I obviously scheduled the date for this post wrong. It ran a day late. The third set of errors about the Eucharist are fixed up this week.
1 Thus, then, with the difficulty solved arising from place, one ought to look into the one which seems to arise from the accidents which remain. For it cannot be denied that the accidents of bread and wine remain, since the senses infallibly point this out.
2 Neither the body of Christ nor His blood is affected by these accidents, because without changing Him this could not be; nor has He the capacity for such accidents. Much the same can he said of the substance of the air. Hence, one concludes that they are without a subject. Nevertheless, they are without a subject in the manner mentioned: namely, that only the quantity tending to measure subsists without a subject, and this supplies a subject to the other accidents.
3 Neither is it impossible that by the divine power an accident can subsist without a subject. For one ought to make the same judgment about the creation of things and about their conservation in being. The divine power, of course, can produce the effects of any second causes whatever without the second causes themselves; so it was able to form a man without seed, and to cure a fever without the operation of nature.
And this happens by reason of the infinity of His power, and because He grants to all second causes their power to act. Wherefore, also, He can conserve the effects of second causes in being without the second causes. And in this way in this sacrament He conserves an accident in being, even after the removal of the substance which was conserving it.
And this, indeed, can especially be said of the quantities tending to measure; these even the Platonists held to subsist of themselves, for this reason: They are separated in the understanding. But it is clear that God can do more in operation than the intellect can in apprehension.
4 Of course, the quantity tending to measure has among the remaining accidents this property: that it is in itself individuated. And the reason is this: Position, which is “the order of parts in the whole,” is essentially included in this quantity, for quantity is “that which has position.” But wherever a diversity of parts of the same species is understood, individuation is necessarily understood, for things which are of the same species are not multiplied except in the individual; accordingly many whitenesses cannot be apprehended except as they are in different subjects, but many lines can be apprehended, even if they are considered in themselves. For diversity of site which is in the line of itself is sufficient for the plurality of lines.
And because only the quantity tending to measure has in its essentials a possible source of the multiplication of individuals in the same species, the first root of this kind of multiplication seems to be from measurement, because even in the genus of substance the multiplication is made according to the division of matter. And this could not even be understood save by the consideration of matter under measurements, for with the quantity gone all substance is indivisible, as is clear from the Philosopher in Physics I .
Notes In case there are any newbies, “the Philosopher” is Aristotle.
5 It is, of course, manifest that in the other genera of accidents, individuals are multiplied in the same species on the part of the subject. And thus one is left to conclude: Since we hold that in this sacrament the measurements subsist of themselves and that the other accidents are founded on these as on a subject, we need not say that accidents of this kind are not individuated; for there persists in the measurements themselves the root of individuation.