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2.1 Theories of Metaphor


..."metaphor" refers to all those processes in which the juxtaposition either of terms or of concrete examples calls forth a network of similarities which help to determine the way in which language attaches to the world.(Kuhn 1993, p539).
The term "metaphor" is used here not in a narrow linguistic sense, but in the sense of rich and complex metaphoric models (Lakoff and Johnson 1980). A metaphoric model is a way to structure the knowledge of one domain (the target) by mapping onto it concepts and relations from an existing domain (the source) that is already familiar. Metaphor in this sense is not a mere linguistic device used only for the figurative embellishment of otherwise straightforward language, but a fundamental way of learning and structuring conceptual systems, a part of everyday discourse. Metaphors are so pervasive that they are sometimes hard to see. For instance, the common model and terminology of the behavior of electrical circuits is based on a metaphoric mapping to fluid flow in pipes, with voltage mapping to water pressure, batteries to pumps, current to flow, and so forth. In a less technical and less obviously metaphorical example, the American conception of anger is metaphorically derived from the image of a heated fluid in a container, giving rise to expressions like "blowing off steam" and "containing his rage" (Lakoff and Kövecs 1987). The metaphoric structure underlying such common concepts indicates that metaphoric models are not merely optional stylistic overlays to a fundamentally objective and literal mode of representation. Rather, they are a fundamental mechanism for encoding knowledge. Much of our common cultural knowledge is in terms of metaphoric models (Lakoff and Johnson 1980).

Since metaphoric processes are a fundamental part of how knowledge is structured, there can be no hard line drawn between metaphoric thought and other kinds. From a certain point of view, all thought is metaphoric:

No two things or mental states ever are identical, so every psychological process must employ one means or another to induce the illusion of sameness. Every thought is to some degree a metaphor (Minsky 1987, p299).
If all thoughts are equally metaphorical, then metaphor is not a very useful analytic category. However, some thoughts seem to be more metaphorical than others. There is a large space of possibilities lying between the purely literal and the obviously metaphorical. Perhaps the most interesting cases are those in which a phrase or thought appears initially to be literal, but upon examination turns out to be based in metaphor after all. We will see that many metaphors used in the discourse of mathematics, science, and technology are like this. It will be useful to distinguish the concept of a structuring metaphor from the closely related idea of an analogy (Winston 1982) (Gentner 1989). Both aim to establish understandings by the creation of mappings between domains, but the two terms connote different aspects of this cognitive process. Analogy usually refers to the construction of explicit mappings between two well-established domains, whereas metaphor is more often implicit. The linguistic form of analogy, the simile, keeps the two domains safely separated by using terms such as like ("life is like a bowl of cherries"), while metaphor draws a more immediate connection ("life is a journey"). More importantly, metaphor often plays a foundational role in the establishment of new, previously unstructured domains. The two terms really connote different views of the same broad cognitive process, with the view through metaphor being more oriented towards the foundations of cognition. Analogies can be powerful learning tools, but if the thing learned is to become an important part of thinking, it must become integrated into the structures of the mind--that is, it must become a structuring metaphor. One draws an analogy, but one lives in metaphor.

2.1.1 The Contemporary Theory of Metaphor

My primary tool for thinking about metaphor will be the theory put forth by George Lakoff and Mark Johnson (1980)(Lakoff and Johnson 1980) and developed further by them, Eve Sweetser (1990)(Sweetser 1990), Mark Turner (1991)(Turner 1991) and others, and more recently labeled "the contemporary theory of metaphor" (Lakoff 1993). In this theory, metaphor is to be understood as any mapping between normally separate conceptual domains. The purpose of this mapping is to structure an abstract, unfamiliar, or unstructured domain (the target) in terms of one that is more concrete, familiar, or structured (the source).

Metaphor is viewed more as a basic tool of cognition rather than a special turn of language, and most concepts are generated by metaphors. The exceptions are those concepts that are thought to be perceptual or cognitive primitives, such as up or cat. Aside from these references to concrete physical objects and experiences, metaphorical understanding is the rule. In Lakoff's words, "metaphor is the main mechanism through which we comprehend abstract concepts and perform abstract reasoning" (Lakoff 1993). The more narrowly linguistic meaning of metaphor is called a "metaphorical expression" to distinguish it from the broader view of metaphor as a conceptual mapping.

2.1.1.1 The Conduit Metaphor

The contemporary theory has its roots in Michael Reddy's work on what he called the Conduit Metaphor (Reddy 1993), a detailed exposition of the system of ideas underlying the concept of communication. Reddy found that there was a consistent metaphorical substrate underlying talk about communications and ideas. This metaphor was based on the idea that ideas were like physical objects, and that the purpose of language was to package up ideas for transfer between minds. This insight was illustrated by example sentences like:

1) He couldn't put his thoughts across well.

2) Try to pack more thoughts into fewer words.

3) I gave him that idea.

4) We tossed the ideas back and forth. The implications of this metaphor are that words function like packing crates for meanings, and that writing or speaking is a process of packing, shipping, and unpacking. Language as a whole is seen as a conduit for transferring meanings from mind to mind. The unstated implication is that meaning is unproblematically conveyed by language. It further implies that the listener is essentially a passive recipient of meanings generated by speakers.


Figure 2.1: Comparing the conduit metaphor and the toolmakers paradigm (after Fig. 1 in (Reddy 1993)).
These usages and their underlying metaphor are so commonplace that their contingent nature might be hard to see. To better illustrate this, Reddy proposed an alternative metaphor system which he called the Toolmakers Paradigm. This metaphor system posits listeners isolated in cells, who transmit and receive crude instructions in the form of blueprints rather than words between neighboring cells. To make any use of these transmissions, they must actively follow the instructions and construct the described object. Naturally transmission is imperfect in this system, and each recreation of meaning is subject to the interpretation of the hearer. The Toolmakers Paradigm is intended to be a metaphorical representation of a constructivist theory of language, in which listeners are active constructors of meanings rather than passive recipients. The existence of an alternate metaphor is a powerful tool for thinking about alternate theories of language. In the conduit metaphor, the sharing of meaning is assumed to be the default case, and any divergence of interpretation is a problem to be explained by faults in the transmission system. By contrast, the Toolmakers Paradigm emphasizes that shared meanings are achievements, requiring careful coordination and interaction through limited channels of communication.

Although the conduit/toolmakers example is a powerful dual metaphor for thinking about constructivist theories of mind, Reddy's main concern is to illustrate the pervasiveness of the conduit metaphor and the way that it can place a strong bias on theories of language. The conduit metaphor plays a dual role in the history of the contemporary theory of metaphor. It stands as an example of a common metaphor worked out in detail, and as an illustration of how linguistic theory itself can be built on and influenced by unquestioned metaphors.

Lakoff and Johnson, inspired by Reddy's effort, embarked on a more comprehensive effort to analyze the metaphor systems underlying everyday thought. They summarize their findings by expressing the metaphors as short declarations of the mapping: LOVE IS A JOURNEY or EMOTIONS ARE SUBSTANCES. According to Lakoff:

Most people are not too surprised to discover that emotional concepts like love and anger are understood metaphorically. What is more interesting, and I think more exciting, is the realization that many of the most basic concepts in our conceptual system are also normally comprehended via metaphor--concepts like time, quantity, state, change, action, cause, purpose, means, modality, and even the concept of a category. These are concepts that enter normally into the grammars of languages, and if they are indeed metaphorical in nature, then metaphor becomes central to grammar (Lakoff 1993, p.212).
Since computer programming concerns itself with many of these same basic concepts, we should not be surprised to find that metaphors underlie the discourse of computation, and that these metaphors are variants of those found in ordinary discourse. To take one example, Lakoff's studies have revealed that the metaphorical representation of events in English involves a basically spatial metaphor, with states being represented as locations, state-change as movement, causes as forces, purposes as destinations, and so forth. This metaphor surfaces in computation through such phrases as "the process is blocked" or "the machine went into a run state". These usages are so much a part of everyday use that, like the conduit metaphor, they hardly seem like metaphors at all.

The viewpoint of the contemporary theory of metaphor leaves us with two points that will inform the rest of this analysis: first, that some of our most fundamental concepts are structured metaphorically, and second, that it is possible (as the Toolmakers Paradigm shows) to gain a new viewpoint on these concepts by proposing alternate metaphors.

2.1.2 Dead Metaphors

We've seen that some metaphorical structures are so ingrained into our habits of thought and language that they are very difficult to see as metaphors. They raise the question of whether such usages are really metaphorical in any meaningful sense. A dead metaphor is one that has become a conventional usage or phrase and so has (according to some theories of metaphor) lost the live mapping between its domains. "Falling in love" is one example--the phrase is so routinized that it does not recall any feelings of physical falling, although the metaphoric mapping is easy enough to recreate. "Kick the bucket" is a better example, since its live roots are even more distant[2].

There is wide diversity of opinion on the question of dead metaphors. According to Black (Black 1962), dead metaphors are not really metaphors at all, but should instead be considered as separate vocabulary items. Lakoff is dubious about the utility of the concept--he believes that most conventionalized phrases still retain traces of their origins in living metaphors (Lakoff and Johnson 1980, p55). Gibbs (Gibbs 1993) points out that if a metaphor was truly dead it would lose its compositional qualities, but in fact they still remain. You can understand expressions like "falling head-over-heels in love" even if you had never heard that particular variant of "falling in love". Since the mapping between domains can be reactivated to comprehend this sort of novel phrase, the metaphor lives on after all. Metaphors used in technical discourse often appear to be dead. Since the technical meanings of phrases like "a blocked process" or "pushing a value onto the stack", are perfectly clear to experts, their metaphorical origins are often dismissed and ignored. Nonetheless the viewpoint of Lakoff and Gibbs is still useful and perhaps necessary to understanding the conceptual bases of technical understanding. In this view, even when technical terms have taken on what seems like an unproblematic formal meaning, they continue to maintain a link back to their metaphor of origin, because the mechanisms for understanding are metaphorical at their roots. Metaphors can differ in the degree to which they are taken for granted and kept out of consciousness, but are rarely so dead as to completely detach themselves from their origins.

Another extremely conventionalized metaphor used in computation is the treatment of memory as space and data as objects that are located and move within that space. The degree of conventionalization of these usages is so high that some people get quite annoyed if attention is drawn to their metaphorical underpinnings. The MEMORY IS SPACE metaphor might be considered dead since it is extremely conventionalized, but it is still alive in Lakoff's sense -- the mapping between domains is still present and can be generative of new constructs, such as the slangy term "bit bucket" (the mythical space where lost bits go) or the endless stream of respectable technical terms that reflect the metaphor ("garbage collection", "partition", "allocation", "compacting", and so forth).

Perhaps transparency is a better metaphor than death to describe the condition of the metaphors underlying technical terminology. They do such a good job of structuring their target domain that they seem to disappear, and the lens of metaphor becomes an invisible pane of glass. The question remains as to what makes particular metaphors achieve transparency. I speculate that metaphors become transparent when they impose a strong structure on a domain that was previously unstructured. These metaphors essentially force one to think about the target domain in their own terms, to the point where any alternative way of structuring the domain becomes forgotten and almost unthinkable. At this point, the winning metaphor is ready to be taken literally. Such metaphors have been labeled theory-constitutive metaphors by some philosophers of science. That is, rather than simply mapping between the concepts and vocabulary of two existing domains, as conventional metaphors do, a theory-constitutive metaphor can be said to create the structure of a new domain, based on the structure of an existing one.

Where one theory-constitutive metaphor is dominant (for instance, the metaphor of electricity as the flow of fluid, or of computer memory as a space), the terms that are brought to the target domain tend to become conventionalized and transparent, such as the term current in electrical theory. But not all theories and metaphors are as well established as these. Even memory is sometimes viewed through alternate metaphors, i.e. as a functional mapping between addresses and values. Computational discourse seems to have a particular need to mix metaphors, as we shall see.

2.1.3 The Metaphorical Nature of Scientific Understanding

The place of metaphor in the discourse of science has always been problematic. The distinction between literal and metaphorical meanings was first promulgated by Aristotle, who grudgingly acknowledged the utility of metaphor in poetry but demanded that it be eliminated from the discourse of natural science. Lloyd argues that this dichotomy was in fact necessary for the creation of a new rhetorical territory in which metaphor would be banned and literalism could flourish:
...the distinction between the literal and the metaphorical...was not just an innocent, neutral piece of logical analysis, but a weapon forged to defend a territory, repel boarders, put down rivals (Lloyd 1989, p23).
So, the domain of science was in a sense brought into being by the very act of banishing metaphor and other poetic forms of language. Scientific thought was to be of a form that dealt only with literal truth. Despite Aristotle, metaphors are commonly employed in scientific discourse, particularly in informal and educational settings. While scientific rhetoric may aspire to the literal, it cannot avoid the need to bootstrap new theories from old concepts using metaphor. Some theories of metaphor in science relegate the use of metaphors for training to a separate category of "exegetical metaphor", but as Kuhn points out (Kuhn 1993), every scientist must be trained and thus such metaphors are not at all marginal, but instead are a crucial part of the way in which a scientific field reproduces itself. The question then becomes whether the exegetical metaphors are like scaffolding, used to erect a formal structure in the mind but discardable when the task of construction is completed, or whether the structure maintains a live, dynamic relationship to the metaphors that allowed it to be built. Given that metaphor is a part of everyday scientific practice, why do most scientists act as literalists, paying little or no attention to metaphor and occasionally expressing hostility to the very idea of investigating them (Gross and Levitt 1994)? The roots of scientific rhetoric's adherence to literalism may be sought in the social practices of scientists. The practice of science demands the use of a rhetoric that promotes literal rather than metaphoric construals of language. Latour (Latour 1987) paints a picture of science as a contest to establish facts, a contest that depends as much on rhetorical moves as it does on laboratories. Scientists jockey to make their statements strong, so they will be taken as facts, while simultaneously working to weaken the statements of rivals by painting them as constructions, hence questionable. The rhetorical tools for making a statement factual Latour calls positive modalities (i.e., a bald statement of fact) while the tools for doing the opposite are negative modalities (i.e., "Dr. X claims that [statement of fact]). "It is around modalities that we will find the fiercest disputes" [Latour, op. cit., p25]. Here, since we are interested specifically in rhetoric rather than ongoing controversies among philosophers of science, we need not trouble ourselves over whether Latour's model of science is complete. It does lead us to speculate that the competitive pressure among scientists to establish facts will also contribute to their tendency to hide or strip the metaphors from the language. A statement that contains obvious metaphors is weaker than one that contains either no metaphors or only those so conventionalized as to be dead. Metaphor use is not exactly a modality in Latour's sense, but it can be seen that similar dynamics might apply and tend to either strip metaphor out of scientific discourse, or disguise it as something else. However, not all science is sufficiently developed that it can maintain the pretense of literalness. Metaphors are commonly used to introduce vocabulary and basic models into scientific fields: "their function is a sort of catachresis--that is, they are used to introduce theoretical terminology where none previously existed." (Boyd 1993). The term catachresis was introduced by Max Black in his influential early work on the interaction theory metaphor (Black 1962). The interaction view posited a dynamic interaction between elements of the two linked domains. But Black did not believe that metaphors used in science were still interactive, since the meanings of the scientific terms were fixed, and that metaphoric vocabulary creation was mere catachresis, rather than a proper metaphor. Boyd disagrees, holding instead that scientific use of metaphor does double duty--it creates vocabulary to describe a new domain, and at the same time makes this new domain interact with the other domain involved in the metaphor.

Boyd terms metaphors that are essential in science theory-constitutive metaphors. He distinguishes these from metaphors used solely for pedagogic purposes, although these might have been more important earlier in the science's history. A good theory-constitutive metaphor is a tool that lets a scientist do his job of "accommodating language to the causal structure of the world" or "carving the world at its joints."[3] His primary example of a theory-constitutive metaphor is the use of computation as a foundational metaphor for cognitive psychology.

The use of metaphor in theory formation and change depends upon this open-endedness, especially in young fields. However, the metaphor persists even as the scientific theory matures and the particular points of analogy become explicit. Sometimes complete explication is impossible, but this is not an indication that metaphor is too imprecise to serve as the basis of scientific theorizing. Rather, it means that metaphors are tools among other tools that scientists use to achieve their goals. Metaphoric interpretation remains open-ended as long as scientific theories remain incomplete.

2.1.4 Formalization and Metaphor

Computer science contains a strong ideological bias against the recognition of metaphor. Its emphasis on formalism might almost be seen as a technology for making metaphors seem as dead as possible. Formalists naturally oppose metaphor as a particularly insidious form of non-rigorous thinking. In computer science, Edsger Dijkstra has made his opinions of metaphor widely known:

By means of metaphors and analogies, we try to link the new to the old, the novel to the familiar. Under sufficiently slow and gradual change, it works reasonably well; in the case of a sharp discontinuity, however, the method breaks down....Coping with radical novelty requires... [that] one must consider one's own past, the experiences collected, and the habits formed in it as an unfortunate accident of history, and one has to approach the radical novelty with a blank mind, consciously refusing to try to link history with what is already familiar, because the familiar is hopelessly inadequate [emphasis added]. ...both the number of symbols involved and the amount of manipulation performed [in complex computations] are many orders of magnitude larger than we can envisage. They totally baffle our imagination, and we must, therefore, not try to imagine them (Dijkstra 1989).
This view, while it seems wildly wrong to me, is at least grounded in a definite epistemological theory. To Dijkstra, certain domains like computation (quantum mechanics is another example) are so radically new that they must be approached with a totally blank mind. This theory is basically the opposite of the one we are developing here, namely that computation, like anything else, is understood in terms of structures defined by mappings from other domains of knowledge. In place of metaphor and imagination, Dijkstra advocates the use of formal mathematics and logic.

However, formalism does not really offer an escape from metaphor, for two separate reasons. First, even formal mathematics is riddled with metaphorical terms and concepts, such as the notion of a function having a slope[4] (a physical metaphor) or being well-behaved (an animate metaphor). Secondly, very few mathematicians would claim that the use of formal methods exempts them from the need to use their imagination!

A more realistic viewpoint on the relationship between metaphor and formalism may be found in Agre's claim that the defining characteristic of technical language is that it links together two separate domains of reference: the real-world domain being formalized and the "Platonic realm of mathematics" (Agre 1992) (Agre 1996). This cross-domain mapping is essentially a metaphorical process in which aspects of the real world target domain are understood in terms of the formalized and well-understood source domain of mathematics.

Such a mapping will always emphasize certain parts of the world at the expense of others. Aspects that are readily translated into mathematical terms will be preserved by the metaphor, while other aspects will become marginalized. The concept of margins derives from Derrida's philosophical deconstructions, in particular the idea that metaphors or world-views can contain "hierarchical oppositions" which classify phenomenon into central and marginal categories. The phenomenon of marginalization will cause research programs to organize themselves around particular central problems (those that the mathematics can describe) while pushing other equally important problems out into subfields, into "areas for future work", or out of consideration entirely. Agre's solution to this form of intellectual tunnel-vision is to deploy new metaphors and more importantly to develop a "reflexive critical awareness" of the role of metaphor in technical work.

Deconstruction is a set of techniques for achieving this sort of awareness by systematically questioning the dominant oppositions and metaphors that structure a field of knowledge. One of these techniques, inversion, is to construct an alternate system that inverts the center and margins created by the dominant metaphor, thereby exposing the assumptions of the original metaphor and bringing the previously marginalized aspects of the phenomenon to attention. Reddy's Conduit metaphor is a good example of such an inversion.

Agre's project is to deconstruct what he sees as the dominant mentalistic metaphors within AI and Cartesian-influenced views in general. Mentalism is a broad structuring metaphor that posits an internal representational space in both humans and computers, in which representational objects dwell and mental processes take place. Mentalism, Agre argues, emphasizes the internal mental processes that take place inside this space at the cost of marginalizing the interactions between inside and outside. To counteract this, he offers the alternative metaphor system of interactionism, which emphasizes precisely the opposite phenomena. From the interactionist perspective, the dynamic relationship of an agent and its environment is of central interest, while the machinery inside the agent that generates its behavior is secondary.

My own project can be viewed, loosely, in deconstructive terms. In the next chapter, I explore use of animism in describing the world in general and computation in particular. The language of computation appears to involve both formal mathematical language and a more informal use of various metaphors, particularly metaphors that map computation on to the domain of animacy. While neither mode is completely dominant, the use of animism is generally confined to pedagogic or informal contexts, and is in some sense marginalized by the strong bias in favor of mathematical formalism that pervades academic discourse. By making animism the central concept of my analysis of programming languages, and designing new agent-based languages that incorporate the use of animate metaphors, I hope in some sense to deconstruct the languages of computation.

The purpose of such deconstruction is to be critical, not destructive. Computation has unquestionably provided powerful new conceptual tools for laying hold of the world. But computation has its limits, as its practitioners are constantly forced to acknowledge. Some of these limitations manifest themselves in reliability problems, brittleness, and the difficulties encountered by both novices and experts in expressing simple ideas in the form of programs. Probing the conceptual underpinnings of the metaphors used to construct computation is one way to try and understand, and possibly circumvent, these limitations.


[2] Apparently the phrase derives from the actions of dying farm animals.

[3]A metaphor introduced by Plato in Phaedrus.

[4] These examples are taken from David Pimm's analysis of mathematical language (Pimm 1987).


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