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Which is nonsense. Thoughts can't exist by themselves. The mere fact that you are having a thought right now guarantees the thought had an originator. Otherwise, the thought would not exist--and if it did, you would have no experience of that thought (if you didn't exist).
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But if I'm fake, so is the thought. You're going off of the fact that living beings think. But thought can be made by a nonexistent being, making the though nonexistent.