You have Vattel, who said that parents were the determining factor of who was natural-born and who was not. And you had Blackstone, who said that where a person was born was the determining factor of who was natural-born and who was not. Vattel defines "Des citoyens et naturels". Blackstone speaks of "Natural Born Subjects."
"Subjects" was the long existing and default term in the colonies. Were it intended to keep this sort of relationship between the state and the individual, the term "Subject" would have continued to be used.
That the term "Subject" was deliberately replaced by the word "Citizen", which at the time was an uncommonly used word in the English language and which possessed a different meaning at the time than what we now understand it to be, (A dictionary of the English language. by Samuel Johnson, 1768.)
clearly demonstrates that we replaced the existing paradigm with a new one.
So which one does the Constitution use? Which one is the "self defined" definition?
As the constitution does not refer to the people of the United States as "Subjects", but instead refers to them as "citizens", it demonstrate that we chose to follow the meaning implicit in the word that is derived from it's origin.
As the American usage of the word is not what was the contemporary English usage of the word, but is instead the Swiss usage of the word, we must therefore conclude that the Vattel definition applies.
Which one is the "self defined" definition?
The one that fits our usage and meaning. The English one does not fit. The Swiss one fits.
The one that fits our usage and meaning. The English one does not fit. The Swiss one fits. Is that so? Well then some people sure didn't get the memo then.
William Rawle in his "A View of the Constitution of the United States" published in 1829: "Therefore every person born within the United States, its territories or districts, whether the parents are citizens or aliens, is a natural born citizen in the sense of the Constitution, and entitled to all the rights and privileges appertaining to that capacity."
James Madison, 1789: "It is an established maxim, that birth is a criterion of allegiance. Birth, however, derives its force sometimes from place, and sometimes from parentage; but, in general place is the most certain criterion; it is what applies in the United States."
James Kent, "Commentaries on American Law", 1826: "Natives are all persons born within the jurisdiction and allegiance of the United States. This is the rule of the common law, without any regard or reference to the political condition or allegiance of their parents, with the exception of the children of ambassadors, who are in theory born within the allegiance of the foreign power they represent."