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Theism / Atheism address 'belief'.
Gnosticism / Agnosticism address 'knowledge'.
Where knowledge is a subset of belief.
The Classical, tripartite definition of knowledge: justified true belief.
Agnostic atheism is a philosophical position on the existence of God. Gnosticism/Agnosticism address knowledge claims; while Theism/Atheism address belief claims. Agnostic atheists are atheistic because they do not hold a belief in the existence of any deity and agnostic because they claim that the existence of a deity is either unknowable in principle or currently unknown in fact.
The agnostic atheist may be contrasted with the agnostic theist, who believes that one or more deities exist but claims that the existence or nonexistence of such is unknown or cannot be known.
Theism and Gnosticism are not mutually exclusive; one can be both. There are four possible combinations:
1. Gnostic Theism - "I believe there is a god, and I know it."
2. Agnostic Theism - "I believe there is a god, but don't know it."
3. Gnostic Atheism - "I believe there is no god, and I know it."
4. Agnostic Atheism - "I do not believe there is a god, but don't know it."
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