 Given this apparatus, we could define incompatibilism and compatibilism in the following way: incompatibilism is the thesis that no deterministic world is a free will world. (Equivalently, incompatibilism is the claim that necessarily, if determinism is true, then the free will thesis is false.) And we could define compatibilism as the denial of incompatibilism; that is, as the claim that some deterministic worlds are free will worlds. (Equivalently, compatibilism is the claim that possibly, determinism and the free will thesis are both true.)