Throughout analytic philosophy, appeals are often made to formal methods for deriving philosophical conclusions. In this paper, I examine a particular instance of this phenomenon according to which it is possible to prove an inconsistency in functionalism --- one of the most popular and well-studied views in philosophy of mind. According to this argument, functionalism can be shown to be self-contradictory by appeal to Beth's definability theorem. I show that this argument misses the mark for reasons both formal and philosophical, and claim that carefully identifying where it goes wrong is instructive for helping clarify what the functionalist position is, how different versions of it might be delineated, and how these variations might be formally expressed.

Dr Owain Griffin's primary areas of research are the philosophy and foundations of mathematics and logic. 

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