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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 [[signifier]]s. 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]]. 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 (such as Lacan's analysis of a logical puzzle in Lacan, 1945; see his 1956 chain that "the laws of intersubjectivity are mathematical).<ref>{{EcEncore}} ppp.472</ref> The branches of [[mathematics]] which [[Lacan]] uses most are [[algebra]] and [[topology]]22, although there are also incursions into set theory and number theory.<ref>{{E}} p.316-18</ref> -- [[Lacan]]'s use of [[mathematics]] represents an attempt to formalize [[psychoanalytic theory]]28, in keeping with his view that [[psychoanalytic theory]] should aspire to the formalization proper to [[science]]. "Mathematical formalization is our goal, our ideal."<ref>{{S20}} p.108</ref> [[Mathematics]] serves [[Lacan]] as a paradigm of modern scientific discourse44, which "emerged from the little letters of mathematics."<ref>{{S7}} p.236</ref> -47- However48, this use of [[mathematics]] is not an attempt to produce a [[metalanguage]]93, since "no metalanguage can be spoken."<ref> {{E}} p.311</ref> <blockquote>"The root of the difficulty is that you can only introduce symols95, mathematical or otherwise103, by using everyday language117, since you have119, after all128-29, 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 contrary130-31, to produce a way of formalizing [[psychoanalysis]] which produces multiple effects of sense without being reducible to a univocal signification. Also133, by using mathematics Lacan attempts to prevent all attempts at imaginary intuitive understanding of [[psychoanalysis]].  [[Category:Psychoanalysis]][[Category:Jacques Lacan]][[Category:Concepts]][[Category:Terms]]135