The non-equilibrium statistical mechanical autocatalytic theory, underlying the "selfish-gene" paradigm, is shown to be at several points insufficient and contradictory for the description of observed facts of biological systems. We analyze at some length these deficiencies as (1) statistical versus individual non-linear self-constraints, (2) the continuous versus discrete cause-effect evolutional transition, and (3) the nature of the emerging aim-directed biological systems. Concerning the latter, it is shown that it can only be described with reference to the origin of the genetic code, which cannot be accounted for by the continuous evolution of non-equilibrium statistical mechanical systems. We point out that these deficiencies might be covered by alternative (quantum) theoretical considerations. The theory of evolution according to which may have lead to aim-directedness in the primordeal times in a more consistent way, concerning both phenotype and genotype. The specific physical model adopted is an affine Hilbert spaces scheme, with a naturally emerging internal dynamics of measurement, monitored internally by (time-inversion) symmetry restoration. In this context, the physical relation of internal molecular symbolism (semiosis) and internal quantum mechanics is discussed.