There is an intriguing question which I have been considering for some time now and which has not yet been resolved and the purpose of this essay is to attempt to clarify: how can plurality coexist with unity? It seems to me that something is either ONE or MANY, and cannot be both at the same time, and yet is as witnessed by our colloquial usage of the word ‘one’ in describing a thing, say a car, which nevertheless is clearly a plurality of parts – steering wheel, passenger seats, engines, and so forth. And even each of these parts, if analysed in this same manner, reveals itself to also be a plurality. So the question is: is there such a thing as unity, and if so, how can it coexist with this apparent plurality?
First, let us examine the origin of this ubiquitous plurality. Any plurality is by definition a coexistence of things which are separated from one another in some way. The two fundamental dimensions by means of which things can be separated from one another are time and space, and this is why Schopenhauer calls these the ‘principium individuationis’. In these two dimensions – or four, for the mathematical purists – individuation takes place, that is, multiple objects can exist at a given time or in a given place across multiple times. Juxtaposition is the characteristic of space as succession is the characteristic of time. In truth there are more such dimensions which can be seen to separate things from one another, and thus individuate them, such as colour, but in the final analysis these can be seen to be contingent upon the original spatiotemporal individuation which is the primary condition for any individuation whatsoever. Any additional differentiating characteristics arise from the properties of matter and the original forces of nature in their endless combinations and permutations.
So, in empirical reality, everything observable is necessarily a plurality since it arises in space and time, and since it will always be possible to question about the contents of any objects occurring therein and to answer this by producing technology which can resolve matter in ever more confined spaces, and analogously for the temporal dimension. An objection to this may be held on the basis of the atomistic theory of modern physics which postulates fundamental particles which cannot be subdivided and which aggregate in varying conformations to produce the richness of our material world. I am disposed to view this as analogous to the proposition regarding the finiteness of time. In effect, these objections stem from the anthropomorphism which projects the finiteness of our own individual lives onto the macrocosmic dimensions of time and space. But it is obvious that such propositions are logically flawed, witnessed most evidently by the questions they beg: ‘what are the contents of these fundamental particles?’, or ‘what was before the beginning of time?’, or ‘where is the universe contained?’, and so on. Such propositions about the finiteness of space and time produce an internal incoherence in these concepts, manifesting as a conflict between their meaning and our beliefs. If the essence of these concepts is sufficiently apprehended, their extrapolation to the infinitesimal and the infinite becomes apparent and undeniable, as counter-intuitive and seemingly inconceivable as this is. As such, space must, by definition, be infinite, and time, beginningless and endless. So, armed with this understanding of space and time, it becomes clear that any object can always be subdivided into parts, whether spatially or temporally. This happens by ‘zooming in’ to the relevant magnification which will show the object to be extended in space or time, and thus separated into parts.
Now, what is unity? While the answer to this seems self-evident, it may be questioned on the basis of lacking an empirical basis. If the consideration given above is accepted, it can no longer be held that atoms or quarks, or even strings, are unities as even these can be shown to consist of parts and are thus pluralities. So, there is nothing in the world that we can observe which fits the definition of unity, so long as this is mutually exclusive to plurality, which it must be according to the law of contradiction, since no thing can be both ONE thing and MANY things. So why, then, do we entertain this concept and use it so widely? Apart from its usage for convenience and as an aid to communication, it has no ground or basis in empirical reality. But, may it be that even the merely casual usage of this term that we entertain lays for us a trap in our minds, leading us on to the delusion that the things we label as ‘one thing’ are in fact true unities? May it even be that this is a primary contributor to our conceptions of ourselves as unities, occasioned in the past as the simple and immortal soul, and today more precariously as our unified consciousness? When it is apprehended that there is no way in which to conceive of ourselves as unities within the spatiotemporal framework, a great fear sets in, alarmed at a potential unravelling of this most insidious yet beloved narrative of our identities. We would begin to fade and eventually disappear into the sea of transient forms, unable any longer to draw up boundaries and demarcate the identities of things from one another, our ‘self’ included, and call these ‘things’. For by calling something a ‘thing,’ we are subtly implying that this ‘thing’ is a unified thing, that it is ONE such ‘thing,’ and thus that its identity is unitary, most vehemently as regards our own identities. In reasonable discourse, however, this cannot be sustained.
If we return to our notion of the infinite divisibility of space and time, we come to a conception of these as necessarily existing across all scales, a nice metaphor for which is afforded by the mathematical notion of fractals, which are said to be self-similar at all scales and can be ‘zoomed in’ or ‘zoomed out’ infinitely. So, if our universe is to be analogised as a fractal, where does unity enter into the picture, if at all? Can it be said that the only unity is that of the entire universe as a whole, even when it is obvious that this is comprised of an infinity of parts? Or, is it rather another erroneous concept that has no grounding in empirical reality, and for which we would need to invoke a metaphysical solution as Schopenhauer does, by postulating a level of existence that is outside of space and time, and thus un-individuated and unitary? Before addressing these questions specifically, let us consider again this idea of zooming in and out. Zooming in, as was previously shown, leads to the realization of a plurality in what had previously seemed to be a unity, as for instance a pixel on my screen appears as such a unity and which, if zoomed in to, will reveal itself as a plurality. Zooming out, on the other hand, produces the opposite effect, that is, that pluralities will converge on to the same point and will take on the appearance of unities, as for instance when travelling to Mars, the Earth will at first appear to us to be a vast plurality, which upon reaching a sufficient distance will appear as a single unitary dot. So, the further away from the universe one gets, or the more one zooms out of it, the more that it will appear to be unifying, but will never reach its end of a final unity, since the universe is infinite, and one can always just zoom out a little bit more. If plurality is hard to reconcile with unity, how difficult and paradoxical does it seem to attempt to reconcile infinity with unity, which are the true diametric opposites. Plurality is just a special case of infinity – or is it the other way around? So, to move closer to something is to see the parts that make it up, and to move away from something is to see of what whole it is the part. This seems to me to establish unequivocally the inherent relativity of this spatiotemporal realm, in which multiplicity is the true and occurring phenomenon and in which unity is nowhere to be found.
One way to reconcile infinity with unity is to treat both in the same manner, as the departing points from both space and time. Infinity is as equally mystifying a concept as is unity, and this can be seen to arise due to the fact of the utter impossibility of the observation of either within spacetime. Since a departure from spacetime is required, a like departure from the inherent relativism of that realm is entailed. However, whether such a departure is truly possible I cannot confirm or refute at this moment, but my inclination is to believe that it is. In such a case, the individuality that so infatuates us disappears and a deeper non-relative state of being is reached, wherein every element of the spatiotemporal infinity is revealed to be one and the same in every instance, appearing in a multitude of places, times, colours, and the like, but in essence all identical. It seems to me that this is the only way to reconcile our concept of infinity with that of unity. The alternative is to claim that spacetime is all there is, and hence that infinity and unity do not exist absolutely. This is the proposition that we are forced to accept so long as we reside in the spatiotemporal manifold, which we must transcend, if this is possible, in order to truly comprehend what infinity and unity signify. At that point, we will come to realize that they signify one and the same thing, as does every other conceivable utterance or concept or representation.
Conclusion: we live in spacetime; spacetime is infinite; there are only pluralities in spacetime; unity is to be sought outside of spacetime; infinity becomes identical with unity therein, infinity since it so appears in spacetime, and unity since it so reveals itself to truly be.