OF THE DEGREES OF OUR KNOWLEDGE.
1. Of the degrees, or differences in clearness, of our Knowledge:
I. 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 PRAECOGNITIS 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 all secondary qualities and
their modes.
14. III. 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:--I. 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.]