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Algebra

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algebra [[Algebra]] (algËbre''algèbre'') Algebra is a branch of MATHEMATICS Which [[mathematics]] which reduces thesolution 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:
solution of problems 1. Formalisation is necessary for psychoanalysis to manipulations of symbolic expressionsacquire scientific status (see [[science]]). Just as [[Claude Lévi-Strauss]] uses quasi-mathematical formulae in an attempt to set anthropology on a more scientific footing, Lacan beginsattempts to do the same for psychoanalysis.
2. Formalisation can provide a core of psychoanalytic theory which can be transmitted integrally even to use algebraic symbols in his work in 1955 (see scHEMA L), in those who have never experienced psychoanalytic treatment. The formulae thus become an attempt toessential aspect of the training of psychoanalysts which take their place alongside the training analysis as a medium for the transmission of psychoanalytic knowledge.
formalise psychoanalysis3. Three main reasons lie behind this attempt atFormalisation 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, manipulated and read in various different ways.<ref>see E, 313</ref>
formalisationMost 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.<ref>Sheridan, 1977:xi</ref>In this dictionary, in line with Lacan's own preference, the algebraic symbols are left as they are in the original French texts.
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 Others
(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)
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.
==References==
<references/>
==See Also==
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.[[Category:Terms]][[Category:Concepts]][[Category:Science]][[Category:Psychoanalysis]][[Category:Jacques Lacan]]
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