E Qui Va Lence Re La Tions and the Categorization of Mathematical Objects

In [2] Lakoff and Nuñez develop a basis for the cognitive science of embodied mathematics. For them, the abstract concepts and reasonings of mathematics are grounded in the conceptual processes that we develop in our interaction with the physical world. Through the use of conceptual metaphor these cognitive devices are projected to the realm of mathematical reasoning. In this paper we employ the methods spelled out in [2] to make a thorough study of the equivalence relation, a particular mathematical object. In particular we identify the primary cognitive metaphors at play in the conception and understanding of the equivalence relation and discuss some examples. The equivalence relation is a fundamental object in all branches of mathematics and, although a relatively simple construction, its cognitive analysis proves to be a rich source of cognitive methaphors and conceptual blending.