The Church-Turing fallacy is the fallacy of supposing that the Church-Turing thesis (CT) or some other idea of Church and Turing entails that the mind can be explained computationally (i.e., computationalism).  (The term 'Church-Turing fallacy' is due to Jack Copeland.)

IMHO, CT is one of the technical ideas most heavily abused by philosophers of mind.

CT says that if a function is computable, then it is computable by Turing machines.  CT does not say anything about which physical systems perform computations or are explained computationally.

If anyone is interested in following up on this theme, the last issue of Synthese has an article by me discussing the relationship between CT and theories of mind, including a refutation of a variety of recurrent arguments from CT to computationalism (viewing the article requires a subscription).

 

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