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prase comments on Atheism = Untheism + Antitheism - Less Wrong
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The difference is what would happen if they were to encounter evidence for the existence of a deity. A weak atheist would start to believe no matter how weak the evidence, wheras the strong atheist would only start to believe if the evidence was stronger than his prior evidence against god. And the strong atheist would probably be much more dilligent in trying to defeat arguments for god.
Assuming that "believe" in your usage means "p(God exists)>0.5" in my usage, and similarly "disbelieve"="p<0.5", this would mean that weak atheists are at exact p=0.5, which is a zero measure set. Such people don't exist.
Seriously, it is difficult to imagine an opinion which can be reversed by literally any evidence against, no matter how weak.