Objection 1. It would seem unlawful for a bigamist to be granted a dispensation. For it is said (Extra, De bigamis, cap. Nuper): "It is not lawful to grant a dispensation to clerics who, as far as they could do so, have taken to themselves a second wife."
Objection 2. Further, it is not lawful to grant a dispensation from the Divine law. Now whatever is in the canonical writings belongs to the Divine law. Since then in canonical Scripture the Apostle says (1 Timothy 3:2): "It behooveth... a bishop to be... the husband of one wife," it would seem that a dispensation cannot be granted in this matter.
Objection 3. Further, no one can receive a dispensation in what is essential to a sacrament. But it is essential to the sacrament of order that the recipient be not irregular, since the signification which is essential to a sacrament is lacking in one who is irregular. Therefore he cannot be granted a dispensation in this.
Objection 4. Further, what is reasonably done cannot be reasonably undone. If, therefore, a bigamist can lawfully receive a dispensation, it was unreasonable that he should be irregular: which is inadmissible.
On the contrary, Pope Lucius granted a dispensation to the bishop of Palermo who was a bigamist, as stated in the gloss on can. Lector, dist. 34.
Further, Pope Martin [Martinus Bracarensis: cap. xliii] says: "If a Reader marry a widow, let him remain a Reader, or if there be need for it, he may receive the Subdiaconate, but no higher order: and the same applies if he should be a bigamist." Therefore he may at least receive a dispensation as far as the Subdiaconate.
I answer that, Irregularity attaches to bigamy not by natural, but by positive law; nor again is it one of the essentials of order that a man be not a bigamist, which is evident from the fact that if a bigamist present himself for orders, he receives the character. Wherefore the Pope can dispense altogether from such an irregularity; but a bishop, only as regards the minor orders, though some say that in order to prevent religious wandering abroad he can dispense therefrom as regards the major orders in those who wish to serve God in religion.
Reply to Objection 1. This Decretal shows that there is the same difficulty against granting a dispensation in those who have married several wives in fact, as if they had married them in law; but it does not prove that the Pope has no power to grant a dispensation in such cases.
Reply to Objection 2. This is true as regards things belonging to the natural law, and those which are essential to the sacraments, and to faith. But in those which owe their institution to the apostles, since the Church has the same power now as then of setting up and of putting down, she can grant a dispensation through him who holds the primacy.
Reply to Objection 3. Not every signification is essential to a sacrament, but that alone which belongs to the sacramental effect,* and this is not removed by irregularity. [Leonine edition reads "officium," some read "effectum"; the meaning is the same, and is best rendered as above.]
Reply to Objection 4. In particular cases there is no ratio that applies to all equally, on account of their variety. Hence what is reasonably established for all, in consideration of what happens in the majority of cases, can be with equal reason done away in a certain definite case.
Source: Summa Theologica (New Advent)