BEYOND ARISTOTLE: INDIVISIBLES AND INFINITE DIVISIBILITY IN THE LATER MIDDLE AGES John E. Murdoch The basic text for late medieval Latin atomism and its critics was Aristotle’s Physics, especially Book VI. Here the atoms or indivisibles he considered and combatted were extensionless, a conception that can be found in scholastic debate about atoms all the way to Galileo and his atomi non quanti.1 The medieval atomists were clustered in the fourteenth-century,2 as were their Aristotelian critics. Figure 1 provides the basic dramatis personae of the fourteenth-century atomists and their critics. The list of atomists is nearly complete, save for the followers of Wyclif. The list of their critics is naturally less complete, being made up of chiefl y those who name their atomist opponents. Yet even without such identifi cation, we can often tell other critics, such as John Buridan and his school, because they oppose specifi c identifi able atomist arguments. The question of the motives for the late medieval atomism is pretty murky. The motives for Greek atomism are, at least to some extent, an answer to Parmenides’s monism and center in attempts to explain natural phenomena (if not always totally successfully). Equally clear are the motives for the Arabic atomism of the Mutakallimun: namely, to put all causal relations into the hands of God through the mechanism of the doctrine of continuous creation. However, in the case of late medieval atomism there is not such a wholesale application to nature or to a God who creates the universe anew at every instant. 1 Galileo Galilei, Discorsi e dimostrazione matematiche intorno a due nuove scienze, vol. 8, p. 72. There is, of course, the quite separate consideration of minima naturalia that arises out of Aristotle’s criticism of Anaxagoras in Physics, I, ch. 4. For the medieval history, as well as the historiography, of this kind of atomism or corpuscularianism, see Murdoch, “The Medieval and Renaissance Tradition of Minima Naturalia”. 2 For the earlier medieval atomism by the likes of Isidore of Seville, William of Conches, etc., see Pabst, Atomentheorien des lateinischen Mittelalters. For the standard treat- ments of the medieval atomism of the fourteenth century, see Duhem, Le système du monde, vol. 7, pp. 3–157; Maier, “Kontinuum, Minima und aktuell Unendliches,” In Die Vorläufer galileis im 14. Jahrhundert 2nd ed., pp. 155–215; and, more briefl y, Murdoch, “Infi nity and Continuity.” 16 john e. murdoch Dramatis personae INDIVISIBILISTS ARISTOTELIANS E Henry of Harclay William of Alnwick OFM N G Walter Chatton OFM Adam Wodeham OFM L I Crathorn OP Thomas Bradwardine S H John Wyclif William of Ockham OFM Roger Rosetus OFM Walter Burley C Gerard of Odo OFM John the Canon O N Nicholas Bonetus OFM T I John Gedo N E Marcus Trevisano N T Nicholas Autrecourt A L Single line arrows represent (named) criticism Double line arrows represent verbatim borrowing Fig. 1. Fourteenth-Century Indivisibilism and its Critics.