Relational theories of numbers, 1300–1350

Despite the fact that it was heated and sophisticated, the debate concerning the metaphysical status of numbers in the late medieval Latin West (ca. 1250–1350) remains largely a terra incognita. This paper focuses on one of the questions faced by realists about numbers: thinkers positing that a number is a distinct thing over and above the numbered things. The question is: Are numbers relational entities? On the face of it, the answer seems to be a straightforward 'no', given that Aristotle classifies number in the category of quantity, which, from at least the times of Boethius, was almost universally considered to be of a non-relational nature. However, as I show, the matter is far from being simple, since the textual evidence clearly shows that there were thinkers challenging this received view; indeed, as the paper demonstrates, some thinkers, for example, Francis of Meyronnes, argued that not only number but indeed the whole category of quantity should be reclassified from a non-relational to a relational one. The paper goes over some of the most interesting proofs advanced by the proponents of the relational view of number and their criticism by the defenders of the more traditional, non-relational view.