Difference between revisions of "Algebra"

From No Subject - Encyclopedia of Psychoanalysis
Jump to: navigation, search
Line 1: Line 1:
[[Image:Lacan-algebra.jpg|thumb|right]]
 
  
[[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]] [[symbol]]s 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]] [[symbol]]s are to be used, manipulated and read in various different ways.<ref>{{E}} p.313</ref>
 
 
 
 
==Details==
 
 
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.
 
 
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]] [[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]].
 
 
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.
 
 
Even other [[symbol]]s which are relatively stable in [[meaning]] are occasionally used in very different ways.
 
 
==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'')
 
|-
 
|}
 
 
==References==
 
<references/>
 
 
==See Also==
 
[[Category:Terms]]
 
[[Category:Concepts]]
 
[[Category:Science]]
 
[[Category:Psychoanalysis]]
 
[[Category:Jacques Lacan]]
 

Revision as of 19:37, 7 August 2006