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Of Atoms and Perfectly Solid Bodies
by Jonathan Edwards
Proposition. 1. All bodies
whatsoever, except atoms themselves, must of absolute necessity be
composed of atoms, or of bodies that are indiscerpible, that cannot be
made less, or whose parts cannot by any finite power whatsoever, be
separated one from another. And this will be fully seen as soon as it is
seen what bodies those are that are indiscerpible, or what is requisite
in a body in order to cause it to be so. And here we shall lay down this
proposition: that that body that is absolutely plenum, or that has every
part of space included within its surface impenetrable, is indivisible,
and that the parts thereof can by no means [be] separated from each
other by any force how great soever. As for instance, suppose the body B
(see Figure 1) to be what we call an absolute plenum, and suppose the
two bodies A and C to come as impetuously and with as great force as you
please, and strike on each side of the body B: I say the two bodies A
and C could cause no faction in the body B.
And again, suppose the
body D to be a perfectly solid body, and to be as pressingly jammed up
as you please between the two bodies E and F, which are supposed not in
the least to give way to the body D. The surfaces of them which touch
the body D are supposed everywhere perfectly even and plain, and to
continue parallel to each other, and to be every way infinitely
extended. I say the body D could not be broken by the pressure of the
bodies E and F. For suppose the body D to begin to be broken and
crumbled into parts by the pressure of the bodies E and F. If the whole
body D can be broken by that pressure, then the parts of the body D can
still be broken again by the pressure of the same bodies with equal
reason (supposing the bodies still to continue pressing towards each
other). And then, too, their parts can still be broken into other parts,
and so on, and that as fast as the motion of the bodies E and F towards
each other shall require. And truly, I think if it be so that the parts
can be broken still finer and finer, they can be broken so fast as not
to retard the motion of the bodies E and F at all. If so, surely the
bodies E and F will presently meet so as to touch intimately everywhere,
inasmuch as it was said the surfaces of the bodies were perfectly even
and continued parallel. And then I ask what is become of the body D? I
think there can be no other answer but that it is annihilated, since it
was said the two bodies were infinitely extended. So that we see, if the
body D can be broken by the bodies E and F, then it can be annihilated
by them, which I believe nobody will own. And the case is all one, let
the body D be of whatsoever figure. Q.E.D.
For if the two bodies A and C should cause any fractions in the body B,
those fractions must be in some certain places or parts of the body and
not in others. For there cannot be fractions in every part. For I
suppose everybody will own that after the body is supposed to be broken,
there remain parts of the broken body which are unbroken. And so it will
be. Let the body be broken into as fine parts as you please, those fine
parts are still unbroken. The fraction is not through the midst of those
parts, as it is between them. So the fraction must be, if at all, in
some places and not in others. And indeed breaking of a body all over or
in every part is the same as to annihilate it. We say then that the body
B cannot be broken in some parts and not in others by the bodies A and
C, for if it is broken in this part and not in that it must be because
’tis easier broken in this than in that. But a body perfectly solid, and
that is absolutely full, is everywhere equally full, equally solid, and
equally strong, and indeed everywhere absolutely alike, so that there is
nothing that should cause a fraction in one place sooner than in
another. But here I foresee that it will be immediately objected, to
render what has been said invalid, “But what if the body B (see Figure
1) should begin first to be broken off et the corners, where pieces
would be more easily cracked off than in other places? And what if it
were less in some places than others, or what if the bodies A and C were
applied with much greater force in some places than others?” These
objections seem at first quite to render all good for nothing. But I
must say that, notwithstanding these objections, what has been said does
prove that, suppose the perfectly solid body were everywhere equally
bulky, and the bodies A and C were all along applied with equal force,
the perfectly solid body could never be broken. And to them that say it
would first break at the corners, I ask how near the corner the first
fraction would be. If they tell me so near, I ask, “Why was it not
nearer still, since that the nearer the corner, the easier and sooner
broken?” If after that the place for the first fraction be assigned
nearer yet, I ask still, “Why not nearer still?” So that at last they
must be forced to say that the first fraction would be infinitely near
the corner, or that the first piece that would be broken off would be
infinitely little. And they had as good say that none at all would be
broken off first. For as I take it, an actually infinitely little body
and no body at all are the same thing or rather the same nothing.
And as to the other two parts of the objection, ’tis enough for them if
we can discover it to be the nature of perfectly solid bodies not to be
broken, or to resist any however great force, as it will appear rather
more plain by another instance. As suppose the body e (see Figure 3) to
be a perfect solid in that shape (wider at the upper, and by degrees to
come quite to a point at the lower), and to be thrust with indefinitely
great force towards the corner g against the sides fg and gh, which are
supposed not at all to give way. It has been proved already that, if it
would break anywhere, it would be at the lower point first; and what we
have said concerning the corners of the body B (in Figure 1) proves that
it would [not] break there. Now since that nothing but the perfect
solidity can hinder the body e from breaking, we have certainly found
out that a perfectly solid body cannot be broken. For the body e may be
as great or as small, as long and as slender as you please: the case is
the same. And let the force that e is to withstand be as great as you
please — if the weight of the universe falling against it from never so
great a distance, and as much more as you please — we can prove, and
what is said above does prove, that it would neither bend nor break, but
stiffly bear the shock of it all.
Corollary 1. From what was said concerning the first and second figures,
it plainly appears that breaking of a perfectly solid body and the
annihilation of it are the same thing, so far that the breaking of it
would be the annihilating of it.
Corollary 2. Hence [it] appears that solidity and impenetrability and
indivisibility are the same thing, if run up to their first principles.
For, as in the first figure, the solidity of the body B is that whereby
it so far resists the bodies A and C that they shall not be able, till
the body B is out of the way, closely everywhere to touch each other.
That is to say, the force of the two (A and C) endeavoring to meet could
not be the annihilating of the body B, for the meeting of them would be
the annihilating of it. By the second case also. The indivisibility of
the body B in the first figure, and the body D in the second figure, has
been proved to be that also whereby the bodies B and D resist that the
bodies pressing upon them should touch each other; inasmuch as the
breaking of them would certainly admit of it, and would be their
annihilation.
Corollary 3. It appears from the two demonstrations and the two first
corollaries that solidity, indivisibility and resisting to be
annihilated are the same thing, and that bodies resist division and
penetration only as they obstinately persevere to be.
Corollary 4. Since that by the preceding corollary, solidity is the
resisting to be annihilated, or the persevering to be of a body, or to
speak plain, the being of it (for being and persevering to be are the
same thing, looked upon two a little different ways), it follows that
the very essence and being of bodies is solidity; or rather, that body
and solidity are the same. If here it shall be said, by way of
objection, that body has other qualities besides solidity, I believe it
will appear to a nice eye that it hath no more real ones. What do you
say, say they, to extension, figure and mobility? As to extension, I
say, I am satisfied it has none more than space without body, except
what results from solidity. As for figure, ’tis nothing but a
modification of solidity, or of the extension of solidity, and as to
mobility, it is but the communicability of this solidity from one part
of space to another.
Or thus, since that by corollary 1 annihilation and breaking are the
same, their contraries, being and indivisibility, must also be the same;
and since by corollary 2 indivisibility and solidity are the same, it
follows that the solidity of bodies and the being of bodies is the same,
or that body and solidity are the same.
Corollary 5. From what has been said, it appears that the nature of an
atom, or a minimum physicum (that is, if we mean by those terms a body
that can’t be made less — which is the only sensible meaning of the
words) does not at all consist in littleness, as generally used to be
thought. For by our philosophy, an atom may be as big as the universe,
because any body, of whatsoever bigness, were an atom if it were a
perfect solid.
N.B. It will be needful here a little to explain what it is that we mean
by “perfectly solid,” “absolute plenum,” etc., for that we have laid
down that that is an absolutely full, a solid body, that has every part
of space included within its surface solid or impenetrable. Our meaning
is very liable to be mistaken, unless a little explained. We intend not
but that a perfect solid may be very full of pores, though perhaps
improperly so called, interspersed up and down in it, as in the perfect
solid L (see Figure 4). ’Tis only requisite that every part of the body
L should be intimately conjoined with some other parts of it, so as not
only barely to touch in some points or lines thereof (I mean
mathematical points or lines), as two perfect globes do, or as a
cylinder, when it lies on one side, does a plane, and as all atoms do
each other except the surfaces where they happen to be infinitely
exactly fitted to join each other. So that the body L, although it may
have some little holes in it, yet it has an absolute plenum continued
all along between these holes, so that ’tis as impregnable as a body
that has no holes at all; and this will be understood more fully
after we have proved that two atoms touching each other by surfaces can
never be separated.
Now ’tis time to apply what we have said concerning atoms, to prove that
all bodies are compounded of such. For if we suppose that all those
bodies which are any way familiar to our senses yet have interstices so
interspersed throughout the whole body that some parts of [it] do only
touch others, and are not conjoined with them, by which they are
rendered imperfectly solid, yet we must allow that those parcels of
matter that are between the pores (that is, betwixt this and the next
adjacent pore) have no pores at all in them, and consequently are
plenums or absolute solids, or atoms; and surely all bodies that have
pores are made up of parcels of matter which are between the pores —
which we have proved to be atoms.
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