I can feel your anger

[CliveStaples]

If you asked him if he believed in god and he said "no"

Right, so let's call this method M1. That is, if you want to know whether someone is an atheist, under M1 you ask them if they believe in god; if he says no, then you know he's an atheist.

This corresponds to the definition I was using earlier:

A belief system B is atheist if and only if B does not include the belief, "At least one god exists".

Let's call this method M2. That is, if want to know whether someone is an atheist, you look at their belief system; if it doesn't include the belief, "At least one god exists", then it's atheist.


I'll prove the correspondence, in case you don't believe me.



Suppose you ask the guy--let's call him Norman--if he believes in god and he says no. So Norman is an atheist under M1. Let B be Norman's belief system. By definition, x in B <=> Norman believes x is true. By hypothesis, Norman doesn't believe x is true. Therefore x is not in B. Thus Norman is an atheist under M2.

Conversely, suppose Norman is an atheist under M2. Then "At least one god exists" is not in B. Since x in B <=> Norman believes x is true, and x is not in B, "Norman believes 'At least one god exists' is true" is false. Since Norman always responds truthfully, he will answer "no" to the question, "Do you believe in god?" Hence, Norman is an atheist under M1.

Therefore, Norm is an atheist under M1 <=> Norm is an atheist under M2.



Now, suppose that the following is Norm's belief system:

{"Two plus two equals four"}

So the only thing this guy believes is true is "Two plus two equals four". Under M2, Norm is an atheist; therefore, under M1, Norm is an atheist.


Now, we should all agree with this so far, right? This is all demonstrably true stuff.