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No.
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What I need to do is to take a look at each argument
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that gets offered for the existence of a soul and rebut it--
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explain why those arguments are not compelling.
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I don't need to prove that souls are impossible.
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I just need to undermine the case for souls.
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If there's no good reason to believe in souls,
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that actually constitutes a reason
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to believe there are no souls.
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Now, if you want to, you could go on and try to prove
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that souls are impossible in the same way
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that maybe dragons are impossible.