Objection 1. It would seem that the believer who leaves his unbelieving wife cannot take another wife. For indissolubility is of the nature of marriage, since it is contrary to the natural law to divorce one's wife. Now there was true marriage between them as unbelievers. Therefore their marriage can nowise be dissolved. But as long as a man is bound by marriage to one woman he cannot marry another. Therefore a believer who leaves his unbelieving wife cannot take another wife.
Objection 2. Further, a crime subsequent to marriage does not dissolve the marriage. Now, if the wife be willing to cohabit without insult to the Creator, the marriage tie is not dissolved, since the husband cannot marry another. Therefore the sin of the wife who refuses to cohabit without insult to the Creator does not dissolve the marriage so that her husband be free to take another wife.
Objection 3. Further, husband and wife are equal in the marriage tie. Since, then, it is unlawful for the unbelieving wife to marry again while her husband lives, it would seem that neither can the believing husband do so.
Objection 4. Further, the vow of continence is more favorable than the marriage contract. Now seemingly it is not lawful for the believing husband to take a vow of continence without the consent of his unbelieving wife, since then the latter would be deprived of marriage if she were afterwards converted. Much less therefore is it lawful for him to take another wife.
Objection 5. Further, the son who persists in unbelief after his father's conversion loses the right to inherit from his father: and yet if he be afterwards converted, the inheritance is restored to him even though another should have entered into possession thereof. Therefore it would seem that in like manner, if the unbelieving wife be converted, her husband ought to be restored to her even though he should have married another wife: yet this would be impossible if the second marriage were valid. Therefore he cannot take another wife.
On the contrary, Matrimony is not ratified without the sacrament of Baptism. Now what is not ratified can be annulled. Therefore marriage contracted in unbelief can be annulled, and consequently, the marriage tie being dissolved, it is lawful for the husband to take another wife.
Further, a husband ought not to cohabit with an unbelieving wife who refuses to cohabit without insult to the Creator. If therefore it were unlawful for him to take another wife he would be forced to remain continent, which would seem unreasonable, since then he would be at a disadvantage through his conversion.
I answer that, When either husband or wife is converted to the faith the other remaining in unbelief, a distinction must be made. For if the unbeliever be willing to cohabit without insult to the Creator--that is without drawing the other to unbelief--the believer is free to part from the other, but by parting is not permitted to marry again. But if the unbeliever refuse to cohabit without insult to the Creator, by making use of blasphemous words and refusing to hear Christ's name, then if she strive to draw him to unbelief, the believing husband after parting from her may be united to another in marriage.
Reply to Objection 1. As stated above (Article 2), the marriage of unbelievers is imperfect, whereas the marriage of believers is perfect and consequently binds more firmly. Now the firmer tie always looses the weaker if it is contrary to it, and therefore the subsequent marriage contracted in the faith of Christ dissolves the marriage previously contracted in unbelief. Therefore the marriage of unbelievers is not altogether firm and ratified, but is ratified afterwards by Christ's faith.
Reply to Objection 2. The sin of the wife who refuses to cohabit without insult to the Creator frees the husband from the tie whereby he was bound to his wife so as to be unable to marry again during her lifetime. It does not however dissolve the marriage at once, since if she were converted from her blasphemy before he married again, her husband would be restored to her. But the marriage is dissolved by the second marriage which the believing husband would be unable to accomplish unless he were freed from his obligation to his wife by her own fault.
Reply to Objection 3. After the believer has married, the marriage tie is dissolved on either side, because the marriage is not imperfect as to the bond, although it is sometimes imperfect as to its effect. Hence it is in punishment of the unbelieving wife rather than by virtue of the previous marriage that she is forbidden to marry again. If however she be afterwards converted, she may be allowed by dispensation to take another husband, should her husband have taken another wife.
Reply to Objection 4. The husband ought not to take a vow of continence nor enter into a second marriage, if after his conversion there be a reasonable hope of the conversion of his wife, because the wife's conversion would be more difficult if she knew she was deprived of her husband. If however there be no hope of her conversion, he can take Holy orders or enter religion, having first besought his wife to be converted. And then if the wife be converted after her husband has received Holy Orders, her husband must not be restored to her, but she must take it as a punishment of her tardy conversion that she is deprived of her husband.
Reply to Objection 5. The bond of fatherhood is not dissolved by disparity of worship, as the marriage bond is: wherefore there is no comparison between an inheritance and a wife.
Source: Summa Theologica (New Advent)