Hegel has commonly been ridiculed for views expressed in his 1801 dissertation, On the Orbits of the Planets, in the final pages of which he had adopted a series of numbers from Plato’s Timaeus – a cosmological text earlier taken seriously by Kepler – to account for the ratios of the distances from the sun of the then known six planets of the solar system. While defenders of Hegel have usually toned down the extent of these claims, this chapter argues that Hegel’s reference to Plato’s Pythagorean cosmology must be taken seriously – not as cosmology, however, but as instantiating the logic appropriate for empirically based science. Hegel’s allusion to Plato’s mythologically expressed “syllogism” is consistent with his idea that logic as Plato conceived it allowed its application to the empirical world but that this applicability had been compromised by Aristotle adaptation of it. With the proper grasp of logic’s utilization of the category of “singularity” in its difference to “particularity” – available to Plato but not Aristotle – we can appreciate how, while Kepler’s Laws were empirically based, Newton’s were not as they relied on abstract entities that could not be justified empirically.