Defining mathematics

Abstract

Any definition of mathematics falls outside its field of investigation. When mathematics is set theory, the history of mathematics prior to the investing of set theory is eliminated. Arguing that the aspects of number and space delimit mathematics makes it possible to avoid both Platonism and constructivism in mathematics. Every philosophy of mathematics should be able to account for the nature and status of the infinite. That set theory is a spatially deepened theory of numbers cannot be accounted for by what Lakoff and Núñez call the Basic Metaphor of Infinity. Gödel’s 1931 results point to an immediate, evident, intuitive insight.