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
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, nor 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 scare 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 propegate
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 Peripatetic Philosophy into their schools, where it
continued many ages, without teaching the world anything but the art of
wrangling, these maxims were nowhere thought the foundations on which
the sciences were built, nor the great helps to the advancement of
knowledge.]
{Of great use to stop wranglers in disputes, but of little use to the
discovery of truths.}
As to these general maxims, therefore, they are, as I have said, of
great use in disputes, to stop the mouths of wranglers; but not of much
use to the discovery of unknown truths, or to help the mind forwards in
its search after knowledge. For who ever began to build his knowledge on
this general proposition, WHAT IS, IS; or, IT IS IMPOSSIBLE FOR THE SAME
THING TO BE AND NOT TO BE: and from either of these, as from a principle
of science, deduced a system of useful knowledge? Wrong opinions often
involving contradictions, one of these maxims, as a touchstone, may
serve well to show whither they lead. But yet, however fit to lay open
the absurdity or mistake of a man's reasoning or opinion, they are of
very little use for enlightening the understanding: and it will not be
found that the mind receives much help from them in its progress in
knowledge; which would be neither less, nor less certain, were these two
general propositions never thought on. It is true, as I have said, they
sometimes serve in argumentation to stop a wrangler's mouth, by showing
the absurdity of what he saith, [and by exposing him to the shame of
contradicting what all the world knows, and he himself cannot but own to
be true.] But it is one thing to show a man that he is in an error, and
another to put him in possession of truth, and I would fain know what
truths these two propositions are able to teach, and by their influence
make us know which we did not know before, or could not know without
them. Let us reason from them as well as we can, they are only about
identical predications, and influence, if any at all, none but such.
Each particular proposition concerning identity or diversity is as
clearly and certainly known in itself, if attended to, as either of
these general ones: [only these general ones, as serving in all cases,
are therefore more inculcated and insisted on.] As to other less general
maxims, many of them are no more than bare verbal propositions, and
teach us nothing but the respect and import of names one to another.
'The whole is equal to all its parts:' what real truth, I beseech you,
does it teach us? What more is contained in that maxim, than what the
signification of the word TOTUM, or the WHOLE, does of itself import?
And he that knows that the WORD whole stands for what is made up of all
its parts, knows very little less than that the whole is equal to all
its parts. And, upon the same ground, I think that this proposition, 'A
hill is higher than a valley', and several the like, may also pass for
maxims. But yet [masters of mathematics, when they would, as teachers of
what they know, initiate others in that science do not] without reason
place this and some other such maxims [at the entrance of their
systems]; that their scholars, having in the beginning perfectly
acquainted their thoughts with these propositions, made in such general
terms, may be used to make such reflections, and have these more general
propositions, as formed rules and sayings, ready to apply to all
particular cases. Not that if they be equally weighed, they are more
clear and evident than the particular instances they are brought to
confirm; but that, being more familiar to the mind, the very naming them
is enough to satisfy the understanding. But this, I say, is more from
our custom of using them, and the establishment they have got in our
minds by our often thinking of them, than from the different evidence
of the things. But before custom has settled methods of thinking and
reasoning in our minds, I am apt to imagine it is quite otherwise; and
that the child, when a part of his apple is taken away, knows it better
in that particular instance, than by this general proposition, 'The
whole is equal to all its parts;' and that, if one of these have need to
be confirmed to him by the other, the general has more need to be let
into his mind by the particular, than the particular by the general.
For in _particulars_ our knowledge begins, and so spreads itself, by
degrees, to _generals_ [Footnote: This is the order in time of the
conscious acquistion of knowledge that is human. The _Essay_ might be
regarded as a commentary on this one sentence. Our intellectual progress
is from particulars and involuntary recipiency, through reactive doubt
and criticism, into what is at last reasoned faith.]. Though afterwards
the mind takes the quite contrary course, and having drawn its knowledge
into as general propositions as it can, makes those familiar to its
thoughts, and accustoms itself to have recourse to them, as to the
standards of truth and falsehood. [Footnote: This is the philosophic
attitude. Therein one consciously apprehends the intellectual
necessities that were UNCONCIOUSLY PRESUPPOSED, its previous
intellectual progress. In philosophy we 'draw our knowledge into as
general propositions as it can' be made to assume, and thus either learn
to see it as an organic while in a speculative unity, or learn that it
cannot be so seen in a finite intelligence, and that even at the last
it must remain 'broken' and mysterious in the human understanding. ]
By which familiar use of them, as rules to measure the truth of other
propositions, it comes in time to be thought, that more particular
propositions have their truth and evidence from their conformity to
these more general ones, which, in discourse and argumentation, are so
frequently urged, and constantly admitted. And this I think to be the
reason why, amongst so many self-evident propositions, the MOST
GENERAL ONLY have had the title of MAXIMS.
12. Maxims, if care be not taken in the Use of Words, may prove
Contradictions.
One thing further, I think, it may not be amiss to observe concerning
these general maxims, That they are so far from improving or
establishing our minds in true knowledge that if our notions be wrong,
loose, or unsteady, and we resign up our thoughts to the sound of words,
rather than [fix them on settled, determined] ideas of things; I say
these general maxims will serve to confirm us in mistakes; and in such
a way of use of words, which is most common, will serve to prove
contradictions: v.g. he that with Descartes shall frame in his mind
an idea of what he calls body to be nothing but extension, may easily
demonstrate that there is no vacuum, i.e. no space void of body, by this
maxim, WHAT IS, IS. For the idea to which he annexes the name body,
being bare extension, his knowledge that space cannot be without
body, is certain. For he knows his own idea of extension clearly and
distinctly, and knows that it is what it is, and not another idea,
though it be called by these three names,--extension, body, space. Which
three words, standing for one and the same idea, may, no doubt, with
the same evidence and certainty be affirmed one of another, as each of
itself: and it is as certain, that, whilst I use them all to stand for
one and the same idea, this predication is as true and identical in its
signification, that 'space is body,' as this predication is true and
identical, that 'body is body,' both in signification and sound.
13. Instance in Vacuum.
But if another should come and make to himself another idea, different
from Descartes's, of the thing, which yet with Descartes he calls by the
same name body, and make his idea, which he expresses by the word body,
to be of a thing that hath both extension and solidity together; he will
as easily demonstrate, that there may be a vacuum or space without a
body, as Descartes demonstrated the contrary. Because the idea to which
he gives the name space being barely the simple one of extension, and
the idea to which he gives the name body being the complex idea of
extension and resistibility or solidity, together in the same
subject, these two ideas are not exactly one and the same, but in the
understanding as distinct as the ideas of one and two, white and black,
or as of CORPOREITY and HUMANITY, if I may use those barbarous terms:
and therefore the predication of them in our minds, or in words standing
for them, is not identical, but the negation of them one of another;
[viz. this proposition: 'Extension or space is not body,' is] as true
and evidently certain as this maxim, IT IS IMPOSSIBLE FOR THE SAME THING
TO BE AND NOT TO BE, [can make any proposition.]
14. But they prove not the Existance of things without us.
But yet, though both these propositions (as you see) may be equally
demonstrated, viz. that there may be a vacuum, and that there cannot be
a vacuum, by these two certain principles, viz. WHAT IS, IS, and THE
SAME THING CANNOT BE AND NOT BE: yet neither of these principles will
serve to prove to us, that any, or what bodies do exist: for that we are
left to our senses to discover to us as far as they can. Those universal
and self-evident principles being only our constant, clear, and distinct
knowledge of our own ideas, more general or comprehensive, can assure us
of nothing that passes without the mind: their certainty is founded
only upon the knowledge we have of each idea by itself, and of its
distinction from others, about which we cannot be mistaken whilst they
are in our minds; though we may be and often are mistaken when we retain
the names without the ideas; or use them confusedly, sometimes for
one and sometimes for another idea. In which cases the force of these
axioms, reaching only to the sound, and not the signification of the
words, serves only to lead us into confusion, mistake, and error. [It is
to show men that these maxims, however cried up for the great guards of
truth, will not secure them from error in a careless loose use of their
words, that I have made this remark. In all that is here suggested
concerning their little use for the improvement of knowledge, or
dangerous use in undetermined ideas, I have been far enough from saying
or intending they should be laid aside; as some have been too forward
to charge me. I affirm them to be truths, self-evident truths; and so
cannot be laid aside. As far as their influence will reach, it is in
vain to endeavour, nor will I attempt, to abridge it. But yet, without
any injury to truth or knowledge, I may have reason to think their use
is not answerable to the great stress which seems to be laid on them;
and I may warn men not to make an ill use of them, for the confirming
themselves in errors.]
15. They cannot add to our knowledge of Substances, and their
Application to complex Ideas is dangerous.
But let them be of what use they will in verbal propositions, they
cannot discover or prove to us the least knowledge of the nature of
substances, as they are found and exist without us, any further than
grounded on experience. And though the consequence of these two
propositions, called principles, be very clear, and their use not
dangerous or hurtful, in the probation of such things wherein there is
no need at all of them for proof, but such as are clear by themselves
without them, viz. where our ideas are [determined] and known by the
names that stand for them: yet when these principles, viz. WHAT IS, IS,
and IT IS IMPOSSIBLE FOR THE SAME THING TO BE AND NOT TO BE, are made
use of in the probation of propositions wherein are words standing for
complex ideas, v.g. man, horse, gold, virtue; there they are of infinite
danger, and most commonly make men receive and retain falsehood for
manifest truth, and uncertainty for demonstration: upon which follow
error, obstinacy, and all the mischiefs that can happen from wrong
reasoning. The reason whereof is not, that these principles are less
true [or of less force] in proving propositions made of terms standing
for complex ideas, than where the propositions are about simple ideas.
[But because men mistake generally,--thinking that where the same terms
are preserved, the propositions are about the same things, though the
ideas they stand for are in truth different, therefore these maxims
are made use of to support those which in sound and appearance are
contradictory propositions; and is clear in the demonstrations above
mentioned about a vacuum. So that whilst men take words for things,
as usually they do, these maxims may and do commonly serve to prove
contradictory propositions; as shall yet be further made manifest]
16. Instance in demonstrations about Man which can only be verbal.
For instance: let MAN be that concerning which you would by these first
principles demonstrate anything, and we shall see, that so far as
demonstration is by these principles, it is only verbal, and gives us
no certain, universal, true proposition, or knowledge, of any being
existing without us. First, a child having framed the idea of a man, it
is probable that his idea is just like that picture which the
painter makes of the visible appearances joined together; and such a
complication of ideas together in his understanding makes up the single
complex idea which he calls man, whereof white or flesh-colour in
England being one, the child can demonstrate to you that a negro is not
a man, because white colour was one of the constant simple ideas of the
complex idea he calls man; and therefore he can demonstrate, by the
principle, IT IS IMPOSSIBLE FOR THE SAME THING TO BE AND NOT TO BE, that
a negro is NOT a man; the foundation of his certainty being not that
universal proposition, which perhaps he never heard nor thought of, but
the clear, distinct perception he hath of his own simple ideas of black
and white, which he cannot be persuaded to take, nor can ever mistake
one for another, whether he knows that maxim or no. And to this child,
or any one who hath such an idea, which he calls man, can you never
demonstrate that a man hath a soul, because his idea of man includes no
such notion or idea in it. And therefore, to him, the principle of WHAT
IS, IS, proves not this matter; but it depends upon collection and
observation, by which he is to make his complex idea called man.
17. Another instance.
Secondly, Another that hath gone further in framing and collecting the
idea he calls MAN, and to the outward shape adds laughter and rational
discourse, may demonstrate that infants and changelings are no men, by
this maxim, IT IS IMPOSSIBLE FOR THE SAME THING TO BE AND NOT TO BE; and
I have discoursed with very rational men, who have actually denied that
they are men.
18. A third instance.
Thirdly, Perhaps another makes up the complex idea which he calls MAN,
only out of the ideas of body in general, and the powers of language and
reason, and leaves out the shape wholly: this man is able to demonstrate
that a man may have no hands, but be QUADRUPES, neither of those being
included in his idea of man: and in whatever body or shape he found
speech and reason joined, that was a man; because, having a clear
knowledge of such a complex idea, it is certain that WHAT IS, IS.
19. Little use of these Maxims in Proofs where we have clear and
distinct Ideas.
So that, if rightly considered, I think we may say, That where our ideas
are determined in our minds, and have annexed to them by us known and
steady names under those settled determinations, there is little need,
or no use at all of these maxims, to prove the agreement or disagreement
of any of them. He that cannot discern the truth or falsehood of such
propositions, without the help of these and the like maxims, will not be
helped by these maxims to do it: since he cannot be supposed to know the
truth of these maxims themselves without proof, if he cannot know the
truth of others without proof, which are as self-evident as these. Upon
this ground it is that intuitive knowledge neither requires nor admits
any proof, one part of it more than another. He that will suppose it
does, takes away the foundation of all knowledge and certainty; and he
that needs any proof to make him certain, and give his assent to this
proposition, that two are equal to two, will also have need of a proof
to make him admit, that what is, is. He that needs a probation to
convince him that two are not three, that white is not black, that a
triangle is not a circle, &c., or any other two [determined] distinct
ideas are not one and the same, will need also a demonstration to
convince him that IT IS IMPOSSIBLE FOR THE SAME THING TO BE AND NOT TO
BE.
20. Their Use dangerous where our Ideas are not determined
And as these maxims are of little use where we have determined ideas, so
they are, as I have showed, of dangerous use where [our ideas are not
determined; and where] we use words that are not annexed to determined
ideas, but such as are of a loose and wandering signification, sometimes
standing for one, and sometimes for another idea: from which follow
mistake and error, which these maxims (brought as proofs to establish
propositions, wherein the terms stand for undetermined ideas) do by
their authority confirm and rivet.