Abstract A normal form for fuzzy Turing machines is proposed and examined. This normal form is arithmetical in nature since the truth values are substituted by n -ples of natural numbers and the operation interpreting the conjunction becomes a sort of truncated sum. Also, some of the results in the paper enable us to emphasize the inadequacy of the notion of fuzzy Turing machine for fuzzy computability, i.e. that this notion is not a good candidate for a ‘Church thesis’ in the fuzzy mathematics… Expand