Ontology and Logic: The Case of Scholastic and Late-Scholastic Theory of Relations

Abstract

This paper investigates the reason (or reasons) why, in the tradition of Western philosophy, a logic of relations was developed only in the second half of the nineteenth century. To this end, it moves along two different but interconnected paths: on the one hand, it attempts to reconstruct the main views concerning the ontology of relations during the middle ages; on the other, it focuses on the treatment of so-called oblique terms (termini obliqui) in the logical works of some preeminent authors belonging to the scholastic and late-scholastic tradition. From the ontological point of view, realists and nominalist both denied that polyadic expressions of the language (spoken, written or mental) signify polyadic properties in the world extra. Some authors, such as Peter Auriol, claimed that polyadic expressions signify something merely mental (as contrasted with ‘real’), thus recognizing, even though in a limited ontological domain, the existence of full-fledged relations, that is, of ‘things’ simultaneously ‘inhering’ in a plurality of subjects. These authors too, however, were unable to produce a logic of relations analogous to that developed in the nineteenth century by De Morgan. If we look at the treatment of so-called ‘oblique inferences’ in the scholastic and late-scholastic tradition, we find that the validity of the inferences in which oblique terms (relations) are involved, does not depend on specific properties of relations but on some general principles on which the syllogistic theory is based. This is true even of the logical work of Juan Caramuel y Lobkowitz (1606–1682), a Spanish Catholic scholastic, who wrote extensively on oblique inferences and who is credited with having introduced a kind of ‘proto-logic’ of relations. Thus, whereas medieval thinkers, from the ontological point of view, attributed to relations understood as polyadic properties a very poor role in the ‘fabric of the world’, from the strictly logical point of view, they made no attempt to develop a systematic analysis of the main properties governing inferences composed by relational sentences. In the case of relations, thinkers belonging to the scholastic and late scholastic tradition did not develop something analogous to the theory of consequences: in other words, they did not possess a logic of relations.