I see no justification for there having to be two types of atheism as this is inconsistent with the other positions [theism and agnosticism]

When it comes to branching [types of], these can be shown as sub-sets...so subsets of theism are religions {which includes all forms of Gnosticism) and everything to do with having some type of leaning towards support for the existence of "GOD" [including my leaning toward the idea of a Cosmic Mind]
So the 'forms' of atheism [ weak and strong] should be observed as types of atheism [subsets] and agnosticism should not be regarded as branching from atheism as a 'type' [usually said to being 'weak'] but rather, should be regarded as distinct from either theism or atheism.

Graphically, it would look something like;

X4zk7ET.png
Thank you for this! I had a difficult time in an unnamed few atheists versus theist groups with members who were adamant that agnosticism is not separate from atheism or theism; the hard demarcations between 'knowledge' and 'belief' made it challenging to have a legitimate discourse.
 
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I wrote this today in an atheist versus theist group:

Yeah, it gets worded that way often nowadays but it's not accurate in practice even for those who make the claim and it is not compatible with a deep dive in philosophy and logic. Now, if most people really "thought" this way and treated others respectfully under those titles I would most likely be okay with the general definitions you provided. Of course not all theists, atheists, and agnostics agree, but if most did and the logic added up I would be ok with it. Fact is that is not typical. Most theists think they know God exists. Most atheists think they know God does not exist. A truly self proclaimed agnostic is neither a theist or atheist. Of course there are some agnostic atheists and agnostic theists but that is not as common as some claim.
From logic the excluded middle is not absolute and there are real world violations. No, not everything violates it but the "law" is not an absolute law.


The law of noncontradiction by extension can also be violated real world and in mathematical logic.
Again not everything contradicts them but somethings do. Most atheism is positive atheism or a subset of antitheism. I know there are many websites and books that try to argue differently just as the new face of literalist Christianity says it's not a religion but a direct spiritual relationship with the one true God.
Knowledge is a subset of belief where knowledge is a smaller aspect of our beliefs that are true (or asserted as true).
Belief is a subjective requirement of knowledge and belief = knowledge if and only if it is justified truth.
In epistemology S believes P (belief condition),
If P is true (Truth condition),
S is justified in believing P ( The justification condition).
Beliefs are a mental state and subjective and not sufficient on their own to be true knowledge but they are required l, otherwise no knowledge exists. I cannot lack all belief and claim any knowledge.


Thus belief is a necessary, but not sufficient component of knowledge.
Agnostics believe there is not enough knowledge for or against a theist or atheist.
Atheists typically belive there are no deities or on some cases there are no God's. The atheists who actually seem to fir the second definition in real life tend to be highly educated and generally intelligent and not simply because they lack beliefs in God(s). Of course Hitchens and others were very intelligent but they were militant atheists.
Regardless even atheists who "lack belief" when pressed admit they do believe there are no God(s), and "believe" the lack of evidence for God(s) gives them knowledge & some evidence provides evidence to them knowing or gnosis.
Go to many agnostic discussion groups and they disagree with the atheist and theist claims on what they believe. Is that less valid than what theists and atheists believe?