too great a 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, gravitation or mutual attraction,
because it appears in many instances, some are straightway for pronouncing
_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 shew itself; as in the
perpendicular growth of plants, and the elasticity of the air. There is
nothing necessary or essential in the case(698); but it depends entirely
on the will of the Governing Spirit(699), 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 enquire 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(700)) about the final
causes of things. [(701) For, besides that this would prove a very
pleasing entertainment to the mind, it might be of great advantage, in
that it not only discovers to us the attributes of the Creator, but may
also direct us in several instances to the proper uses and applications of
things.] And I must 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 sects. 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 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(702).
108. It appears from sect. 66, &c. that the steady consistent methods of
nature may not unfitly be styled the Language of its Author, whereby He
discovers His attributes to our view and directs us how to act for the
convenience and felicity of life. Those men who frame(703) general rules
from the phenomena, and afterwards derive(704) the phenomena from those
rules, seem to consider signs(705) rather than causes. (706)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(707) the analogy too far, and by that means run into mistakes.
109. [(708) To carry on the resemblance.] 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, methinks it is beneath the dignity of the
mind to affect an exactness in reducing each particular phenomenon to
general rules, or shewing how it follows from them. We should propose to
ourselves nobler views, such as 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. [(709) 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 those 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.
III. 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. Sects. 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 immoveable; and relative space to be the measure
thereof, which, being moveable and defined by its situation in respect of
sensible bodies, is vulgarly taken for immoveable 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
immoveable. 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 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. But, notwithstanding what hath been said, I must confess it does not
appear to me that there can be any motion other than _relative_(710): so
that to conceive motion there must be conceived at least 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.—[(711)Whether others can conceive it otherwise, a little
attention may satisfy them.]
113. 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 [(712)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 follows 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, [(713) I mean relative motion, for other I am
not able to conceive.]
114. As the place happens to be variously defined, the motion which is
related to it varies(714). 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 Newton’s _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, hath, 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(715) 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(716) it (in which sense there may be apparent motion); but then
it is because the force causing the change(717) of distance is imagined by
us to be [(718)applied or] impressed on that body thought to move. Which
indeed shews we are capable of mistaking a thing to be in motion which is
not, and that is all. [(719)But it does not prove that, in the common
acceptation of motion, a body is moved merely because it changes distance
from another; since as soon as we are undeceived, and find that the moving
force was not communicated to it, we no longer hold it to be moved. So, on
the other hand, when one only body (the parts whereof preserve a given
position between themselves) is imagined to exist, some there are who
think that it can be moved all manner of ways, though without any change
of distance or situation to any other bodies; which we should not deny, if
they meant only that it might have an impressed force, which, upon the
bare creation of other bodies, would produce a motion of some certain
quantity and determination. But that an actual motion (distinct from the
impressed force, or power, productive of change of place in case there
were bodies present whereby to define it) can exist in such a single body,
I must confess I am not able to comprehend.]
116. From what has been said, it follows that the philosophic
consideration of motion doth not imply the being of an _absolute Space_,
distinct from that which is perceived by sense, and related to 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 exclusive of all body_. This I must confess seems
impossible(720), as being a most 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 hath 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(721). 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 shewn, 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, viz. 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 shew that the incommunicable
attributes of God agree to it. Which doctrine, how unworthy soever it may
seem of the Divine Nature, yet I must confess I do not see how we can get
clear of it, so long as we adhere to the received opinions(722).
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
118. Hitherto of Natural Philosophy. We come now to make some inquiry
concerning that other great branch of speculative knowledge, to wit,
Mathematics(723). 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, doth 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 no less deeply concerned than
other men in the errors arising from the doctrine of abstract general
ideas, and the existence of objects without the mind.
119. Arithmetic hath 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 hath set a price on the most trifling numerical
speculations, which in practice are of no use, but serve only for
amusement; and hath heretofore 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 narrowly 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(724).
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 or 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 numerable 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(725).
123. From numbers we proceed to speak of _extension_(726), 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 is
it the principal occasion of all that nice and extreme subtilty, which
renders the study of Mathematics so very 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 hath been.