Algebra

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algebra (algËbre) Algebra is a branch of MATHEMATICS Which reduces the

   solution of problems to manipulations of symbolic expressions. Lacan begins
   to use algebraic symbols in his work in 1955 (see scHEMA L), in an attempt to
   formalise psychoanalysis. Three main        reasons lie behind this attempt at
   formalisation:
      1. Formalisation is necessary for psychoanalysis to acquire scientific status
   (see SCIENCE). Just as Claude LÈvi-Strauss uses quasi-mathematical formulae in
   an attempt to set anthropology on a more scientific footing, Lacan attempts to
   do the same for psychoanalysis.
      2. Formalisation can provide a core of psychoanalytic theory which can be
   transmitted integrally   even to those who have       never experienced psycho-

analytic treatment. The formulae thus become an essential aspect of the

training of psychoanalysts which take their place alongside the training

analysis as a medium for the transmission of psychoanalytic knowledge.

      3. Formalisation of psychoanalytic theory in terms of algebraic symbols is a
   means of preventing intuitive understanding, which Lacan regards               as  an

imaginary lure which hinders access to the symbolic. Rather than being

   understood in an intuitive way, the algebraic symbols are to be used, manipu-
   lated and read in various different ways (see E, 313).
      Most English translations of Lacan also translate the algebraic symbols
   which appear in his work. For example, Alan Sheridan, in his translation of
   Ecrits, renders the symbol A (for Autre) as O (for Other). However, Lacan was
   opposed to such a practice, as Sheridan himself points out (Sheridan, 1977: xi).
   In this dictionary, in line with Lacan's own preference, the algebraic symbols
   are left as they are in the original French texts.
       The algebraic symbols used by Lacan, which appear principally in the
   MATHEMES, SCHEMA L and the GRAPH OF DESIRE, are listed below, together with
   their most common meaning. However, it is important to remember that the
   symbols do not always refer to the same concept throughout Lacan's work, but
   are used in different ways as his work develops. The most important example
   of such a shift in meaning is the use of the symbol a, which is used in radically
   different ways in the 1950s and in the 1960s. However, even other symbols
    which are relatively stable in meaning are occasionally used in very different
    ways; for example, s nearly always designates the signified, but is used in one
   algorithm to denote the subject supposed to know (see Lacan, 1967). Therefore
   some caution should be exercised when referring to the following list of
   equivalences.

A = the big Other

     A         = the barred Other
     a         = (see objet petit a)
     a'         = (see objet petit a)
     S          = 1. (before 1957) the subject
                    2. (from 1957 on) the signifier
                     3. (in the schemas of Sade) the raw subject of pleasure
     S          = the barred subject
     Si         = the master signifier
     S2        = the signifying chain/knowledge
     s          = the signified (in the Saussurean algorithm)
     S(A)    = the signifier of a lack in the Other
     s(A)     = the signification of the Other (the messagelsymptom)
     D         = demand
     d          = desire
     m        = the ego (moi)
     i          = the specular image (schema R)
     i(a)      = 1. the specular image (graph of desire)
                     2. the ideal ego (optical model)
     I          = the ego-ideal (schema R)
     I(A)     = the ego-ideal (graph of desire)
     H         = the real phallus
     <fi        = the symbolic phallus [upper-case phi]
     9          = the imaginary phallus [lower-case phi]
      (-9)     = castration [minus phi]
     S          = the symbolic order (schema R)
     R         = the field of reality (schema R)
     I          = the imaginary order (schema R)
      P        = the symbolic father/Name-of-the-Father
     p          = the imaginary father
      M       = the symbolic mother
      J         = jouissance
      Je        = phallic jouissance
      JA       = the jouissance of the other
      E        = the statement
      e         = the enunciation
      V        = the will to enjoy (volontÈ de jouissance)
  The typographical details and diacritics are extremely important in Lacanian

algebra. The difference between upper- and lower-case symbols, the difference

  between italicised and non-italicised symbols, the use of the apostrophe, the
  minus sign, and subscripts; all these details play their part in the algebraic

system. For example the upper-case letters usually refer to the symbolic order,



whereas the lower-case letters usually refer to the imaginary. The use of the

bar is also important, and varies even within the same formula.