Among the many thoughtful details that the founders bequeathed to the rest of us is the purposeful naming of our nation; The United States of America. A single moniker like “America” would have neglected the composure of independence and cooperative defiance necessary to earn the crucial signatures on the Declaration of Independence and, soon afterward, the Articles of Confederation wherein the new country’s name was made official. The basic tenet behind the name is captured plainly in the Ninth and Tenth Amendments.
The Ninth of our Bill of Rights reads, “The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.” The Tenth and final component to our Bill of Rights reads, “The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.”
Together, Amendments Nine and Ten cover all liberties not specifically addressed in Amendments One through Eight. Herein lies the answer to that question you asked yourself back in Algebra II, “When would I ever use axiomatic set theory in real life?”
First, let’s clarify two terms; “enumeration” as used in the Ninth Amendment and “the United States” as used in the Tenth Amendment. To enumerate means to establish or to specify. In the Tenth Amendment, the United States means the federal government. Both amendments are intending to institute restrictions on government by axiomatic set theory.
The Ninth Amendment calls out two sets of rights; those that are specifically named in the United States Constitution and those that are not. The theorem being advanced here is that the Constitution does not “constitute” the citizens’ complete set of rights. The Founding Fathers had always held the concern that documenting a finite set of rights might imply that those not mentioned would be considered nonexistent. Note the careful wording in the Declaration of Independence that people “are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness” [emphasis added].
Founding father Alexander Hamilton was highly skeptical of even adding a bill of rights to the United States Constitution. This signer of the Constitution went so far as to “affirm that bills of rights, in the sense and to the extent in which they are contended for, are not only unnecessary in the proposed Constitution, but would even be dangerous.”