On the Coevolution of Basic Arithmetic Language and Knowledge

Skyrms-Lewis sender-receiver games with invention allow one to model how a simple mathematical language might be invented and become meaningful as its use coevolves with the basic arithmetic competence of primitive mathematical inquirers. Such models provide sufficient conditions for the invention and evolution of a very basic sort of arithmetic language and practice, and, in doing so, provide insight into the nature of a correspondingly basic sort of mathematical knowledge in an evolutionary context. Given traditional philosophical reflections concerning the nature and preconditions of mathematical knowledge, these conditions are strikingly modest. First of all, it has to be noted that mathematical propositions, strictly so called, are always judgments a priori, not empirical; because they carry with them necessity, which cannot be derived from experience. Immanuel Kant, The Critique of Pure Reason, B 14-15 Norman Kemp Smith translation