This note “fleshes in” and generalizes an argument suggested by W. Salmon to the effect that the addition of a requirement of mathematical randomness to his requirement of physical homogeneity is unimportant for his “ontic” account of objective homogeneity. I consider an argument from measure theory as a plausible justification of Salmon's skepticism concerning the possibility that a physically homogeneous sequence might nonetheless be recursive and show that this argument does not succeed. However, I state a principle (the Generalized Salmon Thesis) that is intuitively plausible and reflects this skepticism. The principle entails that one should be just as certain that the limit of such an infinite sequence is irrational as one is certain that the sequence is not computable. But I claim that this consequence is acceptable.