Difference between revisions of "Algebra"

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{{Top}}algèbre{{Bottom}}
 
{{Top}}algèbre{{Bottom}}
  
 +
==Mathematics==
 +
[[Algebra]] is a branch of [[mathematics]] which reduces the solution of problems to manipulations of [[symbolic]] expressions.
  
 +
==Jacques Lacan==
 +
In 1955, [[Lacan]] begins to use [[algebraic]] [[symbol]]s -- in an attempt to [[formalize]] [[psychoanalysis]].
 +
 +
''[[Formalization|Click here]] to read about the [[Formalization|Formalization of Psychoanalysis]]''
  
 +
==List of Algebraic Symbols==
 
[[Image:Lacan-algebra.jpg|thumb|right|[[List of algebraic symbols]]]]
 
[[Image:Lacan-algebra.jpg|thumb|right|[[List of algebraic symbols]]]]
 +
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]].
  
[[Algebra]] is a branch of [[mathematics]]
+
''[[List of algebraic symbols|Click here]] to view the [[List of Algebraic Symbols]]''
* which reduces the solution of problems to manipulations of [[symbolic]] expressions, and
 
* concerned with the properties and relationships of abstract entities represented in symbolic form.
 
 
 
In 1955, [[Lacan]] begins to use [[algebraic]] [[symbol]]s -- in an attempt to [[formalize]] [[psychoanalysis]].
 
 
 
''[[Formalization|Click here]] to read about the [[Formalization|Formalization of Psychoanalysis]]''
 
<BR>
 
==[[List of Algebraic Symbols]]==
 
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]].
 
<BR><BR>
 
{| style="width:75%;" border="1" cellpadding="5" cellspacing="0" align="center"
 
! align="center" | ALGEBRAIC SYMBOL !! align="center" | COMMON MEANING
 
|-
 
| align="center" | '''A'''
 
| align="center" | the [[big Other]]
 
|-
 
| align="center" size="x-large" | <strike>'''A'''</strike>
 
| align="center" | the [[bar]]red [[Other]]
 
|-
 
| align="center" | <i>'''a'''</i>
 
| align="center" | (see ''[[objet petit a]]
 
|-
 
| align="center" | <i>'''a''''</i>
 
| 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'')
 
|-
 
|}
 
<BR><BR>
 
  
 
==Development of the Symbols==
 
==Development of the Symbols==
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==See Also==
 
==See Also==
 
{{See}}
 
{{See}}
 +
* [[Bar]]
 
* [[Formalization]]
 
* [[Formalization]]
 +
||
 
* [[Mathematics]]
 
* [[Mathematics]]
 
* [[Matheme]]
 
* [[Matheme]]
 +
||
 
* [[Science]]
 
* [[Science]]
 +
* [[Symbol]]
 
{{Also}}
 
{{Also}}
  

Revision as of 02:29, 24 August 2006

French: algèbre

Mathematics

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

Jacques Lacan

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

Click here to read about the Formalization of Psychoanalysis

List of Algebraic Symbols

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 of the Symbols

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.

Typographic 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