How rules break down, and how to use them anyway.

2013-01-28 13:20

The world does not lend itself to simple, absolute rules. Mathematicians have known this for a long time; politicians have never really accepted it. Unfortunately, the mathematicians are right. Perhaps more unfortunately, the politicians are in charge.

On tumblr, the many “social justice warriors” (a pejorative term; it denotes people who are more strident than they are concerned with justice) are fond of promoting rules which are emotionally appealing and sound good in simple cases, but which cannot possibly be applied consistently. When I say “cannot possibly”, I don’t mean “they could if people were smarter or tried harder”, but rather “these rules are logically self-contradictory”. If you apply these rules consistently, you end up with questions for which you must accept two mutually-exclusive results.

One such rule is that the oppressor can never decide what is oppressive. For instance, men can’t be the ones to decide what’s sexist, or white people to decide what’s racist, or straight people to decide what’s hostile to gays. As a basic principle? Definitely reasonable. People who don’t experience a thing tend to evaluate it poorly at best, they tend to lack information, and the natural biases the brain has towards not feeling guilty heavily favor concluding that People Like Us are not at fault. Sounds like a good rule, easy for everyone to agree on, right?

Well, let me point out to you a term: “trans-exclusionary radical feminist” (TERF). It’s exactly what it sounds like; feminists who do not consider MTF transsexuals to be women. They often actively campaign against recognition of the gender of transwomen, participation of transwomen in women’s rights monements, and so on. So, how does the rule apply? Interestingly, a lot of people see the answer as so completely obvious that the question is stupid, and refuse to answer it, accusing people of trying to “derail” by asking dumb questions. This becomes a difficulty, because there are two different completely obvious answers:

  1. Allowing men to declare themselves women and expect respect for their beliefs about reproductive rights, sexism, and related topics allows men to undermine feminists. People who are not born biologically female must not be allowed to influence feminist organizations or their goals.
  2. Failure to recognize gender identity is oppressive and destructive. Excluding women from participation based on accidents of birth affirms a bigoted view of gender and identity, and harms everyone.

In each case, we have a group that is pretty widely regarded as subject to oppression and/or marginalization, and we have a person that might reasonably be considered not a member of that group telling them that what they’re complaining about isn’t really oppression. When part of the identified oppression of a particular group is an assertion about which categories they go in, a rule that imposes behavioral restrictions by category is going to have problems. And since at least some trans-exclusionary feminists are lesbians, you can’t take advantage of broader categories like “LGBT” to disambiguate.

The problems are not restricted to disputes over group membership. I recently saw someone arguing that no white person ever has the right to accuse a black artist of selling out. What about accusing a black artist of writing homophobic lyrics? The rapper DMX has a fairly strong reputation for anti-gay lyrics. Can a gay white guy complain about that? Again, the rule fails us; it’s obvious that if it’s a problem for white guys to bash black musicians, complaining about lyrics is probably going to be an issue. But should a straight guy be allowed to tell gay guys they can’t complain about his anti-gay stuff?

A while back, one music reviewer reviewed a new Chris Brown album. His review: “Chris Brown hits women. Enough said.” Does it matter whether the reviewer was white? Female? Did he (assuming the name “Chad” suggests a male reviewer) only do that because of hidden racism, and he would never have said such a thing about a white performer, or is it valid commentary?

The problem here is not that the rule needs fine-tuning. It’s that no simple rule can handle the situations. The fancy term is “intersectionality” — there are multiple categories of “privilege” and oppression, and people can be in one oppressed group while simultaneously being part of the oppression of another group. What that means is that any rule which relies on knowing which of two people should be called “the oppressor” cannot succeed.

The world does not admit simple answers, and it does not admit absolute rules. You can make it useful by replacing the term “absolute rule” with “general principle”. Instead of “it is never the place of the oppressor to dictate what is or isn’t oppression”, try “the opinions of people not subject to a particular form of oppression about that oppression should be taken with a grain of salt, and subjected to a bit of extra scrutiny.”

This eliminates all the unresolvable conflicts. There are cases where this principle doesn’t give you a definite answer. That, to many people, is a fatal flaw. But the rule that gave us those lovely and calming definite answers, which we didn’t have to think about? It gave us lovely, calming, definite answers which were provably wrong — because it could give us two answers which contradicted each other.

The quest for certainty has always been with us. In religious discussions, I regularly encounter people who believe that their church has absolute authority, or that their holy text’s translation was made perfect by God, because if they didn’t have that belief, they couldn’t be certain of anything. There are a lot of people who believe this, and they often disagree on their conclusions, so we know that at the very least a majority of them are wrong about their certainty.

The social justice warriors are not improving on this; replacing holy texts or institutions with respected authors or accepted dogmas does not change the underlying error of clinging to certainty. Clinging to certainty prevents correction of errors; it also requires ignoring contradictions rather than trying to resolve them.

There is a solution. Accept that you have limits, and that you don’t even always know them. Accept that the reason that absolute adherence to simple dogmas has failed us every time is not that we had picked the wrong dogmas, but that the world is not amenable to being fully described by simple rules. When applying rules, remember that the purpose of rules for behavior is to help us behave better; if you have to choose between being basically decent to people, and following a rule to the letter, try being decent to people. The rule doesn’t have feelings.

Peter Seebach




  1. Since I pretty much agree with your fundamental point, allow me to pick nits and derail a bit. When you say that “mathematicians have known” it “a long time” that “the world does not lend itself to simple, absolute rules”, just what it is you have in mind? Several possible readings come to mind, but none seem really apposite.

    — Aatu Koskensilta · 2013-02-03 17:15 · #

  2. Goedel’s Incompleteness theorems. We have proven that you can take a very, very, simple set of rules, which are very well understood, and you can establish that:

    1. You cannot determine whether the set of rules is consistent.
    2. There will be things which are true under these rules, but which cannot be proven using these rules.

    Of course, when it comes to non-mathematical rules, you nearly always also end up with:
    3. There are outright contradictions.

    If you add premises when you can’t answer the questions you need answered, you’ll end up with contradictions. If you don’t, you won’t end up with answers at all.

    seebs · 2013-02-03 17:26 · #

  3. I was afraid you’d say that. People find in the incompleteness theorems all sorts of intriguing implications, analogies, metaphors, metaphysical epiphanies. But it’s a good idea to be a bit more precise when discussing and thinking about these matters.

    The first incompleteness theorem states that for any formal theory T in which Robinson arithmetic is interpretable — that is, in any theory where we can define “natural number”, “multiplication”, “addition”, “0”, “1”, and so on, and prove basic computational facts of the arithmetic of natural numbers — we can find a formal sentence G(T) such that G(T) is unprovable in T, but true when interpreted as an arithmetical assertion, provided T is consistent. The sentence G(T) is equivalent to the consistency of the theory T, provably in T when T satisfies certain slightly more stringent conditions — essentially, when we can prove in T enough instances of the induction scheme to carry out proofs by induction on lengths of proofs. For concreteness, we can (by the MRDP theorem) take G(T) to have the form “the Diophantine equation D(x1, …, xn) = 0 has no solutions” for a specific equation D(x1, …, xn) = 0, depending on (the axiomatization of) T.

    So much for technical precision. What are we to make of this? The first salient observation is that your first point is simply incorrect as stated. For many sets of rules we can easily determine if they’re consistent or not, by mathematical proof. We can prove that Frege’s system is inconsistent, first-order Peano arithmetic is consistent, first-order Peano arithmetic together with the assertion that first-order Peano arithmetic is inconsistent is consistent, Martin-Löf’s constructive type theory with a self-including universe is inconsistent, and so on and so forth, in the sense that we can give a compelling piece of mathematical reasoning establishing these conclusions, exactly as legitimate and convincing as any piece of mathematical reasoning at a similar level of abstraction. (Naturally, the consistency proofs can’t be formalized in the theories they prove the consistency of.) As for your second point, we find in mathematical logic no notion of “true under these or those rules”. Rather, sentences are true or false when their non-logical symbols are interpreted in some way, in a model. In case of the incompleteness theorem, we have that for any consistent extension of Robinson arithmetic — either literally, or through interpretation — there is a Diophantine equation D(x1, …, xn) = 0 that has on solutions but for which the formalization of “D(x1, …, xn) = 0 has no solutions” is not derivable.

    The required Gödel policing out of the way, it remains for me merely to suggest in most cases it’s a good idea to simply leave Gödel out of it altogether. Most invocations of Gödel — such as, I posit, we find in your post — are merely pointless (and often confused) mysticism mongering, serving no actual argumentative or illustrative purpose. The excellent text Gödel’s Theorem — an Incomplete Guide to its Use and Abuse by the sadly late Torkel Franzén is very much recommended to anyone wishing to wax poetical about these matters.

    But as I said, this is nit picking and pointless pedantry. Your actual point stands and is well taken.

    — Aatu Koskensilta · 2013-02-04 05:35 · #

  4. Nah, it’s actually pretty good pedantry.

    seebs · 2013-02-04 20:23 · #