Objection 1. It seems that the accidents do not remain in this sacrament without a subject, because there ought not to be anything disorderly or deceitful in this sacrament of truth. But for accidents to be without a subject is contrary to the order which God established in nature; and furthermore it seems to savor of deceit, since accidents are naturally the signs of the nature of the subject. Therefore the accidents are not without a subject in this sacrament.
Objection 2. Further, not even by miracle can the definition of a thing be severed from it, or the definition of another thing be applied to it; for instance, that, while man remains a man, he can be an irrational animal. For it would follow that contradictories can exist at the one time: for the "definition of a thing is what its name expresses," as is said in Metaph. iv. But it belongs to the definition of an accident for it to be in a subject, while the definition of substance is that it must subsist of itself, and not in another. Therefore it cannot come to pass, even by miracle, that the accidents exist without a subject in this sacrament.
Objection 3. Further, an accident is individuated by its subject. If therefore the accidents remain in this sacrament without a subject, they will not be individual, but general, which is clearly false, because thus they would not be sensible, but merely intelligible.
Objection 4. Further, the accidents after the consecration of this sacrament do not obtain any composition. But before the consecration they were not composed either of matter and form, nor of existence [quo est] and essence [quod est]. Therefore, even after consecration they are not composite in either of these ways. But this is unreasonable, for thus they would be simpler than angels, whereas at the same time these accidents are perceptible to the senses. Therefore, in this sacrament the accidents do not remain without a subject.
On the contrary, Gregory says in an Easter Homily (Lanfranc, De Corp. et Sang. Dom. xx) that "the sacramental species are the names of those things which were there before, namely, of the bread and wine." Therefore since the substance of the bread and the wine does not remain, it seems that these species remain without a subject.
I answer that, The species of the bread and wine, which are perceived by our senses to remain in this sacrament after consecration, are not subjected in the substance of the bread and wine, for that does not remain, as stated above (Question 75, Article 2); nor in the substantial form, for that does not remain (75, 6), and if it did remain, "it could not be a subject," as Boethius declares (De Trin. i). Furthermore it is manifest that these accidents are not subjected in the substance of Christ's body and blood, because the substance of the human body cannot in any way be affected by such accidents; nor is it possible for Christ's glorious and impassible body to be altered so as to receive these qualities.
Now there are some who say that they are in the surrounding atmosphere as in a subject. But even this cannot be: in the first place, because atmosphere is not susceptive of such accidents. Secondly, because these accidents are not where the atmosphere is, nay more, the atmosphere is displaced by the motion of these species. Thirdly, because accidents do not pass from subject to subject, so that the same identical accident which was first in one subject be afterwards in another; because an accident is individuated by the subject; hence it cannot come to pass for an accident remaining identically the same to be at one time in one subject, and at another time in another. Fourthly, since the atmosphere is not deprived of its own accidents, it would have at the one time its own accidents and others foreign to it. Nor can it be maintained that this is done miraculously in virtue of the consecration, because the words of consecration do not signify this, and they effect only what they signify.
Therefore it follows that the accidents continue in this sacrament without a subject. This can be done by Divine power: for since an effect depends more upon the first cause than on the second, God Who is the first cause both of substance and accident, can by His unlimited power preserve an accident in existence when the substance is withdrawn whereby it was preserved in existence as by its proper cause, just as without natural causes He can produce other effects of natural causes, even as He formed a human body in the Virgin's womb, "without the seed of man" (Hymn for Christmas, First Vespers).
Reply to Objection 1. There is nothing to hinder the common law of nature from ordaining a thing, the contrary of which is nevertheless ordained by a special privilege of grace, as is evident in the raising of the dead, and in the restoring of sight to the blind: even thus in human affairs, to some individuals some things are granted by special privilege which are outside the common law. And so, even though it be according to the common law of nature for an accident to be in a subject, still for a special reason, according to the order of grace, the accidents exist in this sacrament without a subject, on account of the reasons given above (75, 5).
Reply to Objection 2. Since being is not a genus, then being cannot be of itself the essence of either substance or accident. Consequently, the definition of substance is not--"a being of itself without a subject," nor is the definition of accident--"a being in a subject"; but it belongs to the quiddity or essence of substance "to have existence not in a subject"; while it belongs to the quiddity or essence of accident "to have existence in a subject." But in this sacrament it is not in virtue of their essence that accidents are not in a subject, but through the Divine power sustaining them; and consequently they do not cease to be accidents, because neither is the definition of accident withdrawn from them, nor does the definition of substance apply to them.
Reply to Objection 3. These accidents acquired individual being in the substance of the bread and wine; and when this substance is changed into the body and blood of Christ, they remain in that individuated being which they possessed before, hence they are individual and sensible.
Reply to Objection 4. These accidents had no being of their own nor other accidents, so long as the substance of the bread and wine remained; but their subjects had "such" being through them, just as snow is "white" through whiteness. But after the consecration the accidents which remain have being; hence they are compounded of existence and essence, as was said of the angels, in I, 50, 2, ad 3; and besides they have composition of quantitative parts.
Source: Summa Theologica (New Advent)