Difference between revisions of "Algebra"

From No Subject - Encyclopedia of Psychoanalysis
Jump to: navigation, search
 
(The LinkTitles extension automatically added links to existing pages (https://github.com/bovender/LinkTitles).)
 
(58 intermediate revisions by one other user not shown)
Line 1: Line 1:
algebra (algËbre)                  Algebra is a branch of MATHEMATICS Which reduces the
+
{{Topp}}algèbre{{Bottom}}
  
    solution of problems to manipulations of symbolic expressions. Lacan begins
+
[[Algebra]] is a branch of [[mathematics]] which reduces the solution of problems to manipulations of [[symbolic]] expressions.
  
    to use algebraic symbols in his work in 1955 (see scHEMA L), in an attempt to
+
==Formalization==
 +
In 1955, [[Lacan]] begins to use [[algebraic]] [[symbol]]s -- in an attempt to [[formalize]] [[psychoanalysis]].
  
    formalise psychoanalysis. Three main       reasons lie behind this attempt at
+
[[Three]] main reasons lie behind this attempt at [[formalization]].
  
    formalisation:
+
:1. [[Formalization]] is necessary for [[psychoanalysis]] to acquire [[scientific]] status.
  
      1. Formalisation 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]]
  
    (see SCIENCE). Just as Claude LÈvi-Strauss uses quasi-mathematical formulae in
+
:[[Lacan]] used quasi-mathematical formulae in an attempt to set [[psychoanalysis]] on a more [[scientific]] footing.
  
    an attempt to set anthropology on a more scientific footing, Lacan attempts to
+
:2. [[Formalization]] can provide a core of [[psychoanalytic theory]] which can be transmitted integrally even to those who have never experienced [[psychoanalytic treatment]].
  
    do the same for psychoanalysis.
+
: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]].
  
      2. Formalisation can provide a core of psychoanalytic theory which can be
+
: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]].
  
    transmitted integrally  even to those who have      never experienced psycho-
+
: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>
  
analytic treatment. The formulae thus become            an essential aspect of the
+
==List==
 +
[[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]].
  
training of psychoanalysts which take their place alongside the training
+
''[[List of algebraic symbols|Click here]] to view the [[List of Algebraic Symbols]]''
  
analysis as a medium for the transmission of psychoanalytic knowledge.
+
==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.
  
      3. Formalisation of psychoanalytic theory in terms of algebraic symbols is a
+
==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.
  
    means of preventing intuitive understanding, which Lacan regards              as  an
+
==See Also==
 +
{{See}}
 +
* [[Bar]]
 +
* [[Formalization]]
 +
||
 +
* [[Mathematics]]
 +
* [[Matheme]]
 +
||
 +
* [[Science]]
 +
* [[Symbol]]
 +
{{Also}}
  
imaginary lure which hinders            access to the symbolic. Rather than being
+
==References==
 +
<div style="font-size:11px" class="references-small">
 +
<references/>
 +
</div>
  
    understood in an intuitive way, the algebraic symbols are to be used, manipu-
+
[[Category:Psychoanalysis]]
 +
[[Category:Jacques Lacan]]
 +
[[Category:Science]]
 +
[[Category:Dictionary]]
 +
[[Category:Concepts]]
 +
[[Category:Terms]]
 +
{{OK}}
  
    lated and read in various different ways (see E, 313).
+
__NOTOC__
 
 
      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 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.
 

Latest revision as of 01:25, 24 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