Even Oddness, Part 1

Here's a bizarre story, in three parts, about just how strangely Audie can behave, and just how clueless we are about what Audie is doing.

It starts with a technical debate in psychology. When Eleanor Rosch and colleagues were discovering prototypes, they were also making a lot of people nervous. For over 2,000 years (since Aristotle) the dominant view of how categories worked was that they were objective (i.e., existed in the world, independent of human categorizers) and organized into a hierarchy (like animal -> mammal -> primate -> human). Crucially, categories were seen as "in or out": either something is or isn't a [you name it: mammal, bird, chair, etc.].

Prototype theory threatened to turn all this on its head — especially the last part about in-or-out membership. How could a robin be a "better bird" than a penguin? Psychologists raised in the Aristotelian tradition couldn't wrap their heads around it. So they tried to disprove it.

The most famous attempt came from Armstrong, Gleitman and Gleitman, in a 1983 paper entitled, "What Some Concepts Might Not Be." (Armstrong, Sharon Lee, Gleitman, Lila R. and Gleitman, Henry. 1983. What some concepts might not be. Cognition, 13. 263-308.) The paper is a classic reductio ad absurdum: take something to its logical extreme, show that the extreme is invalid, and claim that the entire theory is bogus.

They took a category that couldn't possibly show prototype effects and replicated some of Rosch's experiments to see if prototype effects showed up. ("Prototype effects" refers to all the ways in which people saw robins and swallows as "better birds" than ostriches and penguins.) The category they chose was even number. The category has a clear, precise mathematical definition: an even number is a multiple of 2. Any number that is a multiple of 2 is an even number; any number that isn't, isn't. No even number is any "better" than any other, so prototype effects can't show up. That is, no even number could possibly be rated as "better" than any other even number.

But prototype effects did show up. Of the six examples of even number on offer — 4, 8, 10, 18, 34, 106 — 4 was judged to be the "best example" of an even number, followed by the others in rank order.

The authors argue that since even numbers don't have prototypes, and since prototype effects show up anyway, then prototype effects can't say anything about how categories are "really" structured.

It's a seductive argument. The problem is that the authors are comparing two completely different notions of what categories "are." They're confusing Audie and Connie. Prototype effects result from human beings making judgments under time pressure. Anthropologists call these "folk" judgments: they aren't scientific, and they aren't generated by rules; they are intuitive — products of Audie. Even number is an "expert" category: rule-bound, binary, black-and-white. It's also a category human beings designed as binary: even numbers couldn't do what they do if they weren’t defined in such a clear way. The category "even number" is something Connie came up with.

Rosch's studies were of human beings making judgments of category membership. She did not make any strong claims about how or why these judgments were made — that is, she did not present a theory of where prototype effects come from. What Armstrong, Gleitman and Gleitman did was rebut a claim that Rosch never made: that prototype effects somehow reveal the "actual structure" of a category (whatever that means).

In the end what their paper really did was, ironically, to provide even stronger evidence for prototype theory than Rosch's experiments had: with natural categories like bird or tree we feel intuitively that there are "better" examples than others. With "even number" we don't expect it, and yet the prototype effects show up anyway. How could this be? There must be something powerful about human categorization that could take a crisp, simple category like even number and turn it into something fuzzy. It seems Audie must be up to something. But what?

This is worth thinking about for a moment. How could there possibly be one even number that is "better" than another? If we believe that numbers exist in an objective world outside of human experience, and that all we're doing as humans is putting pre-existing categories into boxes, then the finding is complete nonsense. It's an easy trap to fall into: the objectivist trap of believing that categories exist before a human being does some categorizing.

This is when we have to use discipline and remind ourselves that even our very perception of what is "out there" is a fiction created by Audie. Audie is doing a lot behind the scenes. Armstrong, Gleitman and Gleitman's findings, because they seem so strange, urge us to press forward for an explanation. How does the human categorization system work, such that a perfectly "objective" category like even number can be judged by humans to have "better" and "worse" exemplars?

What exactly is Audie up to?