I have presented a case for CI as a process of enculturation, with mathematical cognition as an example of the process of enculturation at work. I began by laying out the 4E landscape and locating CI within it, relative to enactivism and EM. In particular I showed how CI shares the interactive stance of enactivism and the constitutive stance of EM, but how it also differs from these. The main difference between CI and enactivism is that CI does not equate life and mind in the way that enactivism does. The main difference between CI and EM is that CI takes cultural practices to play a central role in the assembly of cognitive systems, whereas EM does not.
I then went on to outline the central concepts required to make sense of enculturation. The CI framework embraces both evolutionary continuity and transformation of existing cognitive circuitry in development. Our modern minds are built on archaic precursors by slow incremental changes. However, modern humans are behaviourally plastic and scaffolded learning drives functional changes in our plastic brains. The developmental change from the ANS to the DNS is an example of how learning-driven changes to cortical function result in new abilities, but this would not happen without the novelty and uniqueness of mathematical symbols and the practices for manipulating them.
I also countered two standard objections: impermanence and shrinkage. The defence of CI rested on the novelty and uniqueness of mathematical practices and symbols.
If the CI framework is on the right track, then human cognitive evolution has resulted in minds that are flexible and interactive. Furthermore, cultural evolution has resulted in written symbol systems and practices for manipulating symbols that can be acquired (in development) by minds like ours. The uniqueness of modern human minds lies in their capacity for transformation.