4 - On the need to re-examine the relationship between the mathematical sciences and philosophy in Greek antiquity

Summary

Scholars tend to assume that the mathematical sciences and philosophy were distinct disciplines in antiquity, as they are today. From the fourth century B.C.E. onward, mathematicians and philosophers did distinguish themselves. They criticized each other’s work and, in some areas of the Greek world, strong rivalries developed between philosophers and mathematicians. I argue, however, that the distinction between philosophers and mathematicians did not entail that their fields of inquiry were distinct. This chapter examines the relationship between the mathematical sciences and philosophy from the perspective of the practitioners of the mathematical sciences, in particular, Archytas of Tarentum, Hero of Alexandria, and Claudius Ptolemy. I argue that these practitioners viewed the relationship between the mathematical sciences and philosophy as more complex, where the mathematical sciences are not only in relation to philosophy but, even stronger, forms of philosophy.  Moreover, the mathematical sciences answer some of the most fundamental questions of philosophy, e.g., how to obtain knowledge, how to form a just society, and how to attain the good life.