On the hierarchy of the Objet Petit 'a
Speaking of the "fall" of the a, Lacan noted that 'the diversity of forms taken by that object of the fall ought to be related to the manner in which the desire of the Other is apprehended by the subject.' The earliest form is 'something that is called the breast...this breast in its function as object, object a cause of desire.'The term "phallus" designates the representation of an erect penis, which plays a key role both intra- and inter-subjectively. Freud barely distinguished between the fantasized phallus and the anatomical penis. He called the period between three and five years of age the "phallic stage." At this stage, infants of both sexes are dominated by the question of who possesses a penis and the related issue of its masturbatory jouissance (gratification), which is clitoral in the case of girls. Up to this point, the mother is imagined as having a penis, and the discovery that she lacks a penis, after an initial denial, precipitates the castration complex.
Next there emerges 'the second form: the anal object. We know it by way of the phenomenology of the gift, the present offered in anxiety.' The third form appears 'at the level of the genital act...[where] Freudian teaching, and the tradition that has maintained it, situates for us the gaping chasm of castration.'
Lacan also identified 'the function of petit a at the level of the scopophilic drive. Its essence is realized in so far as, more than elsewhere, the subject is captive of the function of desire.' The final term relates to 'the petit a source of the superego...the fifth term of the function of petit a, through which will be revealed the gamut of the object in its - pregenital - relation to the demand of the - post-genital - Other.'
Jacques Lacan chose to use the term "phallus" for the imaginary and symbolic representation of the penis in order to better distinguish the role of the penis in the fantasy life of both sexes from its anatomical role. Freud's famous "symbolic equation" of breast, feces, penis, and baby (1916-1917a [1915-1917], 1918b, 1924d) already implied this distinction between the real penis and its phallic representations.
According to Lacan, the phallus at the outset represents what else the mother desires is in addition to the baby. Thus, a pre-oedipal triangle of mother, phallus, and infant arises. At first the infant tries to be the phallus for the mother until the moment of a crucial transformation when the child, after identifying the phallus as a static image of completeness and sufficiency, sees it as representing the mother's desire, and thus her lack. From then on, the phallus takes the form of something missing (-') within any imaginary, and hence libidinal, frame of reference. Thus the phallus comes to signify desire, Lacan says.