I’ve defended, in my two previous posts on JTB+1, a psycho-epistemic model of categorization we can use to analyze Gettier Cases. It occurs to me that, in those first two posts, I kind of just asserted that we play what I called the matching game when we categorize something; that is, given a category2 C, we have a set of traits S such that any object having all the traits in S is a member of C. I used the example of categorizing an animal as a dog. We see the floppy ears, the wet nose, the four legs, the fur, the canines, the snout, whatever else, and at some arbitrary point in that process we realize we’re looking at a dog.
At the time I wrote that, I took the matching game to be kind of self-evident. But I figure I should know what I’m talking about if I’m going to talk about it. So upon doing some research into the psychology literature, I’ve discovered that, while what I describe is one live theory of categorization—and, for a long time, from Aristotle until the 70s, was the dominant one—there are others. The major competing account of categorization is the Prototype Theory, which purports that we have in our heads some prototypical example for each category and, when we categorize an object as belonging to a category, we’re simply saying that object is “similar enough” to the prototype.
There’s a handful of data that the proponent of Prototype Theory can point to.
First of all, on the classical account of categorization with sets of traits, membership in a category is completely binary. You’re either a dog or not. There are no borderline cases, and no dog is a more typical example of a dog than any other.
But this seems to be in conflict with the empirical findings (Rosch & Mervis, 1975) that people do naturally consider some objects in a category more typical of that category than others. In practice, a sparrow is considered a more prototypical example of a bird than a penguin. In practice, the boundaries of categories appear to get fuzzy around the edges. For example, what counts as a piece of furniture? And in practice, people categorize more prototypical examples more quickly and assuredly than edge cases.
I think probably the devoted fan of the classical account of categorization can accommodate these findings. We can argue that typicality entails greater familiarity. In the example of the sparrow and the ostrich, we might determine more quickly that a sparrow is a bird not because it genuinely is a more prototypical example of a bird, but simply because sparrows are more common, and people are more psychologically primed to categorize them through familiarity with them. Of course, this hypothesis should be testable if we can think of examples where the prototypical sort of representative of a category is an uncommon member of that category. To my knowledge, this has not been attempted. We can, if we’re really determined to make the case for the classical account, argue that the boundaries of categories aren’t really fuzzy; rather, as I argued in my first post, the set of traits we have to check to verify that something belongs to a given category is context sensitive, and some contexts are fuzzy.
That seems like a plausible story, albeit a bit ad-hoc and not completely convincing. Regardless, I want for now—maybe I’ll think more on it later—to remain agnostic about which theory of categorization we’re going with. I think for our purposes, getting back to epistemology, it doesn’t matter which account we prefer. In fact, I think my answer to the Gettier Cases is almost entirely independent of which theory of categorization we like; I claim that for any context-sensitive theory of categorization, my solution works.
Let T be a theory of categorization, let C be a category, and let X be the necessary and sufficient condition an object O must satisfy to be a member of C under theory T. Note here that we’re thinking of a series of conditions like “X must have paws to be a dog,” and “X must have a snout to be a dog,” as one long compound condition of the form “X must have paws and X must have a snout to be a dog.” But our condition could equally well be something like “X must be sufficiently similar to the Prototypical Dog to be a dog,” or any sort of condition you like—just so long as it’s context sensitive.
Then the reply to the Gettier Cases will be exactly the same! The person in our Gettier Case has a justified true belief that appears to be true by happenstance, and the reason it isn’t knowledge is that the person in the case is using an underlying false lemma to derive their belief: namely, given the context, they are using too liberal a sub-condition of X to categorize objects.
Notice that we can’t use too strict a sub-condition of X. The strictest sub-condition of X, namely X itself, is always true by assumption. If, in our fake barns example, the person got out of his car and examined the real barn and checked meticulously that it has all the characteristics a bona fide barn needs to have, then surely no one could accuse him of not knowing the real barn is a barn, even if he didn’t realize all the others were fakes. In other words, you will never fall prey to a Gettier Case using the strictest possible condition on category membership. You can only be wrong to use too loose a condition.
Another possible complaint about my answer to Gettier which I’ve alluded to before could be that subconscious beliefs—like “if O meets condition X, then O is a member of category C”—are somehow qualitatively different than ordinary beliefs for the purposes of epistemology.
I think this is implausible. We take for granted that we have subsconsious beliefs that are as genuine as our conscious ones. Some of them we probably can’t even articulate. And yet they do seem to behave like our conscious beliefs. They motivate action, they form a thread of the greater tapestry of our beliefs such that pulling on it has a ripple effect on other beliefs, they play into our conditional probabilistic calculus.
More on that once I’ve had a chance to dig into the epistemology literature to see what people have written about subconscious belief.
Justified true belief+no false lemmas condition.
It is perhaps unfortunate that I can’t think of a better word than category, since this has nothing to do with the mathematical theory of categories. No morphisms to be found here, alas.