On Zeno Beach there are infinitely many grains of sand, each half the size of the last. Supposing Aristotle denied the possibility of Zeno Beach, did he have a good argument for the denial? Three arguments, each of ancient origin, are examined: the beach would be infinitely large; the beach would be impossible to walk across; the beach would contain a part equal to the whole, whereas parts must be lesser. It is attempted to show that none of these arguments (...) was Aristotle’s. Indeed, perhaps Aristotle’s finitism applied to magnitude only, not plurality. (shrink)

John Locke’s treatment of quantity in the Essay Concerning Human Understanding is not nearly as extensive or as well-known as his treatment of quality and his distinction between primary and secondary qualities. Yet I contend that a close examination of Locke’s comments on quantity in the Essay reveals that he endorses a general theory of quantity that not only distinguishes quantities from qualities, but also plays several other important roles in his overall philosophy—particularly in his treatments of infinity and demonstrative (...) knowledge. Moreover, I argue that this theory does not appear out of thin air, but is in certain respects one and the same as the approach to quantity found in Aristotle and developed by medieval Aristotelian thinkers. Identifying the core tenets of this approach in the texts of Aristotle and medieval Aristotelians, and formulating them clearly enough to shed light on Locke’s theory of quantity in the Essay, is the principal task of this paper. (shrink)