§30. Nominal Relations

Ockham's nominalism implies that with the exception of substance and quality, terms in all the other categories (relation, place, quantity, etc.) do not signify distinct things existing in the way individual qualities inhere in indi­vidual substances.

The medieval argument about relations belongs to the story of empiricism and especially radical empiricism because what makes empiricism “radical” is the effort after a more consistently empirical empiricism, where the ob­stacle to consistency is nominalist baggage modern philosophy carries over from the end of the Middle Ages. What scholastic philosophers call a “real relation” is an Aristotelian accident, badly but standardly analyzed in terms of inherence in a subj ect. If R is a real relation, then aRb is true if and only if a and b are really distinct extra-mental things with a real extra-mental founda­tion for R in a. The relation is not real but merely rational if a or b is not real, or not really distinct, or no real foundation exists for R in a. Notice that a rela­tion is “in” one term more than the other or others, founded in one term and not equally in all or really connecting them. This is an awkward implication of the assumption that relation is an accident of a substance.

A principle of medieval Aristotelianism is that one accident cannot be in two subjects. It seems obvious. My white cannot also be yours. It can be like it, similar, but it cannot be one and the same individual quality inhering in you and inhering in me. There are two whites, as there are two individuals, a principle bound to make trouble for relations. As an accident, the relation cannot inhere in both terms, for the reason just explored. That made relation seem less real than terms, and prompted Aristotle to regard relation as min­imally real. “It may happen that when one correlative changes, the other can truly be said not to change at all.” In other words, a can begin to be related to b with no change in a but only in b. If you become taller than me, I without changing become shorter than you. This conclusion was widely taken to imply that relations have no existence without the mind.⁵³

The Latin reception of Avicenna’s Metaphysics stimulated new thinking about relation in the thirteenth century. Avicenna wrote in part responding to the teaching of the mutakallimun, who thought divine omnipotence requires God alone to be effective, and that anything logically consistent is really possible and can occur by God’s will. Their argument was explained to European readers in Latin translations of Maimonides, al-Ghazali, and Averroes. These mutakallimun used (perhaps invented) the infinite regress argument against relations. A relational accident would have to inhere in a substratum, but that inherence is a relation, which has to inhere, and that inherence is another relation, and so on, precluding a single well-founded re­lation. Their conclusion was that relations cannot be full-blooded realities— they have to be ficta, cognitive artifacts.

Thomas Aquinas and Duns Scotus both affirm real relations, physical re­lations founded in nature, which is the thesis Ockham rejects. Precisely be­cause everything is singular and separate, if relations were real then God might make a father without a child. If that is impossible in nature, so too are relations. Ockham does not identify a relation with its foundation, because the relation is an act of understanding, not the quality of a substance. Relation considers substance comparatively, comparing substance to substance or quality to quality, without assuming the inherence in them of something denoted by the relational term, which is merely an act of understanding.

He says a relation “is not any such thing in reality as many imagine,” sum­marizing his argument in an elegant syllogism. “Every thing distinct in re­ality from another thing can be understood without that other thing being understood, and most of all, if neither is a part of the other. But it is impos­sible for some thing which is a relation to be understood without any other thing. Therefore, etc. [sic].” In reality, there is nothing except absolutes, which exclude relations. A relation is a name, a word, a concept. “Relations do not exist except as intentions or concepts in the mind, and these certainly are not the same as external things.” Relations are not things, and have no founda­tion in things; they are connotative terms, names. As connotative, they do not signify physical things but only other terms, signs of things. Under nom­inalist analysis, relation thus disappears into logical syntax. How things are related is not a quality of nature; it is the action of signs.⁵⁵

Ockham's theory of relations proved decisive for modern philosophy. After much discussion, refutation, and reformulation among logicians from the fourteenth to sixteenth centuries, it emerges as logical common sense that need only be pronounced, as we find it in Hobbes and Gassendi; in Spinoza, who viewed relations as “our own creation”; again in Locke, who said that relation “be not contained in the real existence of Things, but something ex­traneous, and superinduced”; and Leibniz, for whom “Paternity in David is one thing, sonship in Solomon is another, but the relation common to both is a merely mental thing whose basis is a modification of the individuals.” Hume says relations arise “from the comparison which the mind makes,” and depend “entirely on the ideas, which we compare together,” while for Kant, “Connection [Verbindung] is solely an affair of the understanding.”⁵⁶

The principal ideas responsible for the theoretical treatment of relations from Plato to Kant are that being and unity are convertible and relation an accident.