Then if one tries to make NOT theist = Atheist, which is an arbitrary semantic substitution, and merely a conceptual relative necessity merely true in virtue of the meanings ascribed to the words by someone rather than some type true logical dichotomy by metaphysical necessity, leaving you with a disjunction of theist V atheist…while not logically invalid it comes with a price (baggage). By doing so it commits the atheist that anything that is not a theist MUST therefore be atheist. This includes everything not in the set of theism such as babies, rocks, atoms, quarks…while some atheist I know accept this baggage, and even promote “we are all born atheist”, some do not. Accepting that these thing are atheist *IS* actually consistent with their preferred schema, but then leads to issues such as taking a census…if one asked how many atheists are their in the world the only consistent answer would have to be something along the lines of “countless” or “immeasurable”.
For the atheist that accepts that non theism=atheism, but not that babies, rocks, atoms, quarks etc are atheist they are then stuck with a different problem as they would then have an internally inconsistent system since for any set {A} there is a complimentary set {A’} both comprising the Universal set {U}:
A’=U\A
(In philosophy atheism is not defined this way to eliminate this type of baggage, but defined to be the belief that theism is false, or ostensibly the belief that ontologically God(s) do not exist)
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If you are interested in the logic here using a hypothetical syllogism pattern:
1. ∀x(R(x) ⇒ N(x))
2. ∀x(N(x) ⇒ A(x))
3. ∀x(R(x) ⇒ A(x))
All Nontheist are Atheists
All Rocks are AtheistsOr
- (For all rocks, if it’s a rock, then it’s a nontheist.)
- (For all nontheists, if it’s a nontheist, then it’s an atheist.)
- (For all rocks, if it’s a rock, then it’s an atheist.)
Nontheist=B
Atheist =C
______________________Or simpler:
p1) A V ~A (LEM)
P2) Theist or Not-Theist (Instantiation)
P3) Rocks are Not-Theist (Assertion)
P4) Not-Theist = Atheist (Assertion)
P5) Rock Are Atheist (Conclusion)
Either way, holding to nontheism=atheism leads to absurdities.