6 - How Euclidean geometry has misled metaphysics

Summary

Introduction

Euclid's geometry is so brilliant that it has always dazzled us. It shone for centuries so brightly as to blind us to any model for an established branch of knowledge but the deductive system based on a few self-evident axioms. Thus it misled metaphysics. But that is not my theme. I want to show how it led Leibniz to some mistaken arguments in the central letters of the Leibniz–Clarke Correspondence. The letters are about quite special issues in the metaphysics of space. But they have dominated philosophy since then as our models of how epistemological arguments should decide metaphysical questions. My theme is to reveal the arguments as mistakes.

Space sets ontology one of its most acute, searching and elegant problems. To change my visual metaphor, the reason why we have not been able to see further into this subject is because a giant has been standing on our shoulders. He is Leibniz. Though the arguments in his letters are fallacious, surely he is a giant. What can make those fallacies clear to us was not available to him nor to his great opponent, Newton. But first, what is the problem space sets for ontology?

On the face of it, space has disconcerting properties. The list below is loosely phrased, and neither exclusive nor exhaustive.