Mathematical symbols as epistemic actions – an extended mind perspective

Why are mathematical models so surprisingly efficient in the sciences? In this paper, adopt an extended mind perspective on human mathematical abilities. I review evidence from animal, infant and neuropsychology studies that the human brain contains several specialized neural circuits which can be co-opted to solve complex mathematical problems. However, mathematics has emergent properties which cannot be reduced to these cognitive subsystems. In particular, experimental evidence suggests that our evolved number sense is only capable of representing approximate quantities. Active externalism, a cognitive mechanism proposed by various authors, including Andy Clark and Merlin Donald, allows humans to overcome these cognitive limitations by performing epistemic actions in the world that could not be performed in the mind alone. I discuss the extensive use of external symbols in the history of early modern European mathematics, and demonstrate that this has led to an increasing efficiency of mathematics as epistemic tool in the sciences. This externalization of mathematical symbols can be traced back in the archaeological record to at least 20 000 years ago. Wider implications of externalist and evolutionary approaches to understanding mathematical cognition are discussed.