A discussion of Nieuwenhuizen’s description for the hidden variables of the detectors in the derivation of Bell’s theorem is presented. This description prevents Bell’s inequalities from being effected. However it will be argued, on mathematical and physical bases, that the flaws attributed by Nieuwenhuizen to Bell’s probability distribution function are unjustified.

Bell’s theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the Einstein–Rosen–Podolsky argument occurs if there exists an ‘element of reality’ but nevertheless addition of complementary results is impossible because they are represented by elements from different arithmetics. A naive mixing of arithmetics leads to contradictions at a much more elementary level than the (...) Clauser–Horne–Shimony–Holt inequality. (shrink)

A common mistake present in the derivation of the usually known as the CHSH form of Bell’s inequalities is pointed out. References and comments to the correct approach are given. This error does not alter the final result and only affects the logical consistency of the derivation, but since it seems to be a widespread misconception regarding the roll and interpretation of the of use of hidden variables in Bell’s theorem it is considered to be of general interest.