What does "jurisdiction" mean, in the 14th Amendment?

The first sentence of the 14th Amendment reads: "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside."
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The question about whether or not a child born in the US is automatically a citizen, comes down to the meaning of "jurisdiction". Are foreigners "subject to the jurisdiction" of the United States, just by being IN the United States (or its territory)?
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The legal definition of jurisdiction is "the authority given by law to a court to try cases and rule on legal matters within a particular geographic area and/or over certain types of legal cases." According to this definition, if foreigners are NOT subject to the jurisdiction of the US then American police could not arrest them - and they could not be tried in American courts. This is the protection foreign diplomats get with "diplomatic immunity". If every foreigner had this protection, there would be no need for a special exemption for diplomats.
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To claim this issue never came before the Supreme Court is mistaken. In United States v. Wong Kim Ark, 169 U.S. 649 (1898), the Supreme Court held that when a child is born in America to non-citizen Chinese parents, that child is a United States citizen. (Note this was 60 years after the Amendment was ratified.) The case highlighted disagreements over the precise meaning of one phrase in the Citizenship Clause—namely, the provision that a person born in the United States who is subject to the jurisdiction thereof acquires automatic citizenship. The Supreme Court's majority (6 -2 decision) concluded that this phrase referred to being required to obey U.S. law.

https://en.wikipedia.org/wiki/U...._Wong_Kim_Ark

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The other side of the argument says that the phrase refers to ONLY being subject to American jurisdiction. (they can't also be subject to the jurisdiction of another country, by being citizens of that country) However, to argue that, one would have to stipulate that the people who wrote the law didn't know enough to state "and subject only to the jurisdiction thereof" or otherwise specify plainly that the parents were not citizens of another nation.