“If you’re not part of the solution, you’re part of the problem.”

This tired old adage sounds accusing and incriminating, like you’re supposed to feel guilty for not working towards a solution, a better world. It’s a bold, shaming aphorism.

Here’s my version.

“If you’re not part of the problem, you’re part of the solution!”

Optimism. Relief. Exoneration.

Mine sounds so much more optimistic than the original. Yet, they are exactly logically equivalent.

Both of them state that “you” are “part of the solution” **or** “part of the problem” (and maybe both). There are two sets: “problem”, “solution” and you are a member of **at least** one.

Don’t believe me? Here’s a rough guide to a formal proof.

Let S = “you are part of the solution” and P = “you are part of the problem”.

The first statement translates to “~S => P”.

The second statement translates to “~P => S”.

We will show that one implies the other. First, we will prove that (~S => P) => (~P => S).

1. ~S => P (assumption) 2. ~P (assumption) 3. ~S (assumption) 4. P (1&3, implication, depends on 1,3) 5. P & ~P (2&4, depends on 1,2,3) 6. ~~S (RAA, 5&3, depends on 1,2) 7. S (double negation, depends on 1,2) 8. ~P=>S (2&7, implication, depends on 1) 9. (~S=>P)=>(~P=>S) (1&8, implication, no dependencies)

The proof that (~P=>S)=>(~S=>P) is virtually identical (just swap the roles of P and S).

Of course, you’re assuming that English is as precise as math, whereby “not being” is the opposite of “being”, and the union of the two encompasses all possible states. I tend to think that many people interpret language (at least English) as more of continuum, where there are many values along the line of “being” and “not being”, some of which are so close to the middle as to be considered neutral, and therefore neither “being” nor “not being”. This is even more apparent when using words that are presented as opposites (eg. “problem” vs. “solution”, “for” vs. “against”). There’s an assumed neutral third value that is considered to be neither part of the problem, nor part of the solution. It is an apathetic state allowing the status quo to continue to exist and not influencing its advance in one direction or the other.

Or maybe that’s just me.