Vervaeke and Green: "Women, Fire, and Dangerous Theories"

This 1997 paper is a critique of George Lakoff's theory of categorization from the perspective of traditional truth-conditional semantics. Lakoff's theory, as presented in Women, Fire, and Dangerous Things (1987), is in itself a critique of both the traditional view and prototype theories of categorization.

Vervaeke and Green are angry. They have a number of problems with Lakoff's style of argumentation, and as the title says, they find his theories "dangerous." In fact, they find that Lakoff is arguing for "cultural relativism" (p. 70), and that his theories have "unacceptable implications for the pursuit of science itself" (p. 77) as well as support "the dangerous result of providing strong grounds for skepticism" (p. 63).

Most of their criticisms regard specific arguments and studies that Lakoff employs, and these are irrelevant to, and largely logically independent of, my critique. I should try to focus on the positive side of their argument, i.e., the alternative model of categorization they assume.

They never explicitly put their own cards on the table, but both the style and the content of their arguments suggest that they think of categories as lists of necessary and sufficient conditions for membership. There is a number of problems with this account, but they briefly sketch a counterargument for two of these problems, prototype effects and bizarre class boundaries.

Prototype effects as distances, input errors, or ambiguities
A prototype effect is the phenomenon that deciding on category membership is sometimes more easy than other times. For instance, a chair can effortlessly be categorized as a piece of furniture, but a rug or a clock is more problematic. The extent of this effect can be measured in terms of reaction times, disagreement between subjects, or by making subjects explicitly rate the difficulty.

Prototype theories explain this by assuming that the further away from a category's central prototype we are, the more cognitive effort is required to decide on its membership. (In fact, they should assume that the problems occur in a belt of borderline cases, not in a large "outside" area; but I haven't seen anyone make that observation in print.)

Lakoff explains these effects by hypothesizing an "idealized cognitive model" that structures the division between furniture and non-furniture. The then assumes that the problems occur because the parameters used by the model to make the membership decisions are absent or ambiguous in the problematic cases.

Thus, a duck is not quite a farm animal but also not quite a non-farm animal. It doesn't quite fit the hole through which we feed our idealized model candidates for farm-animalness.

Vervaeke and Green seems to think that classical semantics will quite suffice:

A far more elegant account, however, might hold that there is simply a quantifier ambiguity in the question, "Are ducks farm animals?" If the intended question is, "Are all ducks farm animals?" the answer is unequivocally "No." If it is, "Are some ducks farm animals?" the answer is unequivocally "Yes." (p. 67)

That's interesting---especially since it implies that prototype effects should occur equally with all objects and not just with borderliners.

OK, if I'm really charitable, I could say that the prototype effect should occur with equal intensity in the "All" set, the "Some-But-Not-All set", and the "No" set. But I would suspect that the question "Is a screwdriver a murder weapon?" would be met with reaction times quite distinct from those of "Is a duck a farm animal?"

"External properties" and "social properties"
More centrally, though, to prototype theory are examples like "Is a priest a bachelor?" or "Is a penguin a bird?" Vervaeke and Green work around these examples by postulating to distinct sets of criteria for membership: "Obejctive or external properties" and "social properties" (p. 67)

Having feathers, flying, and singing, then counts as "social properties" of birds, I guess. Vervaeke and Green can now explain the increased reaction times in the case of priests:

There is a match to external properties, and there is a failure of match to social properties, but the participant is unsure about the relevance of these social properties and so hesitates in responding. (p. 67)

This definitely calls for some explanation. For instance, are social properties actual parts of the definition?

If they are, then definitions seem to be dynamic and change as we acquire experience with the world, and that certainly is outside the realm of classical semantics. If they aren't, then apparently definitions aren't a very good model of how people actually decide on category membership. In fact, the "social properties" of a category would then amount to a codification of the prototype, while the "external properties" would amount to a codification of the most liberal application of the category. Thus, Vervaeke and Green would just have reiterated prototype theory under a different name.

The hypernym ordering: is-a vs. is-a-kind-of
Another strategy that Vervaeke and Green use to save the classic conception of category membership is to accuse Lakoff and others of conflating the is-a hierarchy with the is-a-kind-of hierarchy (p. 71).

If I understand this correctly, their point is that the is-a relation obtains as a matter of contingent fact (all firetrucks happen to be red), while the is-a-kind-of relations builds on essential characteristics (the purpose of a firetruck is per definition to extinguish fires).

Allegedly, this should explain why penguins can't fly even though they are birds:

For example, a styrofoam cup is a cup, and a cup is a kind of tableware. So a styrofoam cup is, thereby, a kind of tableware? Most people would say not. (p. 71; my emphasis)

I really can't see how this could fly (no pun intended). Certainly, we can block inferences as much as we like by hypothesizing two different modal operators (one being a fine-grained version of the other).

But if we really and consistently pursue that strategy, we end up killing all inferences that involve contingent factors, not just penguin-type cases. For instance, if I get 0 points on an exam (as a matter of contingent fact), then I fail (per definition)---we are indeed able to make at least some such inferences, and the theory should reflect that.

Symbolic and nonsymbolic categories
The second explicit argument that Vervaeke and Green make concerns Lakoff's example of the Dyirbal word balan, which means roughly "women, fire, and dangerous things."

Lakoff uses this example to illustrate that there are sometimes quite elaborate chains of perceived similarity between one end of a words meaning and the other. This is not what we would expect if categories were learned by a gradual acquisition of a list of necessary and sufficient properties (which, presumably, would be given in something like conjunctional normal form).

Vervaeke and Green diminish the significance of this observation by introducing a distinction between "symbolic" and "nonsymbolic" category systems (p. 71), very similar to their Fregean distinction between "external" and "social" properties. Symbolic systems are "driven by rational constraints such as consistency," while nonsymbolic systems are a more fuzzy business used to talk about God, the Trinity, and other irrational stuff (p. 71). Such systems "glory in the existence of contradiction and unresolvable conceptual mystery"
(p. 71).

Using this distinction, Vervaeke and Green then state their suspicion that balan is in fact not part of the neat logical vocabulary of Dyirbal, but only part of the messy nonsymbolic vocabulary. Their theory can be saved if it is reformulated as "Real categories---neat, logical, consistent categories---are stored and processed as propositional definitions."

It seems fairly clear that this is a garbage can argument very much like the rejection of "wrong" sentences as data in syntactic theories of the '60s. Any theory can of course be true if you get to choose on a case-by-case basis what counts as proper data.