Metaphor II: "Metaphor Is Like Analogy"

Onward we go to the first contemporary view of metaphor, structure mapping theory. Before I start, though, I want to clear something up. Perhaps no one has actually been confused, but I'm afraid that I haven't made something clear that should be made clear. For the most part, cognitive theories of metaphor -- cognitive linguistic accounts, which purport to be theories of all cognition and, if the cognitive linguists had their way, would also combine to serve as the Unified Field Theory, aside -- are intended to account for common, everyday uses of metaphor. "My surgeon is a butcher" and "my lawyer is a shark" are great examples of this sort of metaphor. "A poem should be... silent as the sleeve-worn stone of casement ledges where the moss has grown" is not a good example of this sort of metaphor. Cognitive scientists usually call this latter sort of metaphor "creative metaphor," and to be honest, these types of metaphor have been neglected in cognitive theories. Unlike commonplace metaphors, creative metaphors are often incompatible with comparison and categorization views of metaphor, and more importantly, they are not easily or automatically processed. In fact, I suspect that most of them are specifically designed to induce deliberative thinking, at the same time they elicit automatic emotional and imaginative responses. So, when I talk about metaphor, I mean commonplace, not creative metaphor. I wish we had a viable cognitive account of metaphor that could capture "an empty doorway and a maple leaf" and "hills like white elephants," but we don't.

OK, now that that's out of the way, I can get started. The structure mapping theory of metaphor treats metaphors as analogies, at least in their underlying cognitive mechanisms. Some metaphors are obviously similar to analogies, and may even be considered analogies. "Encyclopedias are gold mines" (a common metaphor in the cognitive literature), for instance, clearly involves the mapping of relational structure between the encyclopedia and gold mine domains. Other metaphors are less obviously analogical. "My lawyer is a shark" seems primarily designed to map a few specific attributes of sharks onto my lawyer, in order to highlight those attributes in my lawyer. It is thus more like a literal similarity comparison (e.g., "Alligator meat is like chicken") than analogical comparisons (e.g., "The atom is like the solar system."). On the surface, the existence of these two different types of metaphor seems to make the possibility of a general theory of metaphor that treats metaphor as analogy (at least in terms of processes) impossible. However, it turns out that literal similarity comparisons may also involve the same processes as analogies, which means that metaphors that are like literal similarity comparisons could also be like analogies.

Here is the gist of the theory: metaphor is like analogy. Analogies involve the "structural alignment" of two (or more) structured representations (representations containing objects, their relations, and their attributes, along with relations between relations) so that the common elements in the representations are mapped onto each other¹. Structural alignment occurs under three primary constraints: systematicity, one-to-one mapping, and parallel connectivity. Systematicity requires that, all things being equal, higher-order mappings are preferred. This means that mappings involving relations between relations will be preferred to mappings involving relations between objects, and mappings between relations between objects will be preferred to mappings between objects or their attributes. The one-to-one mapping constraint requires that each element in a representation be connected to at most one element in the other domain. For instance, in "The atom is like the solar system" analogy, once we map the planets in the solar system domain onto electrons in the atom domain, we cannot also map the planets onto the nucleus or some other element in the atom domain. The third constraint, parallel-connectivity, requires that when elements are mapped onto each other, their arguments are also mapped. For instance, when we map the "Revolve around" relation in the "Atom is like the solar system" analogy, then parallel connectivity requires that the arguments (planets-sun in the solar system domain, and electrons-nucleus in the atom domain) be mapped as well. These constraints allow analogical comparisons to preserve the maximum amount of common structure between the two (or more) domains being compared, and this in turn makes for easier and more productive inferences, which are what motivates most analogies in the first place.

While structure mapping theory was originally intended as a theory of analogy, it can also be extended to literal similarity comparisons like "Alligator meat is like chicken," which are designed to highlight common objects or attributes, and not common relational structure. To do this, the mappings are restricted to objects or attributes². Since metaphors resemble both types of comparisons, structure mapping has, over the last decade or so, been used as a theory of metaphor. To see how this works, I'm going to let the theorists themselves describe an actual example, because I know I couldn't do it any better. Here is a passage from Bowdle and Gentner (In Press)³:

To better illustrate this approach to metaphoric mappings, consider Socrates was a midwife - a metaphor that was first used in Plato's Theaetetus,, and that has been examined in depth by Kittay and Lehrer (1981)... Structure-mapping theory and SME [Structure Mapping Engine, the computational implementation of Structure-mapping theory] predict the following sequence of events during the interpretation of the metaphor. First, the identical predicates in the target and base concepts (i .e., the relations helps and produce) are matched, and the arguments of these predicates are placed in correspondence by parallel connectivity : midwife --> Socrates, mother --> student and child --> idea. Next, these local matches are coalesced into a global system of matches that is maximally consistent . Finally, predicates that are unique to the base but connected to the aligned structure (i.e., those predicates specifying the gradual development of the child within the mother) are carried over to the target . Thus, the metaphor could be interpreted as meaning something like, "Socrates did not simply teach his students new ideas, but rather helped them realize ideas that had been developing within them all along". (p. 11).

There you have it: the two domains (Socrates and midwife) are aligned so that their common relational structure (Socrates helps the student produce an idea; the midwife helps the mother produce a child) is in correspondence. After the mapping occurs, information from the vehicle is carried over to the topic in the form of inferences, so that we now see Socrates as helping give birth to ideas that had been developing in the minds of students, as the midwife helps give birth to children that had been developing inside of mothers.

I won't get into the evidence for this view until I've posted on the other major theory of metaphor, but since I described the assymetry of metaphorical statements as being one of the most important features for a theory of metaphor to capture, in the first post, I will quickly describe how structure mapping explains this assymetry. Like metaphors, analogies are always assymetrical. The primary purpose of analogy, in most cases, is to compare a lesser-known domain (e.g., the atom) with a better-known one (e.g., the solar system). This allows one to carry structure from the better-known domain over to the lesser-known domain, in the form of inferences, to produce more knowledge about it. This sort of directional production of inferences is what produces the assymetry in metaphors as well. In metaphor, the vehicle corresponds to the better-known domain, and the topic to the lesser-known, and inferences are produced from the vehicle to the topic. The "Socrates was a midwife" metaphor demonstrates this. The inferences about internal development are carried from the vehicle to the topic, and no inferences are made in the other direction.

Finally, as I said in the first post, this theory of metaphor was inspired, in part, but Black's interactive theory. The similarity of this theory of metaphor to Black's interactive theory comes from the fact that it is the interaction between the two domains, the vehicle and topic, in the form of the alignment of common relational structure, that produces the relevant features to carry over from the vehicle to the topic. Unlike Black's theory, however, the way in which the interaction determines the relevant features is made explicit. In fact, the mechanisms for discovering these features are explicit enough for the computational implementation of structure mapping theory, the Structure Mapping Engine (SME), to discover them on its own, and thus produce interpretations of metaphors similar to those of human subjects, without human intervention after the encoding of the initial representations of the two domains.

In the next post, I will detail the attributive categorization model, and after that, we'll get to real empirical evidence. In thinking about what might come after that, I've decided that a discussion of novel vs. dead or conventional metaphors might be interesting, because it has implications for the two major theories. Perhaps after the election I'll talk about cognitive linguistic theories of metaphor, too.

¹ Gentner, D., Bowdle, B., Wolff, P., & Boronat, C. (2001). Metaphor is like analogy. In Centner, D., Holyoak, K.J., & Kokinov, B.N. (Eds.), The analogical mind: Perspectives from
cognitive science (pp. 199-253). Cambridge MA, MIT Press.
² In most metaphors, even those that are ostensibly about specific attributes (e.g., "My lawyer is a shark" is about "aggression," or some similar attribute), there is also relational information that can and will be mapped in the process of understanding the metaphor. However, structure mapping theory can handle similarity comparisons and metaphors that only involve the mapping of attributes.
³ Bowdle, B., & Gentner, D. (in press). The career of metaphor. Psychological Review.