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Divisibility of Matter.       §16. In Matter, we have no clear Ideas of the smalness of Parts,
much beyond the smallest, that occur to any of our Senses: and
therefore when we talk of the divisibility of Matter in infinitum,
though we have clear Ideas of Division and Divisibility, and have
also clear Ideas of Parts, made out of a whole, by Division; yet we
have but very obscure, and confused Ideas of Corpuscles, or minute
Bodies, so to be divided, when by former Divisions, they are reduced
to a smalness, much exceeding the perception of any of our Senses;
and so all that we have clear, and distinct Ideas of, is of what Division
in general, or abstractly is, and the Relation of Totum and Pars: But
of the bulk of the Body, to be thus infinitely divided after certain
Progressions, I think, we have no clear, nor distinct Idea at all. For
I ask any one, Whether taking the smallest Atom of Dust he ever
saw, he has any distinct Idea, (bating still the Number which con-
cerns not Extension,) betwixt the 100 000, and the 1000 000 part
of it. Or if he think he can refine his Ideas to that Degree, without
losing sight of them, let him add ten Cyphers to each of those
Numbers. Such a degree of smalness is not unreasonable to be
supposed, since a Division carried on so far brings it no nearer the
end of infinite Division, than the first Division into two halfs does.
I must confess for my part, I have no clear, distinct Ideas of the differ-
ent Bulk, or Extension of those Bodies, having but a very obscure
one of either of them. So that, I think, when we talk of Division of
Bodies in infinitum, our Idea of their distinct Bulks, which is the
Subject and Foundation of Division, comes after a little progression,
to be confounded, and almost lost in Obscurity. For that Idea,
which is to represent only Bigness, must be very obscure and
confused, which we cannot distinguish from one ten times as big,
but only by Number: so that we have clear, distinct Ideas, we may
say of Ten and One, but no distinct Ideas of two such Extensions.
’Tis plain from hence, that when we talk of infinite Divisibility of
Body, or Extension, our distinct and clear Ideas are only of Numbers:
but the clear, distinct Ideas of Extension, after some Progress of
Division, is quite lost; and of such minute Parts, we have no dis-
tinct Ideas at all; but it returns, as all our Ideas of Infinite do, at last
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to that of Number always to be added; but thereby never amounts
to any distinct Idea of actual, infinite Parts. We have, ’tis true, a
clear Idea of Division, as often as we will think of it; but thereby we
have no more a clear Idea of infinite Parts in Matter, than we have a
clear Idea of an infinite Number, by being able still to add new
Numbers to any assigned Number we have: endless Divisibility
giving us no more a clear and distinct Idea of actually infinite Parts,
than endless Addibility (if I may so speak) gives us a clear and
distinct Idea of an actually infinite Number. They both being only
in a Power still of increasing the Number, be it already as great as it
will. So that of what remains to be added, (wherein consists the
Infinity,) we have but an obscure, imperfect, and confused Idea;
from or about which we can argue, or reason with no Certainty or
Clearness, no more than we can in Arithmetick, about a Number of
which we have no such distinct Idea, as we have of 4 or 100; but
only this relative obscure one, that compared to any other, it is
still bigger: and we have no more a clear, positive Idea of it, when we
say or conceive it is bigger, or more than 400,000,000, than if we
should say, it is bigger than 40, or 4: 400,000,000, having no nearer
a proportion to the end of Addition, or Number, than 4. For he that
adds only 4 to 4, and so proceeds, shall as soon come to the end of
all Addition, as he that adds 400,000,000, to 400,000,000. And so
likewise in Eternity, he that has an Idea of but four Years, has as
much a positive complete Idea of Eternity, as he that has one of
400,000,000 of Years: For what remains of Eternity beyond either
of these two Numbers of Years, is as clear to the one as the other;
i.e. neither of them has any clear positive Idea of it at all. For he that
adds only 4 Years to 4, and so on, shall as soon reach Eternity, as
he that adds 400,000,000 of Years, and so on; or if he please,
doubles the Increase as often as he will: The remaining Abyss being
still as far beyond the end of all these Progressions, as it is from the
length of a Day, or an Hour. For nothing finite bears any proportion
to infinite; and therefore our Ideas, which are all finite, cannot bear
any. Thus it is also in our Idea of Extension, when we increase it by
Addition, as well as when we diminish it by Division, and would
enlarge our Thoughts to infinite Space. After a few doublings of
those Ideas of Extension, which are the largest we are accustomed to
have, we lose the clear distinct Idea of that Space: it becomes a
confusedly great one, with a Surplus of still greater; about which,
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when we would argue, or reason, we shall always find our selves at a
loss; confused Ideas, in our Arguings and Deductions from that part
of them which is confused, always leading us into confusion.
Locke Hum II, 29, §16, pp. 370-371-372