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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 [[Saussurean-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]].
===Mathematical Approach===
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}} p.316-18</ref>
