On the notion of free will in the Free Will Theorem
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The (Strong) Free Will Theorem (FWT) of Conway & Kochen (2009) on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will (allowing physicists to ``freely choose'' the settings of their experiments). This makes the theorem philosophically vulnerable, especially if it is construed as a proof of indeterminism or even of libertarian free will(as Conway&Kochen suggest). However, Cator and the author (Foundations of Physics 44, 781-791, 2014) previously gave a reformulation of the FWT that does not presuppose indeterminism, but rather assumes a mathematically specific form of such ``free choices'' even in a deterministic world (based on a non-probabilistic independence assumption). In the present paper, which is a philosophical sequel to the one just mentioned, I argue that the concept of free will used in the latter version of the FWT is essentially the one proposed by Lewis (1981), also known as `local miracle compatibilism' (of which I give a mathematical interpretation that might be of some independent interest also beyond its application to the FWT). As such, the (reformulated)FWT in my view challenges compatibilist free will a la Lewis (albeit in a contrived way via bipartite EPR-type experiments), falling short of supporting libertarian free will.