Difference between revisions of "Algebra"

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[[Algebra]] ([[French]]: ''[[algèbre]]'')
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[[Algebra]] ([[French]]: ''[[algèbre]]'') is a branch of [[mathematics]] which reduces the solution of problems to manipulations of [[symbolic]] expressions.  
 
[[Algebra]] ([[French]]: ''[[algèbre]]'') is a branch of [[mathematics]] which reduces the solution of problems to manipulations of [[symbolic]] expressions.  
  
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[[Lacan]] begins to use [[algebraic]] [[symbol]]s in his work in 1955 (see [[schema L]]), in an attempt to [[formalise]] [[psychoanalysis]].  
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[[Formalisation]] can provide a core of [[psychoanalytic theory]].
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The [[formulae]] thus become a medium for the transmission of [[psychoanalytic]] [[knowledge]].
  
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Three main reasons lie behind this attempt at [[formalisation]]:
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==Formalization==
  
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1. [[Formalisation]] is necessary for [[psychoanalysis]] to acquire [[scientific]] status.  
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[[Jacques Lacan]] begins to use [[algebraic]] [[symbol]]s in 1955 (in an attempt to [[formalise]] [[psychoanalysis]]).
  
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Just as [[Claude Lévi-Strauss]] uses quasi-mathematical formulae in an attempt to set [[anthropology]] on a more [[scientific]] footing, [[Lacan]] attempts to do the same for [[psychoanalysis]].
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[[Jacques Lacan]] attempted to [[formalize]] [[psychoanalytic theory]] in terms of [[algebraic]] [[symbols]].
  
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2. [[Formalisation]] can provide a core of [[psychoanalytic theory]] which can be transmitted integrally even to those who have never experienced [[psychoanalytic]] [[treatment]].  
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[[Lacan]] used quasi-mathematical formulae in an attempt to set [[psychoanalysis]] on a more [[scientific]] footing.
  
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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]].
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[[Formalisation]] is necessary for [[psychoanalysis]] to acquire [[scientific]] status.  
  
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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]].  
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The [[algebraic]] [[symbol]]s are to be used, manipulated and read in various different ways.<ref>{{E}} p.313</ref>
  
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Rather than being understood in an intuitive way, the [[algebraic]] [[symbol]]s are to be used, manipulated and read in various different ways.<ref>{{E}} p.313</ref>
 
  
  
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Most English translations of [[Lacan]] also translate the [[algebraic]] [[symbol]]s which appear in his work.
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==Details==
  
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For example, [[Alan Sheridan]], in his translation of [[Ecrits]], renders the [[symbol]] A (for [[Autre]]) as O (for [[Other]]).  
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The difference between upper- and lower-case [[symbol]]s, the difference between italicised and non-italicised [[symbol]]s, the use of the apostrophe, the minus [[sign]], and subscripts.  
  
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However, [[Lacan]] was opposed to such a [[practice]], as [[Sheridan]] himself points out.<ref>Sheridan, 1977: xi</ref>
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For example the upper-case letters usually refer to the [[symbolic]] [[order]], whereas the lower-case letters usually refer to the [[imaginary]].  
  
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In this dictionary, in line with [[Lacan]]'s own preference, the [[algebraic]] [[symbol]]s are left as they are in the original [[French]] texts.
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The use of the [[bar]] is also important.
  
  
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The [[algebraic]] [[symbol]]s used by [[Lacan]], which appear principally in the [[matheme]]s, [[schema l]] and the [[graph of desire]], are listed below, together with their most common [[meaning]].  
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His use of [[algebraic]] formulations is in fact unconnected to [[mathematics]] itself, but merely provides a concise way of expressing complex [[psychoanalytic]] [[concepts]].  
  
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However, it is important to remember that the [[symbol]]s do not always refer to the same concept throughout [[Lacan]]'s work, but are used in different ways as his work develops.  
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a generalization of arithmetic in which letters representing numbers are combined
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a branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
  
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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.  
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The [[algebraic]] [[symbol]]s used by [[Lacan]], which appear principally in the [[matheme]]s, [[schema l]] and the [[graph of desire]], are listed below, together with their most common [[meaning]].  
  
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However, even other [[symbol]]s 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]].<ref>Lacan, 1967</ref>
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The [[symbol]]s do not always refer to the same concept throughout [[Lacan]]'s work, but are used in different ways as his work develops.  
  
 
Therefore some caution should be exercised when referring to the following list of equivalences.
 
Therefore some caution should be exercised when referring to the following list of equivalences.
  
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Even other [[symbol]]s which are relatively stable in [[meaning]] are occasionally used in very different ways.
  
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==Algebra==
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<blockquote>
 
A = the big Other
 
A = the big Other
  
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H = the real phallus
 
H = the real phallus
  
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<fi = the symbolic phallus [upper-case phi]
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<? = the symbolic phallus [upper-case phi]
  
 
9 = the imaginary phallus [lower-case phi]
 
9 = the imaginary phallus [lower-case phi]
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V = the will to enjoy (volontÈ de jouissance)
 
V = the will to enjoy (volontÈ de jouissance)
  
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The typographical details and diacritics are extremely important in Lacanian algebra.
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</blockquote>
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The difference between upper- and lower-case [[symbol]]s, the difference between italicised and non-italicised [[symbol]]s, the use of the apostrophe, the minus [[sign]], and subscripts; all these details play their part in the [[algebraic]] system.
 
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For example the upper-case letters usually refer to the [[symbolic]] [[order]], whereas the lower-case letters usually refer to the [[imaginary]].
 
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The use of the [[bar]] is also important, and varies even within the same formula.
 
  
 
==References==
 
==References==
 
<references/>
 
<references/>
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==See Also==
 
==See Also==
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[[Category:Terms]]
 
[[Category:Terms]]
 
[[Category:Concepts]]
 
[[Category:Concepts]]

Revision as of 10:13, 29 June 2006


Algebra (French: algèbre)


Algebra (French: algèbre) is a branch of mathematics which reduces the solution of problems to manipulations of symbolic expressions.

Formalisation can provide a core of psychoanalytic theory.

The formulae thus become a medium for the transmission of psychoanalytic knowledge.

Formalization

Jacques Lacan begins to use algebraic symbols in 1955 (in an attempt to formalise psychoanalysis).

Jacques Lacan attempted to formalize psychoanalytic theory in terms of algebraic symbols.

Lacan used quasi-mathematical formulae in an attempt to set psychoanalysis on a more scientific footing.

Formalisation is necessary for psychoanalysis to acquire scientific status.

The algebraic symbols are to be used, manipulated and read in various different ways.[1]


Details

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.

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.


His use of algebraic formulations is in fact unconnected to mathematics itself, but merely provides a concise way of expressing complex psychoanalytic concepts.

a generalization of arithmetic in which letters representing numbers are combined a branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.

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.

The symbols do not always refer to the same concept throughout Lacan's work, but are used in different ways as his work develops.

Therefore some caution should be exercised when referring to the following list of equivalences.

Even other symbols which are relatively stable in meaning are occasionally used in very different ways.

Algebra

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

S1 = 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

<? = 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)

References

  1. ↑ Lacan, Jacques. Écrits: A Selection. Trans. Alan Sheridan. London: Tavistock Publications, 1977. p.313

See Also

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