Another cluster of metaphysical problems focused on the relation at a time between a thing and those items that compose the thing. One such problem was whether the whole is identical to the sum of its parts. Medieval answers to this question were often informed by the Aristotelian principle that there are degrees of unity. Material composites were typically divided into three classes: aggregates, accidental unities, and substances. Aggregates were the weakest sort of unity, since they exist when some things are present in one location. A thing with a greater degree of unity exists when there are some things in one location and these things are arranged in the right way. These arrangements are due either to accidental forms, or to substantial forms. Composites of some things and an accidental form are accidental unities; composites of some things and a substantial form are substances. Among material composites, substances were thought to have the greatest degree of unity.
Medieval philosophers generally agreed that an aggregate is identical to the sum of its parts, but there was considerable disagreement when they turned to accidental unities and substances.
Most medieval philosophers thought that artifacts - even complicated ones such as houses - were accidental unities. They disagreed about whether an artifact was identical to the sum of its parts, due in some measure to a disagreement over the ontological status of relations. Those who thought that relations were things could answer that the artifact is not identical to the material out of which it is composed, for the composite has an additional part, the relation, which the sum of the material parts lacks. Those who thought that relations were not things could not make this claim, though there was still a feeling among some that it was improper to reduce the artifact to being merely the sum of its parts. Abelard, for example, thought that arrangements were not things, and hence they could not be parts of things. However, this does not imply that an artifact is identical in every respect to the sum of its parts. An artifact and the parts that compose it are the ‘‘same in essentia and in number,’’ but they are ‘‘distinct in property,’’ because there is something true of the latter, which is not true of the former, and vice versa (cf. Theologia Christiana III, } 140:247-248; King 2004:89-92).
There were also differences of opinion about the relation of a substance to its substantial parts. Some thought that a material substance is not a sum of two actual, ontologically independent objects (Aquinas In Metaphys. VII, lec. 13, n. 1588; cf. Normore 2006:740-741). Yet, others believed that the substantial form and the matter were in some sense independent things, and hence, they had to determine whether the composite is identical to the sum of these two things. Those who answered in the affirmative were in effect offering a reductionistic account of material substance; those who answered in the negative were antireductionists. Antireductionists, such as Duns Scotus, asserted that a numerically distinct object comes to be when the substantial form combines with matter (Cross 1995). Otherwise, he argued, material substances would be nothing more than aggregates or accidental unities. Ockham and Buridan thought that the material substance is nothing more than the sum of its substantial parts, but that this reductionistic account of material substance did not imply that substances are aggregates or accidental unities (Normore 2006:744-747).
In more general terms, medieval philosophers felt that there were some items that were numerically or really the same thing, yet not entirely identical. This led to an explosion of senses of the terms ‘‘same’’ (idem) and ‘‘different’’ (differens, or diversum) (the preferred terms for medieval discussions of identity). Many of these senses of sameness and difference corresponded to distinctions in the order of things. Hence, Duns Scotus’ famous ‘‘formal’’ and ‘‘modal’’ distinctions were both in the broad sense, real distinctions, even though he reserved the term ‘‘real’’ for a case where x and y could, at least in principle, exist separately in reality.
The formal and modal distinctions had a number of applications in philosophy and theology. The formal distinction was employed to explain how the essence in itself and the essence in Socrates were related to one another. The modal distinction had applications in Trinitarian theology. Indeed, the utility of these nonconceptual modes of distinction in theological applications was the primary reason that even ardent critics of the formal and modal distinction, such as Ockham, often conceded that the distinction was useful when trying to come up with a rational account of the Trinity.
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