Even Oddness, Part 2
Last post I introduced some research results showing that people judge certain numbers (e.g., 4) to be "better" examples of "even number" than others (e.g., 106). This posed a challenge to Rosch's prototype theory, because how could any even number be "better" than any other? Critics of prototype theory said, well, obviously prototype theory can't be right.
First we have to remember that Rosch didn't claim that the prototype effects — that is, the ways in which people rated some category members (like robins and swallows) as "better birds" than others (like ostriches and penguins) — had anything to do with how the category is "really" structured. Instead, Rosch said that any future theory of categories had to account for prototype effects. Any theory of categories that didn't predict prototype effects would be a bad theory.
The question then becomes: where do prototype effects come from?
We can only begin to look seriously at the question if we keep reminding ourselves that categories are a human phenomenon through and through: categories only appear to exist in the world, independent of human categorizers. As we’ve seen, Audie is masterful at making up a story, in an instant, completely outside of our conscious control, convincing us that everything is just "out there," and that we are passive observers of a pre-existing reality. The story is so convincing that few of us ever call it into question at all.
If we do keep in mind the human-made nature of categories, then we can begin to understand where prototype effects come from. This was one of the major tasks George Lakoff set for himself in his seminal work, Women, Fire and Dangerous Things (1987)[1].
The basic idea Lakoff proposes is that prototype effects result from imperfect, simplified mental “models” that we have of the world. A “model” is basically an idea or “best guess” about how something works. A model tells us what to expect and what to do.
Lakoff coined a term: Idealized Cognitive Model, or ICM. The “idealized” part is key. The world is complex, and to function in the world we need ways of idealizing, or simplifying. This gives us reference points to compare actual events to.
Lakoff offers the example of the category mother. In a standard, idealized notion of motherhood, a mother is all of the following:
the person who gave birth to the child
the primary female nurturer of the child
the female provider of half the child’s genetic material
the person who is married to the genetic father of the child
The world often doesn’t match our idealizations. Imagine the following cases:
The primary female nurturer did not give birth to the child or provide any of the child’s genetic material, but is married to the child’s genetic father.
The primary female nurturer of the child did not give birth to the child or provide any of the child’s genetic material, and is not married to the genetic father of the child.
The female provider of half the child’s genetic material also gave birth to the child, but is neither married to the child’s genetic father nor is the child’s primary female nurturer.
The female provider of half the child’s genetic material did not give birth to the child, is not married to the child’s genetic father, and is not the child’s primary female nurturer.
Some of these cases are more common than others, but they are all familiar, and we have names for all these sub-types of mothers. #1 probably describes a stepmother, but could also describe an adoptive mother if the father donated sperm to fertilize the egg. #2 describes an adoptive mother or a foster mother. #3 could describe either a birth mother or a surrogate mother. #4 describes a donor mother.
Usually we don’t need to worry about disentangling all these attributes from one another. Typically all four attributes converge. When they don’t converge, questions arise. And in the case of motherhood, how we answer these questions can have dire consequences for people’s lives.
Prototype theory, along with Lakoff’s theory of ICMs, makes it easy to understand how this type of disagreement works, from a cognitive perspective: each of us (unconsciously, through Audie) ranks the attributes that make up a category. When attributes converge, we all agree, and our latent disagreements remain hidden; when less prototypical category members are considered, disagreements are brought into the open.
So, now we can see how Lakoff's theory of ICM's offers a plausible explanation for prototype effects: category members for which all the attributes hold are the "best" members; category members for which only some of attributes hold are "less good" members. For birds, robins and swallows are "best" because they have feathers and beaks, they're of a certain size, they fly, etc. Ostriches have feathers and beaks, but they're huge and they don't fly. Penguins not only don't fly, but they don't even have feathers. And so on.
You may be thinking: But biologists tell us that ostriches and penguins are birds, and they don't say anything about "better" or "worse" birds. True. The key is that the biologist version of the category bird is an "expert" category, created by Connie. It's been artificially constructed for scientific purposes. What we're talking about here are "folk" categories: creations of Audie, used by humans to make fast, unconscious judgments about categories.
Now that we have a good working theory of how ICMs generate prototypes, how does this explain the bizarre results about even numbers? Tune in next time.
[1] George Lakoff, 1987. Women, Fire, and Dangerous Things: What Categories Reveal about the Human Mind. Chicago and London: University of Chicago Press.