Breaking the US Constitution Using Boolean Logic

December 8th, 2013

I wrote this when I was fifteen (having begun to memorize the United States constitution, for some reason) after having a spark of inspiration while I was waiting to see my representative on stage that made me realize that this section of the constitution was poorly-worded.

Here’s part of Article I, Section 2 of the US Constitution:

In reference to running for the House of Representatives, the Framers wrote that

No Person shall be a Representative who shall not have attained to the Age of twenty five Years, and been seven Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State in which he shall be chosen.

When I first read that, I couldn’t help but notice how awkwardly that sentence was worded. Indeed, it took me a few read-throughs to completely understand what the Framers meant when they wrote this. Maybe that’s just because I’m too attached to Boolean logic rules. Allow me to demonstrate.

Let’s try to write this out logically. We’ve got the text “No person shall be a Representative who…” and then a set of conditions. So if you meet these conditions, you are NOT allowed to be a representative. If we want to write an expression that will return true if you can run and false if you can’t, we surround the entire thing in a not-gate.

¬( ... )

So just to clarify, let’s pretend the text of the conditions is “is dead”, such that the sentence reads “No person shall be a representative who is dead”, which sounds about right. So if you’re dead, then you’re NOT allowed to be a representative; and if you’re not dead, then you ARE (because there are no requirements listed elsewhere in the constitution about being a representative).

Let’s assign ‘A’ to the age requirement, ‘C’ to the citizenship requirement, and ‘R’ to the residence requirement.
So no person shall be a representative who:

¬( A ∧ C ) ∧ ¬( R )

shall not have attained to the age of twenty-five years and been seven years a citizen of the United States,
and who shall not, when elected, be an inhabitant of that state in which he shall be chosen.

It’s easy to see where this is going. You don’t actually have to be twenty-five years old to run for the House! If you meet the Citizenship requirement and the Residence requirement, but not the Age requirement, look at how the expression evaluates:

¬( ¬( F ∧ T ) ∧ ¬( T ) )
¬( ¬( F ) ∧ F )
¬( T ∧ F )
¬( F )

We can see that the conditions for NOT being a representative evaluate to FALSE, so… you’re allowed to be a representative!

This will apply even if you HAVEN’T been a citizen for seven years; the only requirement that actually matters is being an Inhabitant of the state that you’re currently running in.

Before you argue with me that my argument is invalid because I didn’t follow Boolean precedence rules, let me show you this.

I chose the interpretation I did because it seemed more natural and in-line with the text than the actual Boolean rules (indeed, this was how I originally interpreted this section of the Constitution when I first read it). Still, if we DO use the Boolean logic rules, we can take this even further.

In reality, the NOT operator will always evaluate before the AND operator when there are no parentheses to modify operator precedence (OR would come last if we had any OR gates in this expression). So, let’s write it out again:

No person shall be a representative ¬( )
Who shall NOT have attained to the age of twenty-five years ¬( ¬( A ) )
And been seven years a citizen of the United States ¬( ¬( A ) ∧ C )
And who shall NOT, when elected, be an Inhabitant of that state in which he shall be chosen ¬( ¬( A ) ∧ C ∧ ¬( R ) )

The main difference between this expression and the last one is that we’ve ripped the first AND gate, along with the citizenship requirement, out of the parentheses. Thus, the only way you won’t be allowed to run for the House of Representatives in this situation is if all three of the expressions in the compound AND gate evaluate to true.

So you’re allowed to run as long as you’re not in this exact situation: you’re under twenty-five years old, you HAVE been a citizen for 7 years, and you’re not a resident of the state you’re running for. According to this interpretation, if you’re in any other situation (importantly, including any situation in which you don’t meet the Citizenship requirement), you’re allowed to run.

The conditions for the Senate are worded identically, so all of these arguments apply to those running for the Senate as well.

Well… quod erat demonstrandum. I’m going to go run for Congress.