Criticisms
One criticism against the techniques is that patterns already implement these concepts in Java and C++. However it takes extra work to implement patterns.
Another criticism is that the term post-object does not identify a specific technnology or practice, in the way that structured programming and object-oriented programming do. This means that post-object is more ambiguous. This may simply be necessary, given that object-oriented was such a large step in impact and identity.
The name post-object was chosen to parallel post-impressionism. Most art patrons who say they like impressionist art really prefer post-impressionist art. Impressionism was an important but subtle change in art. Post-impressionism, for example Van Gogh, went whole hog. Objects use implementation inheritance in various ways, but leave many issues unresolved. Post-object resolves some issues, specifically heterogeneous groups, mixins, and delegation.
Origins
One early language was Cecil. Another important language is AspectJ. Other languages in the near future should include Sting.