Over on my post introducing potentiality from first principles, a reader raises some important questions that I thought would be worth answering in a separate post. If you haven’t read that post yet, I would encourage you to before continuing here.
This idea of “relative non-being” is the best explanation I have come across of the idea that potency “limits” act, though I still do not quite understand it. It seems to me that “relative non-being” really presupposes diversity in being rather than explaining that diversity; if so, it would be better just to take the diversity as primitive.
We could say that relative non-being is intrinsically differentiated, since whenever something is not X it is therefore something other than X. Thus, another way of talking about relative non-being is in terms of otherness. This does not presuppose the diversity of being, however, because relative non-being is something outside of being—it influences being without making any positive contribution of being. Perhaps this would be clearer if we noted that by “being” we really mean non-relative being, and that likewise by “non-being” we really mean non-relative non-being. So, non-relative being is, non-relative non-being is not, and relative non-being is not X (for some X). We posit relative non-being in order to account for how it can be the case that more than one thing is. If there is only what is (being) and what is not (non-being), then nothing can diversify “isness” into this and that. On the other hand, if isness is composed with is-not-Xness then this opens up the possibility of isness also being composed with is-Xness (ie. is-not-Y for all Y other than X, more on this later). Since no one thing can be both X and not-X at the same time in the same sense, this gives us diversity of being.
What does it mean for being to compose with relative non-being? At this point, all we can say is that it involves mutual influence: being provides the positive contribution by virtue of which something is, whereas relative non-being provides the limits by virtue of which something is not X, or Y, or Z, etc. Neither exists in this influenced form prior to the composition, meaning that the relative non-being has no existence whatsoever apart from its composition with being, and being has no multiplication to this or that instance apart from its composition with relative non-being.
Maybe another way to put that would be: relative non-being can only account for multiplicity/diversity in being if there is diversity in relative non-being. But Parmenides could just reply that there can’t be diversity in relative non-being either: it couldn’t be differentiated by being (because that presupposes diversity in being, which relative non-being is supposed to account for); it couldn’t be differentiated by non-being (because that is nothing); and it couldn’t be differentiated by relative non-being (because any two things with relative non-being have that in common).
The first sentence here is spot on: relative non-being accounts for the diversity in being by virtue of the diversity that is present in relative non-being. But this diversity is not added to something that is otherwise one, but is an intrinsic feature of relative non-being. The relativity of relative non-being means that there is no such thing as relative non-being simpliciter, that is relative non-being without some qualification. This is because relative non-being is defined in terms of what it is relative to—the X in “is not X”—so that if we take this away then all we are left with is non-relative non-being, which is something else entirely.
Given this, Parmenides’s supposed reply doesn’t work: there can be diversity in relative non-being because there can be diversity in its qualifications. Suppose we have something that is not X, nor Y, nor anything else except Z, and we have something that is not X, nor Z, nor anything else except Y. Despite these both having relative non-being, they must be distinct from one another because the way in which they have relative non-being is different: each is qualified in a different way.
This is analogous to other determinables, such as location. You and I each have a location, but these locations themselves are distinct from one another.
At least as far as I understand Parmenides argument against multiplicity, he could give the same justification against multiplicity in relative non-being as against multiplicity in being – though I’m also not sure I understand Parmenides very well.
Parmenides’ argument seems to be:
(1) For there to be more than one being, they must be differentiated either by being or non-being.
(2) They can’t be differentiated by non-being, since that is nothing.
(3) They can’t be differentiated by being, since they have that in common.
Thus, there cannot be more than one being.
The Thomistic response seems to be to deny premise (1) and postulate relative non-being as a third option. But I don’t see why we cannot deny premise (3) instead and just say that yes, while they have “being” in common in the sense that they both exist, they also exist differently (e.g., by being of different kinds, or different individuals of the same kind). In other words, postulate diversity in being as a primitive principle. “Relative non-being” appears to me to be parasitic on this primitive diversity, and therefore superfluous as a response to Parmenides.
This reconstruction is somewhat accurate, but misses a crucial nuance. The problem in (3) is not simply that they have being in common (as they might have relative non-being, or locatedness in common), but that in both cases being is doing the same thing, namely grounding their isness. If all we can say about X is that it is and all that we can say about Y is that it is, then there is no distinction between them, because there is no sense in which Y is not X or vice versa.
I also don’t quite see how it follows that these two ways of conceiving of potentiality (relative non-being vs. capacity for actuality) are equivalent: in arguing that they are equivalent you describe both conceptions in two different ways and those different ways don’t seem equivalent to me.
Looking back, I certainly could have described the relevant moves in more detail. The basic idea is that we can show that the two accounts of potentiality are equivalent by starting from each one and showing how it can be understood in terms of the other.
Let’s start with relative non-being, which we have said limits being by excluding certain options within some domain. It cannot exclude everything in the domain, however, for then it would just be non-relative non-being. So, it must leave certain options “open.” Suppose we are considering a simple feature which can be one of three states, X, Y, or Z, and our relative non-being excludes X and Z. In this case, it leaves Y open. But remember that relative non-being makes no positive contribution of being itself. So, it grounds a certain openness to being without causing something to be or not—it limits what a thing is, but does not determine whether it is or not. But this is precisely what we said it means to be the passive capacity for act.
A similar series of moves can be applied in the opposite direction. Suppose we have some capacity for being Y. Then this capacity excludes being X and being Z, since when this capacity is realized then the thing is not X or Z. But this is just what relative non-being does.
In both cases, because the capacity is for a specific act and because the non-being is relative to a specific range of options, we can invert this range and get the other. We see that these two accounts are two sides of the same coin. While non-being excludes everything and being includes anything, relative non-being and the passive capacity for act restrict their scope, and therefore allow us to consider that scope in two ways—what is in or what is out. The passive capacity for act focuses on the former while relative non-being focuses on the latter, but in reality they are the same thing viewed from different perspectives.
 Throughout this post I refer to relative non-being in terms of being not-X. When not specified, the X should be understood to include one or many options within some domain. Considering colors, for instance, X could be a specific color or any collection thereof.