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An Essay Concerning Humane Understanding, Volume 2 MDCXC, Based on the 2nd Edition, Books 3 and 4 online

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in us the sensation of a yellow colour, and what sort of figure, bulk,
and texture of parts in the superficies of any body were fit to give
such corpuscles their due motion to produce that colour; would that be
enough to make universal propositions with certainty, concerning the
several sorts of them; unless we had faculties acute enough to perceive
the precise bulk, figure, texture, and motion of bodies, in those minute
parts, by which they operate on our senses, so that we might by those
frame our abstract ideas of them. I have mentioned here only
corporeal substances, whose operations seem to lie more level to our
understandings. For as to the operations of spirits, both their thinking
and moving of bodies, we at first sight find ourselves at a loss; though
perhaps, when we have applied our thoughts a little nearer to the
consideration of bodies and their operations, and examined how far our
notions, even in these, reach with any clearness beyond sensible matter
of fact, we shall be bound to confess that, even in these too, our
discoveries amount to very little beyond perfect ignorance and
incapacity.


15. Whilst our complex Ideas of Substances contain not ideas of their
real Constitutions, we can make but few general Propositions concerning
them.

This is evident, the abstract complex ideas of substances, for which
their general names stand, not comprehending their real constitutions,
can afford us very little universal certainty. Because our ideas of them
are not made up of that on which those qualities we observe in them, and
would inform ourselves about, do depend, or with which they have any
certain connexion: v.g. let the ideas to which we give the name MAN be,
as it commonly is, a body of the ordinary shape, with sense, voluntary
motion, and reason joined to it. This being the abstract idea, and
consequently the essence of OUR species, man, we can make but very few
general certain propositions concerning man, standing for such an idea.
Because, not knowing the real constitution on which sensation, power of
motion, and reasoning, with that peculiar shape, depend, and whereby
they are united together in the same subject, there are very few other
qualities with which we can perceive them to have a necessary connexion:
and therefore we cannot with certainty affirm: That all men sleep by
intervals; That no man can be nourished by wood or stones; That all men
will be poisoned by hemlock: because these ideas have no connexion nor
repugnancy with this our nominal essence of man, with this abstract idea
that name stands for. We must, in these and the like, appeal to trial in
particular subjects, which can reach but a little way. We must content
ourselves with probability in the rest: but can have no general
certainty, whilst our specific idea of man contains not that real
constitution which is the root wherein all his inseparable qualities are
united, and from whence they flow. Whilst our idea the word MAN stands
for is only an imperfect collection of some sensible qualities and
powers in him, there is no discernible connexion or repugnance between
our specific idea, and the operation of either the parts of hemlock or
stones upon his constitution. There are animals that safely eat hemlock,
and others that are nourished by wood and stones: but as long as we want
ideas of those real constitutions of different sorts of animals whereon
these and the like qualities and powers depend, we must not hope to
reach certainty in universal propositions concerning them. Those few
ideas only which have a discernible connexion with our nominal essence,
or any part of it, can afford us such propositions. But these are so
few, and of so little moment, that we may justly look on our certain
general knowledge of substances as almost none at all.


16. Wherein lies the general Certainty of Propositions.

To conclude: general propositions, of what kind soever, are then only
capable of certainty, when the terms used in them stand for such ideas,
whose agreement or disagreement, as there expressed, is capable to be
discovered by us. And we are then certain of their truth or falsehood,
when we perceive the ideas the terms stand for to agree or not agree,
according as they are affirmed or denied one of another. Whence we may
take notice, that general certainty is never to be found but in
our ideas. Whenever we go to seek it elsewhere, in experiment or
observations without us, our knowledge goes not beyond particulars. It
is the contemplation of our own abstract ideas that alone is able to
afford us general knowledge.




CHAPTER VII. OF MAXIMS


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. Where in 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,
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. As to Identity and Diversity all Propositions are equally
self-evident.

I. 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 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 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. In Co-existance we have few self-evident Propositions.

II. SECONDLY, as to CO-EXISTANCE, 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 EXISTANCE, 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 PRAECOGNITIS 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. (Book I. chap, 1.) 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 more abstract,
comprehensive, and difficult,) for it must be neither oblique nor
rectangle, neither equilateral, equicrural, nor scalinon; but all and
none of these at once. In effect, it is something imperfect, that cannot
exist; an idea wherein some part of several different and inconsistant
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 all 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.

{Of no use to prove less general propositions, nor as foundations on
consideration of which any science has been built.}

(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
principles. 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) Nor as helps in the discovery of yet unknown truths.

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



Online LibraryJohn LockeAn Essay Concerning Humane Understanding, Volume 2 MDCXC, Based on the 2nd Edition, Books 3 and 4 → online text (page 19 of 29)