Abstract It is a known mathematical fact that the introduction of statistical indeterminacy by means of quantum mechanics (including statistical mechanics) has not loosened up theoretical physics enough so that theoretical biologists could go essentially beyond reductionism. A different type of indeterminacy, designated biological, is introduced here, which conforms with all the known principles of conventional physics. A biochemical model is suggested that embodies this indeterminacy: the catalytic activity of an enzyme depends critically on its electrical environment, but the local electrical states are in turn determined by the ready mobility, within the tissue, of carriers of both signs. The existence of biological indeterminacy arises then from the vast degree of quantum-theoretical near-degeneracy of such a system.