Coincidentally, a paper based on Yudkowsky and Herreshoff’s paper has appeared a few days ago on the arXiv. It’s Paradoxes of rational agency and formal systems that verify their own soundness by Nik Weaver. Here’s the abstract:
We consider extensions of Peano arithmetic which include an assertibility predicate. Any such system which is arithmetically sound effectively verifies its own soundness. This leads to the resolution of a range of paradoxes involving rational agents who are licensed to act under precisely defined conditions.
It seems that simply bombarding the brain isn’t sufficient, even for language, and that social interaction is required (see this study), so that playing math games with the child would be a better idea.