WOMEN, FIRE, AND DANGEROUS THEORIES:
A CRITIQUE OF LAKOFF'S THEORY OF CATEGORIZATION

George Lakoff has put forward a new account of the standard prototype effects in Women, fire, and dangerous things (WF&DT) that has become increasingly popular since the book's publication in 1987. We believe, however, that the theory presented in WF&DT remains untenable for a number of reasons. Briefly, we argue that (1) confusions about the difference between concepts and conceptualizations lead to apparent contradictions in his position; (2) his removal of prototypes from the explanation of "prototype effects" leaves open a wide range of possible and plausible explanations of such effects, many of which derive from the very objectivist paradigm he criticizes; (3) his attempt to replace the compositionality of language with the notion of "motivation" fails, primarily because his account of "motivation" leaves it underspecified and, ultimately, takes his theory out of the realm of scientific investigation; and (4) his "idealized cognitive models"--the core of his cognitive theory--are inadequate explanations that seem to reduce either to something very much like "mental pictures," which fail as theories of representation for a host of well-known reasons, or to "mental propositions," which are most amenable to the traditional models of cognition that Lakoff most strongly opposes.

The idea that cognitive processes operate over concepts that take the form of prototypes, stereotypes, or otherwise "typical" examples of things has been increasingly influential in both empirical and philosophical psychology over the last two decades (e.g., Putnam, 1975; Rosch, 1978; Johnson-Laird, 1987). At times it seems that such a view has very nearly replaced the traditional view that concepts are defined by sets of necessary and sufficient conditions that strictly delineate between what is inside and what is outside the conceptual boundary. The crucial cognitive phenomena--widely known as "prototype effects"--that have favored the newer view over the older include such facts as people being slower and less certain of their categorizations of certain "atypical" items (e.g., Is a penguin a bird? Is a lamp a piece of furniture? Is a priest a bachelor?). No adequate account of these phenomena was put forward by the advocates of the classical view. Prototype theorists argued that the effects are due to concepts having an inherently prototypical nature; viz., that there is a "typicality gradient" that organizes group- membership in terms of an item's similarity to a prototype.

Since the early 1980s, however, a number of important critiques have demonstrated some critical weaknesses in the prototype view as well. In particular, the formalization of prototype theory in terms of fuzzy logic (Zadeh, 1965) was shown to lead to paradoxical results (Osherson & Smith, 1981). As well, "prototype effects" were found even for those concepts that unquestionably have explicit classical boundaries (e.g., negative numbers; Armstrong, Gleitman, & Gleitman, 1983).

A significant revision of the prototype view appears in George Lakoff's 1987 book Women, Fire, and Dangerous Things (WF&DT) Lakoff's account does not put prototypes at the center of cognition but, rather, explains prototype effects by means that are allegedly not subject to the standard criticisms of traditional prototype accounts, while still maintaining the spirit of that tradition. We believe, however, that the theory presented in WF&DT remains untenable for a number of reasons. It is the aim of this paper to outline and examine some of these (see also Kennedy & Vervaeke, 1994). Briefly, we argue that (1) Lakoff is led into inconsistencies by an apparent confusion about the difference between concepts and conceptualizations. (2) By removing prototypes from the explanation of "prototype effects," he leaves open a wide range of plausible alternative explanations of such effects, many of which derive from the very objectivist paradigm he criticizes. (3) Besides difficulties with prototypes, Lakoff's analysis also has difficulties with a key property of language, viz., compositionality. His attempt to replace the compositionality of language with the notion of "motivation" fails, primarily because his account of "motivation" leaves it underspecified and, ultimately, takes his theory out of the realm of scientific investigation. (4) Finally we turn to what Lakoff term "idealized cognitive models" (ICMs). These are at the core of his cognitive theory, but we argue that they are inadequate explanatory devices and, in the end, reduce either to something very much like "mental pictures," which fail as theories of representation for a number of reasons, or to "mental propositions," which are most amenable to the traditional models of cognition that Lakoff most strongly opposes. With the foundations of Lakoff's general theory called into question, his specific application of the theory to the problem of metaphor becomes highly suspect as well.

In this section we identify and discuss (1) a conflict in Lakoff's descriptions of the differences between ICMs and classical categories, (2) a difficulty in his attempt to exemplify the failure of classical categories with reference to the biological concept of species, and (3) the reasons that, contrary to Lakoff's claims, philosophers have been, and must continue to be, concerned about the presence of incompatible accounts of a single intellectual domain, such as that of species in biology. Finally, we show that these difficulties with Lakoff's account are, at least in part, attributable to his failure to distinguish between people's folk-theoretic conceptualizations of such domains, and the actual concepts that ground such conceptualizations.

1.1. ICMs and classical categories: Folk theories or bloodless abstractions?

Lakoff criticizes the "classical" categorization theory for being too abstractly logical; not sufficiently grounded in our bodily interactions with things in the world. He argues, instead, that our thought processes operate over "idealized cognitive models" (ICMs) of the world. ICMs are said to be "directly embodied with respect to their content.... [usually] with respect to use," and that they, "structure thought and are used in forming categories" (p. 13). Thus, as opposed to abstract classical categories, they are said to be derived from our everyday interactions with the world. At another point, however, Lakoff claims that the "classical" model of categorization is derived from a "folk theory" of categorization, derived presumably from "folks'" everyday use of categories. ICMs, he argues, are a more sophisticated account. Thus, it seems, Lakoff wants it both ways: he criticizes "classical" categories for being too technical and abstruse, on the one hand, and for being too crude and "folksy", on the other. Conversely, he praises ICMs for being "grounded" in ordinary people's interactions with the world, and for being the more sophisticated approach to categorization. If, as Lakoff claims, the "classical" theory of categories derives from a "folk theory", and if a "folk theory" is grounded in everyday experience, and if, as he also claims, all our knowledge is ultimately grounded in such experience, then he leaves little room for an account of how we might come to understand his own new theory of categorization, since it is not, by contrast, grounded in the folk theory we have derived from our everyday experience.

1.2. Lakoff's attempt at the refutation of classical categories in biology.

In his critique of the classical model of categorization Lakoff explicitly relies on empirical studies from outside of psychology; studies which show us what the world is really like apart from our usual conceptualization of it. Some of his key examples derive from biological studies of what a species is. Such studies show that the ordinary way we group biological entities does not correspond to the "objective" relations biologists have found to hold between living things. In short, our folk taxonomy conflicts with the scientific taxonomy. Lakoff uses this point to convince the reader that our language use does not mirror the "true" structure of reality. However, there is a question as to the source of such scientific objective reference. Lakoff argues that we have two contradictory ICMs of how words refer, each controlling some of our thoughts on the matter. The first is the model in which words fit the world in virtue of their inherent meaning. The second is that there is a group of people--viz., "experts"--who get to stipulate the meanings of words. Lakoff purports to show that these two models conflict, but that neither is the privileged account of how reference works. Thus, he argues, when the two come into conflict, as they allegedly do when scientific biology challenges folk biology, there is no principled reason for scientific biology to be given priority. The scientific expert may be able to say, for instance, that "tree" does not really name a botanical category, on the grounds that there are two distinct and only distantly related (from an evolutionary perspective) groups of things that ordinarily answer to that name. The folk biologist, however, can say equally well that tree is a perfectly good category because, evolutionary considerations notwithstanding, the members of this class all play similar roles in experience. This may seem contradictory, but rather than abjure it and decide which account is correct, Lakoff embraces the contradiction as characteristic of the flexibility of thought.

Let us summarize Lakoff's argument concerning biological categories. On the one hand, he employs a contradiction between expert stipulation of reference and folk reference in order to show that folk categorization does not mirror the structure of reality. On the other, however, when he comes to explain how reference works and again notes this contradiction, he argues that we should not attempt to resolve the contradiction by giving priority to one of the accounts of reference (pp. 122-125). In short, at one point in his argument he needs to give priority to expert stipulation of reference, but elsewhere he explicitly denies the appropriateness of establishing such priority.

Lakoff claims that it "is apparently intolerable to philosophers of language to have to conflicting models of reference", but that we must shed this dogmatic prejudice and simply accept the conflict (p. 125). As we have just seen, however, the embracing of a contradiction calls one of Lakoff's key arguments into serious question.

1.3. Why people's concern with consistency in explanation is not simply a dogmatic prejudice.

The inability to come up with a consistent account of reference is typically counted as very good evidence for skepticism, i.e., for the claim that we really do not have knowledge of the world. If we cannot even refer to the world in a consistent way then it would follow that we could not have consistent propositions about the world, which in turn would mean that we can not have knowledge of the world. This is the reason philosophers have worried about a consistent account of reference for something over two millennia. It is not a result of

the dogmatic prejudice Lakoff seems to imply. Lakoff does not seem to see this, and so his account has the dangerous result of providing strong grounds for skepticism. We take it as self-evident that any theory the main aim of which is to explain categorization and knowledge, but ends up with an argument for skepticism has gone seriously off course.

One important source of the difficulties discussed in this section is that Lakoff seems to have confused conceptualizations with concepts, i.e., he seems to have confused the proto-theories and folk accounts we have about how language works with the actual cognitive mechanisms that are actually responsible; viz., those that instantiate our referential abilities. There is no reason for believing that these folk theories are true theories of concepts; the fact that folk and scientific theories contradict each other, in fact, counts as good evidence that at least one of them is false. This failure to note the distinction between conceptualizations and actual concepts causes one to fall into a particular kind of error. The problem is that language, per se, in contrast to the folk models or proto-theories built from language use, does not commit one to a particular epistemology or ontology. Language can be used to express common sense naive realism, for sophisticated realism, for empiricism, for nominalism, and for skepticism. Thus, what we really need is an account of meaning that is neutral with respect to all these epistemologies and ontologies. Of course, many people may have a conceptualization of some aspect of language use, such as reference, that entails naive realism. However, if we say that reference really relies on naive realism we are confronted with the implication that theories that contradict naive realism would be self-contradictory and could not have reference, i.e., that they would be literally meaningless. This is a danger inherent in any attempt to identify semantic properties and relations with epistemic properties and relations. Semantic properties and relations must be distinct from epistemic relations if we are to be able to explain how we can use language to overturn even our deepest presuppositions about language and its relation to reality. In short, contra Lakoff, the true account of meaning cannot just be a theory of how people understand or model the world. If it were, it would leave people hopelessly hamstrung; completely unable in principle to change their understandings.

In this section we begin by showing that in spite of his explicit rejection of traditional logic, Lakoff is forced to resort to it to explain certain prototype-like phenomena important to his overall case, viz., Colman and Kay's (1981) study of lies. We then go on to review some serious drawbacks to this research, first articulated by Tsohatzidids (1990), that call into question the very nature of the phenomena themselves. Finally, we show how "prototype effects" might be explained by recourse to traditional logical distinctions that are rejected by Lakoff.

2.1. Lakoff's ambivalent relationship to traditional logic.

Lakoff categorically rejects standard logic as an appropriate tool for linguistic and cognitive analysis. This stems from the intimate connection between logic and classical set theory, which Lakoff sees as the ultimate source of the classical theory of categorization, discussed above, which he also rejects. In light of this, we find it paradoxical that he resorts to the use of just such logic in exemplifying his notion of the ICM. In particular, his account of the category "lie", adopted from the work of Coleman and Kay (1981), relies almost wholly on the derivation of deductive logical consequences from his proposed propositional ICMs for "ordinary communication" and for "justified belief" (pp. 72­73).

To summarize the situation, Coleman and Kay found that there is a cluster of three conditions that differentially contribute to the judgment of whether a given statement is a lie. First and foremost the speaker must not believe what he or she is saying. Second, there must be an intent on the part of the speaker to deceive the listener. Third, but least important according to Coleman and Kay, there must be factual falsity. Why this last aspect is least important is easy enough to see. Imagine that someone says something she believes to be false, with the intent of deceiving another, but is simply wrong in her belief, and has inadvertently uttered a truth. This stills counts as an instance of lying in most people's eyes, according to Colman and Kay's research.

Nevertheless, when asked, most people will define "lie" as a "false statement" when factual falsity is, in fact, the least important of the three conditions. Lakoff purports to explain why subjects do this by way of ICMs. He claims, pace Sweetser (1984), that the ICM for "ordinary communication" consists of two propositions: (a) that if people say something, they're intending to help if and only if (hereafter "iff") they believe it, and (b) people intend to deceive iff the don't intend to help. Notice that neither of these claims is invariably true, only in the "idealized" situation. This is typical of ICMs. The ICM for "justified belief" is also said to consist of two propositions: (c) people have adequate reason for their beliefs, and (d) what people have adequate reason to believe is true. Lakoff goes on to write:

These ICMs provide an explanation of why speakers will define a lie as a false statement, when falsity is by far the least important of the three factors discovered by the Kay-Coleman study. These two ICMs each have an internal logic and when they are taken together, they yield some interesting inferences. For example, it follows from (c) and (d) that if a person believes something, he has adequate reason for his beliefs, and if he has adequate reasons for believing the proposition, then it is true. Thus, in the idealized world of these ICMs if X believes proposition P, then P is true, Conversely, if P is false, then X doesn't believe P. Thus falsity entails lack of belief. (p. 72, italics added)

The explanation continues, but the important point is that Lakoff is employing in his explanation precisely the standard propositional logic that he explicitly rejects as the source of most of the problems in cognitive theory. The italicized terms in the above quotation compellingly evince this claim.

In addition, he overlooks some serious defects in the very work he cites in support. Tsohatzidis (1990) notes that the Coleman and Kay study fails to make several important distinctions. Coleman and Kay presented their subjects with a series of stories and then asked them to decided if the actions of one of the story characters is constitutive of a lie. Consider one such story:

John and Mary have recently started going together.
Valentino is Mary's ex-boyfriend. One evening John asks Mary "Have you seen Valentino this week?" Mary answers, "Valentino's been sick from mononucleosis for the past two weeks." Valentino has in fact been sick from mononucleosis for the past two weeks, but it is also the case that Mary has a date with Valentino the night before. Did Mary lie? (Tsohatzidis, 1990, p. 442).

Coleman and Kay's subjects did not answer this with an unqualified "yes" or "no", but rather with varying degrees of certainty that given statements were, in fact, lies. Coleman and Kay took this as evidence that the meaning of "lie" is indeterminate, and subject to "prototype effects." Tsohatzidis responds, however, that what is actually going on here is a conflict between what Mary explicitly stated and what she "implicated," in Grice's (1975/1989) sense. What she said was true, but what she implicated was false. In order to catch this, one needs to make the standard distinctions between the proposition asserted, propositions logically implied by the proposition asserted, and the propositions that are pragmatically implicated by the proposition asserted. Coleman and Kay fail to make these important logical distinctions and, as a result, seriously undermine their own conclusion.

Tsohatzidis goes on to point out that the scale Coleman and Kay gave their subjects only allows for variation between something clearly being a lie and something clearly not being a lie. The problem is that "not being a lie" can either mean being anything other than a lie, or it can mean being the opposite of a lie, i.e., a truthful statement sincerely uttered. Coleman and Kay seem to have failed to distinguish between the logical relations contradiction and contrariety. A pair of contradictory propositions can neither be both true nor both false. Contraries, however, may both be false, though they cannot both be true. Truth and falsity may be contradictory, but truthfulness and lying, as we saw above, are only contraries; there are other possibilities (viz., of speaking falsely but not lying). The subjects' slow reaction times could be explained as a response to such ambiguity in the scope and nature of the "not" that was used in scale presented to subjects.

2.2. Might logic be precisely what is needed to explain prototype effects, Lakoff's rejection of it notwithstanding?

All of this leads us to wonder whether some of the phenomena that Lakoff would label as "prototype effects" are not more easily explained in terms of the very logic that he rejects. It is important to realize that Lakoff does not believe that prototype effects are the result of mental prototypes, per se, as some earlier prototype theorists claimed. Lakoff claims, rather, that they emerge from an interaction between ICMs and given cognitive tasks. He argues, for instance, that people do not hesitate in classifying priests as bachelors because priests are distant from the prototypical bachelor, but rather because bachelorhood is defined relative to the ICM for marriage, and priests do not fall within the parameters of that ICM. Thus, it is hard for people to say whether priests are bachelors or not; the classic prototype effect. One implication of this account is that almost any effect not predicted by the simplest version of "classical" category theory comes to be called a "prototype effect" even though prototypes are not really thought by Lakoff to be directly involved at all.

Once the prototypes have been taken out of the explanation of "prototype effects," however, alternative explanations abound, many involving perfectly classical explanations. Moreover, there is no longer any compelling reason to expect that a single underlying mechanism is the cause of them all. For instance, consider the situation in which a subject is presented with a list of terms to be classified as to whether each term names a member of the category "farm animals". At a given point during the experimental procedure, the subject is faced with the word, "duck." He hesitates. The inflated RT would be taken by many to be a prototype effect. Depending on the "brand" of prototype theory subscribed to by the researcher, she may claim either (1) that ducks are further from the prototype for farm animals than are, say, cows, pigs, horses, and chickens or, (2) if she is more Lakoffian, that ducks somehow fall outside of the ICM that guides the division of animals into, say, "farm," "wild," and "pet" types (in much the way that priests are said to fall outside of the marriage ICM, thereby leading to a prototype effect when one is set to classifying men as bachelors or not). 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." It might be that the processing of the ambiguity, not a "prototype effect," would lead to the increased RT. So, in addition the dynamics described above--viz., ambiguities caused by a failure to distinguish between assertion and implicature, and between contradiction and contrariety--quantifier ambiguity could also be a source of "prototype effects".

What of bachelors and priests? Here we may have difficulties caused by a failure to distinguish to explicitly distinguish between the relevant properties. Wierzbicka (1990) notes that previous attempts to define "bachelor" have presupposed that all the properties of such a definition must be objective or "external" properties; viz., being an unmarried male. If, however, we add to the definition of bachelor as an unmarried male, the social property, "thought to be marriageable," then the liminal cases such as "priest" become clear-cut non-instances of the category. When researchers have questioned subjects on this matter in the past, however, the presupposition that only external characteristics are relevant has led to a failure to make the relevance of such social properties explicit. Because unmarried but ineligible men are relatively rare, this implicit social property is not salient, and therefore may not come readily to mind for subjects classifying priests. Hence, they hesitate when confronted with priests as examples of bachelors. There is a match to external properties, and there is a failure of match to social properties, but the subject is unsure about the relevance of these social properties and so hesitates in responding.

Lakoff claims to solve several problems of traditional, as well as prototype-inspired, versions of semantics with his theory. In this section we discuss and critically examine some of these. First we show that his concept of "motivatoin" cannot replace traditional compositionality. Next, we show that the primary of function that "motivation" is supposed to serve is that of distinguishing Lakoff's theory from more mainstream prototype theories that have failed. Along the way, we examine some research in anthropology that Lakoff draws on, we think mistakenly, in support of his position. Finally, we return to the concept of "motivation" to show that it is so unconstrained that it, far from being an improvement on compositioanlity, has little explanatory value at all.

3.1. Compositionality and "motivation".

Lakoff criticizes what he calls "the objectivist paradigm" for assuming that "the meaning of the whole is a computable function of the meanings of its parts" (p. 148). We take this to be what is commonly called the compositionality of language. It is conventionally invoked to explain, inter alia, how we can understand and produce sentences we have never before encountered. Thus, for example, the meaning of "John runs" is just a strict function of the meanings of "John" and "run" and the general rules of English grammar whereby the action denoted by a verb is attributed to a subject-noun. Surprisingly, Lakoff rejects this simple, powerful account of sentence meaning. He declares,

This is just wrong. There are variety of reasons, but the one that I think should be stressed most is that objectivist theories lack a concept of motivation. (p. 148)

We take it, therefore, that his concept of "motivation" is, at least in part, expected do the work traditionally assigned to compositionality.

"Motivation," in Lakoff's sense, is a mechanism by which the meanings of terms are metaphorically extended to realms beyond their original domains of application. Thus, for instance, Lakoff argues that the Japanese term "hon", which originally referred to long straight things, comes to be predicated to, among other things, safe hits in baseball because they (typically, but not always) follow a long straight trajectory. Moreover, this association is, he claims, over-determined to some degree because of the close association of baseball hits with baseball bats, which are also hon, being long, straight, and rigid (p. 107). Lest one come to believe that a scientific researcher might, through careful observation and calculation, be able to figure out which things the term "hon" will ultimately come to be applied to, by virtue of their hon-ish properties, or associations with other things that are hon, however, Lakoff insists that the original meaning of hon could not have been used to predict in advance that it would come to be applied to baseball hits. The meaning of hon, it is argued, is only one factor in a complex and non­deterministic process of forming a cultural convention; a process that Lakoff suggests is ultimately beyond the bounds of scientific prediction.

Notice that this move protects Lakoff from the usual rigors of scientific disconfirmation. If a rival researcher were to claim, for instance, "Ah ha! Fire extinguishers shoot out long straight streams of foam or water, and they are associated with fire hoses, which are long and, when in use (their most typical form) are full of highly-pressurized water that renders them straight and stiff. Why aren't they considered to be hon?", Lakoff need only claim, "Because that particular use, though perhaps plausible, is not 'motivated' by the culture in which fire extinguishers are embedded." Consequently, Lakoff places his theory squarely beyond the bounds of science; every possible refutation can be explained away by a lack of "motivation." To bring the theory back within the bounds of science, Lakoff must explicate motivation such that predictions can be subjected to empirical test. This he does not do, and he suggests that it cannot, in principle, be done.

Not only does the notion of motivation place Lakoff's theory beyond testing; it also seems to involve him in a circular argument. Namely, we explain the existence of unpredictable variation in category extension in terms of motivation. However, the only measure we have of this motivation is the degree of variation in category extension. Until an independent measure of motivation can be given, not only is Lakoff's account untestable, it really is not explanatory at all.

3.2. The rationality of concepts and taxonomies.

Lakoff may be invoking the concept of motivation to explain how meaning can be extended in ways that, though not predictable, are still rational. This claim seems to involve an implicit over-riding claim that there can be no scientific theory of rationality, at least not of the rationality that is involved with semantics and categorization. This is implied because the functions of such rationality are said to be not predictable. Once we remove the study of rationality from the scientific study of human behavior then most of the higher cognitive processes will be placed permanently beyond the bounds of cognitive psychology.

Part of what Lakoff is trying to do with the concept of motivation is to create a distinction between his position and the more standard versions of prototype theory. As Vandeloise (1990) notes, the only significant difference between Lakoff's models and more traditional prototype theories is the nature of the similarity links, or the transformation links, that bind a category together. For example, in his case study of over, Lakoff argues that the best model for the meaning of over is a complex structure of schemata (p. 436). These schemata are linked together by transformations, such as metaphorical extension and similarity. These transformations are said to explain the polysemous uses of over. The various schemata are not equally important, however. As Vandeloise notes, this complex structure has a central schema. This could easily be construed as just a kind of prototype. If so, Lakoff has essentially produced a version of the very prototype theory he is trying to replace. In order to avoid this conclusion, Lakoff emphasises that the links to this central schema are indirect and non-transitive. When discussing Lakoff's "case study" of the preposition "over," Vandeloise notes that the "non-transitive nature of the chains linking the elements of the network describing over to its center is the only factor that can differentiate it from the representing world Lakoff denounces, a world in which the elements are directly linked with the prototype" (Vandeloise 1990, p. 433). Such chains are formed when x and y are grouped together into a class because of some common feature A, while z is put into the class because it shares a different property B with y. Thus, there is no common property, such as similarity to a prototype, holding the category together, but x is similar to y, and y is similar to z. All that holds a category together is the structure created by the similarity and transformational links. The resulting structure makes sense, but it cannot be predicted in advance since the chaining can take a variety of different possible pathways. It seems, therefore, that Lakoff emphasizes motivation and chaining because it is the crucial distinction between his own position and the prototype position he is trying to replace.

Anthropologists studying folk taxonomy have long been aware of the chaining of concepts together in a variety of languages. Both Hunn (1976) and Hays (1979), the two anthropologists who launched the discussion of such chaining, argue for the existence of important universals in folk-taxonomic chains, contrary to the cultural relativism which Lakoff attempts to bolster with the notion. A great deal of empirical data points to the fact that folk taxonomies, at least for the biological realm, cross-culturally share the same structure and logic, as well has having very significant overlap in content. In short, many peoples tend to classify the biological world in the same way.

Thus we do not need an explanation of categorization in terms of chaining we need an explanation of categorization in spite of chaining. If chaining were the main mechanism at work, we would expect cultures to diverge in their conceptual structures, whereas the evidence is that they seem to converge, at least in the domain of biological kinds. We need to discover that set of powerful conceptual constraints that results in the existence of such universals. To turn chaining effects into the center of a theory of categorization is a misplaced theoretical move. Although categorization behaviour may be accounted for in terms of chains of similarity links, such explanations really cannot account for the existence of taxonomic universals.

We need also to recognize--along with Goodman (1972), Medin (1989), and Douglas (1993)--that similarity is vacuous as an explanatory concept because any two objects are similar in infinitely many different ways. What causes our general agreement on the relative similarity of objects is more strongly a function of the inherent structure of our cognitive mechanisms, which more or less automatically selects those dimensions along which objects are compared. That is, it is an effect of categorization not its cause. Once again we must distinguish between the conceptualizations people have about how they classify and the actual cognitive mechanisms responsible for classification; mechanisms that can produce universals in how people classify the biological world.

This is not to say that cultures do not make use of different kinds of classification systems. Nevertheless, all cultures have similar taxonomic classification systems for the biological world. That is, each culture has a classification system that is hierarchical and built around the "kind of" relation (e.g., a tiger is a "kind of" cat). As Wierzbicka (1984, 1992) has forcefully argued, this "kind of" relation is not equivalent to the class inclusion relation. Every policeman is a son, but that does not mean that a policeman is a kind of son. The "kind of" relation has a different and more constrained semantics than that of simple class inclusion. Wierzbicka argues that the "kind of" relation specifies a semantic head for a concept, namely, its supercategory. However, not all concepts have such semantic heads. Rather, there is a whole set of characteristics given equal (or near equal) weight. A cup, for instance, is a container, a vessel, kitchenware, and tableware. Because of this if we conflate the class inclusion relation and the "kind of" relation it is easy to create violations of transitive deductions involving things such as cups. 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.

Thus, folk taxonomies built on the "kind of" relation support only more constrained transitive deductions, inductive projections (a fact the developmental psychologist are making good use of) and inferences that involve an interaction of the two. Wierzbicka calls such structures "general-purpose" taxonomies. In contrast, people typically have more special purpose categorization schemes as well. These typically do not give rise to a hierarchical structure based on the "kind of" relation, i.e., they tend to be built on the class inclusion relation, and they do not support the rich inferential practices of the more general purpose folk taxonomies.

Not only are anthropologists keenly aware of this distinction, they are also aware of the distinction between symbolic and non-symbolic classification systems. Dan Sperber (1975, 1985) has argued that there is a principled semantic distinction between symbolic and non-symbolic classification systems. Non-symbolic systems are driven by rational constraints such as consistency and criteria for determinate empirical content. Symbolic systems are not really representational. They are meta-representational. They involve beliefs about propositions that amount to statements of faith. They involve assertions such as "the statement that there are three distinct persons yet only one God is true." One may not be able to explain what the statement about "The Trinity" means, but the believer asserts that the statement is true. Such assertions are meta-representations of reality. Such symbolic classification systems do not obey the rational constraints, and glory in the existence of contradiction and unresolvable conceptual mystery (cf. Berntsen & Kennedy, 1994, in press, on the value of contradiction). Because of this, such classification systems tend to be highly evocative. The relations that hold the system together are largely associational. Consequently, chaining is prevalent in such systems.

Lakoff's titular category--women, fire, and dangerous things --is the meaning of a term in the Dyirbal language, balan, that is native to Australia. Lakoff, pace Dixon (1982), reconstructs the etymological history of balan in an effort to show that the variety of things to which it refers only cluster together relative to the customs, rituals, and experience of the native Dyirbal speakers themselves (pp. 92-93). The strong implication is that no such collection could have been grouped together by the hyper-rational, logical, objective theory of cognition that Lakoff opposes. Although it is difficult to know with certainty, it seems to us that the classification system involving women, fire, and dangerous things, is not, in fact, part of the general purpose folk taxonomy of Dyirbal. Our suspicion stems from the observation that it seems to lack all the important features of such a taxonomy. It also seems, because of the mythic elements underlying the etymology (e.g. birds are the spirits of dead women), that it is a symbolic, rather than a non-symbolic, classification system. Drawing conclusions from this example to how classification works in general is therefore highly suspect.

3.3. The motivation for "motivation".

We now return to the critique of "motivation." Lakoff tries to explicate the notion in terms metaphor and metonymy, strategies frequently employed to extend the referents of concepts. Although his account of the metaphorical extension of fundamental concepts may be worthy of serious attention in a variety of other disciplines, it is doubtful that it could serve in place of linguistic compositionality in the determination of the literal meanings of sentences, as Lakoff claims. Consider the sentence, "The cat is on the mat." Surely its meaning is not merely "motivated" by "cultural conventions" involving the meanings of the component terms, but is, in fact, exactly what Lakoff denies: a strict function of the meanings of the terms and the syntax of English. If not, then it stands as a singularly inexplicable fact that sentences of well­nigh identical meaning are formulable in all languages everywhere (to the best of our knowledge); languages that come from cultures having conventions radically different from ours and, thus, in which radically different "motivations" are presumably at work. What is more, contrary to one obvious implication of Lakoff's position, such a sentence could be formed (i.e., the meaning of a particular combination of words could be correctly predicted) by a stranger to a given language, given only possession of the necessary terms and the syntactic rules of the language. The vagaries of cultural convention seem, on the whole, to matter not.

The root of this problem is the relation between ICMs and the components of language; a relation that we suggest is not clear in Lakoff's analysis. Vandeloise (1990, p. 412) notes that ICMs are linked by Lakoff to such diverse entities as particular words, modifying phrases (such as "strictly speaking"), mental process such as vision, scenarios, live individuals, and proportions. Thus, we find Lakoff offering an ICM for the Pope on one page (Lakoff, 1987, p. 71), and another for the proposition expressed by the sentence, "please sit in the apple juice," on another (Lakoff, 1987, p. 148). Moreover, Vandeloise notes that the representation of a single word--e.g., "over"--may require the use of several ICMs. Given the indeterminacy of the relation between the elements of language and ICMs it is understandable that Lakoff wishes to replace compositionality with the motivation relation. When confronted with a sentence, one trying to apply Lakoff's theory would not know if she should postulate an ICM for each word and try and see how theses ICMs relate together or if she should simply produce an ICM for the whole sentence or perhaps ICMs for phrases or proper names. Moreover, there is no principled theoretical way of deciding between these hypotheses. Asserting that meaning is only motivated and not compositional is a way of sidestepping these difficulties. However, to replace compositionality with an unconstrained theoretical relation between language and ICMs would not be advantageous. As Vandeloise (1990, p. 413) concludes, "Since they are polyvalent, it is doubtless the case that ICMs can make miracles when introduced in mental representations."

Lakoff offers two ways out of this bind. The first is that he attempts to regain the universality that he has given up by invoking "basic experiences" that all humans share. If true, this would allow for the grounding of those "motivations" that seem to operate in all cultures, and all languages, everywhere. Although this is an interesting suggestion, its explanatory value (let alone its truth) is by no means a sure thing, and it requires far more in the way of explication and evidence than is provided by a few intriguing examples. Second, and much more controversial, Lakoff contends elsewhere (Lakoff & Johnson, 1980) that there is no such thing as literal meaning; that all meaning is derived from metaphorical extensions of the primitive "image-schemata", grounded in our embodied interactions with the world. For those who are wary of biting quite so big a bullet--i.e., those who believe that there is literal meaning, and that metaphorical meaning is grounded in that literal meaning--abandoning compositionality would prove unsatisfactory.

In any case, the concept of motivation makes it difficult to see how individuals are actually able to build more complex wholes up from parts. Given that the whole has no predictable relation to the parts, individuals would have no criteria for deciding which novel constructions would be likely to be understood and accepted by others. Typically, however, human beings are very good at this sort of thing. They do sometimes fail, but it is more usual for them to succeed. Note, that even probabilistic prediction is not an option within Lakoff's theory since it is predictability per se that it excludes in such matters. Also, recourse to the influence of the culture, or to cultural convention, is not really an answer since such an answer presumes the ability of the individual to actually learn his culture from others of its members, and it is difficult to see how such learning could occur when the child could not form rules that predict how meaning is constructed.

Finally, we return for a fuller examination of the core concept of Lakoff's theory--the Idealized Cognitive Model, or ICM--for a fuller examination. We try to show that, in the final analysis, ICMs reduce to one of the two things that have dominated concept theory back to the time of Plato and Aristotle: pictures or propositions. If this suggestion is correct, then we are left pretty well where we were before we had ICMs.

4.1. Do ICMs do the work of cognition?

It does not seem that the ICMs are actually doing the important cognitive work. The number of ICMs that could be chosen to represent a particular feature of the world are indefinitely large, especially given Lakoff's claim that such models only fit the world in an indirect and loose fashion. Given such a wide selection of alternatives, individuals must have some other mechanism for selecting the appropriate models. This mechanism cannot be itself a model for then the question arises as to how this model is itself chosen. This regress is parallel to Aristotle's third-man critique of Plato's theory of the Forms. By analogy, we call it the "third-schema argument." To avoid such a regress, there must be other cognitive mechanisms that are responsible for the selection and application of the relevant model. But if this were the case then these mechanisms would actually be doing the most significant cognitive work.

The above considerations notwithstanding, one can still ask what is actually doing the cognitive work in the ICM? Lakoff lays out four basic structuring principles, there are image-schemata, metaphorical mappings, metonymic mappings, and propositional models. Lakoff is quite explicit, in his description of metaphoric and metonymic principles, that they are actually mapping or projection mechanisms, i.e., they are responsible for mapping an existing ICM on to a new domain. It is the ICM that is so mapped that does the cognitive work in the new domain. Hence the cognitive work is ultimately done by image-schemata or by propositional models.

Lakoff argues that his whole system has two foundations: basic level concepts and image-schemata (1987, p. 279). However, he does not state what form basic level concepts take. It is not clear whether they are propositional or image-schematic in nature. Lakoff states that they are more richly structured than kinaesthetic image-schemata, and are associated with rich mental images (1987, p. 270). He also argues that their structure is a preconceptual gestalt which is the kind of structure possessed by image-schemata. Thus, such basic level concepts probably have rich image-schematic models as their conceptual basis. In any case, Lakoff argues that all complex ICMs are ultimately built by means of image-schemata (1987, p. 282), and that meaning is ultimately grounded in either image-schemata or basic concepts. He is quite clear, however, that image-schemata are not primitive because they have analyzable structure. This implies that such schemata have parts but that the parts are only meaningful in relation to other parts. In fact, he states that the basic logic of such schemata is "due to their configurations as gestalts--as structured wholes which are more than mere collections of parts" (1987, p. 272). Lakoff calls them "preconceptual" structures of experience; preconceptual structures that are due to structural correlations in our daily experience (p. 276).

A key difficulty here that such correlation, as the term "preconceptual" indicates, does not have any of the necessary semantic properties to provide a basis for representing the world. Such correlation must be assigned an interpretation before it has such important properties as reference. Lakoff often conflates being able to assign an interpretation that is inherently valuable with the claim that the image-schemata inherently have meaning. So he tells us that, "the CONTAINER schema is inherently meaningful to people by virtue of their bodily experience" (1987, p. 273), and he states that such schemata, "are inherently meaningful because they structure our direct experience" (1987, p. 273). There is nothing in the pattern of correlation, i.e., the preconceptual structure, that refers to the world. There are only structural variables that covary. Correlation is a symmetrical relation whereas the assignment of meaning is not. Certain patterns may be assigned an interpretation when we are involved in tasks we find inherently useful, e.g., putting things in containers, and therefore we would find the pattern meaningful, but that meaning is parasitic on assigning a conceptual interpretation to the structure.

We find it odd that Lakoff would ultimately try to ground meaning in structures with inherent meaning since he denies this move to formal semantics. He consistently argues that the failure of formal semantics is due to the fact that you cannot get meaning from pure structure, and that to claim that the structure is inherently meaningful, or is assigned an interpretation, is to beg the question. He states it most plainly when claiming that the problem with formal semantics in not just technical; the "problem is that structure is not enough to confer meaning" (1987, p. 252). Yet, this is exactly what seems to be at work in image-schemata.

Some may think that we have been too quick in our judgment, and that, perhaps, we are supposed to think of image-schemata as closely related to pictures (see related discussions by Kennedy, 1993, chap. 7; and by Kennedy & Vervaeke, 1994). If so, image-schemata would draw on whatever mechanism it is that pictures do in order to represent their subjects. That is, the patterns of covariation in experience somehow "picture" the world, and thereby provide a basis for representation of it. The problems with this approach are legion and well known, and no one would not want to leap into such a morass. Pictures are inherently ambiguous and cannot uniquely determine their referents. Moreover, the resemblance relation that has been widely supposed to provide the basis for their ability to represent is not asymmetrical as is the representation relation; e.g., if the picture resembles Wellington then Wellington resembles the picture, but although the picture represents Wellington, he does not represent it. Attempts to evade the bind of indeterminacy of reference by recourse to talk of resemblance or similarity is, therefore, vacuous and non-explanatory.

Perhaps, alternatively, the image-schemata are to be understood as being more like models or diagrams. If they are mental models, then saying that ICMs are built out of image-schemata is not longer explanatory since it amounts to saying that ICMs are built out of ICMs. If, on the other hand, they are thought of as akin to diagrams, other problems arise. Lakoff and Johnson (1986) often represent image-schemata in diagrammatic form, hoping, no doubt, to exploit their pictorial properties, while avoiding the traditional problems of picture theories of mental representation. A diagram, however, is just a picture, schematic though it may be, that exists "under a description," so to speak. The description alone serves to reduce the referential indeterminacy of the picture. The claim, then, that image-schemata are really something like diagrams amounts to the admission that much of the cognitive work is being done by the descriptive--i.e., propositional--apparatus that assigns a unique referent to the diagram. That is, since what assigns a determinate meaning to a diagram is a description, it is very likely that the conceptual apparatus is, in the final analysis, propositional in nature. Yet this whole approach in which meaning is due to conceptually driven factors would undercut Lakoff's whole attempt to build cognition up from image-schemata and embodied experience.

This analysis brings us to a consideration of propositional structuring. We have noted that it has to be theory-like if it is going to assign interpretations to image-schemata. That is, propositional structures have to be driven by the concerns that drive theories. They must be concerned with reference, consistency, logical structure, and accuracy of representation. In short, a propositional model must be concerned with truth conditions. Yet all these features of a truth-conditional account of meaning are explicitly rejected by Lakoff as a basis for a theory of meaning. So any attempt to see propositional models as theory-like is not open to Lakoff especially if, as we have seen, they are ultimately doing all the important semantic work.

Lakoff does have a possible response. He could claim that the propositional models are like Johnson-Laird's mental models where the cognitive work is done by properties, especially non-logical properties, of the model that are not covered in the classical theory. Mental models (Johnson-Laird, 1983), however, seem to suffer from many of the same difficulties of indeterminacy as diagrams. Johnson-Laird arbitrarily assigns determinate meaning to the arrows, lines, letters, and various other signs of his models with no principled justification. The underlying assumption seems to be that the elements of such models are somehow self-interpreting, but this simply cannot be, as Wittgenstein (1951/1975) himself showed us in the famed "rule-following" argument decades ago (viz., in order to follow a rule one needs to know when to apply it; a process that itself requires a rule, and so on into infinite regress). It is ironic, however, that Wittgenstein, who has been something of a godfather to those people who have most strongly defended the prototype approach to meaning over the years, provided an argument that leads so conclusively to its refutation. Moreover, as Rips (1986) has argued, there is good reason to believe that, inasmuch as mental models can explain anything, they are just "notational variants" of the standard available logics. Thus, both of the main criticisms of diagrams bear equally against mental models.

A final alternative is to claim that the ICMs, in the final analysis, turn out to be just (descriptions of) prototypes after all. Lakoff contends that ICMs are wholly different from prototypes, and for good reason. If they are just prototypes, then by Lakoff's own admission (1987, p. 151), they may well fall, with traditional versions of prototype theory, to the criticisms made by Osherson and Smith (1981), and by Armstrong, Gleitman, and Gleitman (1983) with which we began this paper. If they are not just descriptions of prototypes then Lakoff must provide us with criteria which clearly distinguish ICMs from prototypes, and he must show how such criteria protect his theory from the criticism that he accepts as holding against prototype theory.

Motivation and chaining are supposed to do this but, as we have shown, Lakoff is not clear on these points, and it is far from assured that they would do the job even if he were. So it is best just to conclude that the propositional models are the cognitive core of the whole system, i.e., that they are ultimately responsible for all the representational work, and that such models work according to something very much like classical truth-conditional accounts. This is supported by Vandeloise's critique of Lakoff's case study of "over." He notes that the whole network of ICMs for "over" is essentially based on a central schema whose graphic representation is actually impossible. The schema can only be represented propositionally (Vandeloise, 1990, p. 421). Lakoff himself seems to acknowledge this when he states this central schema "is an abstract schema that cannot be imaged concretely, but which structures images" (Lakoff, 1987, p. 410). So, in the end Lakoff has not really provided a radically different theory of cognition or meaning.

We have, thus far, argued that several important aspects of Lakoff's theory are left critically vague, or fail to constitute a plausible alternative to standard cognitive theory. We close, however, with a metatheoretical critique that we believe shows that, even if his theory could be made adequately rigorous, it would have unacceptable implications for the pursuit of science itself, whether psychological or otherwise.

Lakoff seems at several points to argue for what might be termed "the psychologism of science." Because our "natural" thought processes are based on a wide array of culturally­dependent and sometimes inherently unpredictable mechanisms, Lakoff repeatedly implies that our theory of cognition must be just as "flexible." To maintain the view that scientific theories should ideally be composed of abstract entities and formal transformation rules that run according to the dictates of logic would be, it is suggested, to remain trapped in the grip of an outdated vocabulary and, indeed, an outdated metaphysic. This we simply cannot accept at face value. There are many areas of nature ­­ apparently capricious and whimsical ­­ that we struggle to model with mathematical and logical tools. There is no reason a priori­­at least no reason given in WF&DT -- to believe that we must give up these tools in our attempts to understand cognition. Indeed, as noted above, Lakoff himself cannot abandon them completely; he uses them repeatedly to explicate his position. Quite to the contrary of Lakoff, it might be argued that it is precisely in virtue of the strict constraints imposed by such unyielding masters as math and logic that we come to truly understand what before we only had a glimmer of, or perhaps a suggestive metaphor for. While metaphor may be one of the driving forces behind the development of scientific theories, it is not the whole scientific process. Lakoff must himself rely on some such distinction between embodied metaphorical thought and abstract logical thought, since it is presumably only through use of the latter that we can know that the former is embodied and metaphorical and does not just directly correspond to reality. Given that abstract logical thought has this capacity to better explicate reality (as opposed to our embodied interaction with it) it makes good epistemological sense that our scientific theories, even those of cognition, should try as much as possible to make use of such a form of thought.

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Correspondence concerning this paper should be addressed to either Christopher D. Green, Department of Psychology, York University, North York, Ontario, CANADA, M3J 1P3 (e-mail:christo@yorku.ca, WWW: http://www.yorku.ca/dept/psych//faculty/academic/christo/) or to John Vervaeke, Department of Philosophy, University of Toronto, Toronto, Ontario, CANADA, M5S 1A1 (e-mail: jvervaek@chass.utoronto.ca).

This paper was written in part while the first author held an Individual Research Grant from the Natural Sciences and Engineering Research Council of Canada. We would also like to acknowledge the assistance many members of the University of Toronto Department of Psychology, who discussed and debated these issues with us at some length. Most notable are Dan Chiappe, Michael Gemar, and Philip Groff.