I got the point that genders aren't 1:1 with sex. Anyhow, you need sex to define a gender, in terms of logics. If you say , by example, transgender, you need to say that a transgender is someone which is not aligned with biological sex. In terms of logic, this is a proposition which requires biological sex to exist. The most common definition of "transgender" is "Transgender also an umbrella term: in addition to including people whose gender identity is the opposite of their assigned sex (trans men and trans women), it may include people who are not exclusively masculine or feminine" . But, to make this sentence consistent, you always need to define an "assigned sex" (at least two). Then , you are right when you say that gender and sex may differ. But still, gender is an assertion about sex, so that, if you have 4,000 sexes, you may have an unbelievable number of ways to be transgender . You have the number of possible choices of two into 4000, only if "transgender" means somebody between TWO assigned sex. If you assume that a transgender could be something in between 3 assigned sex, with 4000 possible sex, you are entering very, very big numbers.