  Aristotle's rejection of intermediates involves showing that their advocates are committed to an unwieldy multiplicity of mathematical universes, at least one corresponding to each mathematical science, whether kinematics, astronomy, or geometry. However, he also sets out to show that such ontologies are not merely pleonastic, but also that an alternative account can be given free of all the difficulties mentioned. In other words, Aristotle's strategy is best seen as diffusing some versions of platonism.