ABSTRACT
In The Tree of Knowledge, biologists Humberto Maturana and Francisco Varela (1987) analyze the biological foundations of human cognition. A crucial component of their argument is a simple but profound aphorism: Everything said is said by someone. It follows from this that any concept, idea, belief, definition, drawing, poem, or piece of music has to be produced by a living human being, constrained by the peculiarities of his or her body and brain. The entailment is straightforward: without living human bodies with brains, there are no ideas—and that includes mathematical ideas. This chapter deals with the structure of mathematical ideas themselves and with how their inferential organization is provided by everyday human cognitive mechanisms such as conceptual metaphor.
