my mom made us this way

My brother and I grew up sitting in the living room with my mom, discussing anything and everything--especially if it was controversial--late into the night. The free exchange of ideas was a given in our household. Oftentimes, my mom wore a look that said, "I'm kind of appalled, but I'm listening." A lot of times, she changed her mind about things by the time we all went to bed.

In some ways, this exchange of ideas has continued into adulthood for my brother and me. I respect how much time he spends reading and thinking, even though I don't always agree with him and his opinions. He recently said something to me like, "I don't understand how you can let your personal feelings about an issue affect the way you think about the issue," the issue in question being smoking bans, which I agree with but he doesn't. (He's rather libertarian.)

He stopped over on Monday night to drop of a birthday present for , and he mentioned his currently getting his head wrapped around the idea of atheism being represented by the mathematical idea of the empty set. Not being a strong mathematician, he wanted to know what we thought about it (considering my girlfriend works with numbers for a living and I was always the one helping him with his math homework). Set theory was...a long time ago for both of us...and not very advanced, considering I didn't take calculus. (Hey, it was offered at the same time Hott!Teacher! taught psychology!) I decided to refresh myself on the basic idea of sets, and gave his proposition some thought. Here's what sense I can make of this and his idea:

• A set contains elements. A set can still be a set, even if it contains only one element.
  
• A set that contains no elements is called "the empty set." There is only one set that contains no elements, as it works with any other type of set because it doesn't matter what the elements are (numbers, types of animals, etc.)--the empty set contains no elements.
  
• The empty set is not the same as zero. Zero is an element, so if a set contains zero, it still contains an element. This is most useful in talking about numerical sets.
  
• In religion, you can look at a set of beliefs like you would look at a numerical set. In Christianity, there's a set of beliefs that includes elements like: "God is the creator" and "Jesus died on the cross."

It's pointless in this discussion to argue about whether or not atheism is a religion so that we can talk about "sets of beliefs of religions." The important thing is that religions do have sets of beliefs. (And, I'll note here that even if atheism does have a set of beliefs, it doesn't mean it's a religion. A square is a rectangle, but a rectangle is not necessarily a square.)

The question we're currently debating is whether or not atheism has a set of beliefs. My brother wrote: "i don't BELIEVE that there is no god... i just don't believe there is one. you see? its not a positive belief. there isn't anything else to it." I think he's operationally defining believing as affirming, and I'm arguing that a belief can negate, that you can believe the opposite. I think atheism is a set, a set of one belief: there is no god.

Anyway...this is what I'm thinking about. (And where's a mathematician when you need one!)