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XV. How external place is rightly taken for the superficies of the surrounding body.
And thus we never indeed distinguish space from extension in length, breadth, and depth; we sometimes,
however, consider place as in the thing placed, and at other times as out of it. Internal place indeed differs in
no way from space; but external place may be taken for the superficies that immediately surrounds the thing
placed. It ought to be remarked that by superficies we do not here understand any part of the surrounding
body, but only the boundary between the surrounding and surrounded bodies, which is nothing more than a
mode; or at least that we speak of superficies in general which is no part of one body rather than another, but
is always considered the same, provided it retain the same magnitude and figure. For although the whole
surrounding body with its superficies were changed, it would not be supposed that the body which was
surrounded by it had therefore changed its place, if it meanwhile preserved the same situation with respect to
the other bodies that are regarded as immovable. Thus, if we suppose that a boat is carried in one direction by
the current of a stream, and impelled by the wind in the opposite with an equal force, so that its situation with
respect to the banks is not changed, we will readily admit that it remains in the same place, although the
whole superficies which surrounds it is incessantly changing.
XVI. That a vacuum or space in which there is absolutely no body is repugnant to reason.
With regard to a vacuum, in the philosophical sense of the term, that is, a space in which there is no
substance, it is evident that such does not exist, seeing the extension of space or internal place is not different
from that of body. For since from this alone, that a body has extension in length, breadth, and depth, we have
reason to conclude that it is a substance, it being absolutely contradictory that nothing should possess
extension, we ought to form a similar inference regarding the space which is supposed void, viz., that since
there is extension in it there is necessarily also substance.
XVII. That a vacuum in the ordinary use of the term does not exclude all body.
And, in truth, by the term vacuum in its common use, we do not mean a place or space in which there is
absolutely nothing, but only a place in which there is none of those things we presume ought to be there.
Thus, because a pitcher is made to hold water, it is said to be empty when it is merely filled with air; or if
there are no fish in a fish-pond, we say there is nothing in it, although it be full of water; thus a vessel is said
to be empty, when, in place of the merchandise which it was designed to carry, it is loaded with sand only, to
enable it to resist the violence of the wind; and, finally, it is in the same sense that we say space is void when
it contains nothing sensible, although it contain created and self-subsisting matter; for we are not in the habit
of considering the bodies near us, unless in so far as they cause in our organs of sense, impressions strong
enough to enable us to perceive them. And if, in place of keeping in mind what ought to be understood by
these terms a vacuum and nothing, we afterwards suppose that in the space we called a vacuum, there is not
only no sensible object, but no object at all, we will fall into the same error as if, because a pitcher in which
there is nothing but air, is, in common speech, said to be empty, we were therefore to judge that the air
contained in it is not a substance (RES SUBSISTENS).
XVIII. How the prejudice of an absolute vacuum is to be corrected.
We have almost all fallen into this error from the earliest age, for, observing that there is no necessary
connection between a vessel and the body it contains, we thought that God at least could take from a vessel
the body which occupied it, without it being necessary that any other should be put in the place of the one
OF THE PRINCIPLES OF HUMAN KNOWLEDGE. 31
The Principles of Philosophy
removed. But that we may be able now to correct this false opinion, it is necessary to remark that there is in
truth no connection between the vessel and the particular body which it contains, but that there is an
absolutely necessary connection between the concave figure of the vessel and the extension considered
generally which must be comprised in this cavity; so that it is not more contradictory to conceive a mountain
without a valley than such a cavity without the extension it contains, or this extension apart from an extended
substance, for, as we have often said, of nothing there can be no extension. And accordingly, if it be asked
what would happen were God to remove from a vessel all the body contained in it, without permitting another
body to occupy its place, the answer must be that the sides of the vessel would thus come into proximity with
each other. For two bodies must touch each other when there is nothing between them, and it is manifestly
contradictory for two bodies to be apart, in other words, that there should be a distance between them, and
this distance yet be nothing; for all distance is a mode of extension, and cannot therefore exist without an
extended substance.
XIX. That this confirms what was said of rarefaction.
After we have thus remarked that the nature of corporeal substance consists only in its being an extended
thing, and that its extension is not different from that which we attribute to space, however empty, it is easy
to discover the impossibility of any one of its parts in any way whatsoever occupying more space at one time
than at another, and thus of being otherwise rarefied than in the way explained above; and it is easy to
perceive also that there cannot be more matter or body in a vessel when it is filled with lead or gold, or any
other body however heavy and hard, than when it but contains air and is supposed to be empty: for the
quantity of the parts of which a body is composed does not depend on their weight or hardness, but only on
the extension, which is always equal in the same vase.
XX. That from this the non-existence of atoms may likewise be demonstrated.
We likewise discover that there cannot exist any atoms or parts of matter that are of their own nature
indivisible. For however small we suppose these parts to be, yet because they are necessarily extended, we
are always able in thought to divide any one of them into two or more smaller parts, and may accordingly
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