our thought is an _idea_ existing only in the mind; and consequently each
part thereof must be perceived. If, therefore, I cannot _perceive_
innumerable parts in any finite extension that I consider, it is certain
they are not contained in it. But it is evident that I cannot distinguish
innumerable parts in any particular line, surface, or solid, which I
either perceive by sense, or figure to myself in my mind. Wherefore I
conclude they are not contained in it. Nothing can be plainer to me than
that the extensions I have in view are no other than my own ideas; and it
is no less plain that I cannot resolve any one of my ideas into an
infinite number of other ideas; that is, that they are not infinitely
divisible(727). If by _finite extension_ be meant something distinct from
a finite idea, I declare I do not know what that is, and so cannot affirm
or deny anything of it. But if the terms _extension_, _parts_, and the
like, are taken in any sense conceivable—that is, for _ideas_,—then to say
a finite quantity or extension consists of parts infinite in number is so
manifest and glaring a contradiction, that every one at first sight
acknowledges it to be so. And it is impossible it should ever gain the
assent of any reasonable creature who is not brought to it by gentle and
slow degrees, as a converted Gentile(728) to the belief of
transubstantiation. Ancient and rooted prejudices do often pass into
principles. And those propositions which once obtain the force and credit
of a _principle_, are not only themselves, but likewise whatever is
deducible from them, thought privileged from all examination. And there is
no absurdity so gross, which, by this means, the mind of man may not be
prepared to swallow(729).
125. He whose understanding is prepossessed 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(730) 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 shew how the arguments from Geometry made use of to support the
infinite divisibility of extension are bottomed on them. [(731) But this,
if it be thought necessary, we may hereafter find a proper place to treat
of in a particular manner.] 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
doth 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 indifferent 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, thought 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 any 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. From what has been said the reason is plain why, to the end any
theorem may 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 throughly, 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(732) _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 Infinites 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,
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 ever 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. 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,[(733) and shew how lines and figures may be
measured, and their properties investigated, without supposing finite
extension to be infinitely divisible,] may be the proper business of
another place(734). 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(735) 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. 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 sensibile_: nay, it will
be evident this is never done, it being impossible. [(736) And whatever
mathematicians may think of Fluxions, or the Differential Calculus, and
the like, a little reflexion will shew them that, in working by those
methods, they do not conceive or imagine lines or surfaces less than what
are perceivable to sense. They may indeed call those little and almost
insensible quantities Infinitesimals, or Infinitesimals of Infinitesimals,
if they please. But at bottom this is all, they being in truth finite; nor
does the solution of problems require the supposing any other. But this
will be more clearly made out hereafter.]
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133. By what we have hitherto said, 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_(737)_ existence of corporeal objects_, hath
been shewn 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 subsistence 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(738) 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 [(739) and in effect conversant about nothing at all].
But how great a prejudice soever against our notions this may give to
those who have already been deeply engaged, and made 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 more clear,
compendious, and attainable than they were before.
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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_(740): 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 shewn 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. It will perhaps be said that we want a _sense_ (as some have
imagined(741)) 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_(742).
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 that term. If therefore it is impossible
that any degree of those powers should be represented in an idea [(743)or
notion], it is evident there can be no idea [or notion] 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_. [(744)But if I should say that _I_ was nothing, or
that _I_ was an _idea_ or _notion_, nothing could be more evidently absurd
than either of these propositions.] If it be said that this is only
quarrelling at a word, and that, since the immediate 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(745). 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. In a large sense indeed, we may be said to have an idea [(746)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(747).
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141. [(748)The natural immortality of the soul is a necessary consequence
of the foregoing doctrine. But before we attempt to prove this, it is fit
that we explain the meaning of that tenet.] It must not be supposed that
they who assert the natural immortality of the soul(749) 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 inclosed. And this notion hath 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 hath 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(750). We have shewn 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 befal 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_(751).
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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(752). 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.
[(753)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(754), 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(755), 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(756).
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 [(757)depart from some received prejudices and modes of
speech, and] retire into themselves, and attentively consider their own
meaning. [(758)But the difficulties arising on this head demand a more
particular disquisition than suits with the design of this treatise.]
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145. From what hath 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(759).
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(760) 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 the 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.”