Almost two thousand years after Plato, René Descartes also proposed a geometrically based alternative theory of atomism, without the problematic nothing–everything dichotomy of void and atom. Although Descartes agreed with the contemporary position, that a vacuum does not occur in nature, the success of his namesake coordinate system and more implicitly, the spatial–corporeal component of his metaphysics would come to define the philosophically modern notion of empty space as a quantified extension of volume. By the ancient definition however, directional information and magnitude were conceptually distinct. With the acquiescence of Cartesian mechanical philosophy to the "brute fact" of action at a distance, and at length, its successful reification by force fields and ever more sophisticated geometric structure, the anachronism of empty space widened until "a seething ferment" of quantum activity in the 20th century filled the vacuum with a virtual pleroma.
What did Plato's discoveries about atomism come to define about empty space?
{'text': 'the philosophically modern notion of empty space as a quantified extension of volume', 'answer_start': 429}