Prototypes

What is a prototype? One hypothesis: given a category defining membership over fully specified things, a prototype is a certain underspecified object whose features are individually typical and jointly discriminative\diagnostic of objects within the category, so that each prototype feature probably holds for an object drawn from the category, and category membership is probable for any object having all the prototype features.

This view of prototypes is just a less committal version of the idea that a category is defined by necessary and sufficient criteria; now a category has (or is associated with a prototype object having) individually kind-of-necessary (i.e. typical) features and jointly kind-of-sufficient (i.e. discriminative) features.

I. Centrality
When I posted this on #slatestarcodex at FreeNode, several people said that a definition of prototypy\prototypicality should make reference to "centrality". What does "centrality" introduce that isn't captured by typicality? Here's a guess: central position refers to average feature values for scalar\graded features of a category. Thus instead of saying that a prototypical willow tree has typical proportions, so that most willow trees have those proportions, we now say that prototypical willow trees have average proportions, whether or not most willow proportions are close to the average value. I don't think this is a very good guess! It would probably help if I had intuitions about the importance of centrality to prototypes.

II.  Underspecification and graded membership
Another comment, this one from grognor alone, was that underspecification wasn't playing a well motivated role in my definition of prototypes. To grognor, a prototype can be a fully specified object, and graded judgements of category membership can be made by gauging the similarity of objects to the prototype.

I'm receptive to the idea that prototypes can be fully specified objects, but I don't think I like the second part. People don't say "This tangelo is 70% an orange", and rarely say things like "Tangelos are more oranges than are lemons." Surely they can make judgements of relative similarity, but those judgements aren't then stated as relative partial memberships.

III. Articulating membership
Or consider, if you ask an articulate person to make a hard-ish categorization, like whether curtains are furniture, they're often capable of providing fine introspective criteria distinguishing category membership definitely. They might say, "Curtains are furniture in the sense of semi-functional, semi-stationary materials which I use to decorate my house, but they are not furniture in the sense of bulky objects that I use to support things off the ground in my house." Or they'll say, "Curtains, like pillows and clocks and dishes, are furnishings, not furniture. That's not a hard categorization. Who do you think you're talking to? I am the queen of home decor categorization judgements. Get out of my kitchen, you uncultured swine."

So some people can figure out distinguishing criteria on-the-fly for different categories, and other people who are familiar with a domain might have a remembered repository of more and finer categories with distinguished labels for objects in the domain. I think it's mostly the less articulate people who are sweating about having to make a binary judgement: the ones who know that words are rough equivocations of categories across minds, but who don't have lots of finely distinguished expert category labels or the ability to invent longer phrases on the fly to explain the motivations behind potentially conflicting membership judgements; to them, hard categorization prompts are a trap. Some people recognize the trap and stop sweating: they give up on reductionism and say, "Curtains are kind of furniture. I'm sure there's no binary answer. Fuzzy concepts. Get with the psychological research zeitgeist." I guess that's fine, and I don't want to trap people. But I don't think I want to make "partial membership" part of my own ontology either.

IV. Uncertain membership
We just saw a fictional case where someone was uncertain about category membership because they didn't know what judgements were relevant to another person's label applications. This is maybe a special case of a category judgement depending on unknown empirical features. Another source of membership uncertainty: the person might not be able to make a confident binary judgement because of logical uncertainty, like if the category is not specified directly in terms of objects having membership\non-membership. Most aren't!

Maybe someday I'll work these sources of membership uncertainty into my definition of prototypes, along with an improved understanding the centrality caveat. And maybe a prototype is still a thing which has individually typical (or central) and jointly discriminative features, but it's fine for any other features to be specified also, in a less principled way, like just cutting and pasting from the population as they do in instance-based statistical learning techniques.

My next post will be about stereotypes as privileged objects of categorical cognition. It's gonna be so sweet.