Gödel is Sure Bach, and Trans People Are Sure Their Gender

Reflections on the Pulitzer-winning ‘Gödel, Escher, Bach’ (1979)

Today I read Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter, which is a math book, and since everything is trans, let me tell you something trans.

The idea here is that formal systems encounter truths they can’t prove. In mathematics, anyway. Hofstadter is explaining Gödel’s incompleteness theorem. The true statement — the one you’re having difficulty proving— remains true in the actual world, but you’d need to go find a different system if you needed to prove it, because this system won’t prove this statement.

I’m not sure how much of this applies outside of mathematics. But here’s how I make it applicable to something I care about.

Trans Men are Men. Trans Women are Women.

Some thoughts about this statement, in light of Gödel, Escher, Bach.

Metaknowledge

How do you know what you know? When someone asks “How many…?”, and you know you can get the answer, either you’ve memorized an answer like “five million” (“declarative” stored knowledge) or you must count (“a procedural method of finding the answer”). How do you know how you know this particular answer? Hofstadter: “You have knowledge about how you classify your own knowledge; and what is more, some of that metaknowledge may itself be stored procedurally, so that it is used without your even being aware of how it is done.” (p. 364) Well, so maybe you don’t know how you know the thing, after all. But you do know the thing.

Recursive Definition

A “recursive definition” defines something “in terms of simpler versions of itself.” (p. 127) For example — my example, of course — if you start with “trans”+[gender], dropping the “trans” makes it a little simpler. That’s how trans men are men, trans women are women works as a definition. (In this case, it’s for people who need the concept of transgender made really, really simple.) So that’s how recursive definition works, as far as I can trans it.

Other statements about gender are often expressed in simple definitional terms, too.

It’s True That Trans People Belong to Their Gender, But How Can I Prove It?

Even a formal mathematical system is unable to prove every truth.

We might not be able to prove that cis people belong to their gender either.

But everyone does belong to their gender, whatever it is. Or doesn’t belong to their gender, whatever it isn’t.

You Need to Interpret The System

Consistency is important. What is consistency, for formal systems? It means that “every theorem, when interpreted, becomes a true statement.” (p. 94, emphasis mine) That is, a system’s consistency isn’t purely inherent. It also depends on how people interpret it. Once someone understands and interprets the system’s theorems to perceive that the theorems are true, they’ll judge the system as being consistent.

How Do You Pick A Way to Interpret Symbols?

To some extent, it’s intuitive. Your interpretation works or doesn’t.

“When you confront a formal system you know nothing of, and if you hope to discover some hidden meaning in it, your problem is how to assign interpretations to its symbols in a meaningful way…When you hit a good choice, a ‘meaningful’ choice, all of a sudden things just feel right, and work speeds up enormously. Pretty soon everything falls into place.” (p. 50)

Statements Can Have More Than One Meaning

“Meaning can exist on two or more different levels of a symbol-handling system.” And so, “rightness and wrongness can exist on all those levels,” too. (p. 575)

Saying that someone is “trans”+gender could mean (a) that they are trans, (b) that they have a gender of “man” or “woman,” (c) that they belong to a separate category apart from “man” and “woman” which is “trans man” or “trans woman.” It could mean any or all of these things simultaneously. It can have different meanings on different levels.

And The Truth May Ultimately Be Undecidable

Again, consistency won’t help you prove a truth, since (Hofstadter paraphrasing Gödel): “All consistent axiomatic formulations of number theory include undecidable propositions.” This Incompleteness Theorem of Gödel’s is proven through “the writing of a self-referential mathematical statement.” (p. 17)

That’s OK

“Gödel says that no sufficiently powerful formal system can be perfect, in the sense of reproducing every single true statement as a theorem,” Hofstadter says. “This fact only seems like a defect if you have unrealistic expectations of what formal systems should be able to do.” (p. 86)

A system is incomplete insofar as “truth transcends theoremhood.” Truth is gonna truth anyway. It’s OK for a truth-explaining system to be incomplete. All that means is that axiomatic reasoning won’t get us to every truth.

More obliquely, Hofstadter wagers that “every undecidable proposition is actually a Gödel sentence, asserting its own nontheoremhood in some system via some code.” (p. 708) The undecidables are OK. OK?

The Trap

When people want to “argue” (*cough cough*) about whether “trans men are men, trans women are women,” often what they’re saying is that they want to set the rules of English and they didn’t give permission for other people to use English differently.

The statement “trans men are men, trans women are women” is often expressed as a rule for understanding gender categories. The anti-trans person resists it. The anti-trans response, taken at face-value, means: Where is your meta-rule that gives you permission to have a trans-inclusive rule?

The problem here (apart from the ego-driven supremacist presumption, which is what’s most glaringly obvious when you don’t take the words at face-value) is that the anti-trans objection is an infinite regress. Insofar as they lay an infinite regress, they lay a trap. We don’t need layers of meta-rules. If we needed rules about rules about rules, none of us could ever use language at all. Hofstadter:

“It begins to seem, then, that one cannot get away from a ‘jukebox’ theory of meaning — the doctrine that no message contains inherent meaning, because, before any message can be understood, it has to be used as the input to some ‘jukebox’, which means that information contained in the ‘jukebox’ must be added to the message before it acquires meaning.

This argument is very similar to the trap which the Tortoise caught Achilles in, in Lewis Carroll’s Dialogue. There, the trap was the idea that before you can use any rule, you have to have a rule which tells you how to use that rule; in other words, there is an infinite hierarchy of levels of rules, which prevents any rule from ever getting used. Here, the trap is the idea that before you can understand any message, you have to have a message which tells you how to understand that message; in other words, there is an infinite hierarchy of levels of messages, which prevents any message from ever getting understood. However, we all know that these paradoxes are invalid, for rules do get used, and messages do get understood. How come?” (p. 170)

Am pretty sure the anti-trans person isn’t saying they need rules about rules about rules or else they can’t use language. They are only making the obstacle course for the trans person. It’s important to see that up front to unmask the trap.

My Qualifications

I have lots of experience dissecting transphobic statements.

I am not a mathematician, but I did read this 800-page book on logic.

Also, I have a gender.

Source

Gödel, Escher, Bach: An Eternal Golden Braid was published in 1979. My page numbers are from the Vintage Books 1980 edition.