The charge that the limit-frequency theory of probability is inconsistent due to incompatibility between the required features of randomness and limit convergence is inapplicable when probability sequences are taken to be empirically (i.e., extensionally) generated, as they must be on a strictly empirical conception of probability.

All past attempts to meet this charge by formulating constructive definitions of randomness that would still allow for a demonstrable limit-convergence have, in their exclusive concern with logically (i.e., intensionally) prescribed sequences, left the logic of extensional classes essentially untouched. In the light of a strict differentiation between intensional and extensional classes a generalized approach is possible under which several closely connected senses of randomness, i.e., the formal, material, restricted and unrestricted senses may be easily distinguished and related to the notion of relevance.