Instead, they used a legal term - natural born citizen. Not found in Vattel, but with a specific legal meaning.
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Legal term???
A defined legal term would be Natural Born Citizen - in all caps. This is how legal definitions are documented in a legal document. But this is not what the founders did.
They did used a legally defined term Citizen. It is capitalized. Thus it is a defined term in the Constitution. In English language terms it is a proper noun.
So you have ‘Citizen’ and the base. It means Citizen of one of the United States. Because of this I will go halfway with you and say that this means that in a strict sense Vattel was NOT used, at least exclusively as the basis for the Article II term. Because Vattel would not have written about a “natural born Citizen of one of the United States”. So Vattel writes about “natural born citizens” (lower case c and a common noun) and Article II uses Citizen as the base for “natural born Citizen”. It is not the same citizen Vattel refers to. At least not in a 1 to 1 match.
So lets look at “natural born” is it a special or defined term? Actually it is merely two adjectives. The ‘term’ is not hyphenated (another common mis-characterization that distorts the founders intent). And the words are not capitalized. So that means the founders did not intend and did not mechanically create a new proper noun that is undefined. In short they did not screw up and not define a term that is not a proper noun.
I contend that since these are simple adjectives they have the same meaning as “natural Citizen and born Citizen”. In the same way if you say it is “green short grass” is the same as saying it is “green grass and it is short grass”.
Some say “natural born” means simply ‘at birth’. They say there are only 2 ‘types’ of citizenship - born and naturalized. This is a lie. A pure lie. There are two types of citizenships but it is the ‘natural’ part that comes into play more than the ‘born’ part. There are ‘natural’ citizens and there are citizens by statute. THESE are the true two types of citizens. Naturalized citizens are a SUBSET of Citizens by statute. A naturalization law. But, especially with the introduction of 14th Amendement we can see that you can be born a Citizen but not be a natural citizen. 14th Amendment citizens are not natural. The do not derive their Citizenship from natural forces - i.e. their parentage and their location of birth together.
As for ‘born’ - it means ‘from birth’. It is not simply AT BIRTH. It is FROM BIRTH. You have to be born a natural citizen and stay that way through out your life.
So “natural born Citizen” is not a proper noun and it is not a legally defined term using any acceptable legal constructs. The founders did not fail us by leaving us with an undefined term in the Constitution.
“A defined legal term would be Natural Born Citizen - in all caps. This is how legal definitions are documented in a legal document.”
No. That is not true, and the US Supreme Court has already disagreed with you, at length.