I answer that, There have been three opinions about the damned. For some have said that a twofold distinction must be made in this matter. First, as to time; for they said that after the judgment day no one in hell will be assisted by any suffrage, but that before the judgment day some are assisted by the suffrages of the Church. Secondly, they made a distinction among those who are detained in hell. Some of these, they said, are very bad, those namely who have died without faith and the sacraments, and these, since they were not of the Church, neither "by grace nor, by name" [*Cf. Oratio ad Vesperas, Fer. ii, post Dom. Pass.] can the suffrages of the Church avail; while others are not very bad, those namely who belonged to the Church as actual members, who had the faith, frequented the sacraments and performed works generically good, and for these the suffrages of the Church ought to avail. Yet they were confronted with a difficulty which troubled them, for it would seem to follow from this (since the punishment of hell is finite in intensity although infinite in duration) that a multiplicity of suffrages would take away that punishment altogether, which is the error of Origen (Peri Archon. i; cf. Gregory, Moral. xxxiv): and consequently endeavored in various ways to avoid this difficulty.
Praepositivus [*Gilbert Prevostin, Chancellor of the See of Paris, A.D. 1205-9] said that suffrages for the damned can be so multiplied that they are entirely freed from punishment, not absolutely as Origen maintained, but for a time, namely till the judgment day: for their souls will be reunited to their bodies, and will be cast back into the punishments of hell without hope of pardon. But this opinion seems incompatible with Divine providence, which leaves nothing inordinate in the world. For guilt cannot be restored to order save by punishment: wherefore it is impossible for punishment to cease, unless first of all guilt be expiated: so that, as guilt remains for ever in the damned, their punishment will nowise be interrupted.
For this reason the followers of Gilbert de la Porree devised another explanation. These said that the process in the diminution of punishments by suffrages is as the process in dividing a line, which though finite, is indefinitely divisible, and is never destroyed by division, if it be diminished not by equal but by proportionate quantities, for instance if we begin by taking away a quarter of the whole, and secondly, a quarter of that quarter, and then a quarter of this second quarter, and so on indefinitely. In like manner, they say by the first suffrage a certain proportion of the punishment is taken away, and by the second an equally proportionate part of the remainder. But this explanation is in many ways defective. First, because it seems that indefinite division which is applicable to continuous quantity cannot be transferred to spiritual quantity: secondly, because there is no reason why the second suffrage, if it be of equal worth, should diminish the punishment less than the first: thirdly, because punishment cannot be diminished unless guilt be diminished, even as it cannot be done away unless the guilt be done away: fourthly, because in the division of a line we come at length to something which is not sensible, for a sensible body is not indefinitely divisible: and thus it would follow that after many suffrages the remaining punishment would be so little as not to be felt, and thus would no longer be a punishment.
Hence others found another explanation. For Antissiodorensis [*William of Auxerre, Archdeacon of Beauvais] (Sent. iv, Tract. 14) said that suffrages profit the damned not by diminishing or interrupting their punishment, but by fortifying the person punished: even as a man who is carrying a heavy load might bathe his face in water, for thus he would be enabled to carry it better, and yet his load would be none the lighter. But this again is impossible, because according to Gregory (Moral. ix) a man suffers more or less from the eternal fire according as his guilt deserves; and consequently some suffer more, some less, from the same fire. wherefore since the guilt of the damned remains unchanged, it cannot be that he suffers less punishment. Moreover, the aforesaid opinion is presumptuous, as being in opposition to the statements of holy men, and groundless as being based on no authority. It is also unreasonable. First, because the damned in hell are cut off from the bond of charity in virtue of which the departed are in touch with the works of the living. Secondly, because they have entirely come to the end of life, and have received the final award for their merits, even as the saints who are in heaven. For the remaining punishment or glory of the body does not make them to be wayfarers, since glory essentially and radically resides in the soul. It is the same with the unhappiness of the damned, wherefore their punishment cannot be diminished as neither can the glory of the saints be increased as to the essential reward.
However, we may admit, in a certain measure, the manner in which, according to some, suffrages profit the damned, if it be said that they profit neither by diminishing nor interrupting their punishment, nor again by diminishing their sense of punishment, but by withdrawing from the damned some matter of grief, which matter they might have if they knew themselves to be so outcast as to be a care to no one; and this matter of grief is withdrawn from them when suffrages are offered for them. Yet even this is impossible according to the general law, because as Augustine says (De Cura pro Mort. xiii)---and this applies especially to the damned---"the spirits of the departed are where they see nothing of what men do or of what happens to them in this life," and consequently they know not when suffrages are offered for them, unless this relief be granted from above to some of the damned in spite of the general law. This, however, is a matter of great uncertainty; wherefore it is safer to say simply that suffrages profit not the damned, nor does the Church intend to pray for them, as appears from the authors quoted above.