Books: A Treatise Concerning the Principles of Human Knowledge
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George Berkeley >> A Treatise Concerning the Principles of Human Knowledge
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105. If therefore we consider the difference there is betwixt natural
philosophers and other men, with regard to their knowledge of the
phenomena, we shall find it consists not in an exacter knowledge of the
efficient cause that produces them--for that can be no other than the
will of a spirit--but only in a greater largeness of comprehension,
whereby analogies, harmonies, and agreements are discovered in the works
of nature, and the particular effects explained, that is, reduced to
general rules, see sect. 62, which rules, grounded on the analogy and
uniformness observed in the production of natural effects, are most
agreeable and sought after by the mind; for that they extend our prospect
beyond what is present and near to us, and enable us to make very
probable conjectures touching things that may have happened at very great
distances of time and place, as well as to predict things to come; which
sort of endeavour towards omniscience is much affected by the mind.
106. CAUTION AS TO THE USE OF ANALOGIES.--But we should proceed warily
in such things, for we are apt to lay too great stress on analogies,
and, to the prejudice of truth, humour that eagerness of the mind
whereby it is carried to extend its knowledge into general theorems.
For example, in the business of gravitation or mutual attraction,
because it appears in many instances, some are straightway for
pronouncing it universal; and that to attract and be attracted
by every other body is an essential quality inherent in all bodies
whatsoever. Whereas it is evident the fixed stars have no such
tendency towards each other; and, so far is that gravitation from being
essential to bodies that in some instances a quite contrary principle
seems to show itself; as in the perpendicular growth of plants, and the
elasticity of the air. There is nothing necessary or essential in the
case, but it depends entirely on the will of the Governing Spirit, who
causes certain bodies to cleave together or tend towards each other
according to various laws, whilst He keeps others at a fixed distance;
and to some He gives a quite contrary tendency to fly asunder just as He
sees convenient.
107. After what has been premised, I think we may lay down the following
conclusions. First, it is plain philosophers amuse themselves in vain,
when they inquire for any natural efficient cause, distinct from a mind
or spirit. Secondly, considering the whole creation is the workmanship of
a wise and good Agent, it should seem to become philosophers to employ
their thoughts (contrary to what some hold) about the final causes of
things; and I confess I see no reason why pointing out the various ends
to which natural things are adapted, and for which they were originally
with unspeakable wisdom contrived, should not be thought one good way of
accounting for them, and altogether worthy a philosopher. Thirdly, from
what has been premised no reason can be drawn why the history of nature
should not still be studied, and observations and experiments made,
which, that they are of use to mankind, and enable us to draw any general
conclusions, is not the result of any immutable habitudes or relations
between things themselves, but only of God's goodness and kindness to men
in the administration of the world. See sect. 30 and 31 Fourthly, by a
diligent observation of the phenomena within our view, we may discover
the general laws of nature, and from them deduce the other phenomena; I
do not say demonstrate, for all deductions of that kind depend on a
supposition that the Author of nature always operates uniformly, and in a
constant observance of those rules we take for principles: which we
cannot evidently know.
108. THREE ANALOGIES.--Those men who frame general rules from the
phenomena and afterwards derive the phenomena from those rules, seem
to consider signs rather than causes. A man may well understand
natural signs without knowing their analogy, or being able to say
by what rule a thing is so or so. And, as it is very possible to
write improperly, through too strict an observance of general grammar
rules; so, in arguing from general laws of nature, it is not impossible
we may extend the analogy too far, and by that means run into mistakes.
109. As in reading other books a wise man will choose to fix his thoughts
on the sense and apply it to use, rather than lay them out in grammatical
remarks on the language; so, in perusing the volume of nature, it seems
beneath the dignity of the mind to affect an exactness in reducing each
particular phenomenon to general rules, or showing how it follows from
them. We should propose to ourselves nobler views, namely, to recreate
and exalt the mind with a prospect of the beauty, order. extent, and
variety of natural things: hence, by proper inferences, to enlarge our
notions of the grandeur, wisdom, and beneficence of the Creator; and
lastly, to make the several parts of the creation, so far as in us lies,
subservient to the ends they were designed for, God's glory, and the
sustentation and comfort of ourselves and fellow-creatures.
110. The best key for the aforesaid analogy or natural Science will be
easily acknowledged to be a certain celebrated Treatise of Mechanics. In
the entrance of which justly admired treatise, Time, Space, and Motion
are distinguished into absolute and relative, true and apparent,
mathematical and vulgar; which distinction, as it is at large explained
by the author, does suppose these quantities to have an existence without
the mind; and that they are ordinarily conceived with relation to
sensible things, to which nevertheless in their own nature they bear no
relation at all.
111. As for Time, as it is there taken in an absolute or abstracted
sense, for the duration or perseverance of the existence of things, I
have nothing more to add concerning it after what has been already said
on that subject. Sect. 97 and 98. For the rest, this celebrated author
holds there is an absolute Space, which, being unperceivable to sense,
remains in itself similar and immovable; and relative space to be the
measure thereof, which, being movable and defined by its situation in
respect of sensible bodies, is vulgarly taken for immovable space. Place
he defines to be that part of space which is occupied by any body; and
according as the space is absolute or relative so also is the place.
Absolute Motion is said to be the translation of a body from absolute
place to absolute place, as relative motion is from one relative place to
another. And, because the parts of absolute space do not fall under our
senses, instead of them we are obliged to use their sensible measures,
and so define both place and motion with respect to bodies which we
regard as immovable. But, it is said in philosophical matters we must
abstract from our senses, since it may be that none of those bodies which
seem to be quiescent are truly so, and the same thing which is moved
relatively may be really at rest; as likewise one and the same body may
be in relative rest and motion, or even moved with contrary relative
motions at the same time, according as its place is variously defined.
All which ambiguity is to be found in the apparent motions, but not at
all in the true or absolute, which should therefore be alone regarded in
philosophy. And the true as we are told are distinguished from apparent
or relative motions by the following properties.--First, in true or
absolute motion all parts which preserve the same position with respect
of the whole, partake of the motions of the whole. Secondly, the place
being moved, that which is placed therein is also moved; so that a body
moving in a place which is in motion doth participate the motion of its
place. Thirdly, true motion is never generated or changed otherwise than
by force impressed on the body itself. Fourthly, true motion is always
changed by force impressed on the body moved. Fifthly, in circular motion
barely relative there is no centrifugal force, which, nevertheless, in
that which is true or absolute, is proportional to the quantity of
motion.
112. MOTION, WHETHER REAL OR APPARENT, RELATIVE.--But, notwithstanding
what has been said, I must confess it does not appear to me that
there can be any motion other than relative; so that to conceive
motion there must be at least conceived two bodies, whereof the
distance or position in regard to each other is varied. Hence, if there
was one only body in being it could not possibly be moved. This seems
evident, in that the idea I have of motion doth necessarily include
relation.
113. APPARENT MOTION DENIED.--But, though in every motion it be
necessary to conceive more bodies than one, yet it may be that one
only is moved, namely, that on which the force causing the change
in the distance or situation of the bodies, is impressed. For, however
some may define relative motion, so as to term that body moved
which changes its distance from some other body, whether the force
or action causing that change were impressed on it or no, yet as
relative motion is that which is perceived by sense, and regarded in
the ordinary affairs of life, it should seem that every man of common
sense knows what it is as well as the best philosopher. Now, I ask any
one whether, in his sense of motion as he walks along the streets, the
stones he passes over may be said to move, because they change distance
with his feet? To me it appears that though motion includes a relation of
one thing to another, yet it is not necessary that each term of the
relation be denominated from it. As a man may think of somewhat which
does not think, so a body may be moved to or from another body which is
not therefore itself in motion.
114. As the place happens to be variously defined, the motion which is
related to it varies. A man in a ship may be said to be quiescent with
relation to the sides of the vessel, and yet move with relation to the
land. Or he may move eastward in respect of the one, and westward in
respect of the other. In the common affairs of life men never go beyond
the earth to define the place of any body; and what is quiescent in
respect of that is accounted absolutely to be so. But philosophers, who
have a greater extent of thought, and juster notions of the system of
things, discover even the earth itself to be moved. In order therefore to
fix their notions they seem to conceive the corporeal world as finite,
and the utmost unmoved walls or shell thereof to be the place whereby
they estimate true motions. If we sound our own conceptions, I believe we
may find all the absolute motion we can frame an idea of to be at bottom
no other than relative motion thus defined. For, as has been already
observed, absolute motion, exclusive of all external relation, is
incomprehensible; and to this kind of relative motion all the
above-mentioned properties, causes, and effects ascribed to absolute
motion will, if I mistake not, be found to agree. As to what is said of
the centrifugal force, that it does not at all belong to circular
relative motion, I do not see how this follows from the experiment which
is brought to prove it. See Philosophiae Naturalis Principia Mathematica,
in Schol. Def. VIII. For the water in the vessel at that time wherein it
is said to have the greatest relative circular motion, has, I think, no
motion at all; as is plain from the foregoing section.
115. For, to denominate a body moved it is requisite, first, that it
change its distance or situation with regard to some other body; and
secondly, that the force occasioning that change be applied to it. If
either of these be wanting, I do not think that, agreeably to the sense
of mankind, or the propriety of language, a body can be said to be in
motion. I grant indeed that it is possible for us to think a body which
we see change its distance from some other to be moved, though it have no
force applied to it (in which sense there may be apparent motion), but
then it is because the force causing the change of distance is imagined
by us to be applied or impressed on that body thought to move; which
indeed shows we are capable of mistaking a thing to be in motion which is
not, and that is all.
116. ANY IDEA OF PURE SPACE RELATIVE.--From what has been said it follows
that the philosophic consideration of motion does not imply the
being of an absolute Space, distinct from that which is perceived
by sense and related bodies; which that it cannot exist without the
mind is clear upon the same principles that demonstrate the like
of all other objects of sense. And perhaps, if we inquire narrowly,
we shall find we cannot even frame an idea of pure Space exclusiv
of all body. This I must confess seems impossible, as being a mos
abstract idea. When I excite a motion in some part of my body,
if it be free or without resistance, I say there is Space; but if I
find a resistance, then I say there is Body; and in proportion as the
resistance to motion is lesser or greater, I say the space is more or
less pure. So that when I speak of pure or empty space, it is not to be
supposed that the word "space" stands for an idea distinct from or
conceivable without body and motion--though indeed we are apt to think
every noun substantive stands for a distinct idea that may be separated
from all others; which has occasioned infinite mistakes. When, therefore,
supposing all the world to be annihilated besides my own body, I say
there still remains pure Space, thereby nothing else is meant but only
that I conceive it possible for the limbs of my body to be moved on all
sides without the least resistance, but if that, too, were annihilated
then there could be no motion, and consequently no Space. Some, perhaps,
may think the sense of seeing doth furnish them with the idea of pure
space; but it is plain from what we have elsewhere shown, that the ideas
of space and distance are not obtained by that sense. See the Essay
concerning Vision.
117. What is here laid down seems to put an end to all those disputes and
difficulties that have sprung up amongst the learned concerning the
nature of pure Space. But the chief advantage arising from it is that we
are freed from that dangerous dilemma, to which several who have employed
their thoughts on that subject imagine themselves reduced, to wit, of
thinking either that Real Space is God, or else that there is something
beside God which is eternal, uncreated, infinite, indivisible, immutable.
Both which may justly be thought pernicious and absurd notions. It is
certain that not a few divines, as well as philosophers of great note,
have, from the difficulty they found in conceiving either limits or
annihilation of space, concluded it must be divine. And some of late have
set themselves particularly to show the incommunicable attributes of God
agree to it. Which doctrine, how unworthy soever it may seem of the
Divine Nature, yet I do not see how we can get clear of it, so long as we
adhere to the received opinions.
118. THE ERRORS ARISING FROM THE DOCTRINES OF ABSTRACTION AND EXTERNAL
MATERIAL EXISTENCES, INFLUENCE MATHEMATICAL REASONINGS.--Hitherto of
Natural Philosophy: we come now to make some inquiry concerning
that other great branch of speculative knowledge, to wit, Mathematics.
These, how celebrated soever they may be for their clearness and
certainty of demonstration, which is hardly anywhere else to be
found, cannot nevertheless be supposed altogether free from mistakes, if
in their principles there lurks some secret error which is common to the
professors of those sciences with the rest of mankind. Mathematicians,
though they deduce their theorems from a great height of evidence, yet
their first principles are limited by the consideration of quantity: and
they do not ascend into any inquiry concerning those transcendental
maxims which influence all the particular sciences, each part whereof,
Mathematics not excepted, does consequently participate of the errors
involved in them. That the principles laid down by mathematicians are
true, and their way of deduction from those principles clear and
incontestible, we do not deny; but, we hold there may be certain
erroneous maxims of greater extent than the object of Mathematics, and
for that reason not expressly mentioned, though tacitly supposed
throughout the whole progress of that science; and that the ill effects
of those secret unexamined errors are diffused through all the branches
thereof. To be plain, we suspect the mathematicians are as well as other
men concerned in the errors arising from the doctrine of abstract general
ideas, and the existence of objects without the mind.
119. Arithmetic has been thought to have for its object abstract ideas of
Number; of which to understand the properties and mutual habitudes, is
supposed no mean part of speculative knowledge. The opinion of the pure
and intellectual nature of numbers in abstract has made them in esteem
with those philosophers who seem to have affected an uncommon fineness
and elevation of thought. It has set a price on the most trifling
numerical speculations which in practice are of no use, but serve only
for amusement; and has therefore so far infected the minds of some, that
they have dreamed of mighty mysteries involved in numbers, and attempted
the explication of natural things by them. But, if we inquire into our
own thoughts, and consider what has been premised, we may perhaps
entertain a low opinion of those high flights and abstractions, and look
on all inquiries, about numbers only as so many difficiles nugae, so far
as they are not subservient to practice, and promote the benefit of life.
120. Unity in abstract we have before considered in sect. 13, from which
and what has been said in the Introduction, it plainly follows there is
not any such idea. But, number being defined a "collection of units," we
may conclude that, if there be no such thing as unity or unit in
abstract, there are no ideas of number in abstract denoted by the numeral
names and figures. The theories therefore in Arithmetic. if they are
abstracted from the names and figures, as likewise from all use and
practice, as well as from the particular things numbered, can be supposed
to have nothing at all for their object; hence we may see how entirely
the science of numbers is subordinate to practice, and how jejune and
trifling it becomes when considered as a matter of mere speculation.
121. However, since there may be some who, deluded by the specious show
of discovering abstracted verities, waste their time in arithmetical
theorems and problems which have not any use, it will not be amiss if we
more fully consider and expose the vanity of that pretence; and this will
plainly appear by taking a view of Arithmetic in its infancy, and
observing what it was that originally put men on the study of that
science, and to what scope they directed it. It is natural to think that
at first, men, for ease of memory and help of computation, made use of
counters, or in writing of single strokes, points, or the like, each
whereof was made to signify an unit, i.e., some one thing of whatever
kind they had occasion to reckon. Afterwards they found out the more
compendious ways of making one character stand in place of several
strokes or points. And, lastly, the notation of the Arabians or Indians
came into use, wherein, by the repetition of a few characters or figures,
and varying the signification of each figure according to the place it
obtains, all numbers may be most aptly expressed; which seems to have
been done in imitation of language, so that an exact analogy is observed
betwixt the notation by figures and names, the nine simple figures
answering the nine first numeral names and places in the former,
corresponding to denominations in the latter. And agreeably to those
conditions of the simple and local value of figures, were contrived
methods of finding, from the given figures or marks of the parts, what
figures and how placed are proper to denote the whole, or vice versa. And
having found the sought figures, the same rule or analogy being observed
throughout, it is easy to read them into words; and so the number becomes
perfectly known. For then the number of any particular things is said to
be known, when we know the name of figures (with their due arrangement)
that according to the standing analogy belong to them. For, these signs
being known, we can by the operations of arithmetic know the signs of any
part of the particular sums signified by them; and, thus computing in
signs (because of the connexion established betwixt them and the distinct
multitudes of things whereof one is taken for an unit), we may be able
rightly to sum up, divide, and proportion the things themselves that we
intend to number.
122. In Arithmetic, therefore, we regard not the things, but the signs,
which nevertheless are not regarded for their own sake, but because they
direct us how to act with relation to things, and dispose rightly of
them. Now, agreeably to what we have before observed of words in general
(sect. 19, Introd.) it happens here likewise that abstract ideas are
thought to be signified by numeral names or characters, while they do not
suggest ideas of particular things to our minds. I shall not at present
enter into a more particular dissertation on this subject, but only
observe that it is evident from what has been said, those things which
pass for abstract truths and theorems concerning numbers, are in reality
conversant about no object distinct from particular numeral things,
except only names and characters, which originally came to be considered
on no other account but their being signs, or capable to represent aptly
whatever particular things men had need to compute. Whence it follows
that to study them for their own sake would be just as wise, and to as
good purpose as if a man, neglecting the true use or original intention
and subserviency of language, should spend his time in impertinent
criticisms upon words, or reasonings and controversies purely verbal.
123. From numbers we proceed to speak of Extension, which, considered as
relative, is the object of Geometry. The infinite divisibility of finite
extension, though it is not expressly laid down either as an axiom or
theorem in the elements of that science, yet is throughout the same
everywhere supposed and thought to have so inseparable and essential a
connexion with the principles and demonstrations in Geometry, that
mathematicians never admit it into doubt, or make the least question of
it. And, as this notion is the source from whence do spring all those
amusing geometrical paradoxes which have such a direct repugnancy to the
plain common sense of mankind, and are admitted with so much reluctance
into a mind not yet debauched by learning; so it is the principal
occasion of all that nice and extreme subtilty which renders the study of
Mathematics so difficult and tedious. Hence, if we can make it appear
that no finite extension contains innumerable parts, or is infinitely
divisible, it follows that we shall at once clear the science of Geometry
from a great number of difficulties and contradictions which have ever
been esteemed a reproach to human reason, and withal make the attainment
thereof a business of much less time and pains than it hitherto has been.
124. Every particular finite extension which may possibly be the object
of our thought is an idea existing only in the mind, and consequently
each part thereof must be perceived. If, therefore, I cannot perceive
innumerable parts in any finite extension that I consider, it is certain
they are not contained in it; but, it is evident that I cannot
distinguish innumerable parts in any particular line, surface, or solid,
which I either perceive by sense, or figure to myself in my mind:
wherefore I conclude they are not contained in it. Nothing can be plainer
to me than that the extensions I have in view are no other than my own
ideas; and it is no less plain that I cannot resolve any one of my ideas
into an infinite number of other ideas, that is, that they are not
infinitely divisible. If by finite extension be meant something distinct
from a finite idea, I declare I do not know what that is, and so cannot
affirm or deny anything of it. But if the terms "extension," "parts,"
&c., are taken in any sense conceivable, that is, for ideas, then to say
a finite quantity or extension consists of parts infinite in number is so
manifest a contradiction, that every one at first sight acknowledges it
to be so; and it is impossible it should ever gain the assent of any
reasonable creature who is not brought to it by gentle and slow degrees,
as a converted Gentile to the belief of transubstantiation. Ancient and
rooted prejudices do often pass into principles; and those propositions
which once obtain the force and credit of a principle, are not only
themselves, but likewise whatever is deducible from them, thought
privileged from all examination. And there is no absurdity so gross,
which, by this means, the mind of man may not be prepared to swallow.
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