Determinism is a claim about the laws of nature: very roughly, it is the claim that everything that happens is determined by antecedent conditions together with the natural laws. #
Incompatibilism is a philosophical thesis about the relevance of determinism to free will: that the truth If determinism rules out the existence of free will. The incompatibilist believes that if determinism turned out to be true, it would also be true that we don't have, and have never had, free will.
The compatibilist denies that determinism has the consequences the incompatibilist thinks it has. According to the compatibilist, the truth of determinism does not preclude the existence of free will. (Even if we learned tomorrow that determinism is true, it might still be true that we have free will.) The philosophical problem of free will and determinism is the problem of understanding, how, if at all, the truth of determinism might be compatible with the truth of our belief that we have free will. That is, it's the problem of deciding who is right: the compatibilist or the incompatibilis
http://jillnorth.org/Formulations_of_CM.pdf
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