It is now time to consider some of the implications of Abelard’s treatments of substantial and quantitative change. We can consider the issues under these heads: First, since it appears that increase and decrease can only occur for substances, what does this imply about the ontological stability of complex artifacts such as houses? Second, if there are analogies between houses and substances, does this erode the divide between substance and artifact that Abelard has tried to erect? Finally, what does the analysis of increase and decrease imply about human powers to effect changes in the world?
3.1. Stability of Substances
In the stretch of the
Dialectica where Abelard explicitly discusses the problem of increase, it appears that increase and decrease can only happen to substances, since it is only here that we can get it so that some
X itself can become bigger or smaller. At several places in his logical works, including in the course of his examination of increase, Abelard asserts that “no thing (res) has more or fewer parts at one time than at another”. In addition, it is for this reason that he immediately concludes that “in a case where more parts have come to be when a substance has been changed in quantity, the substance itself cannot be said to have been that substance which had fewer parts” [
7] (p. 423). The key to understanding what is going on here is to see that Abelard is equivocating between two senses of “whole” and “part”, since he does acknowledge that a substance’s “whole”, and, hence, its quantitative parts, can increase. This is the whole, which he later calls an “integral” whole, that tracks the “ambit” of a substance (comprehensionem substantiae) [
7] (p. 546). However, if we are thinking about increases in substance as such, this can only occur when God intervenes:
But it has been said that two kinds of quantitative change can come to pass, since some of these changes occur with respect to the ambit of a substance, and then there are some that involve both, that is, both substance and quantity. For when substance is increased, it is also necessary that the quantity of substance grows. And this [latter] quantitative change has been relegated to [the kind of change] differentiated as the superior, that is, to the one that has been called coming to be substantially. For in a superior change, it is not necessary that the quantity of substance change, only the substance itself. For when the body of a man is changed from animate to inanimate, the quantity of substance is not changed, so long as the members remain the same. But through an addition or subtraction of something it is necessary that the quantity, that is, the ambit of the substance changes [
7] (p. 424).
There is a noticeable tension at work here in Abelard’s treatment of increase and decrease. How seriously should we take his assertion that no res can have more or fewer parts at any given time? Is he really saying, as he seems to be, that a single substance can be different things at different times? After all, as we noted previously, Abelard seems to be committed to the notion that the material of the universe, once it exists, is merely moved about and imbued with various substantial forms for certain limited spans of time.
Perhaps we merely have a case here of Abelard asserting the rule about res and its mereological inflexibility for rhetorical purposes, specifically, in order to motivate the puzzle. One reason, however, to be skeptical of this idea is that later, when thinking about whether things can gain or lose parts, Abelard asserts that strictly speaking
this house cannot persist if even one part is gained or lost. There might be a collection of bits and pieces on the lot that still have the form and function of a house after Rocky the stone is removed, but it is not
this house, the one consisting of all the bits and pieces plus Rocky [
7] (p. 550). Abelard resists this conclusion in the case of a substance, like Socrates. However, his reasoning is not fully filled out, and he seems to be willing to concede that Socrates or any other particular substance can perhaps consist of different things—that is, different collections of substantial material—at different moments in time: “Therefore, it does not appear to be the case that this man consists of all his parts taken together, but only of those apart from which he cannot be found” (p. 552). What is clear is how careful Abelard is to frame the problem of increase as a puzzle about the
quantities of things. He seems to have thought that this thesis is compatible with the view that a substance might be identical with different collections of res governed by the final substantial form over the course of its lifetime.
However, can the center hold? More specifically, can Abelard carve out this position in such a way that substances and artifacts neatly fall on separate sides of a clearly demarcated line?
One way to test Abelard’s position is to approach it from the side of substances. Can the mereological flexibility of substances hold despite the position that certain substances, the products of first creation, appear to be mereologically inflexible? Certain philosophers who are sometimes associated with Abelard and who have subsequently been named “Nominalists” (Nominales), for instance, reportedly maintained the thesis that “nothing grows” (nihil crescit) [
12]. Perhaps the most striking expression of this thesis can be found in an anonymous commentary on the
Categories:
This rule seems to make it possible to lodge a potential difficulty for us, as we say that every removal of a part, every addition, and every transposition of a parts changes the being of the whole (essentiam totius). Yet that which is sick cannot cease to be sick unless either some part is subtracted, or some part is added, or some of the parts are transposed. Therefore, a case of being sick cannot cease unless being ceases. And hence, there cannot be a being healthy [
13] (p. 397).
Here, we seem at first to have precisely the sort of collapse of substances into specific sets of things governed by a dominant substantial form that many later nominalist thinkers are attracted to. For instance, in the fourteenth-century philosophers such as Jean Buridan maintained that natural substantial forms cannot transfer from one set of material bits to another. Hence, if Browny the horse’s material bits change, Browny’s horse form is also different. “Browny”, consequently, turns out to be a substantive noun that behaves more or less in the same way that “the Seine” behaves. It is a noun that picks out different substances at different times, where the governing pragmatic principle at work is the fact that the sets of substances involved are appropriately connected to one another by means of some natural, causal story (for more on Buridan and Browny, see [
14,
15,
16,
17]).
It is interesting, therefore, to see that this particular “Nominalist” does not go down that path: “To this we say that whatever is healthy is by its nature healthy, and whatever is sick is by its nature sick; nevertheless,
the same man who is healthy can be sick” [
13] (p. 397,
my emphasis). In other words, this Nominalist seems to adopt the picture that we are here attributing to Abelard. This is not to say that there were not any in Abelard’s day who maintained this harder position about the tenability of substances. However, if we are looking for a clear example of a work by an early Nominalist that anticipates Buridan’s position, it must be found elsewhere in the mass of manuscripts still waiting for proper, thorough study.
3.2. Analogy of House Forms to Substantial Forms
So far, then, it appears that Abelard and perhaps most twelfth-century thinkers maintain that substances are different from collections of discrete things, in virtue of the fact that while collections of discrete things are determined by the precise components that comprise the collection, substances can gain or lose members of the collection of materials that underlie them, so long as the dominant substantial form is still holding the remaining bits together into a continuous unity.
As mentioned above, it seems that at first Abelard wishes to enforce the divide by appealing to the continuous nature of substances. That is, because the form unifies the substance, its quantitative parts are continuous with one another. For Abelard as well as for many others in this period, artifacts are, by their very nature, things that have discrete parts. Indeed, for some the lack of continuity between the parts of an artifact immediately guarantees that the artifact is somehow less than fully one. Here, for instance, is an anonymous author from the school of Gilbert of Poitiers.
The reason why it is claimed that every contiguous whole is many, that is, [identical] to its parts, but that no continuous whole is: […] Among integral wholes, there are some that are aggregated out of their parts, as a tree is, and there are some that are disaggregated, as a flock is. Of the aggregated wholes, some are continuous (like a stone), others are contiguous (like a corset), and others are successive (like time). Therefore, a continuous whole is one whose parts are naturally conjoined to one another in such a way that they are believed to contain one another or at least to hold themselves together. For this reason the [parts] are said to be continuous, as they are in a stone, for which it is truly said that it is one. But a contiguous whole is one whose parts are naturally disjoint, while being conjoined by means of art, as one sees in a corset or a woven fabric. Here a part is placed next to a part and aggregated so as to make a whole. But since there is no difference between the whole called contiguous and the whole called disaggregated or collected save that the parts of the former are closer to together, whereas those of the latter are dispersed either by art or by chance, what reason can there be why the one that is disaggregated is many, yet the [whole] that is contiguous is one? [
18] (pp. 38–39).
Since a house is merely contiguous, and not truly continuous, it is identical to its parts, and, accordingly, if a part is removed or added, it in the strict sense is no longer there. As we have seen, Abelard seems to endorse this line of reasoning in his discussion of the principal parts of things [
7] (pp. 549–52).
There is a complication, however, that Abelard himself initiates. Recall Abelard’s account of what increase is. It is not a case where we judge that either X or Y, or even the collection of X and Y, is bigger. Prior to being adjoined to one another, X and Y both existed, were each the size that they still are, and, hence, the collection of the two already existed and is the size that it is. Rather, Abelard argues, it is more appropriate to say that prior to joining X and Y, X and Y did not form a composite.
Hence, when we say ‘if something (quid) is added to some thing (cuilibet rei), the whole is made bigger’, this should not be taken to mean that the composite has become bigger than it was before. Rather, a composite that is bigger than each of the parts taken by themselves has been made by an act of joining some of them together. For in fact previously there was no composite [
7] (p. 423).
Later in his
Dialectica, Abelard observes that there are several grades of integral whole [
7] (p. 548). Some integral wholes are mere pluralities. In such cases, the parts X, Y, and Z need not even be spatially proximate, let alone arranged in any meaningful way, in order to be a whole. Others, such as crowds and flocks, are aggregated wholes. In these cases, X, Y, and Z must be spatially proximate to one another for a whole of this sort to exist. However, there is a third sort of whole, whose parts must be more than merely spatially proximate to one another. In these cases, the parts must also possess a “composition” (compositio). Here, Abelard means that the parts must be organized in a specific way. This organization can be due to a substantial form, in which case the parts are united under a single nature. However—and this is the crucial point—there are also wholes that are unified in an important sense, but whose form is accidental in nature. Houses and dresses are such items. For, as Abelard observes, it is not enough to have all the house’s parts on the lot. They must be composed in order to complete a house [
7] (pp. 550–551). In one of his discussions of grades of wholes, Abelard observes that there is a difference in how nouns referring to these objects work [
19] (pp. 170–171). Mere pluralities of discrete particulars take plural nouns. However, organized wholes, including ships and houses, behave syntactically like names for particular substances. That is, the nouns are used in their singular form, even if ontologically the house is many.
It is, perhaps, in part due to this fact about how Latin works that Abelard is tempted to muse about the analogy between the composition of a human and the composition of a house, when he turns from a discussion of integral wholes (which, remember, are tracking the “ambit”—that is, quantity—of a substance) to a discussion of wholes understood “in terms of their substance and their form” (secundum substantiam et formam) [
7] (pp. 559 f.).
Abelard makes it plain that the mereology at work in hylomorphic composition is different from aggregation. A hunk of material, M, and a substantial form, F, must be “conjoined” (coniungere) in order to have an instance of a substance belonging to some substantial kind (the F-en things). However, the substance that arises is not merely an aggregate of M and F. Rather, it is through the conjunction of the two that M “transitions into” a new nature. This allows us to then say that M conjoined to F is nothing other than the item that is materialized (ipsum materietatum).
It is at this point that Abelard observes a parallel between substantial hylomorphic conjunction and accidental hylomorphic conjunction. Statues are not substantial, as the authorities make abundantly clear. Nevertheless, there is a likeness between statues and humans, which suggests that the composition that inheres in the statue is “quasi-substantial” [
7] (p. 561). Specifically, there seem to be two analogies. First, a statue cannot be without its composition, any more than Socrates can be without his rational substantial form. Second, like Socrates, a statue is nothing other than the material that has been arranged in the right way. The statue, in a sense, is nothing other than the bronze shaped in a certain manner. A golden ring is “nothing other than the gold once it has been forged into a round shape”, and “this house is nothing other than this wood and these stones to which this compositio has been superadded” [
7] (pp. 560–561).
Again, Abelard interprets these claims about artifacts in such a way that the house being nothing other than these boards and these stones implies that each of the boards and stones is necessary in order to have this house. However, interestingly, Abelard is challenged on this point by many of his contemporaries. Two exhibits from the twelfth-century milieu stick out. The first is a short fragment on the persistence of houses that has been edited by Peter King as part of a longer treatise on universals, which he believes to be from a follower of one Joscelin of Soissons [
20] (p. 105). The second is an introduction to logic from the school of one of Abelard’s most astute critics, Alberic [
21].
The discussion in the Joscelinian fragment starts with the startling observation that we could think of the house as
either a continuous whole
or as a discrete whole [
20] (p. 122). It is not clear by this remark whether the author seriously believes that houses are continuous wholes. Perhaps instead, this is merely a ploy. For the author proceeds to demonstrate that, in either case, this house can persist as this house even if it were to lose a stone—nay, even half a wall—provided that the half of the wall that is removed does not make it such that the remainder cannot go on as a house. That is, a house can lose a significant portion of one of its walls, provided that this portion is only a quantitative part of the wall. As long as the wall’s substance, and, thus, its capacity to be a wall for this house, is retained, the house is retained (pp. 124–128) (see also the study of these passages in [
22]).
The discussion and even some of the solutions mooted in the Joscelinian fragment echo the discussion of the house and its persistence conditions in the
Introductiones Montanae Maiores. In particular, the author of the
Introductiones observes that the alleged topical rule, that if a part is destroyed, the whole is destroyed, must be restricted to principal parts [
21] (p. 132). The principal parts may be either substantially principal parts, as the heart and brain are for a human, or quantitatively principal parts, as the walls, roof, and foundation are for a house. This suggests that, unlike the Joscelinian work, the author of the
Introductiones is under no illusion that a house might be a true continuous whole.
The Joscelinian author concedes that if a house were a discrete whole, it would depend upon
its parts. However, he argues that it does not follow that any removal of any part
of a part of the house entails the destruction of the house as a whole, because not every removal of parts of parts entails the removal of the house’s part. The example that the author gives is of a flock of sheep [
20] (p. 126). This flock must have, say, A, B, and C. However, if one were to shave A, this would not, thereby, destroy the flock consisting of A, B, and C. Whereas if one were to remove A’s heart, this would destroy this flock, even though another flock might persist. Similarly, some of the parts of a house might be true continua, in which case a reduction in quantity of any of these parts would not entail the destruction of the whole house.
The author of the
Introductiones, by contrast, seems to offer up a much more radical proposal. To say that a wall is a principal part of a house means that houses must have walls in order to be houses. However, it does not entail that this house must have this wall [
21] (pp. 132–33). Likewise, it is true to say that when one of the smallest parts of a house is destroyed, the whole house is destroyed, so long as we interpret this to mean that if there were no smallest parts, there would be no house (p. 134). Again, however, none of this entails that this house must have this determinate little stone. If a specific house, consisting of a set of parts P and a stone S, were to lose S, this is all that is true: the house “does not continue on in the whole’s same distinctive feature” (non remanet in eadem proprietate totius) (p. 134). It is hard to render the notion into eloquent English, but the basic idea is clear enough (remember that for an Aristotelian in this period, a proprium or proprietas is a distinctive or characteristic feature of a thing or kind of thing). If the house loses S, the house loses the distinctive features of a certain whole. In particular, the house is no longer
a whole consisting of P and S. However, this does not entail that the
house ceases to be. The author of the
Introductiones then adds this especially intriguing principle of determining whether “the F” continues to exist: The house is said to continue on when some parts of it remain, just as the king is said to continue on in his sons, even after he has perished, when some one of his sons lives and continues on father’s role as king (pp. 134–135).