Lakoff, conceptual metaphors and the basic of infinity metaphor

Traditionally, mathematics appears to be independent of metaphor with its formal, objective and precise structure. However, contemporary empirical studies argue that this view is wrong. A historical view of traditional metaphor theories reveals it to be a notion that is complicated, controversial and poorly understood; this motivates an non-traditional approach. As the Lakoff and Johnson and other theorists suggest, moving metaphors paradigmatically to the center of thought improves our view of metaphors and concepts. It also raises new philosophical and cognitive questions that can link mathematics and metaphor. Can we find the metaphorical structure of everyday language in mathematical expressions? How does the simplest mathematical ideas lead to complex mathematical ideas? How does an idea such as infinite which is difficult and paradoxical, construct an objective field such as mathematics? The basic ideas that initiated the mathematics project of Lakoff and Núñez are in the context of these questions. It is essentially a mathematical analysis of ideas, but it is also the discovery of how the concepts evoke an unconscious network of metaphors and a bodily connection in creating ideas. This thesis aims to show how metaphor plays an important role in mathematics, starting with the philosophical adventure of the metaphor and ending with the example of 'infinity'.