I'm not sure what you mean by asking if the two beliefs can "co-exist".
If you mean should we be tolerant and respectful of others beliefs, then sure, theism and atheism can certainly co-exist.
If you mean can both positions be true, then the answer is clearly an emphatic
no, and the two positions are the antithesis of each other.
Theism: A god exists (or gods exists).
Atheism: No gods exist.
Suggesting that both are true is entirely equivalent to asserting "A and not-A". In doing so, you are refusing to allow the debate to exist in any kind of logical framework and hence further communication is rendered impossible.
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Originally Posted by DaveMatrix
But we can show that God's existence is far more likely to be a reality than his non-existence.
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Would love to hear it.