ABSTRACT
This chapter examines Klein's discussion of the difference between Plato and Aristotle regarding the ontology of number, the chapter aims to spells out the significance of that debate both in itself and for the development of the later mathematical sciences. It is ultimately argued that Klein's analysis can be used to show that the transition from the ancient to the modern number concept has some roots in this disagreement between Plato and Aristotle regarding number. Jacob Klein's Greek Mathematical Thought and the Origin of Algebra is an immensely rich book, touching on a wide range of topics. Its main goal is to uncover the nature of modern symbolic mathematics, which lies at the heart of modern science. The most important result of Klein's analysis is that the ancients and the moderns relate their concepts to the world in different fashions. Klein begins his investigation with a consideration of the writings of some Neoplatonic commentators and mathematicians.
