Am I the only one who sees this as "a woodchuck would chuck as much wood as a woodchuck could chuck if a woodchuck could chuck wood." ?
Is this stuff really going to give us a definitive answer concerning the definition of atheism and atheist?
It has been argued that we cannot define atheism negatively because this would entail certain inconsistencies, contradictions, or otherwise entail illogical results. Therefore we should define atheists only and wholly as "not theists". And using such a definition would indeed make infants atheists.
The problem is that there actually is no problem defining atheism as "the belief that no gods exist", and if there were any, it would apply to defining atheists as being "not theists".
All of these posts on logic, set theory, etc., are not (in my view) at all useful to define atheism or theism, but they are important if it is claimed that the only logical way to define atheists is to define them as "not theists".
Of course, we could define atheist as "not theists". That would just be
1) pointless
2) not reflect usage
3) render meaningless or confusing a number of other labels
4) entail labeling people as being atheists even if they themselves as other than atheists and also if the definition of their label reflects usage (which the definition of "atheism" as solely and wholly "not theism" does not)
The problem is that no matter how useful it is to make distinctions like that between theists and deists, agnostics and atheists, polytheists and monotheists, etc., if one argues that logic requires a definition of atheists as "not theists" and further that theists are then defined as anybody who beliefs in god, then we have an issue.
On the one hand, there are all the useful distinctions being thrown out the window for the sake of set theory and logic. On the other, it's also useful to have formal definitions and the ability to use definitions in logical arguments.
Luckily, there is nothing whatsoever illogical about defining atheists as those who deny the existence of any gods. If we consider the most recent definition of "theists" put forward and claimed to be a logical one, it includes people who believe in something they consider to be god. If this definition is capable of being formally expressed, then so is the definition of atheists as "those who believe there is nothing they consider to be a god", or (more simply) that "atheists deny any god exists".
I already spent post after post on pragmatic reasons to define atheism as a belief that gods don't exist, including everything from linguistics to neuroscience, but apparently I must also demonstrate that there is nothing illogical with such a definition.
The New Atheism is at least partly to blame. In recent decades the position that atheism does not entail any beliefs has become a popular (if demonstrably false) one, as it allows atheists to argue that believers are the only ones making epistemic claims. Hence we find incredibly awkward and odd phrases like "absence of belief" or "lack any belief" used almost exclusively in discussions of atheism, because whenever anybody (including atheists) wishes to indicate they "neither disbelieve nor believe" they say "I don't know" and if they don't believe they say "I don't believe." However, saying "I don't believe in god" sounds to many to be too similar to a belief claim, and is to be avoided by awkward phrases that entail the exact same thing. It's all pointless and ridiculous nonsense that could be avoided if the new atheists and those influenced by them (and everybody, actually) were required to take argumentation/critical thinking classes and logic courses in high school rather than learn about rationalizing some meaningless algebraic expression so that
if they go on to calculus they will be capable of evaluating the limits of functions through algebraic manipulations they will never use outside of calculus courses.