 A common but spurious argument for the maximality thesis, which we may call the ‘equivalence fallacy’, cites the fact, noted above, that many different attempts to analyze the informal notion of an effective method in precise terms—by Turing, Church, Post, Andrei Andreevich Markov, and others—turned out to be equivalent to one another, in the sense that each analysis provably picks out the same class of functions, namely those functions computable by (standard) Turing machines.