ABSTRACT
For the seventeenth century and for some time afterward, Euclidian geometry was an ideal of knowledge that was both certain and objective. It was taken as giving us unassailable and universal truths about the world. As such, it was an inspiration that gave a hope, an example of what humanity was capable of, a standard of achievement, and a goal for other fields of knowledge. At the same time, it set the philosophers immense problems because they were working with an individualistic picture of humanity that laid on them the requirement that any account of knowledge had to trace its sources back to capacities and conceptions that were vested in each separated individual independently of any social relation or background. Any such program is faced with immense, even intractable, problems in trying to give an account of the two most striking aspects of geometry, its certainty and necessity on the one hand and its applicability to the things about us on the other.
