# 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
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```   to use algebraic symbols in his work in 1955 (see scHEMA L), in an attempt to
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```   formalise psychoanalysis. Three main        reasons lie behind this attempt at
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```   formalisation:
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```      1. Formalisation is necessary for psychoanalysis to acquire scientific status
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```   (see SCIENCE). Just as Claude LÈvi-Strauss uses quasi-mathematical formulae in
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```   an attempt to set anthropology on a more scientific footing, Lacan attempts to
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```   do the same for psychoanalysis.
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```      2. Formalisation can provide a core of psychoanalytic theory which can be
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```   transmitted integrally   even to those who have       never experienced psycho-
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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
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```   means of preventing intuitive understanding, which Lacan regards               as  an
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```   understood in an intuitive way, the algebraic symbols are to be used, manipu-
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```   lated and read in various different ways (see E, 313).
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```      Most English translations of Lacan also translate the algebraic symbols
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```   which appear in his work. For example, Alan Sheridan, in his translation of
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```   Ecrits, renders the symbol A (for Autre) as O (for Other). However, Lacan was
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```   opposed to such a practice, as Sheridan himself points out (Sheridan, 1977: xi).
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```   In this dictionary, in line with Lacan's own preference, the algebraic symbols
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```   are left as they are in the original French texts.
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```       The algebraic symbols used by Lacan, which appear principally in the
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```   MATHEMES, SCHEMA L and the GRAPH OF DESIRE, are listed below, together with
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```   their most common meaning. However, it is important to remember that the
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```   symbols do not always refer to the same concept throughout Lacan's work, but
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```   are used in different ways as his work develops. The most important example
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```   of such a shift in meaning is the use of the symbol a, which is used in radically
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```   different ways in the 1950s and in the 1960s. However, even other symbols
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```    which are relatively stable in meaning are occasionally used in very different
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```    ways; for example, s nearly always designates the signified, but is used in one
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```   algorithm to denote the subject supposed to know (see Lacan, 1967). Therefore
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```   some caution should be exercised when referring to the following list of
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```   equivalences.
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A = the big Other

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

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