On the notion of free will in the Free Will Theorem∗

The (Strong) Free Will Theorem 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). Although Conway and Kochen informally claim that their theorem supports indeterminism and, in its wake, a libertarian agenda for free will, inferring the former from the Free Will Theorem is a petitio principii (as has been pointed out before). Of course, this also considerably weakens the case for the latter (at least from the theorem). A recent reformulation of the Free Will Theorem due to Cator and the author (2014) uses a mathematically precise formulation of the idea that experimentalists freely choose their settings even in a deterministic world, and thence construes the theorem as providing constraints on determinism (as opposed to proving indeterminism). In the present paper we argue that the concept of free will used in this version of the theorem is essentially the one proposed by Lewis (1981), also known as ‘local miracle compatibilism’. To do so, we give a mathematical reformulation of this idea, which we believe to be well within its spirit and which may be of independent interest. On this double reformulation the Free Will Theorem shows that local miracle compatibilism contradicts the parts of modern physics used in its assumptions. Therefore, although the intention of Conway and Kochen was to support free will through their theorem, what they actually achieved is the opposite: a well-known, philosophically viable version of free will now turns out to be incompatible with physics!