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==Two Approaches - Linguistic and Mathematical==In his attempt to theorize the category of the [[symbolic]], [[Lacan]] adopts two basis 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]].{{Top}}mathématiques{{Bottom}}

The two approaches are complementary, since both are attempts to describe formal systems with precise rules, and both demonstrate the power of the [[signifier]]. ===Mathematical ApproachHistory===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}} ppp.316-18</ref>

 <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>

 <blockquote>"The root of the difficulty is that you can only introduce symols[[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]].