Since antiquity well into the beginnings of the 20^th century geometry was a central topic for philosophy. In contrast, most philosophers of science, if they took notice of topology at all, considered it as an abstruse subdiscipline of mathematics lacking philosophical inter­est. Here it is argued that this neglect of topology may be conceived of as the sign of a conceptual sea-change in philosophy of science that expelled geometry, and, more generally, mathematics, from its central position in philosophy of science and, instead, placed logic at center stage in the 20^th century philosophy of science. Only in recent decades logic has begun to loose its monopoly and geo­metry and topology received a new chance to find a place in philosophy of science, as an object for philosophical reflection and as a conceptual tool for doing philosophy.