It is sometimes assumed that the extreme view of persistence espoused by Abelard and Albert of Saxony is founded on the principle that a whole is identical to the sum of its parts. If that were so, an easy way to avoid the conclusion that a change in parts entails a change in the whole would be to deny that the whole is ever identical to the sum of its parts (Brown 2005:esp. 150-155).
An orthodox Aristotelian will readily assert that an integral whole is not always identical to its parts. Some integral wholes are weakly bound together. For example, a crowd is a very loose and weak unity: it is a combination of substances and an accidental form (Aquinas In Metaphys. expositio V, lectio 21, sections 1102-1104; Summa theologiae III, q. 90, art. 3, ad 3; Buridan Summulae 8.1.4-5). For this reason, its parts might be identical to the whole, and a removal of one part might compromise the existence of that whole. But a combination of a substantial form and matter yields the truest sort of unity one finds in the sublunar world (Aquinas Summa theologiae I, q. 76, art. 8). In the case of substances, the whole is clearly not the sum of its integral parts. First, a substance is not identical to the elements that make it up, since when the substance exists, its parts exist only in potentiality. As for the functional parts, which exist in act only when the whole exists, the sum of these is not identical to the whole, since the whole consists of all the parts plus something that is not a part, but rather a principle, namely the soul (Aquinas In Metaphys. expositio VII, lectio 17, sections 1674-1680).
It would also be wrong to suppose that Abelard or Albert of Saxony think that an integral whole is identical to its parts. Abelard presents the clearest illustration of this point. Abelard admits that it is not always sufficient to gather together the parts in order to create a whole. Some wholes require the imposition of structure in order to bring about the existence of the whole (Logica ingredientibus II, 171.14-17; Dialectica 550.36-551.4). A house, for example, is a collection of boards, nails, and bricks that have the right arrangement. While this arrangement is not a part, it is a difference maker. Abelard claims that a house and the parts that compose it are the ‘‘same in being (essentia) and in number,’’ but they are ‘‘distinct in property’’ (Theologia Christiana III, §§ 139-154: 247-253; cf. Brower 2004; King 2004:85-92; Arlig 2005:165-194). Essentially, certain characteristics are true of, or can be predicated of the thing, which are not true of its matter, and vice versa. But this fact does not entail that the matter and the thing are numerically distinct entities, for x is the same in being as y if and only if every part of x is a part of y and every part of y is a part of x. If x is the same in being as y, then x is numerically the same as y. Therefore, the house is numerically the same as its parts, even though the house is not identical to its parts. The claim that the whole is something over and above its parts is, in Abelard’s view, too unrefined to capture the relations that obtain between a thing and its parts.
Several medieval authors consider a specific puzzle that is generated by the identification of a whole with its parts, namely the Problem of the Many (Abelard Theologia Christiana III, } 153: 252; Pseudo-Joscelin De generibus §§ 22-25 [=Cousin 1836:511-513]; Albert of Saxony Quaes. inArist. physicam I qq. 7-8, and Sophismata 46, 25va-vb). Contemporary philosophers perhaps best know this puzzle as Peter Geach’s puzzle concerning Tibs and Tibbles (Geach 1980:215). Assume that Socrates’ body is perfectly intact: he has all his limbs, and their parts. Now consider every part of Socrates’ body except one finger. Call this whole W. W is not numerically the same as Socrates, so it appears that Wand Socrates must be numerically distinct.
Socrates’ whole body is imbued with the soul of a man. But it also happens that W is imbued with the soul of a man. So, there are now two numerically distinct men where it initially appeared there was one. But it gets worse. Considering the body apart from one finger was only one of an indefinite number of such considerations. And by the same reasoning, these other bracketed wholes composed from Socrates’ body are also men. Hence, it is easy to generate an indefinite number of numerically distinct men where commonsense tells us that there is only one.
Most medieval philosophers who consider the Problem of the Many reject the premise that while Wis a part, W is a human. If W is a part of a per se being (i. e., an Aristotelian primary substance), then Witself cannot be a per se being. There cannot be many per se beings occupying the same location at the same time. Therefore, there are not innumerably many men. There is only one man consisting of innumerably many parts (Albert of Saxony Sophismata 46, 25vb).
Even Abelard resolves the Problem of the Many in roughly this manner. If x and y are the same in being, then x and y are numerically the same. But, according to Abelard, it does not follow that if x and y are different in being, x and y are numerically distinct. This is because if even one part is not shared by x and y, x and y are different in being, but in order to be numerically distinct, x and y cannot share any parts. This characterization of numerical sameness and difference leaves logical space for overlapping objects, which are neither numerically the same nor numerically distinct. Thus, according to Abelard it is true that W is not numerically the same as Socrates. But it does not follow from this fact that Wis numerically distinct from Socrates. Hence, there is not an indefinite number of numerically different men. But if one asks Abelard to pinpoint which of these overlapping men is Socrates, Abelard might reply that Socrates is that sum of parts that is vivified by Socrates’ soul (Theologia Christiana III, } 153). In other words, Socrates is to be identified with the maximal sum of integral parts that is vivified by Socrates’ soul.
World History
