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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.
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