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Matheme
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The '''[[matheme]]''' is a concept introduced in the work of the [[20th century]] [[France|French]] [[psychoanalyst]] [[Jacques Lacan]]. They are [[formula]]e, designed as [[symbol]]ic [[representation]]s of his [[idea]]s and [[analysis|analyses]]. They were intended to introduce some degree of technical rigour in [[philosophical ]] and [[psychological ]] writing, replacing the often hard-to-understand verbal descriptions with formulae resembling those used in the [[hard science]]s, and as an easy way to hold, remember, and rehearse some of the core ideas of both [[Sigmund Freud|Freud]] and [[Lacan]]. "[[Matheme]]", for [[Lacan]], was not simply the imitation of [[science]] by [[philosophy]], but the ideal of a perfect means for the integral transmission of [[knowledge]]. [[Natural]] [[language]], with its constant "metonymic slide", fails here, where [[mathematics]] succeeds. Contemporary philosopher [[Alain Badiou]] identifies "[[matheme]]" with the scientific procedure.
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In Greek, <i>mathêma</i> means "that which is taught." Following the same path that led [[Freud ]] to the discovery of slips [[slip]]s and jokes[[joke]]s, [[Lacan ]] forged connections between the fields of spoken discourse and logical inscription. In 1955, he introduced what could be called his first [[matheme]], schema L.</p><p>The main Lacanian mathemes [[Lacan]]ian [[matheme]]s in order of their appearance are:</p><ol><li><i>Schema L</i> (1955), which identifies four points in the signifying chain: first, the unconscious, or the discourse of the Other (A), and then the subject (S), which in turn...</li> The term '[[matheme]]'' is a neologism coined by [[Jacques Lacan]] in the early 1950s.
Formed by derivation from '[[mathematics]]' and by analogy with [[phoneme]] and Levi-Strauss's [[mytheme]], the term is an equivalent to ''mathematical sign'.
[[Lacan ]] begins to use a variety of graphs and 'schemata' at any early stage in is work.
In 1955, he introduced what could be called his first [[matheme]], [[schema L]], illustrating the [[imaginary]] function of the [[ego]].
Originally used as teaching aids, these range from teh relatively simple 'schema l' illustrating the [[imaginary ]] function of the [[ego]] in the 1955 paper on [[psychosis]] to the complx complex chart of the workings of [[desire]].
In [[Greek]], ''mathêma'' means "that which is taught."
The main Lacanian mathemes in order of their appearance are:
# [[Schema L]] (1955), which identifies four points in the signifying chain: first, the [[unconscious]], or the [[discourse ]] of the [[Other ]] (A), and then the [[subject ]] (S), which in turn results from the relation between the [[ego ]] (a) to the [[other ]] (a) to the other (d). # The [[formula]] of the [[signifier]] (1957), S/s, links the [[law]]s of the [[unconscious]] discovered by [[Freud]] to the [[law]]s of [[language]] ([[metaphor]] and [[metonymy]]).
Perhaps the most familiar is the 'algorithm' which in 1957 replaces [[Saussure]]'s simple diagram of the [[sign]] / arbor with the notation S/s.
This is to be understood as demonstrating that the [[signifier]] is above the [[signified]], and that the two are separated by a [[bar]] that resists [[signification]] and forces the [[signifier]] to slide endlessly. # The "[[big graph]]" (1957) represented two different stages of the [[signifying chain]]. [[Lacan ]] situated [[jouissance]], [[castration]], the [[signifier]], and the [[voice ]] at the various points of intersection on this graph. # The [[four discourses]] (1969) were used to link the discourses of the [[master]], the [[university]], the [[hysteric]], and the [[analyst]]. Four terms—S1, the [[master signifier]]; S2, [[knowledge]]; /S, the [[subject]]; and a, [[surplus enjoyment—turn enjoyment]]—turn in a circular motion to take up four successive positions defined by the [[discourse ]] of the [[master]]: the [[agent]], the [[other]], the production of the discourse, and [[truth]]. # The [[formulas of sexuation]] (1972) present [[sexual difference ]] as a logical inscription. Using the signs ∃x, Φx, and ∀x outside of the field of [[mathematics ]] where they originated, [[Lacan ]] inscribed a [[masculine ]] [[psychical ]] [[structure ]] on one side and a [[feminine ]] [[psychical ]] [[structure]] on the other. The graphs and schemata gradually become more complex, and are eventually replaced by an '[[algebra]]' of 'little letters' or [[matheme]]s. The function of the [[formalization]] that results in the emergence of the [[matheme]] is said by [[Lacan]] to be the integral tranmission of his teachings on [[psychoanalysis]]. The [[Lacanian]] [[matheme]] is characterized by being both open and asymmetrical. It does not tend towards closing discourse, and in spite of its character as a [[statement]], it is primarily an [[enunciation]]. And there lies the paradoxical aspect of the enterprise—to found a [[science]] of the [[subject]]. Even though [[Lacan]] finally concluded that there can be no transmission of [[psychoanalysis]], he always situated [[psychoanalysis]] within [[knowledge]]: access to the [[unconscious]] is legible and transmissible. [[Matheme]]s advance and illustrate the theses that in relation to [[speech]] and writing, another [[structure ]] besides that of grammar or syntax organizes [[speech]], namely the [[structure]] of the [[signifier]]. The [[Lacan]]ian [[matheme]] proceeds neither by faith nor by pure [[mathematics]]. [[Lacan]] situates [[religion]] on the side of making [[real]], or "realizing," the [[symbolic]] of the [[imaginary]], or RSI. On the otherhand, [[Lacan]] defined [[mathematics]] as imagining the [[real]] of the [[symbolic]], or IRS. If such were the case with the [[matheme]], then it could become a model of the [[real]].
==See Also==