Not much information exists on why the Third Congress (under the lead of James Madison and the approval of George Washington) deleted "natural born" from the Naturalization Act of 1790 when it passed the Naturalization Act of 1795. There is virtually no information on the subject because they probably realized that the First Congress committed errors when it passed the Naturalization Act of 1790 and did not want to create a record of the errors.
It can be reasonably argued that Congress realized that under Article I, Section 8 of the Constitution, Congress is given the power to make uniform laws on naturalization and that this power did not include the power to decide who is included or excluded from being a presidential Article II "natural born Citizen." While Congress has passed throughout United States history many statutes declaring who shall be considered nationals and citizens of the United States at birth and thereby exempting such persons from having to be naturalized under naturalization laws, at no time except by way of the short-lived "natural born" phrase in Naturalization Act of 1790 did it ever declare these persons to be "natural born Citizens."
The uniform definition of "natural born Citizen" was already provided by the law of nations and was already settled. The Framers therefore saw no need nor did they give Congress the power to tinker with that definition. Believing that Congress was highly vulnerable to foreign influence and intrigue, the Framers, who wanted to keep such influence out of the presidency, did not trust Congress when it came to who would be President, and would not have given Congress the power to decide who shall be President by allowing it to define what an Article II "natural born Citizen " is.
Additionally, the 1790 act was a naturalization act. How could a naturalization act make anyone an Article II "natural born Citizen?" After all, a "natural born Citizen" was made by nature at the time of birth and could not be so made by any law of man.
I don't think it is "reasonable" to assume that Congress simply had a flash of inspiration five years after the fact that "gee, I guess what we did five years ago was unconstitutional".
However, even if you do think that's a "reasonable" assumption, that doesn't prove it as a fact, and you can't build your "I am certain I am right" on a foundation that is based on nothing more than something being a "reasonable possibility". So, the elimination of the phrase "natural born citizen" in the Act of 1795 was nothing more than standard legislative housecleaning of eliminate redundant language in a statute.
You may not agree with that, but that's certainly as "reasonable" as assuming they all realized five years after the fact that they had acted unconstitutionally. In fact, if their motive was to correct an error, wouldn't it have been prudent of them to pass some clarifying measure to ensure that people born during 1790-1795 were not considered natural born citizens?
Madison led the committee which drafted the 1795 statute. He was not involved with the drafting of the 1790 statute.
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