The Queer Psychoanalysis Society

The Logic of Sex: Heteronormativity, Gender, and the Law of the Excluded Middle

In Gender Studies, LGBT, Philosophy, Politics, The End of Heterosexuality? on March 3, 2014 at 2:18 pm

The first in our on-going series of articles on “The End of Heterosexuality?”


by Joe Weinberg

It has long been thought that there are two and only two genders: male and female. While some (such as Butler in Gender Trouble) have argued that there is actually only one gender (Male being the norm, and female, as not-male, being the only gender) and used as a basis for justifying patriarchal mistreatment,[1]  it seems more accurate to say that there are more than ‘just’ two genders. That heteronormative binary is not only inaccurate, but actively hurtful to large groups of people, those who fall ‘between’ or ‘outside’ that binary.

Once we accept that there is more to the world of gender than male and female, certain questions arise. Do we look at gender as a spectrum? How many genders are there? And where does sex come into the picture? The simple answers are “No,” “I don’t know,” and “Everywhere.” For more nuanced and complex answers, we have to take a step back and define a few terms.

First, heteronormative binary. The heteronormative binary is a very fancy way of saying “two genders.” Basically, it’s referring to the idea that there are only two genders (male and female) and that being one means NOT being the other. Similarly, it refers to the idea that sexuality is pure, either homo or hetero. I don’t like binaries; there is more to being a woman than NOT being a man, and vice versa. I also think it is possible to have aspects of both without being ‘in transition’ from one to the other. And, it’s possible to be neither one, and be perfectly satisfied with that. Similarly, even if we throw in bisexuality to the homo/hetero split, I STILL think there’s more. That’s a matter of simple logic.

Speaking of logic, there are two other principles I need to get out of the way: The Law of the Excluded Middle (LotEM) and the Sorites paradox. The LotEM basically just says that there are other more than two options, and that sometimes the decision that seems to be between two things is actually between more than two things. For some nicely inflammatory examples, abortion isn’t a matter of Pro Choice or Pro Life; someone can be opposed to abortion in all cases EXCEPT incest or rape, or can be in favor of the right to choose while choosing for themselves not to have an abortion. There’s more than just black and white. The LotEM basically reminds us that there are shades of gray.

Sorites is a bit more complex. That’s the question of when something becomes a pile. Sorites himself used millet seeds, but I prefer the image going bald. If I lose one hair, I’m not bald. If I lose all my hair, I’m bald. But one hair isn’t going to make a difference one way or the other, right? But at the same time, if I take my hair away one at a time, sooner or later I cross into the bald category. That means that there is a point where one hair DOES make a difference. So a single hair both does and doesn’t matter. That’s why it’s a paradox.

Okay. Back to the spectrum of gender. If we see gender as a spectrum with male on one side and female on the other, we run into a Sorites paradox. Look:

Screen Shot 2014-07-17 at 10.16.34 AM

Somewhere along that line, a person goes from being female to being male. At some point, a single quality changes the gender. While there is a fluid space in between, a space where someone could be ‘partly male’ or ‘mostly female,’ even then their gender identity is directly linked to that same binary. Riki Wilchins writes that “when you look closer, every spectrum turns out to be anchored by the same familiar two poles – male/female, man/woman, gay/straight. The rest of us are just strung out between them, like damp clothes drying on the line. The spectrum of gender turns out to be a spectrum of heterosexual norms, only slightly less oppressive but not less binary than its predecessors” (30-31). A spectrum really just is a binary. It’s just a binary that looks at the places between. But not as places in themselves so much as portions of one or the other side of the binary. So we have that paradox.

What’s the solution? How can we have transgenderism if we really have only two genders? Well, now we go back to the LotEM. It’s a really simple answer, when you think about it. The way to not have a binary is, simply, to have more than two options. But those other options can’t be a mixture of the first two; it can’t be a spectrum. It needs to be something else. Gender is more than a spectrum. It’s bigger than that. There is androgyny, there are genders that are more than male or female, more than male and female. They can’t be on a spectrum, and having a spectrum between three points is not only hard to draw, it’s hard to conceptualize. Also, no matter how many points we put on whatever shape we decide to make for gender (a gender triangle? Maybe a rhombus?), there may very well be others that are excluded. Some might suggest a ‘galaxy’ of genders, where any gender has the same value as any other. But I think that goes back to the LotEM. Gender isn’t either a shape or a galaxy. It’s not that solid. Not that cemented.

Gender is a performance. Lots of people (Butler, Paasonen, Kogan, West and Zimmerman, etc.) have pointed that one out. Gender is fluid, and it doesn’t necessarily have a singular point where anyone finally settles down.

So how do we throw sex into the mix? The best option would probably be to remind everyone that it doesn’t matter what prefix they put on ‘-sexual’; but seeing as that is unlikely to happen, and is a bit of a lazy way out of the problem, let’s turn back to logic. Gender is fluid and performed. But at any given time, it’s in a single place.[2] So determining sexuality is just a matter of determining preferred sexual partners. In the world of the heteronormative binary, there are three possible sexualities: hetero-, homo-, and bi-. That’s just a matter of logic. But logic changes a lot when we start adding in genders.

Most of us understand logic as being a binary system (bivalent, as the philosophers say): something is either True or it is False. So a truth table with two variables (p and q) has only four possible lines:

Screen Shot 2014-02-28 at 3.20.15 PM

The LotEM tells us that there’s more than two options, so we have to go beyond bivalence. And what is beyond bivalence? Well, you could have something be neither true nor false; it could be both true AND false. Or it could partially true or partially false. Moving into regular language, it’s not hard to see. But it IS hard to represent in a truth table.

Take something as simple as negation (~p or ‘not p’). In bivalent logic, there are only two lines. If p is true, ~p is false. If p is false, ~p is true. Simple. But when we have four possibilities, there are many more possibilities. We have to decide if ~p means “p is false” or “p is not true” or “p is completely false” or “p is not entirely true” or “p is neither true nor false” or “p isn’t completely true or completely false” etc.

Coming back to sexuality, then, we see a similar explosion. If we add a third gender (let’s call it xemale, and define it as having aspects of BOTH male and female), then sexuality expands quite a bit:

  1. MM/FF: homosexuality
  2. MF/FM: Heterosexuality
  3. MX: ?
  4. FX: ?
  5. XX: ?

That’s without even considering people spanning multiple categories. And if we add a Neuter gender (neither male nor female), it gets even bigger:

  1. MM/FF: homosexuality
  2. MF/FM: heterosexuality
  3. MX
  4. FX
  5. XX
  6. MN
  7. FN
  8. XN
  9. NN

With four different genders, we have nine different couplings. And that’s not counting threesomes, foursomes, or other fun weekend activities. A fifth gender puts us up to fifteen. Six puts us to twenty-one. Seven to twenty-eight. Not quite exponential, but the increase in possibilities gets bigger every time we add a gender; by the time we have ten genders, we have almost sixty different pairing possibilities.

Does this destroy heterosexuality? No. But it certainly puts it in perspective, doesn’t it? How important a place does heterosexuality have when there are five, or ten, or fifty-six other possibilities? Getting back to the idea of gender being fluid, how can we classify ourselves as heterosexual, knowing that our partners may or may not continue to be the gender they currently identify as at any given moment?

Defining gender in any specific way, and defining sexuality in a specific way, seems doomed to failure. Or, at best, confusion. Once we accept that there are more than two genders, heterosexuality either becomes less significant or goes away altogether. Both options are good.

Though there’s probably a third option, too, if the LotEM has anything to say about it.

Works Cited:    

Butler, Judith. “Performative Acts and Gender Constitution: An Essay in Phenomenology and Feminist Theory.” Theatre Journal. Vol 40. No 4 (Dec 1998).

Butler, Judith. Gender Trouble: Feminism and the Subversion of Identity. Routledge. First published 1990. reprinted 2008.

Ely, Robin and Irene Padavic. “A Feminist Analysis of Organizational Research on Sex Differences.” Academy of Management Review. Vol 32, No 4: 2007.

Kogan, Terry S. “Transsexuals and Critical Gender Theory: The Possibility of a Restroom Labeled ‘Other’.” Hastings Law Journal. Volume 48 (1996-1997).

Paasonen, Susanna. “Chapter 6: Binary Code, Binary Gender.. And Things Beyond.” from Figures of Fantasy: Internet, Women, & Cyberdiscourse. Peter Lang, New York: 2005.

West, Candace and Don H. Zimmerman. “Doing Gender.” Gender and Society. Vol. 1, No. 2: June 1987.

Wilchins, Riki. “It’s your gender, stupid!” GenderQueer: Voices from Beyond the Sexual Binary. Nestle, Joan, Clare Howell, Riki Wilchins, Eds. Alyson Books, Los Angeles: 2002.

End Notes:

[1]“Establishing difference (obvious, for example, in such coinage as the ‘opposite’ sex) is essential for the accomplishment of inequality because it provides the ideological foundation for unequal treatment” (Ely and Padovic, 1128).

[2] Now we’re getting into Zeno’s paradoxes, saying that if something is unmoving at any given time, it is unmoving at all given times, and therefore it isn’t moving at all. But let’s not think too hard about that one, okay?


About the Author:

Joe Weinberg recently finished his PhD in Rhetoric and Scientific & Technical Communication, writing about identity formation in online communities. He continues to research, think, and write while lecturing at the University of Minnesota Crookston. Self-identified as a cisgendered heterosexual queer, he can be reached at

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