  Schnorr’s theorem is evidence that we really have captured the intuitive notion of randomness. Different intuitive starting points have generated the same set of random sequences. This has been taken to be evidence that ML-randomness or equivalently (prefix-free) Kolmogorov randomness is really the intuitive notion of randomness, in much the same way as the coincidence of Turing machines, Post machines, and recursive functions was taken to be evidence for Church’s Thesis, the claim that any one of these notions captures the intuitive notion of effective computability. Accordingly, Delahaye (1993) has proposed the Martin-Löf-Chaitin Thesis, that either of these definitions captures the intuitive notion of randomness. If this thesis is true, this undermines at least some sceptical contentions about randomness, such as the claim of Howson and Urbach (1993: 324) that ‘it seems highly doubtful that there is anything like a unique notion of randomness there to be explicated’.