SPRING 2005 I discovered something this semester that I think people would find interesting. I was teaching propositional logic to my discrete math class (CS205 at Rutgers) by translating passages from the US Constitution from English into logic. We were looking at the clause defining who could serve as a US Senator and we discovered a bug in the logic! Here's the relevant clause: No Person shall be a Senator who shall not have attained to the Age of thirty Years, and been nine Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State for which he shall be chosen. Article I, Section 3, Clause 3. See: http://www.house.gov/Constitution/Constitution.html or http://www.usconstitution.net/const.html or http://www.gpoaccess.gov/constitution/html/art1.html (The incorrect wording also appears in the requirements for US Representatives, but not the requirements for President, which is worded entirely differently.) It's clear what the Framers had in mind here: You can't be a Senator unless you're at least 30, have been a US Citizen for 9 years, and live in the state you'd be representing. However, the lack of grouping of clauses and the twisted negation at the front make it hard to understand. Using what is known among logicians as DeMorgan's Law (not a legal term!), we can rewrite the clause to the logically equivalent form: Every person who is a Senator must: * have attained to the Age of thirty Years, and been nine Years a Citizen of the United States * or, when elected, be an Inhabitant of that State for which he shall be chosen. In other words, the language here states that *either* being 30 and a 9-year citizen of the US *or* an inhabitant of the state is sufficient. So, according to the clause, a teenager from Alabama can be Senator from Alabama, or a 60-year old lifelong Texan can be Senator from Maine. If it's not obvious to you (it's certainly not obvious to me!) where the flaw is, this simplified example might help. If you are working as an usher in a movie theater and you are told, "Don't admit anyone who is under 18 and has no ticket", it literally says that patrons who are both under 18 and have no ticket should not be admitted. So, if you are under 18 with a ticket, that's ok. A simple fix in this case, which also works with the analogous clause in the Constitution, is to change the "and" to "or" as in "Don't admit anyone who is under 18 or has no ticket." It says that either being under 18 or having no ticket is sufficient to deny someone admittance, which is the desired meaning. OBJECTIONS: Here are some objections I have heard to this analysis, along with my responses. "GROUPING": The problem isn't with the clause, it is that English is ambiguous with respect to grouping and you've grouped it wrong. RESPONSE: It is true that there are multiple possible groupings, but none of them gives the appropriate meaning. Schematically, the sentence says: not Senator and not Thirty and nineYearsCitizen and not Inhabitant It can be regrouped in two natural ways: 1. not (Senator and not (Thirty and nineYearsCitizen) and not Inhabitant) or 2. not (Senator and not (Thirty and nineYearsCitizen and not Inhabitant)). The first is equivalent to: If Senator then ((Thirty and nineYearsCitizen) or Inhabitant) , in other words, you only need to be an inhabitant of a state to be its Senator or you could also be Thirty and a nine-year US citizen. Either is sufficient. This interpretation is the one I think is the natural one for this passage. The second regrouping is equivalent to: If Senator then (Thirty and nineYearsCitizen and not Inhabitant) , in other words, the requirements for being a senator are to be at least 30, a nine-year US citizen, and *not* an inhabitant of the state. So, the alternate grouping actually makes things even worse. "AND DOESN'T MEAN AND": The Framers didn't make a real distinction between "and" and "or" in this setting. I don't see a reason to think this claim is true. First, these logical words are a lot older than our country. Second, they are used consistently throughout the document. For example, there is a negated enumeration in Article I Section 10 Clause 1, which has the form: "No State shall A; B; ...; C, or D". The critical bit here is the use of "or" as the connective in a negated list. Contrast this construction with the positive enumeration in Article II Section 1 Clause 7, which has the form: "The President shall X, and shall not Y". Here, "and" is used as the connective. In both of these cases, the use of "or" and "and" is in keeping with the semantics used in formal logic. I have not yet found anything written on the historical uses of these words, but I'm continuing to look. "YEAH, BUT IT'S CLEAR WHAT THEY MEANT": I totally agree. However, acknowledging a flawed word choice such as this one could provide a jumping off point for discussing the role of interpretation in applying the Constitution---a topic often hotly debated. "IT'S ELLIPSIS": Pat Hawley points out that a more likely description of what happened in this passage is ellipsis. That is, consider the following (logically correct but awkwardly worded) passage: NO PERSON SHALL BE A SENATOR who shall not have attained to the Age of thirty Years, and been nine Years a Citizen of the United States, and NO PERSON SHALL BE A SENATOR who shall not, when elected, be an Inhabitant of that State for which he shall be chosen. Perhaps this passage is the intended one, and then the duplicated words were removed because they are implied by the context and therefore redundant. Actually, this theory sounds reasonable to me. I was beginning to feel the same way about the movie example above---the wrong sentence seems right if you imagine that repeated words were removed. That is, using ellipsis "DON'T ADMIT ANYONE WHO is under 18 and DON'T ADMIT ANYONE WHO has no ticket" becomes "DON'T ADMIT ANYONE WHO is under 18 and has no ticket". So, hmmm, maybe no bug after all! Finally, please note that I am truly awed by the Constitution and the men who wrote it. Pointing out a blemish is not an attempt at dismissing the document as a whole. I believe that it is a visionary document that has changed the human condition for the better. In many ways, it is the most important artifact standing between freedom and chaos. I fervently hope that it will continue to inspire citizens to transcend their baser instincts for the good of the nation.