Philosophy and history of mathematics: a brief introduction

We begin by looking at the place of mathematics, geometry and logic in Greek thought with a focus on the philosophers Plato and Aristotle and the geometer Euclid. Euclid’s book, The Elements, defined mathematical truth for two millennia. Aristotle and Plato disagreed fundamentally about the nature and purpose of mathematics and its relation to scientific knowledge, establishing concepts and attitudes that continue to frame contemporary thinking.
Aristotle is particularly important to subsequent science because his novel concept of ‘the continuum’ was seen to have resolved the paradoxes attributed to Zeno regarding motion and change in the physical world. We will examine in detail these classic riddles including whether Achilles can ever catch a Tortoise.
From Aristotle and Euclid we will also learn about the classical conceptions of valid proof, axiomatic method and logical deductions, all of which underpin mathematics’ claim to be the science of truth.
We conclude our course with modern responses to these ideas in light of the 16th and 17th century revolutions in natural science and mathematics and their new claims to knowledge. Here we will discuss the contemporary debates and disputes over the relationships between mathematics, reason and truth.