2.1 the Comparison Theory and the Substitution Theory
Black (1954) summed up Aristotle's theory as comparison theory and Quintilian's as substitution theory. As Aristotle put forward that metaphor involves a similarity or comparison between two objects or more, the comparison theory considers metaphor at a rhetorical level. Thus, Black defines the comparison theory as a presentation of preexisting similarities (Black 1954: 66). The comparison theory thinks that metaphor is the shortened form of simile, just as "A is B" is short for "A is like B". Aristotle implied that metaphor helped human to perceive and understand something new by something else that was named. Although Aristotle talked about metaphor in great detail, he was trapped in a vicious circle by imposing restrictions to the use of metaphor, believing that metaphor should be used in poetry only. Different from the comparison theory, the substitution theory embodies the substitution of a kind of literal expression with a metaphorical one. To be simple, "A is B" is the substitution of "A is C", if B and C have some mutual features. Feng Xiaohu, scholar at home, points out that the comparison theory and the substitution theory have a mutual foundation, thus metaphor is a variant of simile, and the comparison theory is a special situation of the substitution theory (Feng Xiaohu 2004: 7). Both of them view metaphor only as a rhetorical device, rather than a cognitive method.
2.2 the Interaction Theory
In 1930s, Richards initially advanced the interaction theory in his book The Philosophy of Rhetoric, placing metaphor study on an unprecedented cognitive stage. Richards does not think that metaphor is a figure of speech. "Thought is metaphoric, and proceeds by comparison, and the metaphors of language derive there from" (Richards 1936: 94). On this point, metaphor brings similarities between two or more things. The interaction theory studies metaphor from the image angle, and the so called interaction is the combination of the two images whose fruit is the metaphor. This theory breaks a brand-new path for metaphor study. However, Richards did not interpret the process of the interaction theory. This job is done by Black afterwards.
Black inherits and further develops the interaction theory by explaining the process of interaction in large detail in his book More about Metaphor. He indicates that in the process of interaction between two different thoughts metaphor does bring similarity, but without noting that the similarity is a preexisting one.

Due to the interaction theory, metaphors can create new meanings and they are regarded as semantic phenomena (Shu Dingfang 2000: 4). Metaphor is also a process of thinking and a way of understanding other things. So the theory blazes a new trail in metaphor study and lays the first stone for the later cognitive theory.

2.3 The Conceptual Metaphor Theory
On the basis of the interaction theory proposed by Richards and further developed by Black, Lakoff and Johnson have conducted some fruitful explorations by proposing the conceptual metaphor theory in their collaborated book Metaphors We Live By in 1980. They regard metaphor not as a rhetorical device but as a cognitive tool. "Metaphor is pervasive in everyday life, not just in language but in thought and action. Our ordinary conceptual system, in terms of which we both think and act, is fundamentally metaphorical in nature" (Lakoff ﹠Johnson 1980: 3). Due to what Lakoff and Johnson suggested, metaphor roots in the way of our thinking and action, or we perceive and experience the world in a metaphorical way.

2.3.1 Definition of Conceptual Metaphor
There are a large amount of concepts in our thoughts and they affect the way we perceive the world greatly. Among these concepts, some are concrete that we directly experience from the outside world and others are abstract such as time, happiness, love, friendship and so on. In order to understand those abstract notions, we resort to the concrete ones which depends on human experience of the world, which is called "experimentalist synthesis" by Lakoff and Johnson (Lakoff ﹠Johnson 1980: 192). Lakoff interpreted metaphor as follows: Metaphor is fundamentally conceptual, not linguistic in nature. Metaphorical language is a surface manifestation of conceptual metaphor. Metaphor allows us to understand a relatively abstract or inherently unstructured subject matter in terms of a more concrete, or at least a more highly structured subject matter (Lakoff, 1993). Thus conceptual metaphor is not simply the metaphor in literary expressions or in daily ordinary language but a kind of abstract conceptual system, which roots deeply in human thoughts and actions without being aware of. In conceptual metaphor, there are three basic elements called target domain, source domain and mapping, respectively matching with abstract concepts, concrete concepts and connections between them. In short, conceptual metaphor is a kind of partial mapping between target domain or abstract concepts and source domain or concrete notions. 美剧《复仇》的语篇分析(3):http://www.751com.cn/yingyu/lunwen_9177.html