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Objection 1: It would seem that not even by a miracle is it possible
for two bodies to be in the same place. For it is not possible that,
by a miracle, two bodies be at once two and one, since this would
imply that contradictions are true at the same time. But if we suppose
two bodies to be in the same place, it would follow that those two
bodies are one. Therefore this cannot be done by a miracle. The
minor is proved thus. Suppose two bodies A and B to be in the same
place. The dimensions of A will either be the same as the dimensions
of the place, or they will differ from them. If they differ, then
some of the dimensions will be separate: which is impossible, since
the dimensions that are within the bounds of a place are not in a
subject unless they be in a placed body. If they be the same, then
for the same reason the dimensions of B will be the same as the
dimensions of the place. "Now things that are the same with one and
the same thing are the same with one another." Therefore the
dimensions of A and B are the same. But two bodies cannot have
identical dimensions just as they cannot have the same whiteness.
Therefore A and B are one body and yet they were two. Therefore
they are at the same time one and two.
Objection 2: Further, a thing cannot be done miraculously either
against the common principles---for instance that the part be not
less than the whole; since what is contrary to common principles
implies a direct contradiction---or contrary to the conclusions of
geometry which are infallible deductions from common principles---for
instance that the three angles of a triangle should not be equal to two
right angles. In like manner nothing can be done to a line that is
contrary to the definition of a line, because to sever the definition
from the defined is to make two contradictories true at the same time.
Now it is contrary to common principles, both to the conclusions of
geometry and to the definition of a line, for two bodies to be in the
same place. Therefore this cannot be done by a miracle. The minor is
proved as follows: It is a conclusion of geometry that two circles
touch one another only at a point. Now if two circular bodies were in
the same place, the two circles described in them would touch one
another as a whole. Again it is contrary to the definition of a line
that there be more than one straight line between two points: yet this
would be the case were two bodies in the same place, since between two
given points in the various surfaces of the place, there would be two
straight lines corresponding to the two bodies in that place.
Objection 3: Further, it would seem impossible that by a miracle a
body which is enclosed within another should not be in a place, for
then it would have a common and not a proper place, and this is
impossible. Yet this would follow if two bodies were in the same
place. Therefore this cannot be done by a miracle. The minor is
proved thus. Supposing two bodies to be in the same place, the one
being greater than the other as to every dimension, the lesser body
will be enclosed in the greater, and the place occupied by the greater
body will be its common place; while it will have no proper place,
because no given surface of the body will contain it, and this is
essential to place. Therefore it will not have a proper place.
Objection 4: Further, place corresponds in proportion to the thing
placed. Now it can never happen by a miracle that the same body is at
the same time in different places, except by some kind of
transformation, as in the Sacrament of the Altar. Therefore it can
nowise happen by a miracle that two bodies be together in the same
place.
On the contrary, The Blessed Virgin gave birth to her Son by a
miracle. Now in this hallowed birth it was necessary for two bodies to
be together in the same place, because the body of her child when
coming forth did not break through the enclosure of her virginal
purity. Therefore it is possible for two bodies to be miraculously
together in the same place.
Further, this may again be proved from the fact that our Lord went in
to His disciples, the doors being shut (Jn. 20:19, 26).
I answer that, As shown above (Article 2) the reason why two
bodies must needs be in two places is that distinction in matter
requires distinction in place. Wherefore we observe that when two
bodies merge into one, each loses its distinct being, and one
indistinct being accrues to the two combined, as in the case of
mixtures. Hence it is impossible for two bodies to remain two and yet
be together unless each retain its distinct being which it had
hitherto, in so much as each of them was a being undivided in itself
and distinct from others. Now this distinct being depends on the
essential principles of a thing as on its proximate causes, but on God
as on the first cause. And since the first cause can preserve a thing
in being, though the second causes be done away, as appears from the
first proposition of De Causis, therefore by God's power and by
that alone it is possible for an accident to be without substance as in
the Sacrament of the Altar. Likewise by the power of God, and by
that alone, it is possible for a body to retain its distinct being from
that of another body, although its matter be not distinct as to place
from the matter of the other body: and thus it is possible by a miracle
for two bodies to be together in the same place.
Reply to Objection 1: This argument is sophistical because it is
based on a false supposition, or begs the question. For it supposes
the existence, between two opposite superficies of a place, of a
dimension proper to the place, with which dimension a dimension of the
body put in occupation of the place would have to be identified:
because it would then follow that the dimensions of two bodies occupying
a place would become one dimension, if each of them were identified
with the dimension of the place. But this supposition is false,
because if it were true whenever a body acquires a new place, it would
follow that a change takes place in the dimensions of the place or of
thing placed: since it is impossible for two things to become one
anew, except one of them be changed. Whereas if, as is the case in
truth, no other dimensions belong to a place than those of the thing
occupying the place, it is clear that the argument proves nothing, but
begs the question, because according to this nothing else has been
said, but that the dimensions of a thing placed are the same as the
dimensions of the place; excepting that the dimensions of the thing
placed are contained within the bounds of the place, and that the
distance between the bounds of a place is commensurate with the distance
between the bounds of the thing placed, just as the former would be
distant by their own dimensions if they had them. Thus that the
dimensions of two bodies be the dimensions of one place is nothing else
than that two bodies be in the same place, which is the chief question
at issue.
Reply to Objection 2: Granted that by a miracle two bodies be
together in the same place, nothing follows either against common
principles, or against the definition of a line, or against any
conclusions of geometry. For, as stated above (Article 2),
dimensive quantity differs from all other accidents in that it has a
special reason of individuality and distinction, namely on account of
the placing of the parts, besides the reason of individuality and
distinction which is common to it and all other accidents, arising
namely from the matter which is its subject. Thus then one line may be
understood as being distinct from another, either because it is in
another subject (in which case we are considering a material line),
or because it is placed at a distance from another (in which case we
are considering a mathematical line, which is understood apart from
matter). Accordingly if we remove matter, there can be no
distinction between lines save in respect of a different placing: and
in like manner neither can there be a distinction of points, nor of
superficies, nor of any dimensions whatever. Consequently geometry
cannot suppose one line to be added to another, as being distinct
therefrom unless it be distinct as to place. But supposing by a
Divine miracle a distinction of subject without a distinction of
place, we can understand a distinction of lines; and these are not
distant from one another in place, on account of the distinction of
subjects. Again we can understand a difference of points, and thus
different lines described on two bodies that are in the same place are
drawn from different points to different points; for the point that we
take is not a point fixed in the place, but in the placed body,
because a line is not said to be drawn otherwise than from a point which
is its term. In like manner the two circles described in two spherical
bodies that occupy the same place are two, not on account of the
difference of place, else they could not touch one another as a whole,
but on account of the distinction of subjects, and thus while wholly
touching one another they still remain two. Even so a circle described
by a placed spherical body touches, as a whole, the other circle
described by the locating body.
Reply to Objection 3: God could make a body not to be in a place;
and yet supposing this, it would not follow that a certain body is not
in a place, because the greater body is the place of the lesser body,
by reason of its superficies which is described by contact with the
terms of the lesser body.
Reply to Objection 4: It is impossible for one body to be
miraculously in two places locally (for Christ's body is not locally
on the altar), although it is possible by a miracle for two bodies to
be in the same place. Because to be in several places at once is
incompatible with the individual, by reason of its having being
undivided in itself, for it would follow that it is divided as to
place. on the other hand, to be in the same place with another body is
incompatible with the individual as distinct from aught else. Now the
nature of unity is perfected in indivision (Metaph. v), whereas
distinction from others is a result of the nature of unity. Wherefore
that one same body be locally in several places at once implies a
contradiction, even as for a man to lack reason, while for two bodies
to be in the same place does not imply a contradiction, as explained
above. Hence the comparison fails.
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