Kantian Philosophy of Mathematics and Young Robots

摘要

A child, or young human-like robot of the future, needs to develop an information-processing architecture, forms of representation, and mechanisms to support perceiving, manipulating, and thinking about the world, especially perceiving and thinking about actual and possible structures and processes in a 3-D environment. The mechanisms for extending those representations and mechanisms, are also the core mechanisms required for developing mathematical competences, especially geometric and topological reasoning competences. Understanding both the natural processes and the requirements for future human-like robots requires AI designers to develop new forms of representation and mechanisms for geometric and topological reasoning to explain a child's (or robot's) development of understanding of affordances, and the proto-affordances that underlie them. A suitable multi-functional self-extending architecture will enable those competences to be developed. Within such a machine, human-like mathematical learning will be possible. It is argued that this can support Kant's philosophy of mathematics, as against Humean philosophies. It also exposes serious limitations in studies of mathematical development by psychologists.