Franciscan Studies

Introduction

John Punch (or Ponce; Latin Joannes Poncius, or, occasionally, Pontius, 1599/1603–1661), an Irish Franciscan in exile, unorthodox Scotist and a skilled collaborator of the famous Luke Wadding, is interesting for his fresh and open-minded approach to traditional Scotist doctrines. His take on the theory of relations, which is the topic of this paper, is no exception. As I will show, in his Integer philosophiae cursus ad mentem Scoti¹ he only pretends to be defending a doctrine considered to be traditionally "Scotist," his true mind being apparently quite different.

Some Background

In Punch's time, several competing theories of relations were in currency. The basic insight common, at least as a point of departure, to all scholastics was the one adopted from Aristotle, viz. that a relation is an accidental property of a substance. Quite obviously, substances can enter in and forfeit various relations such as "being similar/dissimilar to," "acting/being acted upon," or "cognizing/desiring" something, without ceasing to exist themselves. In other words, in many cases starting or ceasing to be related to something is clearly a mere accidental change (as opposed to the radical substantial change, i.e., the corruption of one substance and generation of another). However, not all scholastics deduce from this common-sense, pre-philosophical datum the metaphysical thesis that a relation is, ontologically speaking, a true accidental form, distinct from, and inhering in, a substance.

This traditional view was typically maintained by the Scotists and (putting aside certain important qualifications) the Thomists. In this theory, a relation indeed is a real accidental form in its own right, inhering in a single substance and formally causing it to be related to some other substance. According to this theory, these so-called "categorial" [End Page 137] relations—that is, relations pertaining to the category of relation—are not to be identified with (or reduced to) other non-relative accidental forms that are present in the subject and constitute a necessary condition of the relation. The traditional theory thus distinguishes:

1. A. the subject of the relation, i.e., the related thing itself;

2. B. the foundation of the relation, i.e., a non-relative form in virtue of which the subject is related in a certain way;

3. C. the relation itself, which is the form that makes the thing formally related; and

4. D. the object or terminus of the relation, which is the thing to which the related thing is related.²

However, it soon became clear to scholastic thinkers that it would be impossible for every relation without exception to be of the kind just described, that is, a form really distinct from the related thing: for such a theory would generate manifold infinite regresses almost everywhere. They soon realised that there must be kinds of relations which are identical to the related entity: such relations would not then belong to the category of relation, but rather to the category of the given related thing. This is why such relations are called "transcendental"—they "transcend," i.e., "wade across," the categories, that is, are found in more than one category. A transcendental relation's identity with the related thing has an important consequence: whereas the reality of a categorial relation requires the existence of the terminus (e.g., if a red apple is to be similar to another apple, that other apple must exist and must actually be red), for a transcendental relation the real existence of its object is not, generally speaking, required—because an absolute thing (with which a transcendental relation is identified) can, generally speaking, exist without any other absolute thing existing (but cannot exist without the transcendental relation). For example, every potency is transcendentally related to [End Page 138] its proper act, even though the act does not yet exist (or even never will exist).

Following Aristotle's treatise on relations in Metaphysics ∆, the scholastics traditionally recognized three kinds of such categorial relations: relations based on a certain unity (or lack thereof) of form (similarity based on quality, equality based on quantity, and specific identity, based on substantial form; and their opposites, including all mathematical relations), causal...