Metaphor in game-theoretical semantics

Game theory is the study of strategic decision-making through mathematical models founded by John von Neumann (1944), and it is mainly utilized in the field of economics. Despite its formal roots, game theory has been applied to all facets of decision-making, which includes deriving metaphorical meaning out of language. Ohkura (2003: 1-2) presents a game-theoretical template, based on Richards’ (1936: 125) notion of metaphorical tension, as a substitute for such Tarskian truth-conditional semantics as proposed by Davidson, which interpret metaphor as a zero-sum game with only a literal meaning. First, the interactive tension between a metaphor’s tenor and vehicle—the literal and the metaphorical component—is extended to cover the interaction between the metaphorical and the literal meaning of the whole metaphor (Richards 1936: 96-7; Ohkura 2003: 6). This is a very logical extension of the interaction theory. Similar to the previous analysis of metaphor theories, Ohkura (2003: 3-4) acknowledges that metaphors cannot be paraphrased without corrupting their unique meaning, and that a metaphor’s structure is not dependent on similarity—which actually is the source of a metaphor’s tension. It is also acknowledged that a successful metaphor can create new and vivid meanings (op.cit.). These theoretical assumptions act as the basis for the game-theoretical model.

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Traditional models of game-theoretical semantics are constructed as a zero-sum game between a verifier and a falsifier; the former tries to assert that a sentence is true and the latter does the opposite (Ohkura 2003: 5). The winner of this zero-sum game is declared when the truth value of the sentence is determined. This truth value is determined by the literal meaning which acts as the strategic equilibrium of the game. Ohkura (2003: 5) modifies this approach by adopting Lewis’ (1969) definition of a coordination problem game with at least two equilibria. The players of this game coordinate their strategies so that a desired outcome is achieved. This model is applied to metaphor semantics, so that the two equilibria are the literal and the metaphorical meanings of a metaphor, and determining the desired meaning is the coordination problem (Ohkura 2003: 6). Figure 3.1 illustrates this game-theoretical template for a metaphor.

Figure 3.1. Metaphor presented as a coordination problem between its meanings.

The virtue of this approach is that it does not assume that the metaphorical meaning is automatically inferior to the literal as Davidson (1979) asserts. The presence of the two equilibria justifies the claim that a metaphor builds tension between the metaphorical and the literal (Ohkura 2003: 6). Richards (1936: 118) himself suggests that the presence of multiple meanings plays a part in arriving at the right meaning. In addition, this game-theoretical

Coordination Equilibrium A:

Literal meaning

Coordination Equilibrium B:

Metaphorical meaning

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approach supports the conceptual notion that indirect, metaphorical understanding uses the resources of the direct, literal understanding (Lakoff and Johnson 1980: 117). Theoretically, if needed, this template could also be modified to include more than two meanings as equilibria.

Importantly, Ohkura (2003: 6) states that this polysemous quality of a metaphor in itself does not determine which equilibrium—the metaphorical or the literal meaning—is the correct one.

The winning equilibrium is based on convention, context, and domain of use, which fits the points of emphasis of the previously analyzed theories about metaphor structure and meaning.

In a sense, the semantic stalemate between equilibria requires a pragmatic solution. A conventional, i.e. frequent equilibrium can be equated with Richards’ (1936: 11) notion about the persistence of a specific meaning which is ascribed to a metaphor. Thus, Ohkura’s game-theoretical model for a metaphor only expresses the state of a metaphor’s meanings—a coordination problem—but does not specify which meaning is understood.

The first hypothesis of this study states that, in regard to scientific metaphors, the equilibrium of the metaphorical meaning prevails, because, based on reality, a false truth value can be assigned to the literal meaning—which would be unintuitive in academic writing. This is supported by the notion that the falsehood of the literal meaning provides a capacity for metaphorical truth, i.e. it directs the focus to the metaphorical aspect (Davies 1984: 292, 295).

Thus, context-based metaphorical truth is compatible with the literally false statement. Because it has been determined that a paraphrase cannot express an accurate metaphorical truth, the metaphorical meaning can only be attained indirectly through the literal falsehood. This negotiation between the metaphorical truth and the literal falsehood can be elegantly articulated as “the very brink of a misunderstanding” (White 1996: 51). If we can arrive at the metaphorical equilibrium based on the above process, the existence of metaphorical meaning is justified.

Interestingly, if the hypothesis is proven to be accurate, Davidson’ claim about the patent falsehoods of the metaphors’ literal meanings becomes vital for attaining the metaphorical

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meaning. The contrast between a true and a false literal meaning of a metaphor is evident in the following examples.

(13) No man is an island.

(14) Large-star explosions overwhelm those from their smaller and rarer brethren.

The literal meaning of example (13) is true—no male representative of the human species is an isolated piece of land surrounded by a large body of water—while in example (14) it is false—

large-star explosions do not have siblings with whom they share biological parents.

In addition, it has been argued that in science metaphorical meanings have a logical priority over the literal ones, because every traditional principle and definition of space, time, matter, and causality has been violated as modern physics—and science in general—has advanced (Hesse 1993: 50-1, 54). The literal occurs as a limiting case, and the aforementioned instability of a word’s meanings makes it possible to portray the multifaceted and ever-developing nature of reality through language (op.cit.). This is by no means a new sentiment: “ordinary words convey only what we know already; it is from metaphor that we can best get a hold of something fresh” (Aristotle 1410b). Many interpret the semantic instability as leading to an endless circular loop between rivaling meanings, but the game-theoretical template shows that the meanings actually settle into an equilibrium based on context, convention, and domain of use (Richards 1936: 39; Hesse 1993: 57, 64; Ohkura 2003: 6). Thus, the instability of a meaning is not without rules.