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
- 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!)