A. Nobody in their right mind believes this. |
B. You can't help believing this. |
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C. Everyone believes this to begin with, but philosophising cures them of it. | D. You only have to play a game or two of billiards to see how true this is. | ||
Hume thinks C, so he can't believe A, and unless he thinks that all those who don't philosophise are out of their trees he can't believe A either.
Hume resorts to billiards when philosophising leads him to perplexity or to beliefs he can't handle. I don't think he sees billiards as reversing philosophical conclusions, but as letting him not bother about them.