ABSTRACT
In this chapter the author charts the trajectory of his thinking on a kaleidoscope of issues, and how those have been influenced by Annette Karmiloff-Smith's work in Beyond Modularity. Through points of agreement and disagreement with Annette, he discusses his work on Kantian aspects of the development of mathematical competences, his Meta-Configured Genome project exploring the possible evolutionary origins of knowledge of necessary truths and impossibilities, the influence of developmental robotics and artificial intelligence on developmental theory, and even the mathematical knowledge required by trapeze artists and spider monkeys. Immanuel Kant argued that mathematical knowledge, including knowledge of Euclidean geometry and elementary arithmetic, had features that distinguish it from both of the two kinds of knowledge identified by Hume, namely analytic knowledge and empirical knowledge. In response to the author's vague conjecture about altricial species, Jackie Chappell suggested that the basic distinction was not between species, or even individuals, but between competences.
