Like students of comparative religion, the Structuralists take their main inspiration from linguistic research; but the source of their inspiration and the goal of their inquiry differ from those of the comparatists. Comparative linguistics accounts for differences among the world's languages by positing their descent from a common ancestor. Originally it was felt that this linguistic ancestor might be a more transparent medium of communication than the various, mutually incomprehensible languages descended from it. That is to say, it was hoped that the relationship between the sounds of the original language and the things to which these sounds referred might be intuitively obvious. With the reconstruction of Proto- Indo-European this proved not to be the case. As a result, the Swiss linguist Ferdinand de Saussure developed a new theory of language positing that meaning resides not in the actual sounds that are common to all languages, but in the relationships between those sounds, relationships that take on different meanings in each language. For example, the sounds represented by the letters p-a-i-n are similar in English and French, but have very different meanings ("pain" and "bread", respectively). And the English homonyms "pain" and "pane" also possess different meanings, which are attached to the sound of the words only by convention, not by any intrinsic relationship. When this idea is applied to the study of myth, the hypothesis becomes one in which meaning is not found in any specific motif, such as the incest motif in the Oedipus myth, but rather in the relationship between the various motifs that make up the myth--as, for example, in the relationship between the motif of killing the father and solving the riddle of the Sphinx.
The question therefore becomes one of how to analyze properly the structural relationship that is thought to exist among the various motifs contained within a single myth. Levi-Strauss makes several key points, some of them explicit, others implicit:
| Overrating of blood relations | Underrating of blood relations | Slaying monsters | Difficulty walking and standing upright |
| Cadmus seeks his sister Eurpoa, ravished by Zeus | Cadmus kills the dragon | ||
| The Spartoi kill one another | |||
| Labdacus (Laius' father) = lame (?) | |||
| Laius (Oedipus' father) = left-sided (?) | |||
| Oedipus marries his mother, Jocasta | Oedipus kills his father, Laius | Oedipus kills the Sphinx | Oedipus = swollen-foot (?) |
| Eteocles kills his brother, Polynices | |||
| Antigone buries her brother, Polynices, despite prohibition |
Levi-Strauss analyzes the myth first by looking for recurring motifs, such as the motif of killing. But rather than identify killing per se as a meaningful category, he breaks it down further into the two recurring types of killing found in the story: killing a close relative, and killing a monster. This involves a basic procedure of structuralist analysis, which works by identifying pairs of opposites that are taken as defining an area of significance. In this myth, charcters kill only those who are very much like themselves (blood relations) or those who are entirely different from themselves (monsters). Therefore, part of the myth's meaning presumably has to do with this dichotomy.
Note that this dicotomy is not the only or even the most important one that Levi-Strauss identifies. In fact, he places the category of "killing a close relative" in opposition to a class of acts that involve extreme love for a close relative (Cadmus' pursuit of his sister, Europa; Oedipus' marriage to his mother, Jocasta; Antigone's burial of her brother, Polynices). The opposition Levi-Strauss sees between these categories has nothing to do with killing or with incest per se, but rather with the more abstract motifs that he labels "overvaluing" or "undervaluing blood relations". Similarly, killing monsters, a feat of heroic prowess, stands in opposition to some sort of debility (lameness, vel. sim.). For Levi-Strauss, this opposition involves contradictory positions on the question of whether humans are born from the earth: killing earth-born monsters would be a denial, acknowledgement of debility an admission of this origin.
In sum, then, Levi-Strauss reads the myth as being not at all about killing or incest, but about a contrast between the belief that human beings were originally born from the earth, which is the area of concern marked out by the two right-hand columns (and a major element of the Theban cycle), and the knowledge that they are born now of a sexual union between man and woman, the major concern of the two left-hand columns. The point is not so much that the myth solves a problem as that it outlines a problem or a set of problems and provides, in Levi-Strauss' words, "a kind of logical tool which relates the original problem -- born from one or born from two? -- to the derivative problem: born from different or born from the same? By a correlation of this type, the overrating of blood relations is to the underrating of blood relations as the attempt to escape autochthony is to the impossibility to succeed in it. Although experience contradicts theory, social life validates cosmology by its similarity of structure. Hence cosmology is true" (p. 216).