The Cognitive Foundations of Mathematics: The Role of Conceptual Metaphor - eScholarship

Handbook of Mathematical Cognition New York : Psychology Press J. Campbell (Ed.). The Cognitive Foundations of Mathematics: The Role of Conceptual Metaphor Rafael Nunez and George Lakoff In The Tree of Knowledge, biologists Humberto Maturana and Francisco Varela (1987) analyze the biological foundations of human cognition. A crucial component of their arguments 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. The Cognitive Study of Ideas and their Inferential Organization The approach to Mathematical Cognition we take in this chapter is relatively new, and it differs in important ways from (but is complementary to) the ones taken by many of the authors in this Handbook. In order to avoid potential misunderstandings regarding the subject matter and goals of our piece, we believe that it is important to clarify these differences right upfront. The differences reside mainly on three fundamental aspects:

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