One of the proposed hallmarks of an integral whole is that it is actually composed out of its parts. This thought naturally implies that the whole depends upon its parts for its existence. In On the Trinity Boethius tells us that the composite ‘‘gets its being from those things which compose it’’ (De trin. II). In one sense, this claim is not controversial, for in the case of a composite being, some parts are required to bring the composite into existence. Many medieval philosophers would also concede that in order for a composite to exist at some time, the right sort of parts must exist at that time. For example, in order for a human to exist at time t, there must be a substantial human form and the right sort of matter at t.
But some medieval philosophers consider an even stronger reading, namely, that in order for this whole to exist at t, these parts (and no others) must exist at t. Boethius suggests this stronger thesis in his treatments of parts and wholes (De divisione 879c):
> If a part of the whole perishes the whole, whose one part is
Destroyed, will not exist. But if the whole perishes the
Parts, although scattered, remain.
Boethius reiterates his claim that the removal of a part removes the whole in his treatments of the topics (In Ciceronis topica III, 331.23-29 and I, 289.35-39). Taken at his word, the thesis is remarkable, for it suggests that if Socrates’ fingernail is a part of Socrates, then the removal of the fingernail removes Socrates.
There is an innocent way to interpret Boethius’ maxim that the removal of the part entails the removal of the whole. In his Metaphysics, Aristotle notes that one sense of ‘‘x is whole’’ is that x is complete (V, 26, 1023b26-27). Accordingly, if one were to remove y from the whole of which it is a part, the whole consisting ofy and some other parts is removed. For example, if I cut off Socrates’ finger, the whole that consists of Socrates’ finger as well as all of his other parts is compromised. But this just means that Socrates has been ‘‘mutilated’’ (cf. Aristotle Metaphysics V, 27). The removal of Socrates’ finger does not entail the destruction of Socrates. Radulphus Brito seems to have this interpretation of Boethius’ maxim in mind. He claims that in the case of heterogeneous wholes, if one part of the whole is destroyed, the whole itself is not destroyed, but the ‘‘shape of the whole’’ is (Commentary on Boethius’ ‘‘De differentiis topicis’’ II q. 9:45).
Other philosophers insist that Boethius’ rule must be restricted in some manner. Most commonly, the rule is restricted in this way: the whole is removed only if one removes a ‘‘principal'' part. If one were to amputate Socrates' right hand, Socrates would not cease to exist. He would merely lack a hand. Hence, a hand is a ‘‘secondary part.’’ Yet, if someone were to remove Socrates’ heart or brain, Socrates will be destroyed. Thus, hearts and brains are ‘‘principal parts.'' The distinction between principal and secondary parts is in place by the middle of the twelfth century (Pseudo-Joscelin De generibus §§ 6-10 [=Cousin 1836:507-508]; anonymous Introductiones maiores Montane 71va-72rb). The restriction of the Boethian maxim to principal parts is common throughout later Scholastic treatments of mereology (cf. Buridan Summulae 6.4.4; Joachim Jungius Logica Hambergensis XI, §§ 16-18).
What often underwrites this distinction between principal and secondary parts is a metaphysical commitment to forms that are not dependent upon their matter.
If a form is independent of its matter, it can be the metaphysical glue that holds an object together as it changes material components. For example, Walter Burley draws a distinction between the whole secundum formam and the material whole. The formal whole persists so long as the form persists (De toto etparte, 301). Most common-sense objects are identified with a whole secundum formam, not a material whole. Hence, Socrates is not substantially compromised by material changes.
However, there are a few medieval philosophers who argue that the removal of any part entails the removal of the whole. Peter Abelard insists that every integral whole is composed by a unique set of integral parts. This house must be composed out of these nails, these boards, and this cement (Dialectica 551.4-9). If I use other nails or other boards, I could make a house, but not this very house. Given that each whole is composed by a unique set of parts, if any part is removed, that whole is destroyed. Another whole similar to the original might exist after the mereological change takes place, but strictly speaking the two wholes are not identical (cf. Henry 1972:118-129, 1991:92-151; Arlig 2007).
Buridan and Albert of Saxony also flirt with the notion that any mereological change brings about the destruction of the whole (Buridan Quaestiones in physicam I, q. 10; Albert of Saxony Quaestiones in Aristotelis physicam I, q. 8; cf. King 1994; Pluta 2001). There are three senses of numerical sameness: there is a proper sense, a less proper sense, and an improper sense. Something is properly the same in number if all its parts remain the same and it neither acquires nor loses any parts. In this strictest of senses, no corruptible thing persists through mereological change. Something is less properly the same in number if its ‘‘most principal part’’ remains numerically the same. This is the sense that allows us to claim that Socrates is numerically the same man now as that man ten years ago, since Socrates’ intellective soul persists through the change (Buridan In Metaphysicen VII, q. 12, 48va). Finally, something is improperly the same in number if there is a continuous succession of beings that maintain a similar shape, disposition, and form. This improper mode of numerical sameness allows us to claim that the Nile River here today is numerically the same river as the Nile back in Caesar’s time. The reason why these philosophers flirt with an extreme notion of persistence is this: Albert claims that plants and animals can only be numerically the same in the third, improper sense, for these creatures do not have the sort of soul that can act as a guarantor of less proper identity (Quaes. in phys. I, q. 8:131). Oddly, Buridan does not discuss nonhuman substances. It may be that the substantial form of the horse is sufficient to preserve the persistence of the object through change, provided that the substantial form of the horse can play the role of a principal part, for in his Summulae Buridan endorses the distinction between principal and secondary parts (6.4.4). Or it could be that Buridan follows Albert of Saxony’s line when it comes to nonhuman substances.
The extreme view of persistence held by Abelard and Albert of Saxony (and perhaps Buridan) threatens the Aristotelian distinction between substantial and accidental change. Strictly speaking, we do not have one substance, but rather a succession of substances loosely unified by three facts: these successive beings have some of the same parts, this line of succession is continuous, and each member in the line of succession belongs to the same species of substance.
Abelard and Albert of Saxony resort to some interesting antirealist strategies to maintain at the least the appearance of Aristotelian orthodoxy. First, all three philosophers make an exception for human beings. Personal identity is guaranteed by the persistence of the intellective soul (Abelard Dialectica 552.36-37; Albert Quaes. in phys. I, q. 8:125, and p. 130). When it comes to other objects, such as houses and horses, Abelard suggests that these items are convenient fictions, that is, conceptual items constructed from ephemeral things. They are analogous to days and utterances, which strictly speaking do not exist since their putative parts do not exist all at once (Arlig 2007:esp. 217-223). Albert denies that his analysis entails that every mereological change entails substantial change, but he does so by reinterpreting substantial change. Substantial change occurs only in those cases where the specific substantial name is changed (op. cit.:128). So long as one can apply the name and definition of ‘‘horse’’ to the whole in question, no substantial change has occurred.
Given that most medieval philosophers do not endorse an unrestricted reading of the claim that the whole is posterior to its parts, it is interesting to note that they appeal to this very principle in order to demonstrate the absolute simplicity of God (Anselm Monologion 17; Anselm Proslogion 18; Aquinas Summa theologiae I, q. 3, a. 7; Maimonides Guide of the Perplexed II, prop. 21 and II, 1). These philosophers argue that if something is complex, then that thing has parts. But if something has parts, then that thing is posterior to and depends upon its parts. Hence, if God is complex, then God has parts and God depends upon these parts. If God depends upon any x, then x is a higher form of being than God is. So, if God is complex, then God is not the highest form of being. But God is the supreme being. Therefore, God cannot possess any parts whatsoever. God is absolutely simple. Medieval philosophers typically take this to mean that God is not divisible in any respect. God is not a composite of hylomorphic parts, He is not a composite of subject and accident, He is not a composite of genus and differentia, and He is not a composite of being and essence. He is utterly noncomposite (Summa theologiae I q. 3, art. 7).
The thesis that God is absolutely simple has interesting metaphysical and theological implications. For example, if God is absolutely simple then God cannot occupy space or time, since occupying space and time divides the occupant into parts (Anselm Monologion 21).
God’s simplicity also entails that anything that is identical to God’s essence is identical to the whole of God’s essence (Anselm Monologion 17; cf. Boethius De trin. IV). In particular, God is traditionally identified with the Good itself, Justice itself, and Being itself. But since God has no parts, the Good, Justice, and Being cannot be parts of God’s essence. Since identity is transitive, the Good is identical to Justice, Justice is identical to Being, and Being is identical to the Good. Many medieval philosophers are willing to accept and defend this odd result rather than deny that God is absolutely simple. Those who deny that God’s Goodness and Justice are identical do not in turn think that God has parts. Rather, they insist that names such as ‘‘Good’’ and ‘‘Just’’ do not name the essence of God. The best way to describe God’s essence is to say what God is not (Maimonides Guide I 58). In other words, the so-called negative way is motivated by an unwavering commitment to the absolute simplicity of God, which is in turn founded on the principle that a whole depends upon its parts.
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