Abstract
Metaphysics M 10 is the only place where Aristotle provides a solution to the "greatest difficulty" from Book B: If the principles of substances are particular, but objects of scientific knowledge must be universal, how can there be any scientific knowledge of these principles?The nub of Aristotle's solution is that in an important sense scientific knowledge is concerned with particulars. The paper shows why this solution neither compromises Aristotle's official account of scientific knowledge, nor assimilates scientific knowledge to perception, nor does it presuppose any metaphysically loaded conception of forms (as either particular in themselvesor as neutral with respect to universality and particularity).
Rather, Aristotle's point can be understood against the background of his analysis of geometrical thought in Θ 9. At various points, the geometrician must choose or "set out" one particular actualization of the potential inherent in the respective figure, but she must do so in a way that is conducive to a grasp of this potential in its full universality.
The paper explores Aristotle's promise (most explicit in On Memory 1) to take the interplay between universality and particularity in geometrical diagramsas the model for scientific thinking in general.