive: in each of which there are different degrees and ways of
evidence and certainty.
15. Knowledge not always clear, where the ideas that enter into it are clear. But since our
knowledge is founded on and employed about our ideas only, will it not follow from thence that it is
conformable to our ideas; and that where our ideas are clear and distinct, or obscure and confused,
our knowledge will be so too? To which I answer, No: for our knowledge consisting in the perception
of the agreement or disagreement of any two ideas, its clearness or obscurity consists in the
clearness or obscurity of that perception, and not in the clearness or obscurity of the ideas
themselves: v.g. a man that has as clear ideas of the angles of a triangle, and of equality to two right
ones, as any mathematician in the world, may yet have but a very obscure perception of their
agreement, and so have but a very obscure knowledge of it. But ideas which, by reason of their
obscurity or otherwise, are confused, cannot produce any clear or distinct knowledge; because, as
far as any ideas are confused, so far the mind cannot perceive clearly whether they agree or
disagree. Or to express the same thing in a way less apt to be misunderstood: he that hath not
determined ideas to the words he uses, cannot make propositions of them of whose truth he can be
certain.