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[[Algebra]] ([[French]]: ''[[algèbre]]'')
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{{Topp}}algèbre{{Bottom}}
  
 
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[[Algebra]] 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.
 
 
 
[[Formalisation]] can provide a core of [[psychoanalytic theory]].
 
 
 
The [[formulae]] thus become a medium for the transmission of [[psychoanalytic]] [[knowledge]].
 
  
 
==Formalization==
 
==Formalization==
 +
In 1955, [[Lacan]] begins to use [[algebraic]] [[symbol]]s -- in an attempt to [[formalize]] [[psychoanalysis]].
  
[[Jacques Lacan]] begins to use [[algebraic]] [[symbol]]s in 1955 (in an attempt to [[formalise]] [[psychoanalysis]]).
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[[Three]] main reasons lie behind this attempt at [[formalization]].
 
 
[[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.
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:1. [[Formalization]] is necessary for [[psychoanalysis]] to acquire [[scientific]] status.
  
[[Formalisation]] is necessary for [[psychoanalysis]] to acquire [[scientific]] status.
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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]]
  
The [[algebraic]] [[symbol]]s are to be used, manipulated and read in various different ways.<ref>{{E}} p.313</ref>
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:[[Lacan]] used quasi-mathematical formulae in an attempt to set [[psychoanalysis]] on a more [[scientific]] footing.
  
 +
:2. [[Formalization]] can provide a core of [[psychoanalytic theory]] which can be transmitted integrally even to those who have never experienced [[psychoanalytic treatment]].
  
 +
:The [[matheme|formulae]] thus become an essential aspect of the [[training]] of [[psychoanalysis]] which take their [[place]] alongside [[training|training analysis]] as a medium for the transmission of [[psychoanalytic]] [[knowledge]].
  
==Details==
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:3. [[Formalization]] of [[psychoanalytic theory]] in [[terms]] of [[algebraic]] [[symbols]] is a means of preventing [[knowledge|intuitive understanding]], which [[Lacan]] regards as an [[imaginary]] [[lure]] which hinders access to the [[symbolic]].
  
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.  
+
:Rather than [[being]] [[understood]] in an intuitive way, the [[algebraic]] [[symbols]] are to be used, manipulated and read in various different ways.<ref>{{E}} p.313</ref>
  
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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==List==
 +
[[Image:Lacan-algebra.jpg|thumb|right|[[List of algebraic symbols]]]]
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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 [[List of Algebraic Symbols|listed here]], together with their most common [[meaning]].
  
The use of the [[bar]] is also important.
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''[[List of algebraic symbols|Click here]] to view the [[List of Algebraic Symbols]]''
  
 +
==Development==
 +
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.  Therefore some caution should be exercised when referring to the [[list]] of [[equivalences]] above.
  
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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==Details==
 +
The typographic details and diacritics are extremely important in [[Lacan]]ian [[algebra]].
 +
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]].  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.
  
a generalization of arithmetic in which letters representing numbers are combined
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==See Also==
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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{{See}}
 
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* [[Bar]]
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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* [[Formalization]]
 
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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.
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* [[Mathematics]]
 
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* [[Matheme]]
Therefore some caution should be exercised when referring to the following list of equivalences.
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||
 
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* [[Science]]
Even other [[symbol]]s which are relatively stable in [[meaning]] are occasionally used in very different ways.
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* [[Symbol]]
 
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{{Also}}
==Algebra==
 
 
 
{| style="width:75%;" border="1" cellpadding="5" cellspacing="0" align="center"
 
! align="center" | SYMBOL !! align="center" | TRANSLATION
 
|-
 
| align="center" | '''A'''
 
| align="center" | the [[big Other]]
 
|-
 
| align="center" size="x-large" | <strike>'''A'''</strike>
 
| align="center" | the [[bar]]red [[Other]]
 
|-
 
| align="center" | ''a''
 
| align="center" | (see ''[[objet petit a]]
 
|-
 
| align="center" | ''a'''
 
| align="center" | (see ''[[objet petit a]]
 
|-
 
| align="center" | [[Image:BigS.gif]]
 
| align="center" | 1. (before 1957) the [[subject]]<BR>2.(from 1957 on) the [[signifier]]<BR>3. (in the [[matheme|schema]]s of [[Sade]]) the raw [[subject]] of [[pleasure]]
 
|-
 
| align="center" | [[Image:StrikeS.gif]]
 
| align="center" | the [[bar]]red [[subject]]
 
|-
 
| align="center" | [[Image:SS1.gif]]
 
| align="center" | the [[master signifier]]
 
|-
 
| align="center" | [[Image:SS2.gif]]
 
| align="center" | the [[signifying chain]]/[[knowledge]]
 
|-
 
| align="center" | <i>'''s'''</i>
 
| align="center" | the [[signified]] (in the [[Saussure]]an [[sign|algorithm]]
 
|-
 
| align="center" | [[Image:StrikeS(A).gif]]
 
| align="center" | the [[signifier]] of a [[lack]] in the [[Other]]
 
|-
 
| align="center" | [[Image:S(a).gif]]
 
| align="center" | the [[signification]] of the [[Other]] (the [[message]]/[[symptom]])
 
|-
 
| align="center" | '''D'''
 
| align="center" | [[Demand]]
 
|-
 
| align="center" | <i>'''d'''</i>
 
| align="center" | [[Desire]]
 
|-
 
| align="center" | <i>'''m'''</i>
 
| align="center" | the [[ego]] (''[[moi]]'')
 
|-
 
| align="center" | <i>'''i'''</i>
 
| align="center" | the [[specular image]] ([[schema R]])
 
|-
 
| align="center" | <i>'''i(a)'''</i>
 
| align="center" | 1. the [[specular image]] ([[graph of desire]])<BR>2. the [[ideal ego]] ([[optical model]])
 
|-
 
| align="center" | '''I'''
 
| align="center" | the [[ego-ideal]] ([[schema R]])
 
|-
 
| align="center" | '''I(A)'''
 
| align="center" | the [[ego-ideal]] ([[graph of desire]])
 
|-
 
| align="center" | '''Π'''
 
| align="center" | the [[real]] [[phallus]]
 
|-
 
| align="center" | '''Φ'''
 
| align="center" | the [[symbolic]] [[phallus]] [upper-case phi]
 
|-
 
| align="center" | '''(-φ)'''
 
| align="center" | the [[imaginary]] [[phallus]] [lower-case phi]
 
|-
 
| align="center" | <i>'''S'''</i>
 
| align="center" | the [[symbolic]] [[order]] ([[schema R]])
 
|-
 
| align="center" | <i>'''R'''</i>
 
| align="center" | the [[order|field]] of [[reality]] ([[schema R]])
 
|-
 
| align="center" | <i>'''I'''</i>
 
| align="center" | the [[imaginary]] [[order]] ([[schema R]])
 
|-
 
| align="center" | '''P'''
 
| align="center" | the [[symbolic]] [[father]] / [[Name-of-the-Father]]
 
|-
 
| align="center" | <i>'''p'''</i>
 
| align="center" | the [[imaginary]] [[father]]
 
|-
 
| align="center" | '''M'''
 
| align="center" | the [[symbolic]] [[mother]]
 
|-
 
| align="center" | '''J'''
 
| align="center" | ''[[Jouissance]]''
 
|-
 
| align="center" | '''Jφ'''
 
| align="center" | [[phallic]] ''[[jouissance]]''
 
|-
 
| align="center" | '''JA'''
 
| align="center" | the ''[[jouissance]]'' of the [[Other]]
 
|-
 
| align="center" | '''E'''
 
| align="center" | the [[statement]]
 
|-
 
| align="center" | '''e'''
 
| align="center" | the [[enunciation]]
 
|-
 
| align="center" | '''V'''
 
| align="center" | the will-to-enjoy (''volonté de jouissance'')
 
|-|}
 
 
 
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==
 
==References==
 +
<div style="font-size:11px" class="references-small">
 
<references/>
 
<references/>
 +
</div>
  
==See Also==
 
[[Category:Terms]]
 
[[Category:Concepts]]
 
[[Category:Science]]
 
 
[[Category:Psychoanalysis]]
 
[[Category:Psychoanalysis]]
 
[[Category:Jacques Lacan]]
 
[[Category:Jacques Lacan]]
 +
[[Category:Science]]
 +
[[Category:Dictionary]]
 +
[[Category:Concepts]]
 +
[[Category:Terms]]
 +
{{OK}}
 +
 +
__NOTOC__

Latest revision as of 20:25, 23 May 2019

French: algèbre

Algebra is a branch of mathematics which reduces the solution of problems to manipulations of symbolic expressions.

Formalization

In 1955, Lacan begins to use algebraic symbols -- in an attempt to formalize psychoanalysis.

Three main reasons lie behind this attempt at formalization.

1. Formalization is necessary for psychoanalysis to acquire scientific status.
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
Lacan used quasi-mathematical formulae in an attempt to set psychoanalysis on a more scientific footing.
2. Formalization can provide a core of psychoanalytic theory which can be transmitted integrally even to those who have never experienced psychoanalytic treatment.
The formulae thus become an essential aspect of the training of psychoanalysis which take their place alongside training analysis as a medium for the transmission of psychoanalytic knowledge.
3. Formalization 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.[1]

List

The algebraic symbols used by Lacan, which appear principally in the mathemes, schema l and the graph of desire, are listed here, together with their most common meaning.

Click here to view the List of Algebraic Symbols

Development

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

Details

The typographic 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.

See Also

References

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