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 (A) 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 (A), 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.