 (1) Aristotle had argued (Metaph. XIII 3, 1078a5ff) that the work of a geometer is comparable to that of a biologist studying ‘male’ and ‘female’: ‘male’ and ‘female’ are gender attributes of animals that one can discern in isolation when one abstracts from all sorts of other (irrelevant) attributes animals happen to have; just so, the geometer studies his subject-matter by disregarding all irrelevant attributes bodies happen to have, except for points, lines, planes, and their positions and quantities. Moreover, Aristotle argues, the biologist does not suppose that ‘male’ and ‘female’ exist as separate ideal entities (substances) over and above and prior to the concrete living substances that are either male or female, nor should he suppose such a thing. In a similar vein, the points, lines, planes, and solids the geometer studies are neither physical attributes of bodies nor do they enjoy a separate existence independent of them; rather, they exist in the mind of the geometer by virtue of his powers of abstraction. Now Syrianus objects to this line of reasoning that the required kind of abstraction would be impossible unless we assume that the human mind is already equipped with an a priori grasp of precise mathematical entities and principles. He writes: