Suppose that “weak atheism” is defined as “non-belief that God exists.” We can take this as equivalent to “I do not believe that God exists.” Suppose also that “strong atheism” is defined as “belief that God does not exist.” This would be equivalent to the claim “I believe that God does not exist.”
There are essentially two components to these. First is the stance toward a particular proposition, “I believe” or “I do not believe.” Second is the contents of the proposition, “God exists” or “God does not exist.” Take the first part to be a function Blf(x), which is equivalent to “I believe that x”, where x is some proposition. The contrary would be ~Blf(x) which is “I do not believe in x.”
Each of these two components has only two possible values: either “I believe that” or “I do no believe that” (Blf(…) and ~Blf(…)) and x or ~x. The total combinations are four:
- Blf(x) = “I believe that God exists.”
- Blf(~x) = “I believe that God does not exist.”
- ~Blf(x) = “I do not believe that God exists.”
- ~Blf(~x) = “I do not believe that God does not exist.”
1 is theism or the response of a theist. However, 1 implies 4, because it is impossible to hold 1 and hold either 2 or 3. If I believe that God exists (Blf(x)), then I cannot believe that God does not exist (Blf(~x)). I would both believe both that God does and does not exist, which is a contradiction. Further, if 1, then I cannot not believe that God exists (~Blf(x)). I would both believe and not believe the same thing at the same time. Consequently, since I cannot Blf(~x) since I Blf(x), then I must ~Blf(~x). That is since I believe in God it follows that I do not believe that God does not exist. I do not believe the negation of what I do believe. Hence, there are logical implications between the different values.
Weak atheism would hold 3, while not holding 2. This is what would distinguish it from strong atheism which holds 2. Agnosticism would hold 3 and 4. I contend that weak atheism as understood necessarily reduces to agnosticism. One cannot hold 3 and not hold 2 without simultaneously holding 4.
Weak atheism holds to ~Blf(x). However, with regard to 2, either the weak atheism either a) Blf(~x) or b) ~Blf(~x). These are the only possibilities. If a) then weak atheism is actually strong atheism. If b) then weak atheism reduces to Agnosticism. From our presupposition about weak atheism, a) is impossible. Therefore, weak atheism reduces to agnosticism.
Even more, if the weak atheist denies Blf(~x), that is strong atheism, this is by definition ~Blf(x). The weak atheist says, “I do not believe that God exist, but I am not a strong atheist (i.e. ~strong atheist = ~(Blf(~x))).” To accept 3 and deny 2 logically implies agnosticism, that is 3 and 4.
It should be noted that 3 does not imply 2, or ~Blf(x) -\-> Blf(~x). This is the main point that is exploited in the discussion. However, ~Blf(x) cannot be held in isolation. Certain, ~Blf(x) and Blf(x) cannot be held simultaneously, but either Blf(~x) or ~Blf(~x) is also held. Weak atheism is an illusion which is a red herring in the discussion about atheism being “just a lack of belief.” Either one believes that God exists, that God does not exist or is agnostic to the question.