The Hume Archives
A Treatise of Human Nature
Book I
David Hume
1739
|
11/20/96
Copyright 1996, James Fieser (jfieser@utm.edu). This text file
was scanned from Green and Grose's 1886 edition of Hume's Treatise.
The file has not yet been completely cleaned of errors and should
be considered inaccurate. The file contains all of Book I (with
about five pages missing, and minus all footnotes) and the first
few sections of Book II. This file is posted here as a courtesy
to Hume Archives patrons until a more accurate and complete file
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and Grose edition.
A TREATISE OF HUMAN NATURE
CONTENTS
BOOK 1: OF THE UNDERSTANDING.
PART 1: OF IDEAS, THEIR ORIGIN, COMPOSITION, ABSTRACTION, CONNEXION,
ETC.
Of the Origin of our Ideas {1:311}
Division of the Subject {1:316}
Of the Ideas of the Memory and Imagination {1:317}
Of the Connexion or Association of Ideas {1:319}
Of Relations {1:322}
Of Modes and Substances {1:394}
Of Abstract Ideas {1:325}
PART 2: OF THE IDEAS OF SPACE AND TIME
Of the Infinite Divisibility of our Ideas of Space and Time {1:334}
Of the Infinite Divisibility of Space and Time . {1:336}
Of the other Qualities of our Ideas of Space and Time {1:340}
Objections answered {1:345}
The same subject continu'd {1:358}
Of the Idea of Existence and of External Existence {1:369}
PART 3: OF KNOWLEDGE AND PROBABILITY.
Of Knowledge {1:372}}
Of Probability; and of the Idea of Cause and effect {1:375}
Why a Cause is always Necessary {1:380}
Of the Component Parts of our reasonings Concerning Cause and
Effect {1:384}
Of the Impressions of the Senses and Memory {1:385}
Of the Inference from the Impression to the Idea {1:388}
Of the Nature of the Idea, or Belief {1:394}
Of the Causes of Belief {1:399}
Of the Effects of other Relations, and other Habits {1:406}
Of the Influence of Belief {1:416}
Of the Probability of Chances {1:423,}
Of the Probability of Causes {1:428}
Of Unphilosophical Probability. {1:439}
Of the Idea of Necessary Connexion {1:450}
Rules by which to judge of Causes and Effects {1:466}
Of the Reason of Animals {1:409}
PART 4: OF THE SCEPTICAL AND OTHER SYSTEMS OF PHILOSOPHY.
Of Scepticism with regard to Reason {1:472}
Of Scepticism with regard to the Senses {1:478}
Of the Antient Philosophy {1:505}
Of the modern Philosophy {1:510}
Of the Immateriality of the Soul {1:516}
Of Personal Identity {1:533}
Conclusion of this Book {1:544}
BOOK 2: OF THE PASSIONS.
PART 1: OF PRIDE AND HUMILITY.
Division of the Subject {2:75}
Of Pride and Humility; their Objects and Causes {2:77}
Whence these Objects and Causes are Deriv'd {2:79}
Of the Relations of Impressions and Ideas {2:81}
Of the Influence of these Relations on Pride and Humility {2:83}
Limitations of this System {2:88}
Of Vice and Virtue {2:92}
Of Beauty and Deformity {2:95}
Of External Advantages and Disadvantages {2:99}
Of Property and Riches {2:105}
Of the Love of Fame {2:110}
Of the Pride and Humility of Animals {2:118}
PART 2: OF LOVE AND HATRED.
Of the Object and Causes of Love and Hatred {2:121}
Experiments to Confirm this System {2:124}
Difficulties {2:137}
Of the Love of Relations {2:140}
Of our Esteem for the Rich and Powerful {2:145}
Of Benevolence and Anger {2:152}
Of Compassion {2:155}
Of Malice and Envy {2:158}
Of the Mixture of Benevolence and Anger with Compassion and Malice
{2:165}
Of Respect and Contempt {2:173}
Of the Amorous Passion, or Love betwixt the Sexes {2:176}
Of the Love and Hatred of Animals {2:179}
PART 3: OF THE WILL AND DIRECT PASSIONS.
Of Liberty and Necessity {2:181}
The same Subject continu'd {2:188}
Of the Influencing Motives of the Will {2:193}
Of the Causes of the Violent Passions {2:198}
Of the Effects of Custom {2:201}
Of the Influence of the Imagination on the Passions {2:202}
Of Contiguity and Distance in Space and Time {2:205}
The same Subject continued {2:209}
Of the Direct Passions {2:214}
Of Curiosity, or the Love of Truth {2:223}
BOOK 3: OF MORALS.
PART 1: OF VIRTUE AND VICE IN GENERAL.
Moral Distinctions not deriv'd from on {2:233}
Moral distinctions deriv'd from a moral sense {2:246}
PART II: OF JUSTICE AND INJUSTICE.
Justice, whether a natural or artificial virtue {2:252}
Of the origin of justice and property {2:258}
Of the Rules, which determine Property {2:273}
Of the transference of property by consent {2:283}
Of the obligation of promises {2:284}
Some farther reflections concerning justice and injustice {2:293}
Of the origin of government {2:300}
Of the source of allegiance {2:304}
Of the measures of allegiance {2:313}
Of the objects of allegiance {2:317}
Of the laws of nations {2:328}
Of chastity and modesty {2:330}
PART III: OF THE OTHER VIRTUES AND VICES.
Of the origin of the natural virtues and vices {2:334}
Of greatness of mind {2:349}
Of goodness and benevolence {2:358}
Of natural abilities {2:361}
Some farther reflections concerning the natural virtues {2:368}
Conclusion of this book {2:371}
A
T R E A T I S E
OF
Human Nature:
BEING
An A/TTEMPT\ to introduce the experimental
Method of Reasoning
I N T 0
MORAL SUBJECTS.
Rara temporum felicitas, ubi sentire, quae belis; & quae sentias,
decere licet.
T/ACIT\.
VOL. 1.
OF THE
U N D E R S T A N D I N G.
ADVERTISEMENT.
My design in the present work is sufficiently explain'd in the
Introduction. The reader must only observe, that all the subjects
I have there plann'd out to myself, are not treated of in these
two volumes. The subjects of the Understanding and Passions make
a compleat chain of reasoning by themselves; and I was willing
to take advantage of this natural division, in order to try the
taste of the public. If I have the good fortune to meet with success,
I shall proceed to the examination of Morals, Politics, and Criticism;
which will compleat this Treatise of Human Nature. The approbation
of the public I consider as the greatest reward of my labours;
but am determin'd to regard its judgment, whatever it be, as my
best instruction.
INTRODUCTION.
N/OTHING\ is more usual and more natural for those, who pretend
to discover anything new to the world in philosophy and the sciences,
than to insinuate the praises of their own systems, by decrying
all those, which have been advanced before them. And indeed were
they content with lamenting that ignorance, which we still lie
under in the most important questions, that can come before the
tribunal of human reason, there are few, who have an acquaintance
with the sciences, that would not readily agree with them. 'Tis
easy for one of judgment and learning, to perceive the weak foundation
even of those systems, which have obtained the greatest credit,
and have carried their pretensions highest to accurate and profound
reasoning. Principles taken upon trust, consequences lamely deduced
from them, want of coherence in the parts, and of evidence in
the whole, these are every where to be met with in the systems
of the most eminent philosophers, and seem to have drawn disgrace
upon philosophy itself.
Nor is there requir'd such profound knowledge to discover the
present imperfect condition of the sciences, but even the rabble
without doors may, judge from the noise and clamour, which they
hear, that all goes not well within. There is nothing which is
not the subject of debate, and in which men of learning are not
of contrary opinions. The most {1:306} trivial question escapes
not our controversy, and in the most momentous we are not able
to give any certain decision. Disputes are multiplied, as if every
thing was uncertain; and these disputes are managed with the greatest
warmth, as if every thing was certain. Amidst all this bustle
'tis not. reason, which carries the prize, but eloquence; and
no man needs ever despair of gaining proselytes to the most extravagant
hypothesis, who has art enough to represent it in any favourable
colours. The victory is not gained by the men at arms, who manage
the pike and the sword; but by the trumpeters, drummers, and musicians
of the army.
From hence in my opinion arises that common prejudice against
metaphysical reasonings of all kinds, even amongst those, who
profess themselves scholars, and have a just value for every other
part of literature. By metaphysical reasonings, they do not understand
those on any particular branch of science, but every kind of argument,
which is any way abstruse, and requires some attention to be comprehended.
We have so often lost our labour in such researches, that we commonly
reject them without hesitation, and resolve, if we must for ever
be a prey to errors and delusions, that they shall at least be
natural and entertaining. And indeed nothing but the most determined
scepticism, along with a great degree of indolence, can justify
this aversion to metaphysics. For if truth be at all within the
reach of human capacity, 'tis certain it must lie very deep and
abstruse: and to hope we shall arrive at it without pains, while
the greatest geniuses have failed with the utmost pains, must
certainly be esteemed sufficiently vain and presumptuous. I pretend
to no such advantage in the philosophy I am going to unfold, and
would esteem it a strong presumption against it, were it so very
easy and obvious.
'Tis evident,, that all the sciences have a relation, greater
or less, to human nature: and that however wide any of them may
seem to run from it, they still return back by one passage or
another. Even. Mathematics, Natural Philosophy, and Natural Religion,
are in some measure dependent on the science of M/AN\; since the
lie under the cognizance of men, and are judged of by their powers
and faculties. 'Tis impossible to tell what changes and improvements
we might make in these sciences were we thoroughly acquainted
with {1:307} the extent and force of human understanding, and
cou'd explain the nature of the ideas we employ, and of the operations
we perform in our reasonings. And these improvements are the more
to be hoped for in natural religion, as it is not content with
instructing us in the nature of superior powers, but carries its
views farther, to their disposition towards us, and our duties
towards them; and consequently we ourselves are not only the beings,
that reason, but also one of the objects, concerning which we
reason.
If therefore the sciences of Mathematics, Natural Philosophy,
and Natural Religion, have such a dependence on the knowledge
of man, what may be expected in the other sciences, whose connexion
with human nature is more close and intimate? The sole end of
logic is to explain the principles and operations of our reasoning
faculty, and the nature of our ideas: morals and criticism regard
our tastes and sentiments: and politics consider men as united
in society, and dependent on each other. In these four sciences
of Logic, Morals, Criticism, and Politics, is comprehended almost
everything, which it can any way import us to be acquainted with,
or which can tend either to the improvement or ornament of the
human mind.
Here then is the only expedient, from which we can hope for success
in our philosophical researches, to leave the tedious lingering
method, which we have hitherto followed, and instead of taking
now and then a castle or village on the frontier, to march up
directly to the capital or center of these sciences, to human
nature itself; which being once masters of, we may every where
else hope for an easy victory. From this station we may extend
our conquests over all those sciences, which more intimately concern
human life, and may afterwards proceed at leisure to discover
more fully those, which are the objects of pore curiosity. There
is no question of importance, whose decision is not compriz'd
in the science of man; and there is none, which can be decided
with any certainty, before we become acquainted with that science.
In pretending, therefore, to explain the principles of human nature,
we in effect propose a compleat system of the sciences, built
on a foundation almost entirely new, and the only one upon which
they can stand with any security.
And as the science of man is the-only solid foundation for {1:308}
the other sciences, so the only solid foundation we can (live
to this science itself must be laid on experience and observation.
'Tis no astonishing reflection to consider, that the application
of experimental philosophy to moral subjects should come after
that to natural at the distance of above a whole century; since
we find in fact, that there was about the same interval betwixt
the origins of these sciences; and that reckoning from T/HALES\
to SOCRATES, the space of time is nearly equal to that betwixt,
my Lord Bacon and some late philosophers in England, who have
begun to put the science of man on a new footing, and have engaged
the attention, and excited the curiosity of the public. So true
it is, that however other nations may rival us in poetry, and
excel us in some other agreeable arts, the improvements in reason
and philosophy can only be owing to a land of toleration and of
liberty.
Nor ought we to think, that this latter improvement in the science
of man will do less honour to our native country than the former
in natural philosophy, but ought rather to esteem it a greater
glory, upon account of the greater importance of that science,
as well as the necessity it lay under of such a reformation. For
to me it seems evident, that the essence of the mind being equally
unknown to us with that of external bodies, it must be equally
impossible to form any notion of its powers and qualities otherwise
than from careful and exact experiments, and the observation of
those particular effects, which result from its different circumstances
and situations. And tho' we must endeavour to render all our principles
as universal as possible, by tracing up our experiments to the
utmost, and explaining all effects from the simplest and fewest
causes, 'tis still certain we cannot go beyond experience; and
any hypothesis, that pretends to discover the ultimate original
qualities of human nature, ought at first to be rejected as presumptuous
and chimerical.
I do not think a philosopher, who would apply himself so earnestly
to the explaining the ultimate principles of the soul, would show
himself a great master in that very science of human nature, which
he pretends to explain, or very knowing 'm what is naturally satisfactory
to the mind of man. For nothing is more certain, than that despair
has {1:309} almost the same effect upon us with enjoyment, and
that we are no sooner acquainted with the impossibility of satisfying
any desire, than the desire itself vanishes. When we see, that
we have arrived at the utmost extent of human reason, we sit down
contented, tho' we be perfectly satisfied in the main of our ignorance,
and perceive that we can give no reason for our most general and
most refined principles, beside our experience of their reality;
which is the reason of the mere vulgar, and what it required no
study at first to have discovered for the most particular and
most extraordinary phaenomenon. And as this impossibility of making
any farther progress is enough to satisfy the reader, so the writer
may derive a more delicate satisfaction from the free confession
of his ignorance, and from his prudence in avoiding that error,
into which so many have fallen, of imposing their conjectures
and hypotheses on the world for the most certain principles. When
this mutual contentment and satisfaction can be obtained betwixt
the master and scholar, I know not what more we can require of
our philosophy.
But if this impossibility of explaining ultimate principles should
be esteemed a defect in the science of man, I will venture to
affirm, that 'tie a defect common to it with all the sciences,
and all the arts, in which we can employ ourselves, whether they
be such as are cultivated in the schools of the philosophers,
or practised in the shops of the meanest artizans. None of them
can go beyond experience, or establish any principles which are
not founded on that authority. Moral philosophy has, indeed, this
peculiar disadvantage, which is not found in natural, that in
collecting its experiments, it cannot make them purposely, with
premeditation, and after such a manner as to satisfy itself concerning
every particular difficulty which may @e. When I am at a loss
to know the effects of one body upon another in any situation,
I need only put them in that situation, and observe what results
from it. But should I endeavour to clear up after the same manner
any doubt in moral philosophy, by placing myself in the same case
with that which I consider, 'tis evident this reflection and premeditation
would so disturb the operation of my natural principles, as must
render it impossible to form any just conclusion from the phenomenon.
We must therefore glean up our experiments in @ science from a
cautious observation of human life, and take them as {1:310} they
appear in the common course of the world, by men's behaviour in
company, in affairs, and in their pleasures. Where experiments
of this kind are judiciously collected and compared, we may hope
to establish on them a science which will not be inferior in certainty,
and will be much superior in utility to any other of human comprehension.
BOOK I.
{1:.
PART 1. OF IDEAS, THEIR ORIGIN, COMPOSITION, CONNEXION, ABSTRACTION,
ETC.
S/ECT\. I. -- Of the Origin of our Ideas.
A/LL\ the perceptions of the human mind resolve themselves into
two distinct kinds, which I shall call IMPRESSIONS and IDEAS.
The difference betwixt these consists in the degrees of force
and liveliness, with which they strike upon the mind, and make
their way into our thought or consciousness. Those perceptions,
which enter with most force and violence, we may name impressions:
and under this name I comprehend all our sensations, passions
and emotions, as they make their first appearance in the soul.
By ideas I mean the faint images of these in thinking and reasoning;
such as, for instance, are all the perceptions excited by the
present discourse, excepting only those which arise from the sight
and touch, and excepting the immediate pleasure or uneasiness
it may occasion. I believe it will -not be very necessary to employ
many words in explaining this distinction. Every one of himself
will readily perceive the difference betwixt feeling and thinking.
The common degrees of these are easily distinguished; tho' it
is not impossible but in particular instances they may very nearly
approach to each other. Thus in sleep, in a fever, in madness,
or in any very violent emotions of soul, our ideas may approach
to our impressions, As on the other hand it sometimes happens,
that our impressions are so faint and low, that we cannot distinguish
{1:312} them from our ideas. But notwithstanding this near resemblance
in a few instances, they are in general so very different, that
no-one can make a scruple to rank them under distinct heads, and
assign to each a peculiar name to mark the difference.
There is another division of our perceptions, which it will be
convenient to observe, and which extends itself both to our impressions
and ideas. This division is into SIMPLE and COMPLEX. Simple perceptions
or impressions and ideas are such as admit of no distinction nor
separation. The complex are the contrary to these, and may be
distinguished into parts. Tho' a particular colour, taste, and
smell, are qualities all united together in this apple, 'tis easy
to perceive they are not the same, but are at least distinguishable
from each other.
Having by these divisions given an order and arrangement to our
objects, we may now apply ourselves to consider with the more
accuracy their qualities and relations. The first circumstance,
that strikes my eye, is the great resemblance betwixt our impressions
and ideas in every other particular, except their degree of force
and vivacity. The one seem to be in a manner the reflexion of
the other; so that all the perceptions of the mind are double.,
and appear both as impressions and ideas. When I shut my eyes
and think of my chamber, the ideas I form are exact representations
of the impressions I felt; nor is there any circumstance of the
one, which is not to be found in the other. In running over my
other perceptions, I find still the same resemblance and representation.
Ideas and impressions appear always to correspond to each other.
This circumstance seems to me remarkable, and engages my attention
for a moment.
Upon a more accurate survey I find I have been carried away too
far by the first appearance, and that I must make use of the distinction
of perceptions into simple and complex, to limit this general
decision, that all our ideas and impressions {1:313} are resembling.
I observe, that many of our complex ideas never had impressions,
that corresponded to them, and that many of our complex impressions
never are exactly copied in ideas. I can imagine to myself such
a city as the New Jerusalem, whose pavement is gold and walls
are rubies, tho' I never saw any such. I have seen Paris; but
shall I affirm I can form such an idea of that city, as will perfectly
represent all its streets and houses in their real and just proportions?
I perceive, therefore, that tho' there is in general a great,
resemblance betwixt our complex impressions and ideas, yet the
rule is not universally true, that they are exact copies of each
other. We may next consider how the case stands with our simple,
perceptions. After the most accurate examination, of which I am
capable, I venture to affirm, that the rule here holds without
any exception, and that every simple idea has a simple impression,
which resembles it, and every simple impression a correspondent
idea. That idea of red, which we form in the dark, and that impression
which strikes our eyes in sun-shine, differ only in degree, not
in nature. That the case is the same with all our simple impressions
and ideas, 'tis impossible to prove by a particular enumeration
of them. Every one may satisfy himself in this point by running
over as many as he pleases. But if any one should deny this universal
resemblance, I know no way of convincing him, but by desiring
him to shew a simple impression, that has not a correspondent
idea, or a simple idea, that has not a correspondent impression.
If he does not answer this challenge, as 'tis certain he can-not,
we may from his silence and our own observation establish our
conclusion.
Thus we find, that all simple ideas and impressions resemble
each other; and as the complex are formed from them, we may affirm
in general, that these two species of perception are exactly correspondent.
Having discovered this relation, which requires no farther examination,
I am curious to find some other of their qualities. Let us consider
how. they stand with regard to their existence, and which of the
impressions and ideas are causes, and which effects.
The full examination of this question is the subject of the {1:314}
present treatise; and therefore we shall here content ourselves
with establishing one general proposition, That all our simple
ideas in their first appearance are deriv'd from simple impressions,
which are correspondent to them, and which they exactly represent.'
In seeking for phenomena to prove this proposition, I find only
those of two kinds; but in each kind the phenomena are obvious,
numerous, and conclusive. I first make myself certain, by a new,
review, of what I have already asserted, that every simple impression
is attended with a correspondent idea, and every simple idea with
a correspondent impression. From this constant conjunction of
resembling perceptions I immediately conclude, that there is a
great connexion betwixt our correspondent impressions and ideas,
and that the existence of the one has a -considerable influence
upon that of the other. Such a constant conjunction, in such an
infinite number of instances, can never arise from chance; but
clearly proves a dependence of the impressions on the ideas, or
of the ideas on the impressions. That I may know on which side
this dependence lies, I consider the order of their first appearance;
and find by constant experience, that the simple impressions always
take the precedence of their correspondent ideas, but never appear
in the contrary order. To give a child an idea of scarlet or orange,
of sweet or bitter, I present the objects, or in other words,
convey to him these impressions; but proceed not so absurdly,
as to endeavour to produce -the impressions by exciting the ideas.
Our ideas upon their appearance produce not their correspondent
impressions, nor do we perceive any colour, or feel any sensation
merely upon thinking of them@ On the other hand we find, that
any impression either of the mind or body is constantly followed
by an idea, which resembles it, and is only different in the degrees
of force and liveliness, The constant conjunction of our resembling
perceptions, is a convincing proof, that the one are the causes
of the other; and this priority of the impressions is an equal
proof, that our impressions are the causes of our ideas, not our
ideas .of our, impressions.
To confirm this I consider Another plain and convincing phaenomenon;.
which is, that, where-ever by any accident the {1:315} faculties,
which give rise to any impressions, are obstructed in their operations,
as when one is born blind or deaf; -not only the impressions are
lost, but also their correspondent ideas; so that there never
appear in the mind the least traces of either of them. Nor is
this only true, where the organs of sensation are entirely destroy'd,
but likewise where they have never been put in action to produce
a particular impression. We cannot form to ourselves a just idea
of the taste of a pine apple, without having actually tasted it.
There is however one contradictory phaenomenon, which may prove,
that 'tis not absolutely impossible for ideas to go before their
correspondent impressions. I believe it will readily be allow'd
that the several distinct ideas of colours, which enter by the
eyes, or those of sounds, which are convey'd by the hearing, are
really different from each other, tho' at the same time resembling.
Now if this be true of different colours, it must be no less so
of the different shades of the same colour, that each of them
produces a distinct idea, independent of the rest. For if this
shou'd be deny'd, 'tis possible, by the continual gradation of
shades, to run a colour insensibly into what is most remote from
it; and if you will not allow any of the means to be different,
you cannot without absurdity deny the extremes to be the same.
Suppose therefore a person to have enjoyed his sight for thirty
years, and to have become perfectly well acquainted with colours
of all kinds, excepting one particular shade of blue, for instance,
which it never has been his fortune to meet with. Let all the
different shades of that colour, except that single one, be plac'd
before him, descending gradually from the deepest to the lightest;
'tis plain, that he will perceive a blank, where that shade is
wanting, said will be sensible, that there is a greater distance
in that place betwixt the -contiguous colours, than in any other.
Now I ask, whether 'tis possible for him, from his own imagination,
to supply this deficiency, and raise up to himself the idea of
that particular shade, tho' it had never been conveyed to him
by his senses? I believe i here are few but will be of opinion
that he can; and this may serve as a proof, that the simple ideas
are not always derived from the correspondent impressions; tho'
the instance is so particular and singular, that 'tis scarce worth
{1:316} our observing, and does not merit that for it alone we
should alter our general maxim.
But besides this exception, it may not be amiss to remark on
this head, that the principle of the priority of impressions to
ideas must be understood with another limitation, <viz>.
that as our ideas are images of our impressions, so we can form
secondary ideas, which are images of the primary; as appears from
this very reasoning concerning them. This is not, properly speaking,
an exception to the rule so much as an explanation of it. Ideas
produce the images of them. selves in new ideas; but as the first
ideas are supposed to be derived from impressions, it still remains
true, that all our simple ideas proceed either mediately or immediately,
from their correspondent impressions.
This then is the first principle I establish in the science of
human nature; nor ought we to despise it because of the simplicity
of its appearance. For 'tis remarkable, that the present question
concerning the precedency of our impressions or ideas, is the
same with what has made so much noise in other terms, when it
has been disputed whether there be any <innate ideas>, or
whether all ideas be derived from sensation and reflexion. We
may observe, that in order to prove the ideas of extension and
colour not to be innate, philosophers do nothing but shew that
they are conveyed by our senses. To prove the ideas of passion
and desire not to be innate, they observe that we have a preceding
experience of these emotions in ourselves., Now if we carefully
examine these arguments, we shall find that they prove nothing
but that ideas are preceded by other more lively perceptions,
from which the are derived, and which they represent. I hope this
clear stating of the question will remove all disputes concerning
it, and win render this principle of more use in our reasonings,
than it seems hitherto to have been.
SECT. III.-Division of the Subject.
Since it appears, that our simple impressions are prior to their
correspondent ideas, and that.the exceptions are very rare, method
seems to require we should examine our impressions, before we
consider our ideas. Impressions way be divided into two kinds,
those Of SENSATION and those of {1:317} REFLEXION. The first kind
arises in the soul originally,from unknown causes. The second
is derived in a great measure from our ideas, and that in the
following order. An impression first strikes upon the senses,
and makes us perceive heat or cold, thirst or hunger, pleasure
or pain of some kin(I or other. Of this impression there is a
copy taken by the mind, which remains after the impression ceases;
and this we call an idea. This idea of pleasure or pain, when
it returns upon the soul, produces the new impressions of desire
and aversion, hope and fear, which may properly be called impressions
of reflexion, because derived from it. These again are copied
by the memory and imagination, and become ideas; which perhaps
in their turn give rise to other impressions and ideas. So that
the impressions of reflexion are only antecedent to their correspondent
ideas; but posterior to those of sensation, and deriv'd from them.
The examination of our sensations belongs more to anatomists and
natural philosophers than to moral; and therefore shall not at
present be enter'd upon. And as the impressions of reflexion,
viz. passions, desires, and emotions, which principally deserve
our attention, arise mostly from ideas, 'twill be necessary to
reverse that method, which at first si-ht seems most natural;
and in order to explain the nature and principles of the human
mind, give a particular account of ideas, before we proceed to
impressions. For this reason I have here chosen to begin with
ideas.
SECT. III.-Of the Ideas of the Memory and Imagination.
We find by experience, that when any impression bas been present
with the mind, it again makes its appearance there a,s an idea;
and this it may do after two different ways: either when in its
new appearance it retains a considerable degree of its @t vivacity,
and is somewhat intermediate betwixt an impression and an idea:
or when it entirely loses that vivacity, and is a perfect idea.
The faculty, by which we repeat our impressions in the first manner,
is called the M/EMORY\, and the other the IMAGINATION. 'Tis evident
at first sight, that the ideas of the memory are much more lively
and strong than those of the imagination, and that {1:318} the
former faculty paints its objects in more distinct colours, than
any which are employ'd by the latter. When we remember any past
event, the idea of it flows in upon the mind in a forcible manner;
whereas in the imagination the perception is faint and languid,
and cannot without difficulty be preserv'd by the mind steddy
and uniform for any considerable time. Here then is a sensible
difference betwixt one species of ideas and another. But of this
more fully hereafter.
There is another difference betwixt these two kinds of ideas,
which:-s no less evident, namely that tho' neither the ideas,
of the memory nor imagination, neither the lively nor faint ideas
can make their appearance in the mind, unless their correspondent
impressions have gone before to prepare the way for them, yet
the imagination is not restrain'd to the same order and form with
the original impressions; while the memory is in a manner ty'd
down in that respect, without any power of variation."
'Tis evident, that the memory preserves the original form, in
which its objects were presented, and that where-ever we depart
from it in recollecting any thing, it proceeds from some defect
or imperfection in that faculty. An historian may, perhaps, for
the more convenient Carrying on of his narration, relate an event
before another, to which it was in fact posterior; but then he
takes notice of this disorder, if he be exact; and by that means
replaces the idea in its due position. 'Tis the same case in our
recollection of those places and persons, with which we were formerly
acquainted. The chief exercise of the memory is not to preserve
the simple ideas, but their order and position. In short, this
principle is supported by such a number of common and vulgar phaenomena,
that we may spare ourselves the trouble of insisting on it any
farther.
The same evidence follows us in our second principle, of the
liberty of the imagination to transpose and change its ideas.
The fables we meet with in poems and romances put this entirely
out of the question. Nature there is totally confounded, and nothing
mentioned but winged horses, fiery dragons, and monstrous giants.
Nor will this liberty of the fancy appear strange, when we consider,
that all our ideas are {1:310} copy'd from our impressions,' and
that there are not any two impressions which are perfectly inseparable.
Not to mention, that this is an evident consequence of the division
of ideas into simple and complex. Where-ever the imagination perceives
a difference among ideas, it can easily produce a separation.
SECT. IV.-Of the Connexion or Association of Ideas.
As all simple ideas may be separated by the imagination, and
may be united again in what form it pleases, nothing wou'd be
more unaccountable than the operations of that faculty, were it
not guided by some universal principles, which render it, in some
measure, uniform with itself in all times and places. Were ideas
entirely loose and unconnected, chance alone wou'd join them;
and 'tis impossible the same simple ideas should fall regularly
into complex ones (as they Commonly do) without some bond of union
among them, some associating quality, by which one idea naturally
introduces another. This uniting principle among ideas is not
to be consider'd as an inseparable connexion; for that ha,s been
already excluded from the imagination: Nor yet are we to conclude,
-that without it the mind cannot join two ideas; for nothing is
more free than that faculty: but we are only to regard it as a
gentle force, which commonly prevails, and is the cause why, among
other things, languages so nearly correspond to each other; nature
in a manner pointing out to every one those simple ideas, which
are most proper to be united in a complex one. The qualities,
from which this association arises, and by which the mind is after
this manner convey'd from one idea to another, are three, -viz.
RESEMBLANCE., CONTIGUITY in time or place, and CAUSE and EFFECT.
I believe it will not be very necessary to prove, that these
qualities produce an association among ideas, and upon the appearance
of one idea naturally introduce another. 'Tis plain, that in the
course of our thinking, and in the constant revolution of our
ideas, our imagination runs easily from one idea to any other
that resembles it, and that this quality alone is to the fancy
a sufficient bond and association. 'Tis likewise evident that
as the senses, in changing their objects, {1:320} are necessitated
to change them regularly, and take them as they lie <contiguous>
to each other, the imagination must by long custom acquire the
same method of thinking, and run along the parts of space and
time in conceiving its objects. As to the connexion, that is made
by the relation of cause and effect, we shall have occasion afterwards
to examine it to the bottom, and therefore shall not at present
insist upon it. 'Tis sufficient to observe, that there is no relation,
which produces a stronger connexion in the fancy, and makes one
idea more readily recall another, than the relation of cause and
effect betwixt their objects.
That we may understand the full extent of these relations, we
must consider, that two objects are connected together in the
imagination, not only when the one @ immediately resembling, contiguous
to, or the cause of the other, but also when there is interposed
betwixt them a third object, which bears to both of them any of
these relations. This may be carried on to a great length; tho'
at the same time we may observe, that each remove considerably
weakens the relation. Cousins in the fourth degree are connected
by causation, if I may be allowed to use that term; but not so
closely as brothers, much less as child and parent. In general
we may observe, that all the relations of blood depend upon cause
and effect, and are esteemed near or remote, according to the
number of connecting causes interpos'd betwixt the persons.
Of the three relations above-mention'd this of causation is the
most extensive. Two objects may be considered as plac'd in this
relation, as well when one is the cause of any of the actions
or motions of the other, as when the former is the cause of the
existence of the latter. For as that action or motion is nothing
but the object itself, consider'd in a certain light, and as the
object continues the same in all its different situations, 'tis
easy to imagine how such an influence of objects upon one another
may connect them in the imagination.
We may carry this farther, and remark, not only that two objects
are connected by the relation of cause and effect, when the one
produces a motion or any action in the other, but also when it
has a power of producing it. And this we may observe to be the
source of all the relation,; of interest and duty, by which men
influence each other in society, and {1:321} are plac'd in the
ties of government and subordination. A master is such-a-one as
by his situation, arising either from force or agreement, has
a power of directing in certain particulars the actions of another,
whom we call servant. A judge is one, who in all disputed cases
can fix by his opinion the possession or property of any thing
betwixt any members of the society. When a person is possess'd
of any power, there is no more required to convert it into action,
but the exertion of the will; and that in every case is considered
as possible, and in many as probable; especially in the case of
authority, where the obedience of the subject is a pleasure and
advantage to the superior.
These are therefore the principles of union or cohesion among
our simple ideas, and in the imagination supply the place of that
inseparable connexion, by which they are united in our memory.
Here is a kind of ATTRACTION, which in the mental world will be
found to have as extraordinary effects as in the natural, and
to shew itself in as many and as various forms. Its effects are
every where conspicuous; but as to its causes, they are mostly
unknown, and must be resolv'd into original qualities of human
nature, which I pretend not to explain. Nothing is more requisite
for a true philosopher, than to restrain the intemperate desire
of searching into causes, and having established any doctrine
upon a sufficient number of experiments, rest contented with that,
when he sees a farther examination would lead him into obscure
and uncertain speculations. In that case his enquiry wou'd be
much better employ'd in examining the effects than the causes
of his principle.
Amongst the effects of this union or association of ideas, there
are none more remarkable, than those complex ideas, which are
the common subjects of our thoughts and reasoning, and generally
arise from some principle of union among our simple ideas. These
complex ideas may be divided into Relations, Modes, and Substances.
We shall briefly examine each of these in order, and shall subjoin
some considerations concerning our general and particular ideas,
before we leave the present subject, which may be consider'd as
the elements of this philosophy. {1:322}
SECT. V.-Of Relations.
The word RELATION is commonly used in two senses considerably
different from each other. Either for that quality, by which two
ideas are connected together in the imagination, and the one naturally
introduces the other, after the manner above-explained: or for
that particular circumstance, in which, even upon the arbitrary
union of two ideas in the fancy, we may think proper to compare
them. In common language the former is always the sense, in which
we use the word, relation; and tis only in philosophy, that we
extend it to mean any particular subject of comparison, without
a connecting principle. Thus distance will be allowed by philosophers
to be a true relation, because we acquire an idea of it by the
comparing of objects: But in a common way we say, that nothing
can be more distant than such or such things from each other,
nothing can have less relation: as if distance and relation were
incompatible.'
It may perhaps be esteemed an endless task to enumerate all those
qualities, which make objects admit of comparison, and by which
the ideas of philosophical relation are produced. But if we diligently
consider them, we shall find that without difficulty they may
be compriz'd under seven general heads, which may be considered
as the sources of all philosophical relation.
1The first is resemblance: And this is a relation, without which
no philosophical relation can exist; since no objects will admit
of comparison, but what have some degree of resemblance.2 But
tho' resemblance be necessary to all philosophical relation, it
does not follow, that it always produces a connexion or association
of ideas. When a quality becomes very general, and is common to
a great many individuals, it leads not the mind directly to any
one of them; but by presenting at once too great a choice, does
thereby prevent the imagination from fixing on any single object.
2Identity may be esteem'd a second species of relation. This
relation I here consider as apply'd in its strictest sense to
constant and unchangeable objects; without examining the nature
and foundation of personal identity, which shall find {1:323}
its place afterwards. Of all relations the most universal is that
of identity, being common to every being whose existence has any
duration.
3After identity the most universal and comprehensive relations
are those of Space and Time, which are the sources of an infinite
number of comparisons, such as distant, contiguous, above, below,
before, after, &e.
4All those objects, which admit of quantity, or number, may
be compar'd in that particular; which is another very fertile
source of relation.
5W-hen any two objects possess the same quality in common, the
degrees, in which they possess it, form a fifth species of relation.
Thus of two objects, which are both heavy, the one may be either
of greater, or less weight than the other. Two colours, that are
of the same kind, may yet be of different shades, and in that
respect admit of comparison.
6The relation of contrariety may at first sight be regarded
as an exception to the rule, that no relation of any kind can
subsist without some degree of resemblance. But let us consider,
that no two ideas are in themselves contrary, except those of
existence and non-existence, which are plainly resembling, as
implying both of them an idea of the object; tho' the latter excludes
the object from all times and places, in which it is supposed
not to exist.'
7All other objects, such as fire and water, heat and cold, are
only found to be contrary from experience, and from the contrariety
of their causes or effects; which relation of cause and effect
is a seventh philosophical relation, as well as a natural one.
The resemblance implied in this relation, shall be explain'd afterwards."
It might naturally be expected, that I should join difference
to the other relations. But that I consider rather as a negation
of relation, than as anything real or positive. Difference is
of two kinds as oppos'd either to identity or resemblance. The
first is call'd a difference of number; the other of kind. {1:324}
SECT. VI.-Of Modes and Substance.8.
I wou'd fain ask those philosophers, who found so much of their
reasonings on the distinction of substance and accident, and imagine
we have clear ideas of each., whether the idea of substance be
deriv'd from the impressions of sensation pr of reflection? If
it be convey'd to us by our senses, I ask, which of them; and
after what manner? If it be perceiv'd by the eyes, it must be
a colour; if by the ears, a sound; if by the palate, a taste;
and so of the other senses. But I believe none will assert, that
substance is either a colour, or sound, or a taste. The idea,
of substance must therefore be deriv'd from an impression of reflection,
if it really exist. But the impressions of reflection resolve
themselves into our passions and emotions: none of which can possibly
represent a substance. We have therefore no idea of substance,
distinct from that of a collection of particular qualities, nor
have we any other meaning when we either talk or reason concerning
it.'
The idea of a substance as well as that of a mode, is nothing
but a collection of Simple ideas, that are united by the imagination,
and have a particular name assigned them, by which we are able
to recall, either to ourselves or others, that collection. But
the difference betwixt these ideas consists in this, that the
particular qualities, which form a substance, are commonly refer'd
to an unknown something, in which they are supposed to inhere;
or granting this fiction should not take place, are at least supposed
to be closely and inseparably connected by the relations of contiguity
and causation. The effect of this is, that whatever new simple
quality we discover to have the same connexion with the rest,
we immediately comprehend it among them, even tho' it did not
enter into the first conception of the substance. Thus our idea
of gold may at first be a yellow colour, weight, malleableness,
fusibility; but upon the discovery of its dissolubility in aqua
regia, we join that to the other qualities, and suppose it to
belong to the substance as much as if its idea had from the beginning
made a part of the compound one. The principal of union being
regarded as the chief part of the complex idea, gives entrance
to {1:325} whatever quality afterwards occurs, and is equally
comprehended by it, as are the others, which first presented themselves.
themselves.
That this cannot take place in modes, is evident from considering
their mature. The. simple ideas of which modes are formed, either
represent qualities, which are not united by contiguity and causation,
but are dispers'd in different subjects; or if they be all united
together, the uniting principle is not regarded as the foundation
of the complex idea. The idea of a dance -is an instance of the
first kind of modes; that of beauty of the second. The reason
is obvious, why such complex ideas cannot receive any' new idea,
without changing the name, which distinguishes the mode.
SECT. VII. Of Abstract Ideas.
A very material question has been started concerning abstract
or general ideas, whether they be general or particular in the
mind's conception of them. A great philosopher has disputed the
receiv'd opinion in this particular, and has asserted, that all
general ideas are nothing but particular ones, annexed to a certain
term, which gives them a more extensive signification, and makes
them recall upon occasion other individuals, which are similar
to them. As I look upon this to be one of the greatest and most
valuable discoveries that has been made of late years in the republic
of letters, I shag here endeavour to confirm it by some arguments,
which I hope will put it beyond all doubt and controversy.
'Tis evident, that in forming most of our general ideas, if not
all of them, we abstract from every particular degree of quantity
and quality, and that an object ceases not to be of any particular
species on account of every small alteration in its extension,
duration and other properties. It may therefore be thought, that
here is a plain dilemma, that decides concerning the nature of
those abstract ideas, which have afforded so much speculation
to philosophers. The abstract idea of a man represents men of
all sizes and all qualities; which 'tis concluded it cannot do,
but either by representing {1:326} at once all possible sizes
and all possible qualities, or by, representing no particular
One at all. Now it having been esteemed absurd to defend the former
proposition, as implying an infinite capacity in the mind, it
has been commonly infer'd in favour of the letter: and our abstract
ideas have been suppos'd to represent no particular degree either
of quantity or quality. But that this inference is erroneous,
I shall endeavour to make appear, fir@t, by proving, that 'tis
utterly impossible to conceive any quantity or quality, without
forming a precise notion of its degrees: And secondly by showing,
that tho' the capacity of the mind be not infinite, yet we can
at once form a notion of all possible degrees of quantity and
quality, in such a manner at least, as, however imperfect, may
serve all the purposes of reflection and conversation.
To begin with the first proposition, that the mind cannot for,m
any notion of quantity or quality without forming a precise notion
of degrees of each; we may prove this by the three following arguments.
First, We have observ'd, that whatever objects are different are
distinguishable, and that whatever objects are distinguishable
are separable by the thought and imagination.' And we may here
add, that these propositions are equally true in the inverse,
and that whatever objects are separable are also distinguishable,
and that whatever objects are distinguishable, are also different.
For how is it possible we can separate what is not distinguishable,
or distinguish what is not different? In order therefore to know,
whether abstraction implies a separation, we need only consider
it in this view, and examine, whether all the circumstances, which
we abstract from in our general ideas, be such as are distinguishable
and different from those, which we retain as essential parts of
them. But 'tis evident at first sight, that the precise length
of a line is not different nor distinguishable from the line itself.
nor the precise degree of any quality from the quality. These
ideas, therefore, admit no more of separation than they do of
distinction and difference. They are consequently conjoined with
each other in the conception; and the general idea of a. line,
notwithstanding all our abstractions and refinements, has in its@
appearance in the mind a precise degree of quantity and {1:327}
quality; however it may be made to represent others, which have
different degrees of both.
Secondly, 'tis contest, that no object can appear to the senses;
or in other words, that no impression can become present to the
mind, without being determined in its degrees both of quantity
and quality. The confusion, in which impressions are sometimes
involv'd, proceeds only from their faintness and unsteadiness,
not from any capacity in the mind to receive any impression, which
in its real existence has no particular degree nor proportion.
That is a contradiction in terms; and even implies the flattest
of all contradictions, viz. that 'tis possible for the same thing
both to be and not to be.
Now since all ideas are deriv'd from impressions, and are nothing
but copies and representations of them, whatever is true of the
one must be acknowledg'd concerning the other. Impressions and
ideas differ only in their strength and vivacity. The foregoing
conclusion is not founded on any particular degree of vivacity.
It cannot therefore be affected by any variation in that particular.
An idea is a weaker impression:2 and as a strong impression must
necessarily have a determinate quantity and quality, the case
must be the same with its copy or representative.
Thirdly, 'tis a principle generally receiv'd in philosophy that
everything in nature is individual, and that 'tis utterly absurd
to suppose a triangle really existent, which has no precise proportion
of sides and angles. If this therefore be absurd in fact and reality,
it must also be absurd in idea; since nothing of which we can
form a clear and distinct idea is absurd and impossible. But to
form the idea of an object, and to form an idea simply, is the
same thing; the reference of the idea to an object being an extraneous
denomination, of which in itself it bears no mark or character.
Now as 'tis -impossible to form an idea of an object, that is
possest of quantity and quality, and yet is possest of no precise
degree of either; it follows that there is an equal impossibility
of forming an idea, that is not limited and confin'd in both these
particulars. Abstract ideas are therefore in {1:328} themselves
individual, however they may become general in their representation.
The image in the mind is only that of a particular object, tho'
the application of it in our reasoning be the same, as if it were
universal.
This application of ideas beyond their nature proceeds from our
collecting all their possible degrees of quantity and quality
in such an imperfect manner as may serve the purposes of life,
which is the second proposition I propos'd to explain. When we
have found a resemblance I among several objects, that often occur
to us, we apply the same name to all of them, whatever differences
we may observe in the degrees of their quantity and quality, and
whatever other differences may appear among them. After we have
acquired a custom of this kind, the hearing of that name revives
the idea of one of these objects, and makes the imagination conceive
it with all its particular circumstances and proportions. But
as the same word is suppos'd to have been frequently applied to
other individuals, that are different in. many respects from that
idea, which is immediately present to the mind; the word not being
able to revive the idea of all these individuals, but only touches
the soul, if I may be allow'd so to speak, and revives that custom,
which we have acquir'd by surveying them. They are not really
and in fact present to the mind, but only in power; nor do we
draw them all out distinctly in the imagination, but keep ourselves
in a readiness W survey any of them, as we may be prompted by
a present design or necessity. The word raises up an individual
idea, along with a certain custom; and that custom produces any
other individual one, for which we may have occasion. But as the
production of all the ideas, to {1:329} which the name may be
apply'd, is in most eases impossible, we abridge that work by
a more partial consideration, and find but few inconveniences
to arise in our reasoning from that abridgment.
For this is one of the most extraordinary circumstances in the
present affair, that after the mind has produc'd an individual
idea, upon which we reason, the attendant custom, reviv'd by the
general or abstract term, readily suggests any other individual,
if by chance we form any reasoning, that agrees not with it. Thus
shou'd we mention the word triangle, and form the idea of a particular
equilateral one to correspond to it, and shou'd we afterwards
assert, that the three angles of a triangle are equal to each
other, the other individuals of a scalenum and isosceles, which
we overlooked at first, immediately crowd in upon us, and make
us perceive the falshood of this proposition, tho' it be true
with relation to that idea, which we had form'd. If the mind suggests
not always these ideas upon occasion, it proceeds from some imperfection
in its faculties; and such a one as is often the source of false
reasoning and sophistry. But this is principally the case with
those ideas which are abstruse and compounded. On other occasions
the custom is more entire, and 'tis seldom we run into such errors.
Nay so entire is the custom, that the very same idea may be annext
to several different words, and may be employ'd in different reasonings,
without any danger of mistake. Thus the idea of an equilateral
triangle of an inch perpendicular may serve us in talking of a
figure, of a rectilinear figure, of a regular figure, of a triangle,
and of an equilateral triangle. AR these terms, therefore, are
in this case attended with the same idea; but as they are wont
to be apply'd in a greater or lesser compass, they excite their
particular habits, and thereby keep the mind in a readiness to
observe, that no conclusion be form'd contrary to any ideas, which
are usually compriz'd under them.
Before those habits have become entirely perfect, perhaps the
mind may not be content with forming the idea of only one individual,
but may run over several, in order to make itself comprehend its
own meaning, and the compass of that collection, which it intends
to express by the general term. That we may &x the meaning
of the word, figure, we may {1:330} revolve in our mind the ideas
of circles, squares, parallelograms, triangles of different sizes
and proportions, and may not rest on one image or idea. However
this may be, 'tis certain that we form the idea of individuals,
whenever we use any general term; that we seldom or never can
exhaust these individuals; and that those, which remain, are only
represented by means of that habit, by which we recall them, whenever
any present occasion requires it. This then is the nature of our
abstract ideas and general terms; and 'tis after this manner we
account for the foregoing paradox, that some, ideas are particular
in their nature, but general in their representation.' A particular
idea becomes general by being annex'd to a general term; that
is, to a term, which from a customary conjunction has a relation
to many other particular ideas, and readily recalls them in the
imagination.
The only difficulty, that can remain on this subject, must be
with regard to that custom, which so readily recalls every particular
idea, for which we may have occasion, and is excited by any word
or sound, to which we commonly annex it. The most proper method,
in my opinion, of giving a satisfactory explication of this act
of the mind, is by producing other instances, which are analogous
to it, and other principles, which facilitate its operation. To
explain the ultimate causes of our mental actions is impossible.
'Tis sufficient, if we can give any satisfactory account of them
from experience and analogy.
First then I observe, that when we mention any great number,
such as a thousand, the mind has generally no adequate idea of
it, but only a power of producing such an idea, by its adequate
idea of the decimals, under which the number is comprehended.
This imperfection, however, in our ideas, is never felt in our
reasonings; which seems to be an instance parallel to the present
one of universal ideas.
Secondly, we have several instances of habits, which may be reviv'd
by one single word; as when a person, who has by rote any periods
of a discourse, or any number of verses, will be put in remembrance
of the whole, which he is at a loss to recollect, by that single
word or expression, with which they begin.
Thirdly, I believe every one, who examines the situation {1:331}
of his mind in reasoning' will agree with me, that we do not annex
distinct and compleat ideas to every term we make use of, and
that in talking of government, church, negotiation, conquest,
we seldom spread out in our minds all the simple ideas, of which
these complex ones are compos'd. 'Tis however observable, that
notwithstanding this imperfection we may avoid talking nonsense
on these subjects, and may perceive any repugnance among the ideas,
as well as if we had a fall comprehension of them. Thus if instead
of saying, that in war the weaker have always recourse to negotiation,
we shou'd say, that they have always recourse to conquest, the
custom, which we have acquir'd of attributing certain relations
to ideas, still follows the words, and makes us immediately perceive
the absurdity of that proposition; in the same manner as one particular
idea may serve us in reasoning concerning other ideas, however
different from it in several circumstances.
Fourthly, As the individuals are -collected together, said plac'd
under a general term with a view to that resemblance, which they
bear to each other, this relation must facilitate their entrance
in the imagination, and make them be suggested more readily upon
occasion. And indeed if we consider the common progress of the
thought, either in reflection or conversation, we shall find great
reason to be satisfy'd in this particular. Nothing is more admirable,
than the readiness, with which the imagination suggests its ideas,
and presents them at the very instant, in which they become necessary
or useful. The fancy runs from one end of the universe to the
other in collecting those ideas, which belong to any subject.
One would think the whole intellectual world of ideas was at once
subjected to our view, and that we did nothing but pick out such
as were most proper for our purpose. There may not, however, be
any present, beside those very ideas, that are thus collected
by a kind of magical faculty in the soul, which, tho' it be always
most perfect in the greatest geniuses, and is properly what we
call a genius, is however inexplicable by the utmost efforts of
human understanding.
Perhaps these four reflections may help to remove an difficulties
to the hypothesis I have propos'd concerning abstract ideas, so
contrary to that, which has hitherto prevail'd in philosophy,
But, to tell the truth I place my {1:331} chief confidence in
what I have already prov'd concerning the impossibility of general
ideas, according to the common method of explaining them. We must
certainly seek some new system on this head, and there plainly
is none beside what I have propos'd. If ideas be particular in
their nature, and at the same time finite in their number, 'tis
only by custom they can become general in their representation,
and contain an infinite number of other ideas under them.
Before I leave this subject I shall employ the same principles
to explain that distinction of reason, which is so much talk'd
of, and is so little understood, in the schools. Of this kind
is the distinction betwixt figure and the body figur'd; motion
and the body mov'd. The difficulty of explaining this distinction
arises from the principle above explain'd, that all ideas, which
are different, are separable. For it follows from thence, that
if the figure be different from the body, their ideas must be
separable as well as distinguishable: if they be not different,
their ideas can neither be separable nor distinguishable. What
then is meant by a distinction of reason, since it implies neither
a difference nor separation.
To remove this difficulty we must have recourse to the foregoing
explication of abstract ideas. 'Tis certain that the mind wou'd
never have dream'd of distinguishing a figure from the body figur'd,
as being in reality neither distinguishable, nor different, nor
separable; did it not observe, that even in this simplicity there
might be contain'd many different resemblances and relations.'
Thus when a globe of white marble is presented, we receive only
the impression of a white colour dispos'd in a certain form, nor
are we able to separate and distinguish the colour from the form.
But observing afterwards a globe of black marble and a cube of
white, and comparing them with our former object, we find two
separate resemblances, in what formerly seemed, and really is,
perfectly inseparable. After a little more practice of this kind,
we begin to distinguish the figure from the colour by a distinction
of reason; that is, we consider the figure and colour together,
since they are in effect the same and undistinguishable; but still
view them {1:333} in different aspects, according to the resemblances,
of which they are susceptible. When we wou'd consider only the
figure of the globe of white marble, we form in reality an idea
both of the figure and colour, but tacitly carry our eye to its
resemblance with the globe of black marble: And in the same manner,
when we wou'd consider its colour only, we turn our view to its
resemblance with the cube of white marble. By this means we accompany
our ideas with a kind of reflection, of which custom renders us,
in a great measure, insensible. A person, who desires us to consider
the figure of a globe of white marble without thinking on its
colour, desires an impossibility but his meaning is, that we shou'd
consider the figure and colour together, but still keep in our
eye the resemblance to the globe of black marble, or that to any
other globe of whatever colour or substance. {1:334}
PART II.
OF THE IDEAS OF SPACE AND TIME,.
SECT. I. Of the Infinite Divisibility of our Ideas of Space and
Time.
W/HATEVER\ has the air of a paradox, and is contrary to the first
and most unprejudiced notions of mankind, is often greedily embrac'd
by philosophers, as shewing the superiority of their science,
which cou'd discover opinions so remote from vulgar conception.
On the other hand, anything propos'd to us, which causes surprize
and admiration, gives such a satisfaction to the mind, that it
indulges itself in those agreeable emotions, and will never be
persuaded that its pleasure is entirely without foundation. From
these dispositions in philosophers and their disciples arises
that mutual complaisance betwixt them; while the former furnish
such plenty of strange and unaccountable opinions, and the latter
so readily believe them. Of this mutual complaisance I cannot
give a more evident instance than in the doctrine of infinite
divisibility, with the examination of which I shall begin this
subject of the ideas of space and time.
'Tis universally allow'd, that the capacity of the mind is limited,
and can never attain a full and adequate conception of infinity:
And tho' it were not allow'd, 'twould be sufficiently evident
from the plainest observation and experience.' 'Tis also obvious,
that whatever is capable of being divided in infinitum, must consist
of an infinite number of parts, and that 'tis impossible to set
any bounds to the number of parts, without setting bounds at the
same time to the division. It requires scarce any, induction to
conclude from hence, that the idea, which we form of any finite
quality, is not infinitely divisible, but that by proper distinctions
and {1:335} separations we may run up this idea to inferior ones,
which will be perfectly simple and indivisible. In rejecting the
infinite capacity of the mind, we suppose it may arrive at an
end in the division of its ideas; nor are there any possible means
of evading the evidence of this conclusion.
'Tis therefore certain, that the imagination reaches a minimum,
and may raise up to itself an idea, of which it cannot conceive
any sub-division, and which cannot be diminished without a total
annihilation. When you tell me of the thousandth and ten thousandth
part of a grain of sand, I have a, distinct idea of these numbers
and of their different proportions; but the images, which I form
in my mind to represent the things themselves, are nothing different
from each other, nor inferior to that image, by which I represent
the grain of sand itself, which is suppos'd so vastly to exceed
them. What consists of parts is distinguishable into them, and
what is distinguishable is separable. But whatever we may imagine
of the thing, the idea of a grain of sand is not distinguishable,
nor separable into twenty, much less into a thousand, ten thousand,
or an infinite number of different ideas.'
'Tis the same case with the impressions of the senses as with
the ideas of the imagination. Put a spot of ink upon paper, fix
your eye upon that spot, and retire to such a distance, that,
at last you lose sight of it; 'tis plain, that the moment before
it vanish'd the image or impression was perfectly indivisible.
'Tis not for want of rays of light striking on our eyes, that
the minute parts of distant bodies convey not any sensible impression;
but because they are remov'd beyond that distance, at which their
impressions were reduc'd to a minimum, and were incapable of any
farther diminution. A microscope or telescope, which renders them
visible, produces not any new rays of light, but only spreads
those, which always flow'd from them; and by that means both gives
parts to impressions, which to the naked eye appear simple and
uncompounded, and advances to a' 'minimum, what was formerly imperceptible.
We may hence discover the error of the common opinion, that the
capacity of the mind is limited on both sides, and that 'tis impossible
for the imagination to form an adequate {1:336} idea, of what
goes beyond a certain degree of minuteness as well as of greatness.
Nothing can be more minute, than some ideas, which we form in
the fancy; and images, which appear to the senses; since there
are ideas and images perfectly simple and indivisible. The only
defect of our senses is, that they give us disproportion'd images
of things, and represent as minute and uncompounded what is really
great and compos'd of a vast number of parts. This mistake we
are not sensible of: but taking the impressions of those minute
objects, which appear to the senses, to be equal or nearly equal
to the objects, and finding by reason, that there are other objects
vastly more minute, we too hastily conclude, that these are inferior
to any idea of our imagination or impression of our senses. This
however is certain, that we can form ideas, which shall be no
greater than the smallest atom of the animal spirits of an insect
a thousand times less than a mite: And we ought rather to conclude,
that the difficulty lies in enlarging our conceptions so much
as to form a just notion of a mite, or even of an insect a thousand
times less than a mite. For in order to form a just notion of
these animals, we must have a distinct idea representing every
part of them;, which, according to the system of infinite divisibility,
is utterly impossible, and,recording to that of indivisible parts
or atoms, is extremely difficult, by reason of the vast number
and multiplicity of these parts.
SECT. II.-Of the Infinite Divisibility of Space and Time.
Wherever ideas are adequate representations of objects, the relations,
contradictions and agreements of the ideas are all applicable
to the objects; and this we may in general observe to be the foundation
of all human knowledge. But our ideas are adequate representations
of the most minute parts of extension; and thro' whatever divisions
and subdivisions we may suppose these parts to be arriv'd at,
they can never become inferior to some ideas, which we form. The
plain consequence is, that whatever appears impossible and contradictory
upon the comparison of these ideas, must be really impossible
and contradictory, without any farther excuse or evasion.
Every thing capable of being infinitely divided contains {1:337}
an infinite number of parts; otherwise the division would be stopt
short by the indivisible parts, which we should immediately arrive
at. If therefore any finite extension be infinitely divisible,
it can be no contradiction to suppose, that a finite extension
contains an infinite number of parts: And vice versa, if it be
a contradiction to suppose, that a finite extension contains an
infinite number of parts, no finite extension can be infinitely
divisible. But that this latter supposition is absurd, I easily
convince myself by the consideration of my clear ideas. I first
take the least idea I can form of a part of extension, and being
certain that there is nothing more minute than this idea, I conclude,
that whatever I discover by its means must be a real quality of
extension. I then repeat this idea once, twice, thrice, &c.,
and find the compound idea of extension, arising from its repetition,
always to augment, and become double, triple, quadruple, &c.,
till at last it swells up to a considerable bulk, greater or smaller,
in proportion as I repeat more or less the same idea. When I stop
in the addition of parts, the idea of extension ceases to augment;
and were I to carry on the addition in infinitum, I clearly perceive,
that the idea of extension must also become infinite. Upon the
whole, I conclude, that the idea of all infinite number of parts
is individually the same idea with that of an infinite extension;
that no finite extension is capable of containing an infinite
number of parts; and consequently that no finite extension is
infinitely divisible.
I may subjoin another argument propos'd by a noted author,"
which seems to me very strong and beautiful. 'Tis evident, that
existence in itself belongs only to unity, and is never applicable
to number, but on account of the unites, of which the number is
compos'd. Twenty men may be said to exist; but 'tis only because
one, two, three, four, &c. are existent, and if you deny the
existence of the latter, that of the former falls of course. 'Tis
therefore utterly absurd to suppose any number to exist, and yet
deny the existence of {1:338} unites; and as extension is always
a number, according to the common sentiment of metaphysicians,
and never resolves itself into any unite or indivisible quantity,
it follows, that extension can never at all exist. 'Tis in vain
to reply, that any determinate quantity of extension is an unite;
but such-a-one as admits of an infinite number of fractions, and
is inexhaustible in its sub-divisions. For by the same rule these
twenty men may be consider'd as an unite. The whole globe of the
earth, nay the whole universe, may be consider'd as an unite,.
That term of unity is merely a fictitious denomination, which
the mind may apply to any quantity of objects it collects together;
nor can such an unity any more exist alone than number can, as
being in reality a true number. But the unity, which can exist
alone, and whose existence is necessary to that of all number,
is of another kind, and must be perfectly indivisible, and incapable
of being resolved into any lesser unity.
All this reasoning takes place with regard to time; along with
an additional argument, which it may be proper to take notice
of. 'Tis a property inseparable from time, and which in a manner
constitutes its essence, that each of its parts succeeds another,
and that -none of them, however contiguous, can ever be co-existent.
For the same reason, that the year 1737 cannot concur with the
present year 1738 every moment must be distinct from, and posterior
or antecedent to another.2 'Tis certain then, that time, as it
exists, must be compos'd of indivisible moments. For if in time
we could never arrive at an end of division, and if each moment,
as it succeeds another, were not perfectly single and indivisible,
there would be an infinite number of co-existent moments, or parts
of time; which I believe will be allow'd to be an arrant contradiction.
The infinite divisibility of space implies that of time, as is
evident from the nature of motion. If the latter, therefore, be
impossible, the former must be equally so.
I doubt not but, it will readily be allow'd by the most obstinate
defender of the doctrine of infinite divisibility, that these
arguments are difficulties, and that 'tis impossible to give any
answer to them which will be perfectly clear and satisfactory.
But here we may observe, that nothing can be more {1:339} absurd,
than this custom of calling a difficulty what pretends to be a
demonstration, and endeavouring by that means to elude its force
and evidence. 'Tis not in demonstrations as in probabilities,
that difficulties can take place, and one argument counter-ballance
another, and diminish its authority. A demonstration, if just,
admits of no opposite difficulty; and if not just, 'tis a mere
sophism, and consequently can never be a difficulty. 'Tis either
irresistible, or has no manner of force. To talk therefore of
objections and replies, and ballancing of arguments in such a
question as this, is to confess, either that human reason is nothing
but a play of words, or that the person himself, who talks so,
has not a Capacity equal to such subjects. Demonstrations may
be difficult to be comprehended, because of abstractedness of
the subject; but can never have such difficulties as will weaken
their authority, when once they are comprehended.
'Tis true, mathematicians are wont to say, that there are here
equally strong arguments on the other side of the question, and
that the doctrine of indivisible points is also liable to unanswerable
objections. Before I examine these arguments and objections in
detail, I will here take them in a body, and endeavour by a short
and decisive reason to prove at once, that 'tis utterly impossible
they can have any just foundation.
'Tis an establish'd maxim in metaphysics, That whatever the mind
clearly conceives, includes the idea of possible existence, or
in other words, that nothing we imagine is absolutely impossible.
We can form the idea of a golden mountain, and from thence conclude
that such a mountain may actually exist. We can form no idea of
a mountain without a valley, and therefore regard it as impossible.
Now 'tis certain we have an idea of extension; for otherwise
why do we talk and reason concerning it? 'Tis likewise certain
that this idea, as conceiv'd by the imagination, tho' divisible
into parts or inferior ideas, is not infinitely divisible, nor
consists of an infinite number of parts: For that exceeds the
comprehension of our limited capacities. Here then is an idea
of extension, which consists of parts or inferior ideas, that
are perfectly, indivisible: consequently this idea implies no
contradiction: consequently 'tis possible for extension {1:340}
really to exist conformable to it: and consequently all the arguments
employ'd against the possibility of mathematical points are mere
scholastick quibbles, and unworthy of our attention.
These consequences we may carry one step farther, and conclude
that all the pretended demonstrations for the infinite divisibility
of extension are equally sophistical; since 'tis certain these
demonstrations cannot be just without proving the impossibility
of mathematical points; which 'tis an evident absurdity to pretend
to.
SECT. III.-Of the other Qualities of our Idea of Space and Time.
No discovery cou'd have been made more happily for deciding all
controversies concerning ideas, than that abovemention'd, that
impressions always take the precedency of them, and that every
idea, with which the imagination is furnish'd, first makes its
appearance in a correspondent impression. These latter perceptions
are all so clear and evident, that they admit of no controversy;
tho' many of our ideas are so obscure, that 'tis almost impossible
even for the mind, which forms them, to tell exactly their nature
and composition. Let us apply this principle, in order to discover
farther the nature of our ideas of space and time.
Upon opening my eyes, and turning them to the surrounding objects,
I perceive many visible bodies; and upon shutting them again,
and considering the distance betwixt these bodies, I acquire the
idea of extension. As every idea is deriv'd from some impression,which
is exactly similar to it, the impressions similar to this idea
of extension, must either be some sensations deriv'd from the
sight, or some internal impressions arising from these sensations.,
Our internal impressions are our passions, emotions, desires
and aversions; none of which, I believe, will ever be asserted
to be the model, from which the idea of space is deriv'd. There
remains therefore nothing but the senses, which can convey to
us this original impression. Now what impression do oar senses
here convey to us? This is the {1:341} principal question, and
decides without appeal concerning the nature of the idea.
The table before me is alone sufficient by its view to give me
the idea of extension. This idea, then, is borrow'd from, and
represents some impression, which this moment appears to the senses.
But my senses convey to me only the impressions of colour'd points,
dispos'd in a, certain manner. If the eye is sensible of any thing
farther, I desire it may be pointed out to me. But if it be impossible
to shew any thing farther, we may conclude with certainty, that
the idea of extension is nothing but a copy of these colour'd
points, and of the manner of their appearance.
Suppose that in the extended object, or composition of colour'd
points, from which we first receiv'd the idea of extension, the
points were of a purple colour; it follows, that in every repetition
of that idea we wou'd not only place the points in the same order
with respect to each other, but also bestow on them that precise
colour, with which alone we are acquainted. But afterwards having
experience of the other colours of violet, green, red, white,
black, and of all the different compositions of these, and finding
a resemblance in the disposition of colour'd points, of which
they are compos'd, we omit the peculiarities of colour, as far
as possible, and found an abstract idea merely on that disposition
of points, or manner of appearance, in which they agree. Nay even
when the resemblance is carry'd beyond the objects of one sense,
and the impressions of touch are found to be Similar to those
of sight in the disposition of their parts; this does not hinder
the abstract idea from representing both, upon account of their
resemblance. All abstract ideas are really nothing but particular
ones, consider'd in a certain light; but being annexed to general
terms, they are able to represent a vast variety, and to comprehend
objects, which, as they are alike in some particulars, are in
others vastly wide of each other.'
The idea of time, being deriv'd from the succession of our perceptions
of every kind, ideas as well as impressions, and impressions of
reflection as well as of sensations will afford us an instance
of an abstract idea, which comprehends a still greater variety
than that of space, and yet is represented {1:342} in the fancy
by some particular individual idea of a determinate quantity and
quality.
As 'tis from the disposition of visible and tangible objects
we receive the idea of space, so from the succession of ideas
and impressions we form the idea of time, nor is it possible for
time alone ever to make its appearance, or be taken notice of
by the mind.' A man in a sound sleep, or strongly occupy'd with
one thought, is insensible of time; and according as his perceptions
succeed each other with greater or less rapidity, the same duration
appears longer or shorter to his imagination. It has been remark'd
by a great philosopher, that our perceptions have certain bounds
in this particular, which are fix'd by the original nature and
constitution of the mind, and beyond which no influence of external
objects on the senses is ever able to hasten or retard our thought.
If you wheel about a burning coal with rapidity, it will present
to the senses an image of a circle of fire; nor will there seem
to be any interval of time betwixt its revolutions; meerly because
'tis impossible for our perceptions to succeed each other with
the same rapidity, that motion may be communicated to external
objects. Wherever we have no successive perceptions, we have no
notion of time, even tho' there be a real succession in the objects.
From these phenomena, as well as from many others, we may conclude,
that time cannot make its appearance to the mind, either alone,
or attended with a steady unchangeable object, but is always discovered
some <perceivable> succession of changeable objects.
To confirm this we may add the following argument, which to me
seems perfectly decisive and convincing. 'Tis evident, that time
or duration consists of different parts: For otherwise we cou'd
not conceive a longer or shorter duration. 'Tis also evident,
that these parts are not @existent: For that quality of the co-existence
of parts belongs to extension, and is what distinguishes it from
duration. Now as time is compos?d of parts, that are not coexistent:
an unchangeable object, since it produces none but coexistent
impressions, produces none that can give us the idea of time;
and consequently that idea must be deriv'd from a succession of
{1:343} changeable objects, and time in its first appearance can
never be sever'd from such a succession.
Having therefore found, that time in its first appearance to
the mind is always conjoin'd with a succession of changeable objects,
and that otherwise it can never fall under our notice, we must
now examine whether it can be conceiv'd without our conceiving
any succession of objects, and whether it can alone form a distinct
idea in the imagination.
In order to know whether any objects, which are join'd in impression,
be inseparable in idea, we need only consider, if they be different
from each other; in which case, 'tis plain they may be conceiv'd
apart. Every thing, that is different is distinguishable: and
everything, that is distinguishable, may be separated, according
to the maxims above-explain'd. If on the contrary they be not
different, they are not distinguishable: and if they be not distinguishable,
they cannot be separated. But this is precisely the case with
respect to time, compar'd with our successive perceptions. The
idea of time is -not deriv'd from a particular impression mix'd
up with others, and plainly distinguishable from them; but arises
altogether from the manner, in which impressions appear to the
mind, without making one of the number. Five notes play'd on a
flute give us the impression and idea of time; tho' time be not
a sixth impression, which presents itself to the hearing or any
other of the senses. Nor is it a sixth impression, which the mind
by reflection finds in itself. These five sounds making their
appearance in this particular manner, excite no emotion in the
mind, nor produce an affection of any kind, which being observ'd
by it can give rise to a new idea. For that is necessary to produce
a new idea of reflection, nor can the mind, by revolving over
a thousand times all its ideas of sensation, ever extract from
them any new original idea, unless nature has so fram'd its faculties,
that it feels some new original impression arise from such a contemplation.
But here it only takes notice of the manner, in which the different
sounds make their appearance; and that it may afterwards consider
without considering these particular sounds, but may conjoin it
with any other objects. The ideas of some objects it certainly
must have, nor is it possible for it without these ideas ever
to arrive at any conception of time; which since it, appears not
as any {1:344} primary distinct impression, can plainly be nothing
but different ideas, or impressions, or objects dispos'd in a
certain manner, that is, succeeding each other.
I know there are some who pretend, that the idea of duration
is applicable in a proper sense to objects, which are perfectly
unchangeable; and this I take to be the common opinion of philosophers
as well as of the vulgar. But to be convinc'd of its falsehood
we need but reflect on the foregoing conclusion, that the idea
of duration is always deriv'd from a succession of changeable
objects, and can never be convey'd to the mind by any thing stedfast
and unchangeable. For it inevitably follows from thence, that
since the idea of duration cannot be deriv'd from such an object,
it can never-in any propriety or exactness be apply'd to it, nor
can any thing unchangeable be ever said to have duration. Ideas
always represent the Objects or impressions, from which they are
deriv'd, and can never without a fiction represent or be apply'd
to any other. By what fiction we apply the idea of time, even
to what is unchangeable, and suppose, as is common, that duration
is a measure of rest as well as of motion, we shall consider afterwards.
There is another very decisive argument, which establishes the
present doctrine concerning our ideas of space and time, and is
founded only on that simple principle, that our ideas of them
are compounded of parts, which are indivisible. This argument
may be worth the examining.
Every idea, that is distinguishable, being also separable, let
us take one of those simple indivisible ideas, of which the compound
one of extension is form'd, and separating it from all others,
and considering it apart, let us form a judgment of its nature
and qualities.
'Tis plain it is not the idea of extension. For the idea of extension
consists of parts; and this idea, according to t-he supposition,
is perfectly simple and indivisible. Is it therefore nothing?
That is absolutely impossible. For as the compound idea of extension,
which is real, is compos'd of such ideas; were these so many non-entities,
there wou'd be a real existence compos'd of non-entities; which
is absurd. Here therefore I must ask, What is our idea of a simple
and indivisible point? No wonder if my answer appear somewhat
new, since the question itself has scarce ever yet {1:345} been
thought of. We are wont to dispute concerning the nature of mathematical
points, but seldom concerning the nature of their ideas.
The idea of space is convey'd to the. mind by two senses, the
sight and touch; nor does anything ever appear extended, that
is not either visible or tangible. That compound impression, which
represents extension, consists of several lesser impressions,
that are indivisible to the eye or feeling, and may be call'd
impressions of atoms or corpuscles endow'd with colour and solidity.
But this is not all. 'Tis not only requisite, that these atoms
shou'd be colour'd or tangible, in order to discover themselves
to our senses; 'tis also necessary we shou'd preserve the idea
of their colour or tangibility in order to comprehend them by
our imagination. There is nothing but the idea of their colour
or tangibility, which can render them conceivable by the mind.
Upon the removal of the ideas of these sensible qualities, they
are utterly annihilated to the thought or imagination.'
Now such as the parts are, such is the whole. If a point be not
consider'd as colour'd or tangible, it can convey to us no idea;
and consequently the idea of extension, which is compos'd of the
ideas of these points, can never possibly exist. But if the idea
of extension really can exist, as we are conscious it does, its
parts must also exist; and in order to that, must be consider'd
as colour'd or tangible. We have therefore no idea of space or
extension, but when we regard it as an object either of our sight
or feeling.
The same reasoning will prove, that the indivisible moments of
time must be fill'd with some real object or existence, whose
succession forms the duration, and makes it be conceivable by
the mind.
SECT. IV.- Objections answer'd.
Our system concerning space and time consists of two parts, which
are intimately connected together. The first depends on this chain
of reasoning. The capacity of the mind is not infinite; consequently
no idea of extension or duration consists of an infinite number
of parts or inferior ideas, but of a finite number, and these
simple and indivisible:'Tis therefore possible for space and
time to exist {1:346} conformable to this idea: And if it be possible,
'tis certain they actually do exist conformable to it; since their
infinite divisibility is utterly impossible and contradictory.
The other part of our system is a consequence of this. The parts,
into which the ideas of space and time resolve themselves, become
at last indivisible; and these indivisible parts, being nothing
in themselves, are inconceivable when not fill'd with something
real and existent. The ideas of space and time are therefore no
separate or distinct ideas, but merely those of the manner or
order, in which objects exist: Or in other words, 'tis impossible
to conceive either a vacuum and extension without matter, or a
time, when there was no succession or change in any real existence.
The intimate connexion betwixt these parts of our system is the
reason why we shall examine together the objections, which have
been urg'd against both of them, beginning with those against
the finite divisibility of extension.
IThe first of these objections, which I shall take notice of,
is more proper to prove this connexion and dependence of the one
part upon the other, than to destroy either of them. It has often
been maintained in the schools, that extension must be divisible,
in infinitum, because the system of mathematical points is absurd;
and that system is absurd, because a mathematical point is a non-entity,
and consequently can never by its conjunction with others form
a real existence. This wou'd be perfectly decisive, were there
no medium betwixt the infinite divisibility of matter, and the
non-entity of mathematical points. But there is evidently a medium,
viz. the bestowing a colour or solidity on these points; and the
absurdity of both the extremes is a demonstration of the truth
and reality of this medium. The system of physical points, which
is another medium, is too absurd to need a refutation. A real
extension, such as a physical point is suppos'd to be, can never
exist without parts, different from each other; and wherever objects
are different, they are distinguishable and separable by the imagination.
II. The second objection is deriv'd from the necessity there
wou'd be of penetration, if extension consisted of mathematic-.i,l
points. A simple and indivisible atom, that touches another, must
necessarily penetrate it; for 'tis impossible it can touch it
by its external parts, from the very supposition {1:347} of its
perfect simplicity, which excludes all parts. It must therefore
touch it intimately, and in its whole essence, <secundum se,
tota, & totaliter>; which is the very definition of penetration.
But penetration is impossible: Mathematical points are of consequence
equally impossible.
I answer this objection by substituting a juster idea of penetration.
Suppose two bodies containing no void within their circumference,
to approach each other, and to unite in such a manner that the
body, which results from their union, is no more extended than
either of them; 'tis this we must mean when we talk of penetration.
But 'tis evident this penetration is nothing but the annihilation
of one of these bodies, and the preservation of the other, without
our being able to distinguish particularly which is preserv'd
and which annihilated. Before the approach we have the idea of
two bodies. After it we have the idea only of one. 'Tis impossible
for the mind to preserve any notion of difference betwixt two
bodies of the same nature existing in the same place at the same
time.
Taking then penetration in this sense, for the annihilation of
one body upon its approach to another, I ask any one, if he sees
a necessity, that a colour'd or tangible point shou'd be annihilated
upon the approach of another colour'd or tangible point? On the
contrary, does he not evidently perceive, that from the union
of these points there results an object, which is compounded and
divisible, and may be distinguished into two parts, of which each
preserves its existence distinct and separate, notwithstanding
its contiguity to the other? Let him aid his fancy by conceiving
these points to be of different colours, the better to prevent
their coalition and confusion. A blue and a red point may surely
lie contiguous without any penetration or annihilation. For if
they cannot, what possibly can become of them? Whether shall the
red or the blue be annihilated? Or if these colours unite into
one, what new colour will they produce by their union?
What chiefly gives rise to these objections, and at the same
time renders it so difficult to give a satisfactory answer to
them, is the natural infirmity and unsteadiness both of our imagination
and senses, when employ'd on such minute objects. Put a spot of
ink upon paper, and retire to such a distance, that the spot becomes
altogether invisible; you will {1:348} find, that upon your return
and nearer approach the spot first becomes visible by short intervals;
and afterwards becomes always visible; and afterwards acquires
only a new force in its colouring without augmenting its bulk;
and afterwards, when it has encreas'd to such a degree as to be
really extended, 'tis still difficult for the imagination to break
it into its component parts, because of the uneasiness it finds
in the conception of such a minute object as a single point. This
infirmity affects most of our reasonings on the present subject,
and makes it almost impossible to answer in an intelligible manner,
and in proper expressions, many questions which may arise concerning
it.
III. There have been -many objections drawn from the mathematics
against the indivisibility of the parts of extension: tho' at
first sight that science seems rather favourable to the present
doctrine; and if it be contrary in its <demonstrations>,
'tis perfectly conformable in its definitions. My present business
then must be to defend the definitions, and refute the demonstrations.
A surface is defin'd to be length and breadth without dept,h:
A line to be length without breadth or depth: A point to be what
has neither length, breadth nor depth. 'Tis evident that all this
is perfectly unintelligible upon any other supposition than that
of the. composition of extension by indivisible points or atoms.
How else cou'd any thing exist without length, without breadth,
or without depth?
Two different answers, I find, have been made to this argument;
neither of which is in my opinion satisfactory. The first is,
that the objects of geometry, those surfaces, lines and points,
whose proportions and positions it examines, are mere ideas in
the mind; I and not only never did, but never can exist in nature.
They never did exist; for no one will pretend to draw a line or
make a surface entirely conformable to the definition: They never
can exist; for we may produce demonstrations from these very ideas
to prove, that they are impossible.
But can anything be imagin'd more absurd and contradictory than
this reasoning? Whatever can be conceiv'd by a clear and distinct
idea necessarily implies the possibility of existence; and he
who pretends to prove the impossibility of its existence by any
argument derived from the clear {1:349} idea, in reality asserts,
that we have no clear idea of it, because we have a clear idea.
'Tis in vain to search for a contradiction in any thing that is
distinctly conceiv'd by the mind. Did it imply any contradiction,
'tis impossible it cou'd ever be conceiv'd.
There is therefore no medium betwixt allowing at least the possibility
of indivisible points, and denying their idea; and 'tis on this
latter principle, that the second answer to the foregoing argument
is founded. It has been I pretended, that tho' it be impossible
to conceive a length without any breadth, yet by an abstraction
without a separation, we can consider the one without regarding
the other; in the same manner as we may think of the length of
the way betwixt two towns, and overlook its breadth. The length
is inseparable from the breadth both in nature and in our minds;
but this excludes not a partial consideration, and a distinction
of reason, after the manner above explain'd.
In refuting this answer I shall not insist on the argument, which
I have already sufficiently explained, that if it be impossible
for the mind to arrive at a minimum in its ideas, its capacity
must be infinite, in order to comprehend the infinite number of
parts, of which its idea of any extension wou'd be compos'd. I
shall here endeavour to find some new absurdities in this reasoning.
A surface terminates a solid; a line terminates a surface; a
point terminates a line; but I assert, that if the ideas of a
point, line or surface were not indivisible, 'tis impossible we
shou'd ever conceive these terminations: For let these ideas be
suppos'd infinitely divisible; and then let the fancy endeavour
to fix itself on the idea of the last surface, line or point;
it immediately finds this idea to break into parts; and upon its
seizing the last of these parts, it loses its hold by a new division,
and so on in infinitum, without any possibility of its arriving
at a concluding idea. The number of fractions bring it no nearer
the last division, than the first idea it form'd. Every particle
eludes the grasp by a new fraction; like quicksilver, when we
endeavour to seize it. But as in fact there must be something,
which terminates the idea of every finite quantity; and as this
terminating {1:350} idea cannot itself consist of parts or inferior
ideas; otherwise it wou'd be the last of its parts, which finish'd
the idea, and so on; this is a clear proof, that the ideas of
surfaces, lines and points admit not of any division; those of
surfaces in depth; of lines in breadth and depth; and of points
in any dimension.
The school were so sensible of the force of this argument, that
some of them maintained, that nature has mix'd among those particles
of matter, which are divisible in infinitum, a number of mathematical
points, in order to give a termination to bodies; and others eluded
the force of this reasoning by a heap of unintelligible cavils
and distinctions. Both these adversaries equally yield the victory.
A man who hides himself, confesses as evidently the superiority
of his enemy, as another, who fairly delivers his arms.
Thus it appears, that the definitions of mathematics destroy
the pretended demonstrations; and that if we have the idea of
indivisible points, lines and surfaces conformable to the definition,
their existence is certainly possible: but if we have no such
idea,'tis impossible we can ever conceive the termination of any
figure; without which conception there can be no geometrical demonstration.
But I go farther, and maintain, that none of these demonstrations
can have sufficient weight to establish such a principle, as this
of infinite divisibility; and that because with regard to such
minute objects, they are not properly demonstrations, being built
on ideas, which are not exact, and maxims, which are not precisely
true. When geometry decides anything concerning the proportions
of quantity, we ought not to look for the utmost precision and
exactness. None of its proofs extend so far. It takes the dimensions
and proportions of figures justly; but roughly, and with some
liberty. Its errors are never considerable; nor wou'd it err at
all, did it not aspire to such an absolute perfection.
I first ask mathematicians, what they mean when they f,a.y one
line or surface is /EQUAL\ to, or /GREATER\ or /LESS\ than another?
Let any of them give an answer, to whatever sect he belongs, and
whether he maintains the composition of extension by indivisible
points, or by quantities divisible in infinitum. This question
will embarrass both of them. {1:351}
There are few or no mathematicians, who defend the hypothesis
of indivisible points; and yet these have the readiest and justest
answer to the present question. They need only reply, that lines
or surfaces are equal, when the numbers of points in each are
equal; and that as the proportion of the numbers varies, the proportion
of the lines and surfaces is also vary'd. But tho' this answer
be just, as well as obvious; yet I may affirm, that this standard
of equality is entirely useless, and that it never is from such
a comparison we determine objects to be equal or unequal with
respect to each other. For as the points, which enter into the
composition of any line or surface, whether perceiv'd by the sight
or touch, are so minute and so confounded with each other, that
'tis utterly impossible for the mind to compute their number,
such a computation will Never afford us a standard by which we
may judge of proportions. No one will ever be able to determine
by an exact numeration, that an inch has fewer points than a foot,
or a foot fewer than an ell or any greater measure: for which
reason we seldom or never consider this as the standard of equality
or inequality.
As to those, who imagine, that extension is divisible in infinitum,
'tis impossible they can make use of this answer, or fix the equality
of any line or surface by a numeration of its component parts.
For since, according to their hypothesis, the least as well as
greatest figures contain an infinite number of parts; and since
infinite numbers, properly speaking, can neither be equal nor
unequal with respect to each other; the equality or inequality
of any portions of space can never depend on any proportion in
the number of their parts. 'Tis true, it may be said, that the
inequality of an ell and a yard consists in the different numbers
of the feet, of which they are compos'd; and that of a foot and
a yard in the number of the inches. Bat as that quantity we call
an inch in the one is suppos'd equal to what we call an inch in
the other, and as 'tis impossible for the mind to find this equality
by proceeding in infinitum with these references to inferior quantities:
'tis evident, that at last we must fix some standard of equality
different from an enumeration of the parts.
There are some, who pretend, that equality is best defin'd {1:352}
by congruity, and that any two figures are equal, when upon the
placing of one upon the other, all their parts correspond to and
touch each other. In order to judge of this definition let us
consider, that since equality is a relation, it is not, strictly
speaking, a property in the figures themselves, but arises merely
from the comparison, which the mind makes betwixt them.' If it
consists, therefore, in this imaginary application and mutual
contact of parts, we must at least have a distinct notion of these
parts, and must conceive their contact. Now 'tis plain, that in
this conception we wou'd run up these parts to the greatest minuteness,
which can possibly be conceiv'd; since the contact of large parts
wou'd never render the figures equal. But the minutest parts we
can conceive are mathematical points; and consequently this standard
of equality is the same with that deriv'd from the equality of
the number of points; which we have already determined to be a
just but an useless standard. We must therefore look to some other
quarter for a solution of the present difficulty.
[The following paragraph is added from the appendix] There are
many philosophers, who refuse to assign any standard of equality,
but assert, that 'tis sufficient to present two objects, that
are equal, in order to give us a just notion of this proportion.
All definitions, say they, are fruitless, without the perception
of such objects; and where we perceive such objects, we no longer
stand in need of any definition. To this reasoning, I entirely
agree.; and assert, that the only useful notion of equality, or
inequality, is deriv'd from the whole united appearance and the
comparison of particular objects.
'Tis evident, that the eye, or rather the mind is often able
at one view to determine the proportions of bodies, and pronounce
them equal to, or greater or less than each other, without examining
or comparing the number of their minute parts. Such judgments
are not only common, but in many cases certain and infallible.
When the measure of a yard and that of a foot are presented, the
mind can no more question, that the first is longer than the second,
than it can doubt of those principles, which are the most clear
and self-evident.
There are therefore three proportions, which the mind distinguishes
in the general appearance of its objects, and calls by the names
of greater, less and equal. But tho' its {1:353} decisions concerning
these proportions be sometimes infallible, they are not always
so; nor are our judgments of this kind more exempt from doubt
and error than those on any other subject. We frequently correct
our first opinion by a review and reflection; and pronounce those
objects to be equal, which at first we esteem'd unequal; and regard
an object as less, tho' before it appear'd greater than another.
Nor is this the only correction, which these judgments of our
senses undergo; but we often discover our error by a juxtaposition
of the objects; or where that is impracticable, by the use of
some common and invariable measure, which being successively apply'd
to each, informs us of their different proportions. And even this
correction is susceptible of a new correction., and of different
degrees of exactness, according to the nature of the instrument,
by which we measure the bodies, and the care which we employ in
the comparison.'
When therefore the mind is accustomed to these judgments and
their corrections, and finds that the same proportion which makes
two figures have in the eye that appearance, which we call equality,
makes them also correspond to each other, and to any common measure,
with which they are compar'd, we form a mix'd notion of equality
deriv'd both from the looser and stricter methods of comparison.
But we are not content with this. For as sound reason convinces
us that there are bodies vastly more minute than those, which
appear to the senses; and as a false reason wou'd perswade us,
that there are bodies infinitely more minute; we clearly perceive,
that we are not possess'd of any instrument or art of measuring,
which can secure us from ill error and uncertainty. We are sensible,
that the addition or removal of one of these minute parts, is
not discernible either in the appearance or measuring; and as
we imagine, that two figures, which were equal before, cannot
be equal after this removal or addition, we therefore suppose
some imaginary standard of equality, by which the appearances
and measuring are exactly corrected, and the figures reduc'd entirely
to that proportion. This standard is plainly imaginary. For as
the very idea of equality is that of such a particular appearance
corrected by juxtaposition or a common measure. the notion of
any correction beyond what we have instruments and art to make,
is a mere fiction of the mind, and useless {1:354} as well as
incomprehensible. But tho' this standard be only imaginary, the
fiction however is very natural; nor is anything more usual, than
for the mind to proceed after this manner with any action, even
after the reason has ceas'd, which first determined it to begin.
This appears very conspicuously with regard to time; where tho'
'tis evident we have no exact method of determining the proportions
of parts, not even so exact as in extension, yet the various corrections
of our measures, and their different degrees of exactness, have
given as an obscure and implicit notion of a perfect and entire
equality. The case is the same in many other subjects. A musician
finding his ear becoming every day more delicate, and correcting
himself by reflection and attention, proceeds with the same act
of the mind, even when the subject fails him, and entertains a
notion of a compleat <tierce> or <octave>, without
being able to tell whence he derives his standard. A painter forms
the same fiction with regard to colours. A mechanic with regard
to motion. To the one light and shade; to the other swift and
slow are imagin'd to be capable of an exact comparison and equality
beyond the judgments of the senses.
We may apply the same reasoning to /CURVE\ and /RIGHT\ lines.
Nothing is more apparent to the senses, than the distinction betwixt
a curve and a right line; nor are there any ideas we more easily
form than the ideas of these objects. But however easily we may
form these ideas, 'tis impossible to produce any definition of
them, which will fix the precise boundaries betwixt them. When
we draw lines upon paper, or any continu'd surface, there is a
certain order, by which the lines run along from one point to
another, that they may produce the entire impression of a curve
or right line; but this order is perfectly unknown, and nothing
is observ'd but the united appearance. Thus even upon the system
of indivisible points, we can only form a distant notion of some
unknown standard to these objects. Upon that of infinite divisibility
we cannot go even this length; but are reduc'd meerly to the general
appearance, as the rule by which we determine lines to be either
curve or right ones. But tho' we can give no perfect definition
of these lines, nor produce any very exact method of distinguishing
the one from the other; yet this hinders us not from correcting
the first appearance by a more accurate consideration, and by
a comparison {1:355} with some rule, of whose rectitude from repeated
trials we have a greater assurance. And 'tis from these corrections,
and by carrying on the same action of the mind, even when its
reason fails us, that we form the loose idea of a perfect standard
to these figures, without being able to explain or comprehend
it.
'Tis true, mathematicians pretend they give an exact definition
of a right line, when they say, it is the shortest way betwixt
two points. But in the first place I observe, that this is more
properly the discovery of one of the properties of a right line,
than a just deflation of it. For I ask any one, if upon mention
of a right line he thinks not immediately on such a particular
appearance, and if 'tis not by accident only that he considers
this property? A right line can be comprehended alone; but this
definition is unintelligible without a comparison with other lines,
which we conceive to be more extended. In common life 'tis established
as a maxim, that the straightest way is always the shortest; which
wou'd be as absurd as to say, the shortest way is always the shortest,
if our idea of a right line was not different from that of the
shortest way betwixt two points.
Secondly, I repeat what I have already established, that we have
no precise idea of equality and inequality, shorter and longer,
more than of a right line or a curve; and consequently that the
one can never afford us a perfect standard for the other. An exact
idea can never be built on such as are loose and undetermined.
The idea of a plain surface is as little susceptible of a precise
standard as that of a right line; nor have we any other means
of distinguishing such a surface, than its general appearance.
'Tis in vain, that mathematicians represent a plain surface as
produc'd by the flowing of a right line. 'Twill immediately be
objected, that our idea of a surface is as independent of this
method of forming a surface, as our idea of an ellipse is of that
of a cone; that the idea of a right line is no more precise than
that of a plain surface; that a right line may flow irregularly,
and by that means form a figure quite different from a plane;
and that therefore we must suppose it to flow along two right
lines, parallel to each other, and on the same plane; which is
a description, that explains a thing by itself, and returns in
a circle. {1:356}
It appears, then, that the ideas which are most essential to
geometry, viz. those of equality and inequality, of a right line
and a plain surface, are far from being exact and determinate,
according to our common method of conceiving them. Not only we
are incapable of telling, if the case be in any degree doubtful,
when such particular figures are equal; when such a line is a
right one, and such a surface a plain one; but we can form no
idea of that proportion, or of these figures, which is firm and
invariable. Our appeal is still to the weak and fallible judgment,
which we make from the appearance of the objects, and correct
by a compass or common measure; and if we join the supposition
of any farther correction, 'tis of such-a-one as is either useless
or imaginary. In vain shou'd we have recourse to the common topic,
and employ the supposition of a deity, whose omnipotence may enable
him to form a perfect geometrical figure, and describe a right
line without any curve or inflexion. As the ultimate standard
of these figures is deriv'd from nothing but the senses and imagination,
'tis absurd to talk of any perfection beyond what these faculties
can judge of; since the true perfection of any thing consists
in its conformity to its standard.
Now since these ideas are so loose and uncertain, I wou'd fain
ask any mathematician what infallible assurance he has, not only
of the more intricate,,, and obscure propositions of his science,
but of the most vulgar and obvious principles? How can he prove
to me, for instance, that two right lines cannot have one common
segment? Or that 'tis impossible to draw more than one right line
betwixt any two points? Shou'd be tell me, that these opinions
are obviously absurd, and repugnant to our clear ideas; I would
answer, that I do not deny, where two right lines incline upon
each other with a sensible angle, but 'tis absurd to imagine them
to have a common segment. But supposing these two lines to approach
at the rate of an inch in twenty leagues, I perceive no absurdity
in asserting, that upon their contact they become one. For, I
beseech you, by what rule or standard do you judge, when you assert,
that the line, in which I have suppos'd them to concur, cannot
make the same right line with those two, that form so small an
angle betwixt them? You must surely have some idea of a right
line, to which this line does not agree. Do you therefore mean
that it {1:357} takes not the points in the same order and by
the same rule., as is peculiar and essential to a right line?
If so, I must inform you, that besides that in judging after this
manner you allow, that extension is compos'd of indivisible points
(which, perhaps, is more than you intend) besides this, I say,
I must inform you, that neither is this the standard from which
we form the idea of a right line; nor, if it were, is there any
such firmness in our- senses or imagination, as to determine when
such an order is violated or preserv'd. The original standard
of a right line is in reality nothing but a certain general appearance;
and 'tis evident right lines may be made to concur with each other,
and yet correspond to this standard, tho' corrected by all the
means either practicable or imaginable.
[This paragraph is inserted from the appendix.] To whatever side
mathematicians turn, this dilemma still meets them. If they judge
of equality, or any other proportion, by the accurate and exact
standard, viz. the enumeration of the minute indivisible parts,
they both employ a standard, which is useless in practice, and
actually establish the indivisibility of extension, which they
endeavour to explode. Or if they employ, as is usual, the inaccurate
standard, deriv'd from a comparison of objects, upon their general
appearance, corrected by measuring and juxtaposition; their first
principles, tho' certain and infallible, are too coarse to afford
any such subtile inferences as they commonly draw from them. The
first principles are founded on the imagination and senses: The
conclusion, therefore, can never go beyond, much less contradict
these faculties.
This may open our eyes a little, and let us see, that no geometrical
demonstration for the infinite divisibility of extension can have
so much force as what we naturally attribute to every argument,
which is supported by such magnificent pretensions. At the same
time we may learn the reason, why geometry falls of evidence in
this single point,, while all its other reasonings command our
fullest assent and approbation. And indeed it seems more requisite
to give the reason of this exception, than to shew, that we really
must make such an exception, and regard all the mathematical arguments
for infinite divisibility as utterly sophistical. For 'tis evident,
that as no idea of quantity is infinitely {1:358} divisible, there
cannot be imagin'd a more glaring absurdity, than to endeavour
to prove, that quantity itself admits of such a division; and
to prove this by means of ideas, which are directly opposite in
that particular. And as this absurdity is very glaring in itself,
so there is no argument founded on it'. which is not attended
with a new absurdity, and involves not an evident contradiction.
I might give as instances those arguments for infinite divisibility,
which are deriv'd from the point of contact. I know there is no
mathematician, who will not refuse to be judg'd by the diagrams
he describes upon paper, these being loose draughts, as he will
tell us, and serving only to convey with greater facility certain
ideas, which are the true foundation of all our reasoning. This
I am satisfy'd with, and am willing to rest the controversy merely
upon these ideas. I desire therefore our mathematician to form,
as accurately as possible, the ideas of a circle and a right line;
and I then ask, if upon the conception of their contact he can
conceive them as touching in a mathematical point, or if he must
necessarily imagine them to concur for some space. Whichever side
he chuses, he runs himself into equal difficulties. If he affirms,
that in tracing these figures in his imagination, he can imagine
them to touch only in a point, he allows the possibility of that
idea, and consequently of the thing. If he says, that in his conception
of the contact of those lines he must make them concur, he thereby
acknowledges the fallacy of geometrical demonstrations, when carry'd
beyond a certain degree of minuteness; since 'tis certain he has
such demonstrations against the concurrence of a circle and a
right line; that is, in other words, be can prove an idea, viz.
that of concurrence, to be <incompatible> with two other
ideas, those of a circle and right line; tho' at the same time
he acknowledges these ideas to be inseparable.
SECT. V.-The same subject continued.
If the second part of my system be true, that the idea of space
or extension is nothing but the idea of visible or tangible points
distributed in a certain order; it follows, that we can form no
idea of a vacuum, or space, where there is nothing visible or
tangible.' This gives rise to three objections, {1:359} which
I shall examine together, because the answer I shall give to one
is a consequence of that which I shall make use of for the others.
First, It may be said, that men have disputed for many ages concerning
a vacuum and a plenum, without being able to bring the affair
to a final decision; and philosophers, even at this day, think
themselves at liberty to take part on either side, as their fancy
leads them. But whatever foundation there may be for a controversy
concerning the things themselves, it may be pretended, that the
very dispute is decisive concerning the idea, and that 'tis impossible
men cou'd so long reason about a vacuum, and either refute or
defend it, without having a notion of what they refuted or defended.
Secondly, If this argument shou'd be contested, the reality or
at least the possibility of the idea of a vacuum may be prov'd
by the following reasoning. Every idea is possible, which is a
necessary and infallible consequence of such as are possible.
Now tho' we allow the world to be at present a plenum, we may
easily conceive it to be depriv'd of motion; and this idea will
certainly be allow'd possible. It must also be allow'd possible,
to conceive the annihilation of any part of matter by the omnipotence
of the deity, while the other parts remain at rest. For as every
idea, that is distinguishable, is separable by the imagination;
and as every idea, that is separable by the imagination, may be
conceiv'd to be separately existent; 'tis evident, that the existence
of one particle of matter, no more implies the existence of another,
than a square figure in one body implies a square figure in every
one. This being granted, I now demand what results from the concurrence
of these two possible ideas of rest and annihilation, and what
must we conceive to follow upon the annihilation of all the air
and subtile matter in the chamber, supposing the walls to remain
the same, without any motion or alteration? There are some metaphysicians,
who answer, that since matter and extension are the same, the
annihilation of one necessarily implies that of the other; and
there being now no distance betwixt the walls of the chamber,
they touch each other; in the same manner as my hand touches the
paper, which is immediately 'before me. But tho' this answer be
very common, I defy these metaphysicians to conceive the matter
according to {1:360} their hypothesis, or imagine the floor and
roof, with all the opposite sides of the chamber, to touch each
other, while they continue in rest, and preserve the same position.
For how can the two walls, that run from south to north, touch
each other, while they touch the opposite ends of two walls, that
run from east to west? And how can the floor and. roof ever meet,
while they are separated by the four walls, that lie in a contrary
position? If you change their position, you suppose a motion.
If you conceive any thing betwixt them, you suppose a new creation.
But keeping strictly to the two ideas of rest and annihilation,
'tis evident, that the idea, which results from them, is not that
of a contact of parts, but something else; which is concluded
to be the idea of a vacuum.
The third objection carries the matter still farther, and not
only asserts, that the idea of a vacuum is real and possible,
but also necessary and unavoidable. This assertion is founded
on the motion we observe in bodies, which, 'tis maintain'd, wou'd
be impossible and inconceivable without a vacuum, into which one
body must move in order to make way for another.. I shall not
enlarge upon this objection, because it principally belongs to
natural philosophy, which lies without our present sphere.
In order to answer these objections, we must take the matter
pretty deep, and consider the nature and origin of several ideas,,
lest we dispute without understanding perfectly the subject of
the controversy. 'Tis evident the idea of darkness is no positive
idea, but merely the negation of .light, or more properly speaking,
of colour'd and visible objects. A man, who enjoys his sight,
receives no other perception from turning his eyes on every side,
when entirely depriv'd of light, than what is common to him with
one born blind; and 'tis certain such-a-one has no idea either
of light or darkness. The consequence of this is, that 'tis not
from the mere removal of visible objects we receive the impression
of extension without matter; and that the idea of utter darkness
can never be the same with that of vacuum.
Suppose again a man to be Supported in the air, and to be softly
convey'd along by some invisible power; 'tis evident 'he is sensible
of nothing, and never receives the idea of extension, nor indeed
any idea, from this invariable motion. Even supposing he moves
his limbs to and fro, this cannot {1:361} convey to him that idea.
He feels in that case a certain sensation or impression, the parts
of which are successive to each other, and may give him the idea
of time: But certainly are not dispos'd in such a manner, as is
necessary to convey the idea of s ace or the idea of space or
extension.
Since then it appears, that darkness and motion, with the utter
removal of every thing visible and tangible, can never give us
the idea of extension without matter, or of a vacuum; the next
question is, whether they can convey this idea, when mix'd with
something visible and tangible?
'Tis commonly allow'd by philosophers, that all bodies, which
discover themselves to the eye, appear as if painted on a plain
surface, and that their different degrees of remoteness from ourselves
are discovered more by reason than by the senses. When I hold
up my hand before me, and spread my fingers, they are separated
as perfectly by the blue colour of the firmament, as they cou'd
be by any visible object, which I cou'd place betwixt them. In
order, therefore, to know whether the sight can convey the impression
and idea of a vacuum, we must suppose, that amidst an entire darkness,
there are luminous bodies presented to us, whose light discovers
only these bodies themselves, without giving us any impression
of the surrounding objects.
We must form a parallel supposition concerning the objects of
our feeling. 'Tie not proper to suppose a perfect removal of all
tangible objects: we must allow something to be perceiv'd by the
feeling; and after an interval and motion of the hand or other
organ of sensation, another object of the touch to be met with;
and upon leaving that, another; and so on, as often as we please.
The question is, whether these intervals do not afford us the
idea of extension without body?
To begin with the first case; 'tis evident, that when only two
luminous bodies appear to the eye, we can perceive, whether they
be conjoin'd or separate: whether they be separated by a great
or small distance; and if this distance varies, we can perceive
its increase or diminution, with the motion of the bodies. But
as the distance is not in this case any thing colour'd or visible,
it may be thought that there is here a vacuum or pure extension,
not only intelligible to the mind, but obvious to the very senses.
This is our natural and most familiar way of thinking; but which
we shall learn to correct by a little reflection. We {1:362} may
observe, that when two bodies present themselves, where there
was formerly an entire darkness, the only change, that is discoverable,
is in the appearance of these two objects, and that all t-he rest
continues to be as before, a perfect negation of light, and of
every colour'd or visible object. This is not only true of what
may be said to be remote from these bodies, but also of the very
distance; which is interposed betwixt them; that being nothing
but darkness, or the negation of light; without parts, without
composition, invariable and indivisible. Now since this distance
causes no perception different from what a blind man receives
from his eyes, or what is convey'd to us in the darkest night,
it must partake of the same properties: And as blindness and darkness
afford us no ideas of extension, 'tis impossible that the dark
and undistinguishable distance betwixt two bodies can ever produce
that idea.
The sole difference betwixt an absolute darkness and the appearance
of two or more visible luminous objects consists, as I said, in
the objects themselves, and in the manner they affect our senses.
The angles, which the rays of light flowing from them, form with
each other; the motion that is requir'd in the eye, in its passage
from one to the other; and the different parts of the organs,
which are affected by them; these produce the only perceptions,
from which we can judge of the distance. But as these perceptions
are each of them simple and indivisible, they can never give us
the idea of extension.
We may illustrate this by considering the sense of feeling, and
the imaginary distance or interval interpos'd betwixt tangible
or solid objects. I suppose two cases, viz. that of a man supported
in the air, and moving his limbs to and fro, without meeting any
thing tangible; and that of a man, who feeling something tangible,
leaves it, and after a motion, of which he is sensible, perceives
another tangible object; and I then ask, wherein consists the
difference betwixt these two cases? No one will make any scruple
to affirm, that it consists meerly in the perceiving those objects,
and that the sensation, which arises from the motion, is in both
cases the same: And as that sensation is not capable {1:363} of
conveying to us an idea of extension, when unaccompany'd with
some other perception, it can no more give us that idea, when
mix'd with the impressions of tangible objects; since that mixture
produces no alteration upon it.