In Metaphysics A.4 (985b4-19 [DK67 A6]), Aristotle provides crucial information about fundamental aspects of the chemistry and microphysics of the atomic theory of Leucippus and Democritus of Abdera. Besides the plenum and the void, which he identifies as the elements of the atomic theory, he presents what he himself names as differences. These fundamental differences are named so because they ought to be responsible for the emergence of all other differences in the physical world, and especially the ones that hit our senses. Aristotle provides a list of three differences both in what is recognized as autochthonous terminology from Leucippus and Democritus, and in a translation to terms apparently more intelligible to Aristotelian listeners. Among those differences there is one in particular that is harder to comprehend than the other ones: rhysmos. Aristotle’s translation of rhysmos into schēma has led most interpreters to acknowledge that it referred solely to atoms individually, while the other two differences would refer to relations between atoms. In this paper, I want to propose an interpretation in which rhysmos actually refers to several aspects of the chemistry and microphysics of the atomic theory.

According to Glaucus of Rhegium Democritus was “a disciple of a Pythagorean” (dk 68 A1, 38). The tetralogical catalog of his works prepared by Thrasylus begins its section on ethics with the three following works: Pythagoras; On the Disposition of the Wise Man; On the Things in Hades (dk 68 B0a–c). The very order of the first three ethical works of Democritus could point to some sort of dependence on Pythagoreanism. This was suggested earlier by Frank (1923: 67), who believes that this is due to the fact that Democritus saw Pythagoras as basically the founder of an ethic-religious sect. Without being forced to agree with Frank, it is undeniable that there are many similarities between Pythagorean and Democritean ethics. The Democritean sentences that speak about the sense of shame before oneself as a way of preventing evil deeds (dk 68 B84, 244, and 264) recalls the practice of anamnesis, the examination of conscience in the Pythagorean tradition. Even more important are the parallel uses of measure as a basis for ethical reasoning. This paper aims to review this connection between Pythagorean traditions and Democritus, examining what emerges as the most probable core issue to determine how close this relation between atomists and Pythagoreans could have been: the Aristotelian testimony (de An. 1.2 404a16-20 [dk 58 B40]) on the material conception of the Pythagorean soul. In fact, a corpuscular conception of the soul (“dust in the air”), foreshadowing the psychology of Democritus, is attributed to the Pythagoreans. Is the argument of de An. 1.2 404a16-20 a misunderstanding by Aristotle? Or does this testimony represent an actual dialogue that Pythagoreans were having with atomists in the fifth century bce?

In the atomism of Leucippus and Democritus, as transmitted by Aristotle, elements are the atoms and everything else are atomic compounds. Still according to Aristotle, all of the physical features of sensible compounds must be traceable down to their elementary chemical constituents. He puts this same kind of demand to the atomic theory and considers that it falls short, because their impassive and immutable atoms cannot suffer the fundamental chemical processes that we witness in nature: generation and alteration. According to Aristotle, there is the atomism of Leucippus and Democritus something we could name as a theory of differences. Chemical processes (as he conceives them) would not be real, but only the expression of the aggregation and segregation of atoms moving through the void. The differences observed in compounds and attested by the senses would be caused by differences between atoms and by their relative positions. In this paper, I explore this theory of differences, showing that it makes sense, but also that it is more complex than Aristotle’s initial suggestion. In atomism, not only the different geometric shapes of the atoms matter, but also the relationships that atoms establish among themselves, as well as the structure of the compound, which presupposes the void, and the atomic motion, summing up a total of seven fundamental differences that respond for most of the functions that Aristotle would like to find in the elements of a chemical theory.

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