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Objet (petit) a
This term has sometimes been translated into English as "object (little) a", but Lacan insisted that it should remain untranslated, "thus acquiring, as it were, the status of an algebraic sign."<ref>Sheridan, Alan. "Translator's note." Lacan, Jacques. Écrits: A Selection. Trans. Alan Sheridan. London: Tavistock Publications, 1977. p.vii-xii</ref>
The symbol a (the first letter of the word autre, or "other") is one of the first algebraic signs which appears in Lacan's work, and is first introduced in 1955 in connection with schema L. It is always lower case and italicized to show that it denotes the little other, in opposition to the capital 'A' of the big Other. Unlike the big Other, which represents a radical and irreducible alterity, the little other is "the other which isn't another at all, since it is essentially coupled with the ego, in a relationship which is always reflexive, interchangeable."<ref>Lacan, Jacques. The Seminar. Book II. The Ego in Freud's Theory and in the Technique of Psychoanalysis, 1954-55. Trans. Sylvana Tomaselli. New York: Nortion; Cambridge: Cambridge Unviersity Press, 1988. p. 321</ref> In schema L, then, a and a' designate indiscriminately the ego and the counterpart/specular image, and clearly belong to the imaginary order.
Object of Desire
In 1957, when Lacan introduces the matheme of fantasy ($ <> a), a begins to be conceived as the object of desire. This is the imaginary part-object, an element which is imagined as separable from the rest of the body. Lacan now begins to distinguish between a, the object of desire, and the specular image, which he now symbolizes i(a).
In the seminar of 1960-1, Lacan articulates the objet petit a with the term agalma (a Greek term meaning glory, an ornament, an offering ot the gods, or a little statue of a god) which he extracts from Plato's Symposium. Just as the agalma is a precious object hidden inside a relatively worthless box, so the objet petit a is the object of desire which we seek in the other.<ref>Lacan, Jacques. Le Séminaire. Livre VIII. Le transfert, 1960-61. Ed. Jacques-Alain Miller. Paris: Seuil, 1991. p. 177</ref>
Object-Cause of Desire
From 1963 onwards, a comes increasingly to acquire connotations of the real, although it never loses its imaginary status; in 1973 Lacan can still say that it is imaginary.<ref>Lacan, Jacques. Le Séminaire. Livre XX. Encore, 1972-73. Ed. Jacques-Alain Miller. Paris: Seuil, 1975. p. 77</ref> From this point on, a denotes the object which can never be attained, which is really the cause of desire rather than that towards which desire tends; this is why Lacan now calls it the "object-cause" of desire.
Object of Drive
Objet petit a is any object which sets desire in motion, especially the partial objects which define the drives. The drives do not seek to attain the objet petit a, but rather circle round it.<ref>Lacan, Jacques. The Seminar. Book XI. The Four Fundamental Concepts of Psychoanalysis, 1964. Trans. Alan Sheridan. London: Hogarth Press and Institute of Psycho-Analysis, 1977. p. 179</ref>
Object of Anxiety, Libido
Position of the Analyst
In the seminars of 1962-3 and of 1964, objet petit a is defined as the leftover, the remainder (Fr. reste), the remnant left behind by the introduction of the symbolic in the real. This is developed further in the seminar of 1969-70, in which Lacan elaborates his formulae of the four discourses. In the discourse of the master, one signifier attempts to represent the subject for all other signifiers, but inevitably a surplus is always produced; this surplus is objet petit a, a surplus meaning, and a surplus enjoyment (Fr. plus-de-jouir). This concept is inspired by Marx's concept of surplus value; a is the excess of jouissance which has no "use value" but persists for the mere sake of enjoyment.
In 1973, Lacan links objet petit a to the concept of semblance, asserting that 'a' is a "semblance of being."<ref>Lacan, Jacques. Le Séminaire. Livre XX. Encore, 1972-73. Ed. Jacques-Alain Miller. Paris: Seuil, 1975. p.87</ref>