Objection 1. It would seem that consanguinity is not by natural law an impediment to marriage. For no woman can be more akin to a man than Eve was to Adam, since of her did he say (Genesis 2:23): "This now is bone of my bones and flesh of my flesh." Yet Eve was joined in marriage to Adam. Therefore as regards the natural law no consanguinity is an impediment to marriage.
Objection 2. Further, the natural law is the same for all. Now among the uncivilized nations no person is debarred from marriage by reason of consanguinity. Therefore, as regards the law of nature, consanguinity is no impediment to marriage.
Objection 3. Further, the natural law is what "nature has taught all animals," as stated at the beginning of the Digests (i, ff. De just. et jure). Now brute animals copulate even with their mother. Therefore it is not of natural law that certain persons are debarred from marriage on account of consanguinity.
Objection 4. Further, nothing that is not contrary to one of the goods of matrimony is an impediment to marriage. But consanguinity is not contrary to any of the goods of marriage. Therefore it is not an impediment thereto.
Objection 5. Further, things which are more akin and more similar to one another are better and more firmly united together. Now matrimony is a kind of union. Since then consanguinity is a kind of kinship, it does not hinder marriage but rather strengthens the union.
On the contrary, According to the natural law whatever is an obstacle to the good of the offspring is an impediment to marriage. Now consanguinity hinders the good of the offspring, because in the words of Gregory (Regist., epis. xxxi) quoted in the text (Sent. iv, D, 40): "We have learnt by experience that the children of such a union cannot thrive." Therefore according to the law of nature consanguinity is an impediment to matrimony.
Further, that which belongs to human nature when it was first created is of natural law. Now it belonged to human nature from when it was first created that one should be debarred from marrying one's father or mother: in proof of which it was said (Genesis 2:24): "Wherefore a man shall leave father and mother": which cannot be understood of cohabitation, and consequently must refer to the union of marriage. Therefore consanguinity is an impediment to marriage according to the natural law.
I answer that, In relation to marriage a thing is said to be contrary to the natural law if it prevents marriage from reaching the end for which it was instituted. Now the essential and primary end of marriage is the good of the offspring. and this is hindered by a certain consanguinity, namely that which is between father and daughter, or son and mother. It is not that the good of the offspring is utterly destroyed, since a daughter can have a child of her father's semen and with the father rear and teach that child in which things the good of the offspring consists, but that it is not effected in a becoming way. For it is out of order that a daughter be mated to her father in marriage for the purpose of begetting and rearing children, since in all things she ought to be subject to her father as proceeding from him. Hence by natural law a father and mother are debarred from marrying their children; and the mother still more than the father, since it is more derogatory to the reverence due to parents if the son marry his mother than if the father marry his daughter; since the wife should be to a certain extent subject to her husband. The secondary essential end of marriage is the curbing of concupiscence; and this end would be forfeit if a man could marry any blood-relation, since a wide scope would be afforded to concupiscence if those who have to live together in the same house were not forbidden to be mated in the flesh. Wherefore the Divine law debars from marriage not only father and mother, but also other kinsfolk who have to live in close intimacy with one another and ought to safeguard one another's modesty. The Divine law assigns this reason (Leviticus 18:10): "Thou shalt not uncover the nakedness" of such and such a one, "because it is thy own nakedness."
But the accidental end of marriage is the binding together of mankind and the extension of friendship: for a husband regards his wife's kindred as his own. Hence it would be prejudicial to this extension of friendship if a man could take a woman of his kindred to wife since no new friendship would accrue to anyone from such a marriage. Wherefore, according to human law and the ordinances of the Church, several degrees of consanguinity are debarred from marriage.
Accordingly it is clear from what has been said that consanguinity is by natural law an impediment to marriage in regard to certain persons, by Divine law in respect of some, and by human law in respect of others.
Reply to Objection 1. Although Eve was formed from Adam she was not Adam's daughter, because she was not formed from him after the manner in which it is natural for a man to beget his like in species, but by the Divine operation, since from Adam's rib a horse might have been formed in the same way as Eve was. Hence the natural connection between Eve and Adam was not so great as between daughter and father, nor was Adam the natural principle of Eve as a father is of his daughter.
Reply to Objection 2. That certain barbarians are united carnally to their parents does not come from the natural law but from the passion of concupiscence which has clouded the natural law in them.
Reply to Objection 3. Union of male and female is said to be of natural law, because nature has taught this to animals: yet she has taught this union to various animals in various ways according to their various conditions. But carnal copulation with parents is derogatory to the reverence due to them. For just as nature has instilled into parents solicitude in providing for their offspring, so has it instilled into the offspring reverence towards their parents: yet to no kind of animal save man has she instilled a lasting solicitude for his children or reverence for parents; but to other animals more or less, according as the offspring is more or less necessary to its parents, or the parents to their offspring. Hence as the Philosopher attests (De Animal. ix, 47) concerning the camel and the horse, among certain animals the son abhors copulation with its mother as long as he retains knowledge of her and a certain reverence for her. And since all honest customs of animals are united together in man naturally, and more perfectly than in other animals, it follows that man naturally abhors carnal knowledge not only of his mother, but also of his daughter, which is, however, less against nature, as stated above.
Moreover consanguinity does not result from carnal procreation in other animals as in man, as stated above (1, ad 5). Hence the comparison fails.
Reply to Objection 4. It has been shown how consanguinity between married persons is contrary to the goods of marriage. Hence the Objection proceeds from false premises.
Reply to Objection 5. It is not unreasonable for one of two unions to be hindered by the other, even as where there is identity there is not likeness. In like manner the tie of consanguinity may hinder the union of marriage.
Source: Summa Theologica (New Advent)