"Critical thinking, like that in all area of human interest, has been in considerable part thinking in parallels , and critical argument has to that extent been an argument from analogy. " (M.H. Abrams, The Mirror and the Lamp, Preface.)
According to Giambattista Vico, the ancient language, before the formation of society, must have been full of the boldest metaphor, since this is the natural character of "words taken wholly from rough Nature, and invented under some Passion, as Terror, Rage, or Want." A distant echo of Vico's theories can be heard in Steven Pinker's Darwinian accounts of language. For Pinker, metaphors of space and force are quite possibly part of our evolutionary inheritance and are so basic to language that they are hardly metaphors at all, at lease not in the literary sense.
Metaphors depend on drawing attention to the similar in the apparently dissimilar, and they trade on secondary comparisons between the two terms. Max Black describes the "interaction" model of metaphor as not reducible to a literal paraphrase. Unlike the "substitution" or "comparison" views of metaphor, the interaction view identifies the cognitive (and emotional) content of a metaphor with its demand for simultaneous awareness of two subjects, the "principal" and "subsidiary" subjects, with their respective systems of implication. Thus the metaphor "selects, emphasizes, suppresses, and organizes features of the principal subject by implying statements about it that normally apply to the subsidiary subject." Models and Metaphors, p.45 (there is also a certain backflow process ...the secondary subject comes to appear more like the primary.) The extended meanings that result from a metaphor can neither be antecedently predicted nor subsequently paraphrased.
For Gorgio Agamben, this kind of description still obscures the fact that the "ressemblance" or semic intersections do not preexist the metaphor, but are rendered possible by it and assumed subsequently as its explanation, Just as Oedipus' answer to the sphynx does not preexist the enigma, but, having been created by it, pretends to offer its solution. (cf theory)
Metaphors are made and also wear out. They become clichés... or perhaps they just lose their figure. In metaphors that are crystallized by usage (and thus no longer metaphors) it is possible to distinguish a proper and an improper signified. Effective metaphors require shared social conventions and some measure of authority on the part of their makers. (do they confer authority? Or are they supposed to be expressed by the the proper authorities? -- who gets to say?) Sarah Kofman's analysis of the "camera obsura of ideology" focusses on the constraints of metaphor, especially when metaphors "join together as a system."
(see schizophrenia for the systematic inability to distinguish metaphors)
For Max Black, theoretical models in science work very much like metaphors, requiring analogical transfer and revealing new relationships. Models, however, require a greater degree of structural identity, or isomorphism, so that assertions made about the secondary domain can yield insight into the original field of interest, and usually the properties of the second field are better known that those of their intended field of application. Mathematical models are paradigmatic examples for science, and in physics and engineering, at least, their primary function is conventionally taken to be the enabling of predictions and the guiding of experimental research. Kant went so far as to identify science with mathematization....dass in jeder besonderen Naturlehre nur so viel eigentliche Wissenschaft angetroffen können als darin Mathematik anzutreffen ist. For Max Black, "perhaps every science must start with metaphor and end with algebra, and perhaps without the metaphor there would never have been any algebra." (p.242)
"In technical metalogic, a "model" is a system of objects (any kind of objects) that make all of the sentences in a theory true , where a "theory" is a list of sentences in a language. Even in matalogic, though, "model" has two meanings: the term refers either to the assignment of terms in the theory to objects (the interpretation ) or to the objects themselves (the structure ). For example, we could have as a theory the sentences: "object A is touching object B"; "Object C is touching object B"; and "Object C is not touching object A." We can easily imagine a structure that satisfies or makes true all of the sentences in this little theory -- it would consist of three objects in a row, 1,2,3, each only touching the next. Notice that they could be any kinds of objects, including cats, jars of jam, cars, or some mixture of these. The interpretation of the theory might map A onto 1, B onto 2, and C onto 3. (Equally, it could map A onto 3, B onto 2, and C onto 1.) "(Elizabeth Lloyd, The Structure and Confirmation of Evolutionnary Theory, preface (1994.)
Models are "speculative instruments" (I.A. Richards) part of the imaginative aspect of scientific thought, which enable us to see new connections, and their fictionality is sometimes fully acknowledged. James Clerk Maxwell famously acknowledged the explanatory value of fictional construction in his description of electrical potential. "We have no reason to believe," he wrote, "that anything answering to this function has a physical existence in the various part of space, but it contributes not a little to the clearness of our conceptions to direct our attention as if it were a real property of the space in which it exists."
In science metaphors become cognitively and technologically productive insofar as they mobilize social, technical, and natural resources. Thomas Kuhn calls these particular unities of theory and practice "exemplars." (cf. paradigm) In contemporary biology, organisms such as the fruit fly, drosophilia melanogaster, the round worm, and the house mouse are natural models and used to represent a class of biological phenomena across a wide range of species.
One might draw out from this distinction that metaphors somehow mobilize the difference between the two domains, even by cutting accross them, while scientific models attempt to eliminate those differences, even while taking advantage of them (eg: using mathematics as a tool in physics.) Yet, as R. Lewontin points out, science still relies on metaphors, and there is a great risk of confusing the metaphor with the thing of real interest. "We cease to see the world as if it were like a machine and take it to be a machine. The result is that the properties we ascribe to our object of interest and the questions we ask about it reinforce the original metaphorical image and we miss the aspects of the system which do not fit the metaphorical approximation." As Alexander Rosenbluth and Norbert Wiener have written, "The price of metaphor is eternal vigilance." ("Purposeful and non-purposeful behavior," Philosophy of Science 18 (1951)--quoted in R. Lewontin, The Triple Helix, p. 4)
The most pervasive current metaphor in the life sciences is precisely the one developed by Wiener and his associates: that of biological activity (life) as computation.
"We employ a dualism of models only in order to arrive at a process that challenges all models. Each time, mental correctives are necessary to undo the dualisms we had no wish to construct but through which we pass" (Thousand Plateaus, p. 20)