A Treatise of Human Nature
PART I.2: Of The Ideas Of Space And Time
SECT. I. OF THE INFINITE DIVISIBILITY OF OUR IDEAS OF SPACE AND TIME.
Whatever has the air of a paradox, and is contrary to the first and most unprejudiced
notions of mankind, is often greedily embraced by philosophers, as shewing the
superiority of their science, which coued discover opinions so remote from vulgar
conception. On the other hand, anything proposed 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
It is universally allowed, that the capacity of the mind is limited, and can never attain a
full and adequate conception of infinity: And though it were not allowed, it would be
sufficiently evident from the plainest observation and experience. It is also obvious, that
whatever is capable of being divided in infinitum, must consist of an infinite number of
parts, and that it is 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 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.
It is 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 supposed 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.
It is 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; it is plain, that the moment before it vanished the image or
impression was perfectly indivisible. It is not for want of rays of light striking on our
eyes, that the minute parts of distant bodies convey not any sensible impression; but