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Is it possible to have a sincere discussion about this? If I falsely believe in free will then surely I don't have a choice in the matter.

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Even if you have no free will, that doesn't mean that your mind can't be changed by arguments.

But, he can only be persuaded by the arguments that will necessarily persuade him, not necessarily those which correspond to reality. What merit is it to simply find the right button to push?

Lots of merit, because pushing that button will give an enjoyment feedback of being right.

Compare with adventure games that more or less consists of finding the right buttons to push in some order :)

You experience adventure games pretty differently from how I do.

Also note that "merit" and "enjoyment" are different things.

Of course they are. "Enjoyment" is something that can objectively defined, "merit" means whatever you want it to.

That is not really how I experience adventure games, but given the context of comparing a discussion with finding buttons to push, I thought it was apt :)

As for merit vs. enjoyment, I believe that the best merit of discussions is the enjoyment one can derive from it.

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