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The Story of Space: Aristotle’s Container View Of Space And Place As Extendable Limit

If you want to understand how change is possible, even in the simplest sense of movement from one place to another, you need an account of the space across which that thing moves. This is Aristotle’s concern in the Physics, his work on natural philosophy. Even though everyone agrees that space has some sort of existence, he tells us, it is not an easy thing to say exactly what it is. As Zeno’s paradox underscores, if space or place exists, and everything that exists has a place, then there must be a place of place, and a place of place of place, to infinity. But Parmenides (of whom Zeno was a student) established that Being is a finite, continuous whole, so place cannot be infinite.

Does this mean that change and movement is impossible, that all the change we see and experience is a lie or illusion? For if place can’t exist, there is no place from, and into, which a thing can move. And further, if there is no place, then things can’t exist in the first place, since they must be somewhere in order to exist. You will recall Timaeus’ declaration 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” (1).

Unlike some other philosophers, Aristotle doesn’t want to deny change, but to give an account that can bring together seeming opposite camps. His task is to make what had previously been described as limitless (aperion) finite; to subsume Timaeus’ tripartite of the Intelligible, visible, and space-chora under one singular Being; all the while also maintaining the denial of the Atomist void. In his typical fashion, he reviews all the claims of his predecessors (in virtue of which we have most of the extant record for Presocratic philosophers of nature) and lays out four possibilities for what space is. Space must be one of either form, matter, interval, or extendable limit.

Immediately he eliminates both form and matter (although arguably matter is much more akin to Plato’s space-chora) because, he says, neither of these can be separated from the thing itself. (2) You cannot remove neither the form nor the matter from a gold statue without destroying that statue. But you can separate the thing from the space it is in. For example, as you pour water from a glass, the water leaves the space it used to occupy. Since space seems to survive the destruction or change of the thing itself, it must be separate and different from that thing.

That leaves us with two candidates — extendable limit and interval. Aristotle asserts space is extendable limit, and renames it as“place” (topos), without offering much argument against the interval model of space. This may be because the interval view, identified with the Atomists and their conception of the void, is not a legitimate candidate for Aristotle — this must have seemed so obvious to him that he didn’t feel he needed to argue the point.

So the obvious candidate for space is extendable limit, described as: “the limit of the surrounding body, at which it is in contact with that which is surrounded [i.e., the thing]” (3) Space is an envelope that surrounds a thing, and it changes, grows, and is destroyed with the thing. Using our example from before, as water passes out of the glass, it is replaced by air, continuously and without break; no gap or overlap is possible, and the envelope that holds the water passes out of the glass with it.

“The primary sense in which a thing can be said to be in place is as a thing (say, water) is in a vessel; but Aristotle is careful to add that place itself is unchanging and unmovable, as the river is a unity/one even though waters flow within it. Thus, the Heraclitean image for radical flux — of the river you cannot step into more than once, if the once — is put in the service of the Parmenidean One. Change, motion, and becoming take place always within the context of a superseding nature of reality as the unchanging One.” (4)

The view of space as extendable, as an envelope surrounding the thing, raises a couple new questions that Aristotle wants to address: First, can a thing have more than one place or envelope at the same time? Only in the sense that a thing — say water — can be in a cup that is in a kitchen that is in a house, etc. Envelopes are embeddable, but the place proper for a thing is only its first envelope, where it finds its own limit or boundary as a thing.

The second question is the opposite of the first: Can more than one thing occupy the same place? If I stick my foot in a river, are both my foot and the water in the same place? Aristotle says no, because the first envelope coincides perfectly with its thing, and it is destroyed, grows, and changes along with the thing. Your foot has its place that it brings into the river, and both your foot and the water are in the river, sharing this place as a secondary place.

Aristotle remarks that this is the main difference between his place-as-extendable-limit and Plato’s space-chora, a distinction that is today preserved in the difference between the concept of place as concrete and specific, versus a more abstract and even mathematical matrix of space. (5) But I would argue that what he does is something else entirely: in a sleigh of hand, while renaming space as place here, elsewhere we will find him folding Plato’s space-chora into his account of the underlying substrate (hupokeimenon), later identified as matter (hule).

Most interesting, there is a mathematical principle of two-ness that Aristotle enlists to back up his claim: two things cannot be in the same place at the same time and still be two and different. This is fascinating because the concept of difference (against which we understand identity) is here tied to the history of concepts of space. What it means for one thing to be different from some other thing is its having its own proper envelope of being. Difference is, in the first instance, understood spatially.

References

(1) Timaeus 52d. Plato’s Cosmology, Francis M. Cornford, (1935).

(2) Physics, 209b 20–33.

(3) Physics, 212a 5–6.

(4) Alfonso, D. Rita, “Space and Irigaray’s Theory Of Sexual Difference” in Thinking With Irigaray, eds. Rawlinson, Hom, Khader, State University of New York Press, 2011, pp.99–109. I have re-written a section of this essay, which I published in 2011, and repurposed it here.

(5) Physics, 209b 15.

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