All That Space Is Not
The Story of Space: The Strange Non-Being of Space and the Logic of Negation
Up to this point in this series, we have examined the first figuration of space as a receptacle of being that is (1) analogous to women’s bodies in reproduction, and (2) akin to Necessity in its power to sift the elements into place. This post will focus on the logic of negation in Timaeus’ description of the receptacle, and touch upon its relationship to Platonic metaphysics and Plato’s theory of forms. After this, we’ll be ready to examine Timeaus’ inauguration of space as chora in the next installment of this series.
The Strange Logic of Negation
You may remember the first installment of this series where I dissected the grammar of Anaximander’s aperion as the negation of boundary or limit? Timaeus uses this same grammatical technique when describing the receptacle. He tells us that the receptacle is strange (atopou) being without or out of place (topos). He accents this with a-ethous, the unaccustomed and unfamiliar, arrived at through the alpha-privative negation of ethos, the root for our word “ethics.” Finally, the receptacle’s participation in what is real is aporotata, puzzling or aporetic (uses the same root as Anaximander’s aperion). The receptacle is further described as invisible (anoraton eidos) and without shape (amudron). Given that it can neither be perceived through the senses nor known through reason, it can only be apprehended vaguely through a bastard logic akin to the hazy logic of dreams.
Imagine having to describe something only by saying what it is not. It is not easy and yet this is precisely what Timaeus is doing. Why? Because the receptacle, like Anaximander’s aperion, cannot be known or spoken of directly. It occupies a strange position between being and non-being. It has some sort of existence, because without it nothing else would exist, but it is not itself a thing in the same way other beings are things in the world.
A Third Kind Between Being and Non-being
“Our new starting point is describing the universe must, however, be a fuller classification than we made before. We then distinguished two things; but now a third must be pointed out. For our earlier discourse the two were sufficient: one postulated as model, intelligible and always unchangingly real; second, a copy of this model, which becomes and is visible. A third we did not distinguish, thinking that the two would suffice; but now, it seems, the argument compels us to attempt to bring to light and describe a form difficult and obscure. What nature must we, then, conceive it to posses and what part does it play? This, more than anything else: that it is the receptacle [hupodoche] — as it were, the nurse — of all becoming” (Timeaus 48e-49a; Cornford).1
The Timaeus is considered a late dialogue, reportedly one of the last written by Plato. Some theorists suggest that in this work, Plato revises his signature dualistic metaphysics. You might be familiar with how, in The Republic, the visible, sensible world of change is modelled after the invisible, intelligible world of eternal, unchanging Forms or Ideas. The physical world is perceived through the senses and is only a shadow or imitation of the true reality, which is the world of Forms, accessible only through reason and intellectual understanding. This dualism underpins Plato's belief that knowledge of the Forms is the only true knowledge, as opposed to mere opinion derived from sensory experience.
Now, in the Timeaus, the receptacle acts as an interface between the intelligible realm of the Forms and the sensible world filled with physical phenomena. This new, third kind of being stands between being and non-being, mediating the transition of intelligible Forms into sensible reality. As such, the receptacle is a solution to the “problem of participation” from the Parmenides: How do particular things in the physical world partake in or "participate" in the abstract Forms (or Ideas) that are supposed to give them their characteristics. In the dialogue, Parmenides questions how a Form, which is a single, unified, and perfect entity, can be present in multiple particular things without being divided or diminished. This raises issues about the relationship between the one (the Form) and the many (the particulars), as well as how Forms can be both transcendent and immanent. The problem highlights potential contradictions in Plato's theory of Forms, leading to difficulties in understanding how the physical world relates to the realm of Forms.
It seems Plato was looking for a fix to his metaphysics in his latter years, but mainstream academic Platonists consider this a controversial position for various reasons, chief among them being that Plato has Timeaus, and not Socrates (his usual spokesperson), present the theory. Whether Timeaus is here speaking for Plato or not, the receptacle cleverly solves two problems at the same time: the “problem of origins” in Presocratic philosophy as described in the first installment of this series, and the “problem of the participation” of the Forms in the the phenomenal world.
Space-chora
The receptacle to which we have been referring though a series of reproductive and productive metaphors (i.e., recall the odorless base that is used in perfume making, or the smooth and pliant wax surface on which marks can be made) is finally given the name of space-chora near the end of the discourse on Necessity. Going back the the Presocratic context, the elements do not transmute the one into the other, but only in and through the receptacle do beings take form and materialize. We can now name this chora, Timeaus declares, thereby inaugurating the concept of space.
The difference between this and that water is now understood in spatial terms - this water is here and that water is there. Just as two things cannot occupy different spaces and be one and the same, as a corollary, two things cannot occupy the same space and still be two, giving rise to the first principle of difference: that “so long as the two things are different, neither can ever come to be in the other in such a way that the two should become at once one and the same thing, and two.” The intelligible realm of the Forms and the sensible realm of experience are two and not the same because of chora, which guarantees both (1) their separation and difference, and (2) the interface or communication between them.2
Beings take up space by definition: we “say that everything that exists must be in some place [topos] and occupy some room [chora], and that what is not somewhere on earth or heaven is nothing” (Timaeus 52d, Cornford). Famously, Parmenides’ student Zeno will take this assertion and turn it on its head in his paradox of place: if everything that exists must have a place, and place exists, then there must be a place of place, and a place or place of place, ad infinitum. This puzzle will serve as Aristotle’s starting point into the question of space.
Plato’s Cosmology, Francis M. Cornford, (1935).
As an aside, difference in the Western Philosophy context is imagines as a difference between two, and two that are really two sides of the same one, making it very difficult for us to imagine differences beyond binary differences, plurality or multiplicity.