Nominalism Meets Indivisibilism
Medieval Philosophy and Theology, vol. 3 (1993)
Nominalists, it is said, are defined by their opposition to the needless multiplication of entities. For most fourteenth-century nominalists, parsimony was in the first instance a logico-semantic matter, raising the question of how one should explain the truth conditions of sentences without assuming any kind of strictly isomorphic relation between individual sentences and what makes them true.
In their analyses of the structure of continuous spatial magnitudes, this question was presented in an especially clear and unambiguous form: “Is it necessary to posit indivisible entities to explain the truth conditions of sentences containing terms such as ‘point’, ‘line’, and ‘surface’ ?” Affirmative answers offered one route to indivisibilism, the thesis that continua are divisible into finitely or infinitely many indivisible parts, or mathematical atoms.