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
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 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 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.