So my last round of musing was on the subject of “emptiness.” Connected to that idea is the concept of “fullness,” of “plenum.” I suspect that one of the primary failures of contemporary metaphysics is misunderstanding which is really which: that is to say, what is really full, and what is really empty. Here again, Whitehead’s process metaphysics offers us important insights. Because how we think of “fullness” – of a thing, a region of space, or whatever – is directly correlated to what we believe to be genuinely real. I argued earlier against the naïve concept of “empty” space, pointing out that not only is that space (according to physics) a broiling froth of micro events and virtual particles, but that it is also densely awash in relational connections to the rest of the universe. Adding to that earlier discussion, one could say that the space itself is a kind of “thing”: it is an event in its own right, it is a process of space relating itself to other spatial events. In this regard, Whitehead rejected the “material aether” that dominated astrophysical thought in the days between James Clerk Maxwell and Albert Einstein (the last quarter of the 19^th C. to the first decade or two of the 20^th), and argued instead for an “aether of events” as the dominating characteristic of space.

Without assuming – indeed, explicitly denying – any absolute sense of either “emptiness” or “fullness,” what sorts of relative conditions might lead us to characterize one sort of collection as generally more full, and another as comparatively more empty? Well, for that we need a notion of what it is that fills, hence that which is not there when things are empty. My argument is that what “fills” are events and relations.

Consider an object, a really, really, solid object. Often times, the first thing that will pop to mind from such a description will be a rock. But few rocks will be as dense and mass-ive (recall that mass does not refer to a thing’s size, and massive originally referred to a thing’s enormous weight and density) as products of refined metallurgy. So we might suppose instead something like a large weight for a barbell, or a heavy digging spike for breaking up packed earth. There is a great deal of matter there, but what can we say about the events and relations that comprise our massive object?

Well for all that there is a lot of “stuff” in that rock or metal object, for all its great density of matter, such objects are, in reality, extremely simple. Indeed, that simplicity approaches the kind of uniform non-event-hood of a crystal, with the denser metal object being even further in that direction than the natural rock. This is a kind of relational “vacuum” that is only a few small steps above that of “empty space.” Now, I have already pointed out that “empty” space really isn’t empty; it remains relationally connected to the rest of the universe, and stands forth as the various kinds of processes (recall the “quantum foam”) that characterize space-like events.

Consider, now, a comparable unit of pond water.

Actually, before we can do that, we must address what we might mean by “comparable.” Comparable how? Comparable in terms of volume of stuff? In terms of mass? In terms of the displacement of pond water by the rock or metal object? In order to compare one thing to another – to say, for example, that A is equivalent or equal to B – there must be a standard by which this comparability (let’s say “equality,” just so we have a concrete example) must be established and determined. Whitehead was very conscious of this fact, addressing it in the earliest pages of his first major work (his Treatise on Universal Algebra) and devoting an entire chapter to it in his critique of Einstein’s presuppositions regarding space and gravity (his Principle of Relativity.) In that latter book, Whitehead represented the idea that A is equal to B according to principle gamma using the formula:

A = B → γ

But a more contemporary (and arguably clearer) way of formulating what is intended might be,

A =_γ B

as this makes it clearer that the modifying characteristic of γ is associated with the equals sign. Unnoticed in the literature (and, at least, uncommented on by Whitehead) is the fact that this shows that any such concept of comparison is inherently modal in nature – the γ changes the mode of equality in play. This is extremely problematic for a great deal of formal logic, which will often enough introduce “=” as a non-logical primitive, giving no thought to, or even noting, the complex of relational factors that have been insinuated into the system without any (much less, any proper) analysis. Since relational factors are precisely what we are most concerned with here, such blithe disregard is something we cannot allow.

So with the above in mind, consider a “comparable” unit of pond water. If the γ is mass, then the volume will be greater, if it is volume, then the mass will be less. Regardless of the choice of γ, we can begin to look at the ways the two different structures relate to the outside world, but also relate “internally” to themselves.

On both of these accounts, the solid object shows a diminutive relational profile. It can be dropped off in the garage, or left out in the yard, with little difference to how it relates to the world. The exposure in the yard will, over sufficient time, cause wear and incremental destruction to the surface of the solid object. Allowed to proceed without let, such destruction will ultimately degrade the internal integrity of the solid object. But meanwhile, internally, the solid object has an even smaller degree of cohesive relatedness. There is nothing more than a static “thereness” of parts that are, for all intents and purposes, indistinguishable, the one from the other. Relationally, it is practically a vacuum.

The pond water, however, is a very different matter. This isn’t just water; it is a teeming, almost feverish, living environment. An event of enormous complexity, it is thrashing and churning with organic activity within, while each of those individual cells and bits of living matter is itself a thrashing and churning event of staggering relational depth. But just as rich and complicated as the pond water’s internal relatedness, is the overwhelming importance of its external connections to the world. Having once been ripped out of its native habitat of the pond, the sample of pond water has already begun to die. The rock can be dropped here, the metal object dumped over there, and such impacts on its overall integrity as will accrue, will only do so very slowly. The relational connectedness of the pond water is so absolute, that if it remains separated from its over-arching natural environment for very long, it will become as dead and inert as the rock. The rock can ignore its external relations, because its internal relations are themselves nothing more than a repetition of dead events by dead matter.

So the ultimate relational density is that of organic reality, and it is for this reason that Whitehead referred to his own metaphysical speculations as “the philosophy of organism.”

One last word here about my use of the words “external” and “internal” in the above. There is a broader metaphysical sense in which these terms are used, which is implied in the above, but which now needs to be made explicit, and the pivot here is the relation of “identity.” Recall from above that “A is B” (A is identical to B, that is, A and B are the same) is treated as a simple primitive in most logic, but for Whitehead it is a modal concept where A =γ B only with reference to some standard γ. Metaphysically, external relations treat identity (like many logicians), as an unanalyzable, originally given relational fact of the world. Internal relations, however, treat identity as an ultimately achieved relational fact of the world: external begins with identity, while internal ends with identity. Part of Whitehead’s genius was recognizing how both are necessary.