Books: A Treatise Concerning the Principles of Human Knowledge

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125. He whose understanding is possessed with the doctrine of abstract
general ideas may be persuaded that (whatever be thought of the ideas of
sense) extension in abstract is infinitely divisible. And one who thinks
the objects of sense exist without the mind will perhaps in virtue
thereof be brought to admit that a line but an inch long may contain
innumerable parts--really existing, though too small to be discerned.
These errors are grafted as well in the minds of geometricians as of
other men, and have a like influence on their reasonings; and it were no
difficult thing to show how the arguments from Geometry made use of to
support the infinite divisibility of extension are bottomed on them. At
present we shall only observe in general whence it is the mathematicians
are all so fond and tenacious of that doctrine.

126. It has been observed in another place that the theorems and
demonstrations in Geometry are conversant about universal ideas (sect.
15, Introd.); where it is explained in what sense this ought to be
understood, to wit, the particular lines and figures included in the
diagram are supposed to stand for innumerable others of different sizes;
or, in other words, the geometer considers them abstracting from their
magnitude--which does not imply that he forms an abstract idea, but only
that he cares not what the particular magnitude is, whether great or
small, but looks on that as a thing different to the demonstration. Hence
it follows that a line in the scheme but an inch long must be spoken of
as though it contained ten thousand parts, since it is regarded not in
itself, but as it is universal; and it is universal only in its
signification, whereby it represents innumerable lines greater than
itself, in which may be distinguished ten thousand parts or more, though
there may not be above an inch in it. After this manner, the properties
of the lines signified are (by a very usual figure) transferred to the
sign, and thence, through mistake, though to appertain to it considered
in its own nature.

127. Because there is no number of parts so great but it is possible
there may be a line containing more, the inch-line is said to contain
parts more than any assignable number; which is true, not of the inch
taken absolutely, but only for the things signified by it. But men, not
retaining that distinction in their thoughts, slide into a belief that
the small particular line described on paper contains in itself parts
innumerable. There is no such thing as the ten--thousandth part of an
inch; but there is of a mile or diameter of the earth, which may be
signified by that inch. When therefore I delineate a triangle on paper,
and take one side not above an inch, for example, in length to be the
radius, this I consider as divided into 10,000 or 100,000 parts or more;
for, though the ten-thousandth part of that line considered in itself is
nothing at all, and consequently may be neglected without an error or
inconveniency, yet these described lines, being only marks standing for
greater quantities, whereof it may be the ten--thousandth part is very
considerable, it follows that, to prevent notable errors in practice, the
radius must be taken of 10,000 parts or more.

128. LINES WHICH ARE INFINITELY DIVISIBLE.--From what has been said
the reason is plain why, to the end any theorem become universal in
its use, it is necessary we speak of the lines described on paper
as though they contained parts which really they do not. In doing
of which, if we examine the matter thoroughly, we shall perhaps
discover that we cannot conceive an inch itself as consisting of,
or being divisible into, a thousand parts, but only some other line which
is far greater than an inch, and represented by it; and that when we say
a line is infinitely divisible, we must mean a line which is infinitely
great. What we have here observed seems to be the chief cause why, to
suppose the infinite divisibility of finite extension has been thought
necessary in geometry.

129. The several absurdities and contradictions which flowed from this
false principle might, one would think, have been esteemed so many
demonstrations against it. But, by I know not what logic, it is held that
proofs a posteriori are not to be admitted against propositions relating
to infinity, as though it were not impossible even for an infinite mind
to reconcile contradictions; or as if anything absurd and repugnant could
have a necessary connexion with truth or flow from it. But, whoever
considers the weakness of this pretence will think it was contrived on
purpose to humour the laziness of the mind which had rather acquiesce in
an indolent scepticism than be at the pains to go through with a severe
examination of those principles it has ever embraced for true.

130. Of late the speculations about Infinities have run so high, and
grown to such strange notions, as have occasioned no small scruples and
disputes among the geometers of the present age. Some there are of great
note who, not content with holding that finite lines may be divided into
an infinite number of parts, do yet farther maintain that each of those
infinitesimals is itself subdivisible into an infinity of other parts or
infinitesimals of a second order, and so on ad infinitum. These, I say,
assert there are infinitesimals of infinitesimals of infinitesimals, &c.,
without ever coming to an end; so that according to them an inch does not
barely contain an infinite number of parts, but an infinity of an
infinity of an infinity ad infinitum of parts. Others there be who hold
all orders of infinitesimals below the first to be nothing at all;
thinking it with good reason absurd to imagine there is any positive
quantity or part of extension which, though multiplied infinitely, can
never equal the smallest given extension. And yet on the other hand it
seems no less absurd to think the square, cube or other power of a
positive real root, should itself be nothing at all; which they who hold
infinitesimals of the first order, denying all of the subsequent orders,
are obliged to maintain.

131. OBJECTION OF MATHEMATICIANS.--ANSWER.--Have we not therefore
reason to conclude they are both in the wrong, and that there is
in effect no such thing as parts infinitely small, or an infinite
number of parts contained in any finite quantity? But you will
say that if this doctrine obtains it will follow the very foundations
of Geometry are destroyed, and those great men who have raised
that science to so astonishing a height, have been all the while
building a castle in the air. To this it may be replied that whatever is
useful in geometry, and promotes the benefit of human life, does still
remain firm and unshaken on our principles; that science considered as
practical will rather receive advantage than any prejudice from what has
been said. But to set this in a due light may be the proper business of
another place. For the rest, though it should follow that some of the
more intricate and subtle parts of Speculative Mathematics may be pared
off without any prejudice to truth, yet I do not see what damage will be
thence derived to mankind. On the contrary, I think it were highly to be
wished that men of great abilities and obstinate application would draw
off their thoughts from those amusements, and employ them in the study of
such things as lie nearer the concerns of life, or have a more direct
influence on the manners.

132. SECOND OBJECTION OF MATHEMATICIANS.--ANSWER.--If it be said
that several theorems undoubtedly true are discovered by methods
in which infinitesimals are made use of, which could never have
been if their existence included a contradiction in it; I answer
that upon a thorough examination it will not be found that in any
instance it is necessary to make use of or conceive infinitesimal parts
of finite lines, or even quantities less than the minimum sensible; nay,
it will be evident this is never done, it being impossible.

133. IF THE DOCTRINE WERE ONLY AN HYPOTHESIS IT SHOULD BE RESPECTED
FOR ITS CONSEQUENCES.--By what we have premised, it is plain that very
numerous and important errors have taken their rise from those false
Principles which were impugned in the foregoing parts of this treatise;
and the opposites of those erroneous tenets at the same time appear to be
most fruitful Principles, from whence do flow innumerable consequences
highly advantageous to true philosophy. as well as to religion.
Particularly Matter, or the absolute existence of corporeal objects, has
been shown to be that wherein the most avowed and pernicious enemies of
all knowledge, whether human or divine, have ever placed their chief
strength and confidence. And surely, if by distinguishing the real
existence of unthinking things from their being perceived, and allowing
them a subsistance of their own out of the minds of spirits, no one thing
is explained in nature, but on the contrary a great many inexplicable
difficulties arise; if the supposition of Matter is barely precarious, as
not being grounded on so much as one single reason; if its consequences
cannot endure the light of examination and free inquiry, but screen
themselves under the dark and general pretence of "infinites being
incomprehensible"; if withal the removal of this Matter be not attended
with the least evil consequence; if it be not even missed in the world,
but everything as well, nay much easier conceived without it; if, lastly,
both Sceptics and Atheists are for ever silenced upon supposing only
spirits and ideas, and this scheme of things is perfectly agreeable both
to Reason and Religion: methinks we may expect it should be admitted and
firmly embraced, though it were proposed only as an hypothesis, and the
existence of Matter had been allowed possible, which yet I think we have
evidently demonstrated that it is not.

134. True it is that, in consequence of the foregoing principles, several
disputes and speculations which are esteemed no mean parts of learning,
are rejected as useless. But, how great a prejudice soever against our
notions this may give to those who have already been deeply engaged, and
make large advances in studies of that nature, yet by others we hope it
will not be thought any just ground of dislike to the principles and
tenets herein laid down, that they abridge the labour of study, and make
human sciences far more clear, compendious and attainable than they were
before.

135. Having despatched what we intended to say concerning the knowledge
of IDEAS, the method we proposed leads us in the next place to treat of
SPIRITS--with regard to which, perhaps, human knowledge is not so
deficient as is vulgarly imagined. The great reason that is assigned for
our being thought ignorant of the nature of spirits is our not having an
idea of it. But, surely it ought not to be looked on as a defect in a
human understanding that it does not perceive the idea of spirit, if it
is manifestly impossible there should be any such idea. And this if I
mistake not has been demonstrated in section 27; to which I shall here
add that a spirit has been shown to be the only substance or support
wherein unthinking beings or ideas can exist; but that this substance
which supports or perceives ideas should itself be an idea or like an
idea is evidently absurd.

136. OBJECTION.--ANSWER.--It will perhaps be said that we want a sense
(as some have imagined) proper to know substances withal, which,
if we had, we might know our own soul as we do a triangle. To this
I answer, that, in case we had a new sense bestowed upon us, we
could only receive thereby some new sensations or ideas of sense.
But I believe nobody will say that what he means by the terms soul
and substance is only some particular sort of idea or sensation.
We may therefore infer that, all things duly considered, it is
not more reasonable to think our faculties defective, in that they do not
furnish us with an idea of spirit or active thinking substance, than it
would be if we should blame them for not being able to comprehend a round
square.

137. From the opinion that spirits are to be known after the manner of an
idea or sensation have risen many absurd and heterodox tenets, and much
scepticism about the nature of the soul. It is even probable that this
opinion may have produced a doubt in some whether they had any soul at
all distinct from their body since upon inquiry they could not find they
had an idea of it. That an idea which is inactive, and the existence
whereof consists in being perceived, should be the image or likeness of
an agent subsisting by itself, seems to need no other refutation than
barely attending to what is meant by those words. But, perhaps you will
say that though an idea cannot resemble a spirit in its thinking, acting,
or subsisting by itself, yet it may in some other respects; and it is not
necessary that an idea or image be in all respects like the original.

138. I answer, if it does not in those mentioned, it is impossible it
should represent it in any other thing. Do but leave out the power of
willing, thinking, and perceiving ideas, and there remains nothing else
wherein the idea can be like a spirit. For, by the word spirit we mean
only that which thinks, wills, and perceives; this, and this alone,
constitutes the signification of the term. If therefore it is impossible
that any degree of those powers should be represented in an idea, it is
evident there can be no idea of a spirit.

139. But it will be objected that, if there is no idea signified by the
terms soul, spirit, and substance, they are wholly insignificant, or have
no meaning in them. I answer, those words do mean or signify a real
thing, which is neither an idea nor like an idea, but that which
perceives ideas, and wills, and reasons about them. What I am myself,
that which I denote by the term I, is the same with what is meant by soul
or spiritual substance. If it be said that this is only quarreling at a
word, and that, since the immediately significations of other names are
by common consent called ideas, no reason can be assigned why that which
is signified by the name spirit or soul may not partake in the same
appellation. I answer, all the unthinking objects of the mind agree in
that they are entirely passive, and their existence consists only in
being perceived; whereas a soul or spirit is an active being, whose
existence consists, not in being perceived, but in perceiving ideas and
thinking. It is therefore necessary, in order to prevent equivocation and
confounding natures perfectly disagreeing and unlike, that we distinguish
between spirit and idea. See sect. 27.

140. OUR IDEA OF SPIRIT.--In a large sense, indeed, we may be said
to have an idea or rather a notion of spirit; that is, we understand
the meaning of the word, otherwise we could not affirm or deny
anything of it. Moreover, as we conceive the ideas that are in the
minds of other spirits by means of our own, which we suppose to be
resemblances of them; so we know other spirits by means of our own
soul--which in that sense is the image or idea of them; it having
a like respect to other spirits that blueness or heat by me perceived
has to those ideas perceived by another.

141. THE NATURAL IMMORTALITY OF THE SOUL IS A NECESSARY CONSEQUENCE
OF THE FOREGOING DOCTRINE.--It must not be supposed that they who
assert the natural immortality of the soul are of opinion that it
is absolutely incapable of annihilation even by the infinite power
of the Creator who first gave it being, but only that it is not
liable to be broken or dissolved by the ordinary laws of nature
or motion. They indeed who hold the soul of man to be only a thin
vital flame, or system of animal spirits, make it perishing and
corruptible as the body; since there is nothing more easily dissipated
than such a being, which it is naturally impossible should survive
the ruin of the tabernacle wherein it is enclosed. And this notion
has been greedily embraced and cherished by the worst part of mankind,
as the most effectual antidote against all impressions of virtue
and religion. But it has been made evident that bodies, of what frame or
texture soever, are barely passive ideas in the mind, which is more
distant and heterogeneous from them than light is from darkness. We have
shown that the soul is indivisible, incorporeal, unextended, and it is
consequently incorruptible. Nothing can be plainer than that the motions,
changes, decays, and dissolutions which we hourly see befall natural
bodies (and which is what we mean by the course of nature) cannot
possibly affect an active, simple, uncompounded substance; such a being
therefore is indissoluble by the force of nature; that is to say, "the
soul of man is naturally immortal."

142. After what has been said, it is, I suppose, plain that our souls are
not to be known in the same manner as senseless, inactive objects, or by
way of idea. Spirits and ideas are things so wholly different, that when
we say "they exist," "they are known," or the like, these words must not
be thought to signify anything common to both natures. There is nothing
alike or common in them: and to expect that by any multiplication or
enlargement of our faculties we may be enabled to know a spirit as we do
a triangle, seems as absurd as if we should hope to see a sound. This is
inculcated because I imagine it may be of moment towards clearing several
important questions, and preventing some very dangerous errors concerning
the nature of the soul. We may not, I think, strictly be said to have an
idea of an active being, or of an action, although we may be said to have
a notion of them. I have some knowledge or notion of my mind, and its
acts about ideas, inasmuch as I know or understand what is meant by these
words. What I know, that I have some notion of. I will not say that the
terms idea and notion may not be used convertibly, if the world will have
it so; but yet it conduceth to clearness and propriety that we
distinguish things very different by different names. It is also to be
remarked that, all relations including an act of the mind, we cannot so
properly be said to have an idea, but rather a notion of the relations
and habitudes between things. But if, in the modern way, the word idea is
extended to spirits, and relations, and acts, this is, after all, an
affair of verbal concern.

143. It will not be amiss to add, that the doctrine of abstract ideas has
had no small share in rendering those sciences intricate and obscure
which are particularly conversant about spiritual things. Men have
imagined they could frame abstract notions of the powers and acts of the
mind, and consider them prescinded as well from the mind or spirit
itself, as from their respective objects and effects. Hence a great
number of dark and ambiguous terms, presumed to stand for abstract
notions, have been introduced into metaphysics and morality, and from
these have grown infinite distractions and disputes amongst the learned.

144. But, nothing seems more to have contributed towards engaging men in
controversies and mistakes with regard to the nature and operations of
the mind, than the being used to speak of those things in terms borrowed
from sensible ideas. For example, the will is termed the motion of the
soul; this infuses a belief that the mind of man is as a ball in motion,
impelled and determined by the objects of sense, as necessarily as that
is by the stroke of a racket. Hence arise endless scruples and errors of
dangerous consequence in morality. All which, I doubt not, may be
cleared, and truth appear plain, uniform, and consistent, could but
philosophers be prevailed on to retire into themselves, and attentively
consider their own meaning.

145. KNOWLEDGE OF SPIRITS NOT IMMEDIATE.--From what has been said,
it is plain that we cannot know the existence of other spirits
otherwise than by their operations, or the ideas by them excited
in us. I perceive several motions, changes, and combinations of ideas,
that inform me there are certain particular agents, like myself,
which accompany them and concur in their production. Hence, the
knowledge I have of other spirits is not immediate, as is the
knowledge of my ideas; but depending on the intervention of ideas, by me
referred to agents or spirits distinct from myself, as effects or
concomitant signs.

146. But, though there be some things which convince us human agents are
concerned in producing them; yet it is evident to every one that those
things which are called the Works of Nature, that is, the far greater
part of the ideas or sensations perceived by us, are not produced by, or
dependent on, the wills of men. There is therefore some other Spirit that
causes them; since it is repugnant that they should subsist by
themselves. See sect. 29. But, if we attentively consider the constant
regularity, order, and concatenation of natural things, the surprising
magnificence, beauty, and perfection of the larger, and the exquisite
contrivance of the smaller parts of creation, together with the exact
harmony and correspondence of the whole, but above all the
never-enough-admired laws of pain and pleasure, and the instincts or
natural inclinations, appetites, and passions of animals; I say if we
consider all these things, and at the same time attend to the meaning and
import of the attributes One, Eternal, Infinitely Wise, Good, and
Perfect, we shall clearly perceive that they belong to the aforesaid
Spirit, "who works all in all," and "by whom all things consist."

147. THE EXISTENCE OF GOD MORE EVIDENT THAN THAT OF MAN.--Hence,
it is evident that God is known as certainly and immediately as
any other mind or spirit whatsoever distinct from ourselves. We may
even assert that the existence of God is far more evidently perceived
than the existence of men; because the effects of nature are infinitely
more numerous and considerable than those ascribed to human agents. There
is not any one mark that denotes a man, or effect produced by him, which
does not more strongly evince the being of that Spirit who is the Author
of Nature. For, it is evident that in affecting other persons the will of
man has no other object than barely the motion of the limbs of his body;
but that such a motion should be attended by, or excite any idea in the
mind of another, depends wholly on the will of the Creator. He alone it
is who, "upholding all things by the word of His power," maintains that
intercourse between spirits whereby they are able to perceive the
existence of each other. And yet this pure and clear light which
enlightens every one is itself invisible.

148. It seems to be a general pretence of the unthinking herd that they
cannot see God. Could we but see Him, say they, as we see a man, we
should believe that He is, and believing obey His commands. But alas, we
need only open our eyes to see the Sovereign Lord of all things, with a
more full and clear view than we do any one of our fellow--creatures. Not
that I imagine we see God (as some will have it) by a direct and
immediate view; or see corporeal things, not by themselves, but by seeing
that which represents them in the essence of God, which doctrine is, I
must confess, to me incomprehensible. But I shall explain my meaning;--A
human spirit or person is not perceived by sense, as not being an idea;
when therefore we see the colour, size, figure, and motions of a man, we
perceive only certain sensations or ideas excited in our own minds; and
these being exhibited to our view in sundry distinct collections, serve
to mark out unto us the existence of finite and created spirits like
ourselves. Hence it is plain we do not see a man--if by man is meant that
which lives, moves, perceives, and thinks as we do--but only such a
certain collection of ideas as directs us to think there is a distinct
principle of thought and motion, like to ourselves, accompanying and
represented by it. And after the same manner we see God; all the
difference is that, whereas some one finite and narrow assemblage of
ideas denotes a particular human mind, whithersoever we direct our view,
we do at all times and in all places perceive manifest tokens of the
Divinity: everything we see, hear, feel, or anywise perceive by sense,
being a sign or effect of the power of God; as is our perception of those
very motions which are produced by men.

149. It is therefore plain that nothing can be more evident to any one
that is capable of the least reflexion than the existence of God, or a
Spirit who is intimately present to our minds, producing in them all that
variety of ideas or sensations which continually affect us, on whom we
have an absolute and entire dependence, in short "in whom we live, and
move, and have our being." That the discovery of this great truth, which
lies so near and obvious to the mind, should be attained to by the reason
of so very few, is a sad instance of the stupidity and inattention of
men, who, though they are surrounded with such clear manifestations of
the Deity, are yet so little affected by them that they seem, as it were,
blinded with excess of light.

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