Before going too far down this road, I’d like some attention given to the notion of approximation.
For example, consider two theories of category formation:
CFT1: categories have necessary and sufficient conditions for membership, and to answer “Is X a Y?” we evaluate the truth-value of the conjunction of Y.conditions as applied to X. CFT2: categories have prototypical members, and to answer “Is X a Y?” we evaluate the similarity of X to Y.prototype.
It’s pretty easy to show, using more or less the arguments you present here, that CFT2 is a much better approximation of real human categorization behavior than CFT1.
But it’s also clear that CFT2 is nevertheless an approximation, not a full explanation. For example, it’s pretty easy to show that human similarity judgments aren’t symmetrical—the classic though somewhat outdated example is “Cuba is more like Red China than Red China is like Cuba”—which means that “the similarity of X to Y.prototype” is ill-defined: do we mean S(X, Y.prototype) or X to S(Y.prototype, Y) or something else?
But before we discard CFT2 for that reason, we should ask what we’re trying to accomplish. Approximate solutions are useful in real-world situations, as long as we keep in mind that they are approximate. Prototype theory is adequate for a wide range of tasks. So we might want to hold onto CFT2 even knowing it’s wrong.
Similarly, if we want to discard CFT1, it’s not enough to show that it’s wrong. We should also have some confidence that it’s useless.
Before going too far down this road, I’d like some attention given to the notion of approximation.
For example, consider two theories of category formation: CFT1: categories have necessary and sufficient conditions for membership, and to answer “Is X a Y?” we evaluate the truth-value of the conjunction of Y.conditions as applied to X.
CFT2: categories have prototypical members, and to answer “Is X a Y?” we evaluate the similarity of X to Y.prototype.
It’s pretty easy to show, using more or less the arguments you present here, that CFT2 is a much better approximation of real human categorization behavior than CFT1.
But it’s also clear that CFT2 is nevertheless an approximation, not a full explanation. For example, it’s pretty easy to show that human similarity judgments aren’t symmetrical—the classic though somewhat outdated example is “Cuba is more like Red China than Red China is like Cuba”—which means that “the similarity of X to Y.prototype” is ill-defined: do we mean S(X, Y.prototype) or X to S(Y.prototype, Y) or something else?
But before we discard CFT2 for that reason, we should ask what we’re trying to accomplish. Approximate solutions are useful in real-world situations, as long as we keep in mind that they are approximate. Prototype theory is adequate for a wide range of tasks. So we might want to hold onto CFT2 even knowing it’s wrong.
Similarly, if we want to discard CFT1, it’s not enough to show that it’s wrong. We should also have some confidence that it’s useless.