  (3) The KS theorem, by its mathematical nature, is not empirically testable. However, we could, along the lines of the previous paragraphs, try to measure a subset of a suitable KS-uncolourable set. Especially, it should be possible to produce cases along the lines of Clifton’s example (3.5) where QM and a noncontextual HV theory make measurably different predictions. It seems as if such cases could provide empirical tests of whether Nature is contextual (though not whether such contextuality is of the causal or ontological type).(For a recent version of such an approach see Tang and Yu 2017.)  From the 1980s on, it has been argued that such testing is impossible. The KS theorem, it was claimed, leaves enough loopholes for a HV theory at variance with QM, but able to reproduce the theory’s empirical predictions. Pitowsky (1983, 1985) argued that it is possible to restrict attention to a subset of directions in R3 which are colourable. His argument, however, relies on a non-standard version of probability theory that is regarded as physically implausible. Meyer (1999) has exploited the mathematical fact that a set DM of directions in R3 approximating the KS-set arbitrarily closely, but with rational coordinates is KS-colourable. Meyer argues that real measurements have finite precision and thus can never distinguish between a direction in R3 and its approximation from DM. Kent (1999) has generalized the result for all Hilbert spaces, and Clifton and Kent (2000) have shown that also a set of directions DCK such that every one direction is a member of just one orthogonal triple approximates any direction arbitrarily closely. In DCK there are no interlocking triples, the question of contextuality does not arise and DCK trivially is KS colourable. Clifton and Kent, in addition, have explicitly shown that DCK is large enough to allow probability distributions over value assignments arbitrarily close to all QM distributions. Meyer, Kent and Clifton (MKC) can be understood as thus arguing that even an empirical test of KS-uncolourable directions confirming the QM predictions cannot prove the contextuality of Nature. Because of the test’s finite precision it is impossible to disprove the contention that unwittingly we have tested close-by members of a KS-colourable set. One quite obvious objection to this type of argument is that the original KS argument works for possessed values, not measured values, so the MKC argument, dealing on finite precision of measurement, misses the mark. We might not be able to test observables which are exactly orthogonal or exactly alike in different tests, but it would be a strange HV interpretation that asserts that such components do not exist (see Cabello 1999 in Other Internet Resources). Of course, such a noncontextual HV proposal would be immune to the KS argument, but it would be forced to either assume that not for every one of the continuously many directions in physical space there is an observable, or else that there are not continuously many directions in physical space. Neither assumption seems very attractive. 