My impression is that gender is a social essence of what men and women are thought to be like in the ideal which emerges from actual conditions in which men and women exist and are set to relate to one another. So although there may be struggles over what a man or woman is constituted by, there only two primary sexes with devistions from the two that the general idea can be materially imbued in and readily made sense of as a legitimate and real identity.
[url]criticaltheorylibrary.blogspot.com/2011/02/slavoj-zizek-key-ideas.html?m=1[/url]
The big Other is then a kind of collective lie to which we all individually subscribe. We all know that the emperor is naked (in the Real) but nonetheless we agree to the deception that he is wearing new clothes (in the Symbolic). When Zizek avers that "the big Other no longer exists" is that in the new postmodern era of reflexivity we no longer believe that the emperor is wearing clothes. We believe the testimony of our eyes (his nakedness in the Real) rather than the words of the big Other (his Symbolic new clothes). Instead of treating this as a case of punctuting hypocrisy, Zizek argues that "we get more than we bargained for - that the very community of which we were a member has disintegrated" (For They Know Not What They Do). There is a demise in "Symbolic efficiency".
Symbolic efficiency refers to the way in which for a fact to become true it is not enough for us just to know it, we need to know that the fact is also known by the big Other too. For Zizek, it is the big Other which confers an identity upon the many decentered personalities of the contemporary subject. The different aspects of my personality do not claim an equal status in the Symbolic - it is only the Self or Selves registered by the big Other which display Symbolic efficiency, which are fully recognized by everyone else and determine my socio-economic position.
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Even with idea of transgender gaining traction it still seems to assume a man or woman binary and the language they ise to describe it suggests being a man or a woman is so essential as to be part of some metaphysical self/soul.
https://www.ethicalpolitics.org/ablunden/pdfs/For%20Ethical%20Politics.pdf#page90
-For Ethical Politics