Logic

Today I made a few observations of my mental state. It amused me to put them in an ordered list:

1. Being depressed makes it hard to get work done.
2. When I get work done, I feel good.
3. Feeling good is the opposite of being depressed.
4. Therefore, in order to feel good, I must first feel good.

I was going to post something like the above on facebook with some pithy comment about my brief training in formal logic. "Haha, logic shows the impossibility of ever breaking the cycle of depression!" I would say, then sit back and marvel in my own cleverness.

Then I actually thought about the formal logic of it... it turns out I made a pretty basic error. To show you how, we have to translate the above statements into symbols, which lay bare their meanings by removing the shiny words. We will use the following definitions:

• A = being depressed
• B = getting work done
• C = feeling good

Each statement is conditional - it can either be true or false. If it is false, then its opposite is true, indicated by "Not". So if A is false, then Not A is true.

My list of observations links together these individual statements by "if - then" connections. Though I never actually say, "If I'm depressed then I don't get work done," that is the meaning of observation number 1. Let's now translate them all:

1. If A then Not B
2. If B then C
3. C = Not A
4. If C then C

Let me first make it clear that there's no logical error in the above. The conclusion is obviously a pretty meaningless tautology. The error was in my thinking that 4 follows from 1, 2, and 3, by an implicit, "If I feel good, then I get work done," which translates to:

• If C then B

With 2 above that leaves us with "If C then B" and "If B then C", thus:

• If C then C,

or, "If I feel good then I get work done then I feel good." What a hilariously depressing joke!

Unfortunately, "If C then B" DOES NOT FOLLOW. It is a common mistake to assume that "If A then B" implies "If Not A then Not B", which wikipedia helpfully informs us is called denying the antecedent. What does follow, however, is:

• If B then Not A,

from the transposition of number 1. Then we can see, by number 3, that this is exactly the same as number 2, "If B then C". And since we can't have a discussion of logic without any Latin, I will point out that this is the same as the rule of modus tollens: If A then B; Not B; Therefore Not A. So my observations amount to two equivalent statements, a definition, and a tautology.

I hope we all have learned something today. I think at least a cursory introduction to formal logic should be required, perhaps in secondary education; no reason to wait for college. In practice it mixes algebra with reading comprehension, and the result is better reasoning and critical thinking skills. Plus, it can help you avoid making a fool of yourself on facebook, and by God we need more of That!