Sovereignty attained through birth
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Which parent has “paternal dominion” or the main authority over children is determined by contract; or else the mother has it.
The right of dominion by generation is that which the parent hath over his children, and is called paternal. And is not so derived from the generation, as if therefore the parent had dominion over his child because he begat him, but from the child's consent, either express or by other sufficient arguments declared. For as to the generation, God hath ordained to man a helper, and there be always two that are equally parents: the dominion therefore over the child should belong equally to both, and he be equally subject to both, which is impossible; for no man can obey two masters. And whereas some have attributed the dominion to the man only, as being of the more excellent sex, they misreckon in it. For there is not always that difference of strength or prudence between the man and the woman as that the right can be determined without war. In Commonwealths this controversy is decided by the civil law: and for the most part, but not always, the sentence is in favour of the father, because for the most part Commonwealths have been erected by the fathers, not by the mothers of families. But the question lieth now in the state of mere nature where there are supposed no laws of matrimony, no laws for the education of children, but the law of nature and the natural inclination of the sexes, one to another, and to their children. In this condition of mere nature, either the parents between themselves dispose of the dominion over the child by contract, or do not dispose thereof at all. If they dispose thereof, the right passeth according to the contract. We find in history that the Amazons contracted with the men of the neighbouring countries, to whom they had recourse for issue, that the issue male should be sent back, but the female remain with themselves: so that the dominion of the females was in the mother.
If there be no contract, the dominion is in the mother. For in the condition of mere nature, where there are no matrimonial laws, it cannot be known who is the father unless it be declared by the mother; and therefore the right of dominion over the child dependeth on her will, and is consequently hers. Again, seeing the infant is first in the power of the mother, so as she may either nourish or expose it; if she nourish it, it oweth its life to the mother, and is therefore obliged to obey her rather than any other; and by consequence the dominion over it is hers. But if she expose it, and another find and nourish it, dominion is in him that nourisheth it. For it ought to obey him by whom it is preserved, because preservation of life being the end for which one man becomes subject to another, every man is supposed to promise obedience to him in whose power it is to save or destroy him.
Hobbes, Lev XX 4-5
Concerning the circumstances under which monarchs of different sexes have and pass on “paternal dominion” (authority over children).
If the mother be the father's subject, the child is in the father's power; and if the father be the mother's subject (as when a sovereign queen marrieth one of her subjects), the child is subject to the mother, because the father also is her subject.
If a man and a woman, monarchs of two several kingdoms, have a child, and contract concerning who shall have the dominion of him, the right of the dominion passeth by the contract. If they contract not, the dominion followeth the dominion of the place of his residence. For the sovereign of each country hath dominion over all that reside therein.
He that hath the dominion over the child hath dominion also over the children of the child, and over their children's children. For he that hath dominion over the person of a man hath dominion over all that is his, without which dominion were but a title without the effect.
The right of succession to paternal dominion proceedeth in the same manner as doth the right of succession to monarchy, of which I have already sufficiently spoken in the precedent chapter.
Hobbes, Lev XX 6-9