City Size, Boundaries and Objects

Kenneth Vernon’s wonderful CfAS blog post on How Big is the Smallest City raised some provocative questions, and I found myself, well, provoked.

Itself a response to Hagit Nol’s excellent earlier post on the difficulties of defining a city in archaeological contexts, Vernon followed Smith and Lobo in distinguishing between functional and sociological definitions of a city. He recognized that functional definitions were vague and fuzzy, essentially because most functions were necessary but insufficient.

Vernon suggests sociological definitions are simpler, and the challenge for us is simply to define a standard threshold and encourage its adoption. If we “can reach some consensus around a set of standards,” he argues, the question becomes “what we will do as archaeologists to encourage their adoption? When it comes to advancing the archaeological study of cities, this is where the rubber really meets the road.”

Maybe, maybe not, but the part that provoked me was using the Sorites paradox to advance the argument.

Simply stated, the paradox is a challenge to classical logic stating that if one grain of wheat doesn’t make a pile, and adding another doesn’t make a pile, then adding one more grain can never make a pile. Vernon suggests it’s simply a reminder that language evolves, and if we define the threshold the paradox goes away. To make a pile, Vernon suggests, we simply define how many grains are needed, and can do the same for defining a city.

Wait, what?

Have we really advanced our understanding by stating, say, that at 9,999 persons a settlement is not a city, but at the next birth it becomes one? If we think so, then the paradox is resolved. If not, the paradox is only drawn more starkly.

For my part, I think a sociological definition (understood as size) has the same kinds of underlying complexity and nuance as functional definitions, with boundaries equally fuzzy. Groups of people sociologically organized in one way may constitute a city at a given scale, but it may take more or less if they’re organized in very different ways.

I suppose that poses the risk of sending us down the endless rabbit holes of what number of people makes a city if organized in a particular way, or whether size should be measured in terms of number or density per unit area.  And there’s a presumed temporal dimension as well—surely a University of Arkansas football game doesn’t satisfy the scalar requirement (or even a University of Michigan game, if we wish to require a higher population).

Or, alternately, we can understand “city” less in terms of arbitrary boundaries applied to imprecise and indirect measures of underlying dimensions, and more as what Star and Griesemer called “boundary objects,” which are analytically useful precisely because of their imprecision, because they allow sufficient fuzziness around the edges for scholars in different contexts to discuss phenomena like cities without rigid and shared a priori definitions.

Understanding city as a boundary object allows the concept to have both granularity for scholars working on a single example in a single context, while also allowing enough abstraction for comparison with other contexts and other communities of scholars. It’s this back-and forth tacking between the concrete and the abstract—rather than mere imprecision—that makes boundary objects distinctive.

And because what constitutes a city also implicates a whole range of value judgments and potential asymmetries of power (past and present), it also lets us foreground the reasons why different communities construct the concept in different ways, as Isto Huvila has argued.

Certainly there’s a risk of problematizing definitions in ways that prevent rather than promote comparison and synthesis (as Smith and Lobo note), and that’s not my intent. Whether my view is a rabbit hole obscuring the need for a shared standard minimum population size for a city is thus a fair question.

So too, according to the Sorites paradox, is where the edge of a rabbit hole starts. Both may be slippery slopes, but that doesn’t make them any less real.

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3 thoughts on “City Size, Boundaries and Objects”

  1. Alex centers on a powerful flaw in ordinary science practice: naive, thoughtless use of ordinary-language words as if they were sharply defined. In the case of “city” the word is sharply defined by federal and state governments, and these boundaries for current U.S. populations are clearly too particular for general use. LIDAR and other methods including more foot surveying has been revealing how much settlement data has been obscured, e.g. in Maya cities and in Angkor; these revelations should be cautions against supposing current data are sufficient for assessing nature and size of settlements. More deeply, these efforts to numerically define Western entities and extend to non-European societies are Enlightenment science (Bristow, W. F. (2010) “Enlightenment”. Zalta, E. (Ed). Stanford Encyclopedia of Philosophy , Summer 2011. Metaphysics Research Lab, Center for Study of Language and Information, Stanford University -updated online 2017). We need to free archaeology from ethnocentric Western categories, ponder what questions reveal more of societies and histories–recognize multiplicities (aka historical particularism) rather than try to formulate general laws.

  2. Fuzzy borders are commonplace in archaeology (and in life, by the way). They concern any time-space concept and resist to any attempt to removing the uncertainty. They are better understood when time is concerned, as it has a one-dimensional extension: expressions as “young” or even “culture” cannot be resolved by arbitrarily fixing a starting – or ending – point in time. Humans understand that fixing the expression “the Villanovan culture started in Italy in the 11th century BC” with a statement such as “the Villanovan culture started in Italy at 00:00 on 1st January 1100 BC” is silly, but unfortunately computers don’t. So, digitization requires more sophisticated ways of dealing with fuzziness.
    The same is true for space concepts, where the boundaries of a spatial region (a city, for example) according to a much-discussed categorization by Varzi may be fiat boundaries – those defined arbitrarily by a human decision – or bona fide boundaries – those defined (?) by physical properties. There is an extensive bibliography on this subject, analyzing why and how archaeologists (notably those using digital technologies) should be concerned with it.

  3. Thanks for your thoughtful comments on my post!

    Based on the responses here, I think I did not state my point clearly enough. I was not trying to suggest that we can overcome the Sorites Paradox by mere fiat. Rather, I wanted to suggest that we see the paradox as a tool for describing an important constraint on natural languages that is relevant to debates about the nature of cities.

    My own view is that where possible we should prefer to work with a continuous variable like population density rather than ordinal categories like ‘town’ or ‘city’. But, of course, even density isn’t free from methodological and conceptual hurdles. It also assumes a well-defined area, after all. Plus, it’s really hard to measure, especially in archaeology. And so, it’s sometimes easier to ask “why are cities where they are?” rather than “why are there more people in some places rather than others?” In those cases, I think we’d be better off if everyone used the same criteria for identifying cities because it would make it easier to aggregate data and compare models.


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