The binned distribution densities of magnitudes in both the complete and th
e declustered catalogs of earthquakes in the Southern California region hav
e two significantly different branches with crossover:magnitude near M = 4.
8. In the case of declustered earthquakes, the b-values on the two branches
differ significantly from each other by a factor of about two. The absence
of self-similarity across a broad range of magnitudes in the distribution
of declustered earthquakes is an argument against the application of an:ass
umption of scale-independence to models of main-shock earthquake occurrence
, and in turn to the use of such models to justify the assertion that earth
quakes are unpredictable. The presumption of scale-independence for complet
e local earthquake catalogs is attributable, not to a universal process of
self-organization-leading to future large earthquakes, but to the universal
ity of the process that produces aftershocks, which dominate complete catal
ogs.