Abstract
I am concerned mainly with linguistic metaphors. There are, however, non-linguistic metaphors to which structural or analogical theories probably apply. Paradigmatic among such metaphors are pictorial or visual metaphors (Carroll, 1994; Stafford, 2000). To deal with linguistic metaphors, I set up some syntactic and semantic equipment. Section 2 deals with the distinction between the external language of words (the language of English1 surface structures) and the internal language of concepts (the logical language of deep structures). It also deals with literal and metaphorical meanings. Section 3 discusses grammars and gives re-write rules for many grammatical forms of metaphor. I talk about metaphorical identifications and predications. Section 4 introduces the extended predicate calculus (XPC) as the internal logical language. The XPC is an intensional predicate calculus. The XPC extends the ordinary predicate calculus in three ways: (1) it adds thematic roles; (2) it adds symbols for generalized events (occurrences); (3) it has tools for dealing with parts of worlds (situations). Section 5 shows how propositions in the XPC are encoded in networks or graphs. Since the semantic machinery behind the XPC is technical, I put it into Appendix 2.1. If you’re familiar with the semantics of the ordinary predicate calculus, Appendix 2.1 is easily accessible. Appendix 2.1 describes logical spaces as models for the XPC; it describes XPC situations and XPC semantics.
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Notes
The structural theory of metaphor should be directly extensible to other natural languages in the Indo-European family besides English.
NETMET works with a language that resembles the XPC but that is less expressive; still, the language used by NETMET is powerful enough to generate and to partially interpret metaphors. NETMET’s language consists of expressions like [Pl:produce(AGENT: student, PATIENT: idea); P2:express(AGENT: student, PATIENT: idea); P3: if P2 then P3;]. NETMET contains text-generation routines that translate such expressions into human-readable English surface structures: “Students express ideas”. NETMET does not contain any routines for translating English texts into its internal language.
My notions of surface structure and deep structure are derived more from Kintsch (1972) and Woods (1981) than from Chomsky.
The concept of the literal is not entirely clear (see Rumelhart, 1979).
My formalisms for working with grammars (and the languages they generate) are derived from Chomsky (1957a; 1957b; 1959) and are standard in computational approaches to both natural and artificial languages (Grishman, 1986: ch. 2). Though I choose this classical account for its familiarity, my approach is also consistent with more recent statistical approaches to syntax and semantics (Charniak, 1993).
In their discussion of LOVE IS A FORCE, Lakoff & Johnson(1980: 49) give the metaphor: “I was magnetically drawn to her”. However, in that metaphor “magnetically” does not seem to function adverbially by specifying a way of being drawn; rather, it seems to qualify the woman who is attracting the person who is drawn to her: she is a magnet.
There are many classical rhetorical figures of speech (Lanham, 1991). Some of these are merely syntactical (metaplasm permutes letters or syllables); some are merely pragmatic (eulogy is discourse with the purpose of praising). I am interested in semantic figures. Semantic figures are those that determine distinct classes of meanings (truth-conditional combinations of their component and associated words). Metaphors are semantic figures. Figures close to metaphor include: (1) absurdities (e.g. “Socrates is and is not human”); (2) oxymorons (e.g. “single wife”, “married bachelor”, “military intelligence”); (3) paradoxes (e.g. “Get closer to be far way”, “This sentence is false”); (4) adynata (e.g. “In the middle of the night in the broad daylight, two dead boys got up to fight; back to back they faced each other, pulled their swords and shot each other; two deaf policemen heard the noise and went and arrested those two dead boys”); (5) hypallage (e.g. in Shakepeare, with Bottom playing Pyramus: “I see a voice. Now will I to the chink, To spy and I can hear my Thisby’s face” (A Midsummer Night’s Dream, V, i); (6) synecdoche (e.g. “One hundred hands marched up the hill”; (7) metonymy (e.g. “The White House announced the legalization of marijuana”); (8) simile (e.g. “She was as beautiful as a sunset”, “My love is like a red red rose”). Irony and hyperbole are semantic figures that are less similar to metaphor. There are many other semantic figures and many taxonomies thereof.
The view that metaphors are linguistic manifestations of underlying analogies is not new. Aristotle (1984: 57b1–30) claims that metaphors are derived from analogies. Following Aristotle, Arendt (1971: Vol. 1, p. 103) argues that metaphors are based on analogies. Kintsch (1972: 280) asserts that metaphors are produced and understood using “analogy rules.” Miller (1979: 231) argues that proportional metaphors of the form “X is the Y of Z” are based on analogical comparisons. Carbonell & Minton (1985: 407) assert that analogical reasoning is the “underlying cognitive process” of which metaphors are linguistic manifestations. Indurkhya (1987: 446) assumes that “there is a structural analogy underlying every metaphor.” Kittay (1987:169) posits a metaphorical function that is an analogical mapping function. Lakoff (1987: 276) claims that “Each metaphor has a source domain, a target domain, and a source-to-target mapping.” Gentner, Falkenhainer, and Skorstad (1988) claim that relational metaphors can be analyzed as analogies. Finally, the Oxford English Dictionary defines a metaphor as “The figure of speech in which a name or descriptive term is transferred to some object different from, but analogous to, that to which it is properly applicable.”
Kittay (1987: 292) suggests that conceptual fields in natural languages have a hierarchical organization: subfields are nested inside superfields, with entire lexicon of the language as the largest superfield. For instance: the field of child-birth and the field of philosophy are both subfields of the much larger superfield field of human activity. Depending on context, the concepts [philosopher] and [midwife] are either from the same field (human activity), or from distinct subfields within it. If Kittay is right that conceptual fields are hierarchically nested, then it is likely that the hierarchy of fields has the kind of structure Rosch (1978) posits for other conceptual hierarchies. According to Rosch, concepts occur on three levels: the subordinate levels, the basic level, and superordinate levels. For instance: [cocker-spaniel] is on some subordinate level; [dog] is a basic level concept; [mammal] is on some superordinate level. The basic level is central. I suspect the most intense metaphors occur when concepts from distinct basic level conceptual fields are combined by identification or predication. As fields grow larger and more abstract (as they become superordinate), the identifications and predications become more literal. There is much work to be done in this area. Since that work is for psychology, I don’t pursue it.
It’s important to recognize that the sortal “metaphor” denotes a natural language kind; natural language kinds are vague and naturally permit exceptions; so, for any definition of “metaphor” there will be exceptional and borderline cases. Just as there are whole classes of exceptions in other areas of natural languages (such as the formations of plurals and past tenses in English), so also there are likely to be classes of exceptions to any definition of metaphor. While the definition I gave is defensible, it isn’t like a definition in mathematics or physics. Linguistic definitions like this one may be only stipulative.
Miller (1995) defines metaphor as a statement whose logical form is (x behaves as if it were a y). He gives an example from J. C. Maxwell: “The electromagnetic field behaves as if it were a collection of rubber bands and pulleys”; an early atomic metaphor: “The 1913 Bohr atom behaves as if it were a miniscule quantitized solar system” (p. 206); a later atomic metaphor “The 1923 Bohr atom behaves as if it were comprised of a denumerable infinity of harmonic oscillators each one of which emits continuous radiation with the frequency of a possible atomic transition” (p. 208). Here’s an example I found in a biology article: “the phosphorylated receptors did not necessarily alter the chemistry of the SH2-containing proteins. Instead, many simply induced the SH2 domains to latch onto the phosphate-decorated tyrosines, as if the SH2 domains and the tyrosines were Lego blocks being snapped together.’ (Scott & Pawson, 2000: 74). Statements of logical form are based on analogies. For instance: “The editors of New Scientist treat physicists as if they were priests” expresses the analogy just as superstitious believers treat priests, so the editors of New Scientist treat physicists. See Fauconnier (1996) for a discussion of analogical counterfactuals (I obviously don’t agree with his anti-logical rhetoric).
Counterfactual conditionals have the form “If X were Y, then Z” (e.g. “If I were rich, then I’d buy a farm in Vermont”). Counterfactual conditionals seem to require possible worlds for their interpretations: “If I were a rich man, then I would buy a farm in Vermont” is true if and only if there is some world W such that my counterpart in W is a rich man and my counterpart in W buys a farm in the counterpart of Vermont in W. Tormey (1983) suggests that metaphors are condensed counterfactuals: “Juliet is the sun” means that “If Juliet were a celestial object, then she would be the sun”. I do not agree with Tormey’s theory (for the reasons given by Hintikka & Sandu, 1994: 158); still, I think his work shows that ideas from possible worlds semantics are useful for metaphors.
I heard this on the History Channel’s show on Marco Polo on 18 July 2000.
In terms of classical syntactic analysis, the subscripts “LIT” and “MET”, and those for the fields “S” and “T”, are decorations on the nodes of the parse tree of the utterance.
Consider these sentences: (1) “The boy broke the vase with the hammer” and (2) “The boy broke the vase with the handle”. The preposition “with” marks two distinct roles in sentences (1) and (2); these roles ought to be explicitly distinguished.
Thagard clearly recognizes the need for something like indexes. Thagard (1995: 28) refers to indexes as names of propositions. He gives this example: “chase(Hercules, Fifi) name: chase-1; run(Fifi) name: run-1; cause(chase-1, run-1) name: cause-1”.
Although I’ve equated the relations in R with English thematic role relations, nothing prevents R from containing other relations. It makes good sense to use R to model the relations that are pervasive in a domain. If the universe of discourse is set-theory, then the membership relation ∈ goes into R. Besides thematic role relations, R is likely to include: the identity relation =; part-whole relations; subtype-supertype relations.
Helman (1986) suggests that situations are more natural than conceptual graphs, but they seem to be equivalent. The conceptual graph models of analogy developed by Thagard & Holyoak (1989, 1989b) seem to solve all the problems that Helman raises. Conceptual graphs are certainly easier to visualize than situations.
Mori & Nakagawa (1991) aim to apply situation semantics to metaphor. Unfortunately, their article is not well-informed (“There is no research . . . which refers to the analysis of metaphorical expressions in discourse”, p. 450 — how about Kittay (1987)?; or just look at the many, many references in Steen (1992) that appeared before 1991; and, hey, how about Helman (1986)?). Their formal work appears to involve little more than what one might do with some LISP in a few afternoons. Alas.
While there can be little doubt that reality is filled with objective analogies that hold between relationally indiscernible situations, it is easy to take this idea too far. Emerson’s Nature (1990/1836) takes it to the extreme: “man is an analogist, and studies relations in all objects. He is placed in the centre of beings, and a ray of relation passes from every other being to him” (p. 28); “The world is emblematic. Parts of speech are metaphors, because the whole of nature is a metaphor of the human mind. The laws of moral nature answer to those of matter as face to face in a glass. . . . The axioms of physics translate the laws of ethics. Thus ‘the whole is greater than its part;’ ‘reaction is equal to action;’ the smallest weight may be made to lift the greatest, the difference of weight being compensated by time;’ and many the like propositions, which have an ethical as well as a physical sense” (p. 31); finally, “The law of harmonic sounds reappears in the harmonic colors, the granite is differenced in its laws only by the more or less of heat from the river that wears it away, the river, as it flows, resembles the air that flows over it; the air resembles the light which traverses it with more subtile currents; the light resembles the heat which rides with it through Space” (p. 37). The question Emerson raises in my mind is to wonder just how deeply and extensively nature really is analogically structured.
Propositional graphs or diagrams are like structured meanings (Cresswell, 1985) or like structured propositions (King, 1995, 1996).
Descriptions are known by many names: Schemas (Goodman, 1976); scripts (Schank & Abelson, 1977); the linguistic sides of experiential gestalts (Lakoff & Johnson, 1980); domains (Gentner, 1983); the linguistic sides of mental models (Johnson-Laird, 1983); schema (Rumelhart et al., 1986a); semantic fields (Kittay, 1987); description groups (Falkenhäiner et al., 1989); domains (Holyoak & Thagard, 1989, 1990).
Compressions like [Ql: on(cat, mat)] resemble generic propositions (e.g. “Dogs eat meat”, “Birds fly”). Dahl (1975: 109) and Quine (1992: 26) translate generics into the predicate-calculus using universal quantifiers; the many difficulties with this approach are discussed by Lyons (1977: Vol. 1, pp. 193–197). Generics permit exceptions: “Dogs eat meat” is true even if there are a few vegetarian canines (like my grandmother’s beloved poodle Fifi). Metaphors often involve generics (e.g. “Man is a wolf” and “Light is a wave”). Generic quantification functions in metaphors exactly as in literal language. For more on generics, see Carlson & Pelletier (1995).
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Steinhart, E.C. (2001). Language. In: The Logic of Metaphor. Synthese Library, vol 299. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9654-1_2
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