And Where Is That, Mr Aristotle?

“Not very many people have defended Aristotle’s account of place. Virtually no ancient or medieval philosopher accepted it.” So Ben Morison begins his book, On Location, in which, he says, he hopes to rehabilitate Aristotle’s account “as a piece of philosophy.”

 

Aristotle’s theory has had a modest degree of support in more modern times. In a 1972 Synthese paper, Patrick Suppes noted that Aristotle’s theory is “philosophical”, by contrast with Euclid’s mathematical theory, and Ptolemy’s physical theory. Suppes’ aim was to talk about mathematical theories, and he doesn’t explain what he took a philosophical theory to be, as distinguished from a mathematical one. But he compared Aristotle favourably with later philosophical theorists: “From a philosophical standpoint, it is evident that the closeness of argument characteristic of Aristotle's Physics is not matched, and there is a general degradation of intellectual standard.”

The main aims of Aristotle’s theory were (a) to give a theory of place that permits one body to replace another in a place, and (b) to account properly for natural places. Obviously, we don’t care about (b) these days, but (a) is still important. Newton was keenly aware of this consideration, which he accommodated by making place a contiguous bounded region of space completely independent of material body. “The material delineation of any figure is not a new presentation of that figure with respect to space, but only a corporeal representation of it,” he wrote.

Famously, Aristotle defined the place of a thing as the innermost motionless boundary of what contains it. Since place is thus distinct from that which occupies it, the replacement desideratum (a) is secure.

The funny thing about Aristotle’s theory, though, is that, contrary to the title of Morison’s book, it is precisely not a theory of location. The basic fact about locations is that if you know where x is relative to y, and where y is relative to z, then you know where x is relative to z  (and vice versa). Aristotle nowhere notes this very basic fact.

And yet the ancient world knew about maps. Above is a reproduction of a fairly creditable map of the Mediterranean world—look at the shape of Italy and Greece, for instance—that must have been constructed from pairwise relative locations. (How else could it have been constructed?) It was drawn long before Aristotle. Yet Aristotle says nothing about the relations among places that enable places to be mapped. His examples of places are the Lyceum and the Agora: yet he never tells us how to navigate to either of these. How would you tell a visitor where he can find the Agora?

Aristotle’s blind spot leads to all sorts of oddities. Because he is interested in places as what substances occupy, his places are tied to substances in a way that Newton’s is pointedly not. If you trace a ball as it is thrown from one boy to another, it occupies a place at each moment of its flight, but the places that it vacates as it flies through the air cease (actually) to exist. There is no (actual) place except one that is occupied by a substance, and though the places that the ball vacates are occupied by air, a body of air without boundaries is not a substance. (Of course, a place that ceases actually to exist may continue to exist potentially.)

So take the room in which you are currently sitting, dear reader. The inner surface of the roof, walls, and floor are (arguably) a place because they bound the air within. But knock out a wall and that very volume of air is not in a place. Rather it is a merely a part of a larger body of air, and as such it potentially exists. So places don’t have places inside them in the usual way. Moreover, as Hintikka once noted, Euclid’s geometry is falsified in Aristotle’s theory because lines don’t extend infinitely. (The Parallels Postulate fails, but for all the wrong reasons.)

So what’s the bottom line? Is it just that Aristotle’s theory of place is a failure? Even if so, so what? No: I think there is a lesson of greater urgency for historians of philosophy. Aristotle’s theory is not about what we today construe as place. It is a theory of something else altogether. It’s just wrong to compare his theory with that of Euclid or Newton.