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If my decision to forego the money was the result of mental analysis and rumination...
...then when does the determinism come into play? The whole idea of free will is that I can reflect upon and choose a course of action.
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Rigid determinism states that everything that happens is a result of physical interactions. In your scenario, the mugger pulls the gun, which causes certain chemical reactions in your brain, which trigger more reactions, which eventually lead to your decision. Basically, given a certain stimulus and a certain brain state, determinism says there is only one possible outcome - thus, no free will, because while it may have appeared that you made the decision, it was dictated by the chemicals in your brain.
I'm personally not a fan of determinism, but I'm not a fan of much theoretical science at all, so I don't have a counterpoint.
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