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==Symbolic==
In his attempt to theorize the [[category ]] of the [[symbolic]], [[Lacan]] adopts two basic approaches.# The first approach is to describe it in [[terms ]] borrowed from [[linguistics]], using a [[Saussure]]an-inspired [[model ]] of [[language]] as a [[system ]] of [[signifiers]].
# The second approach is to describe it in terms borrowed from [[mathematics]].
The two approaches are complementary, since both are attempts to describe [[formal ]] systems with precise rules, and both demonstrate the [[power ]] of the [[signifier]].
===History===
Although there is a general shift in [[Lacan]]'s [[work ]] from the [[linguistic]] approach which predominates in the 1950s to a [[mathematical]] approach which predominates in the 1970s, there are traces of the [[mathematical]] approach as early as the 1940s. The branches of [[mathematics]] which [[Lacan]] uses most are [[algebra]] and [[topology]], although there are also incursions into set [[theory ]] and [[number ]] theory.<ref>{{E}} pp. 316-18</ref>
==Formalization==
[[Lacan]]'s use of [[mathematics]] represents an attempt to [[formalize]] [[psychoanalytic theory]], in keeping with his view that [[psychoanalytic theory]] should aspire to the [[formalization]] proper to [[science]].
<blockquote>"Mathematical formalization is our [[goal]], our [[ideal]]."<ref>{{S20}} p. 108</ref></blockquote>
[[Mathematics]] serve [[Lacan]] as a paradigm of modern [[scientific]] [[discourse]], which "emerged from the little letters of mathematics."<ref>{{S7}} p. 236</ref>
==Metalanguage==
However, this use of [[mathematics]] is not an attempt to produce a [[metalanguage]], since "no metalanguage can be spoken."<ref> {{E}} p.311</ref>
<blockquote>"The root of the difficulty is that you can only introduce [[symbols]], mathematical or otherwise, by using everyday language, since you have, after all, to explain what you are going to do with [[them]]."<ref>{{S1}} p.2</ref></blockquote>Thus [[Lacan]]'s use of [[mathematics]] is not an attempt to escape from the ambiguity of [[language]], but, on the contrary, to produce a way of [[formalization|formalizing]] [[psychoanalysis]] which produces multiple effects of [[sense ]] without [[being ]] reducible to a univocal [[signification]]. Also, by using [[mathematics]] [[Lacan]] attempts to prevent all attempts at [[imaginary]] [[knowledge|intuitive understanding]] of [[psychoanalysis]].
==See Also==
