Exceptions Matter

rare exceptions to your theory are still exceptions to your theory

Biologist Richard Dawkins recently posted this thread on Twitter/X arguing that the existence of intersex people is not a counterexample to the view that biological sex is a binary because intersex people are extremely rare.

Obviously this generated all sorts of discourse about intersex people and trans people that I’m not going to get into here. Instead my focus is on the form of Dawkins’ argument:

1. There are exceptions to a set of particular claims (The existence of intersex people as exceptions to the claims that sex is binary and all people are either male or female)

2. These exceptions are incredibly rare (Excluding those with Klinefelter syndrome and Turner syndrome, intersex people make up around 0.018% of the population)¹

3. Incredibly rare exceptions should be discounted when evaluating sets of particular claims

4. Therefore, the set of particular claims remains true (Sex is binary)

This is an infuriatingly common form of reasoning, often summed up by the phrase ‘the exception that proves the rule’. The thought is that the rarity of the exception means that we should discount it. The existence of a rare exception supposedly illustrates how often the ‘rule’ gets it right. I suppose when Dutch explorers saw black swans for the first time in Australia, they must have declared “That settles it! Now we know for sure that all swans are white.”

When we’re speaking generally, this kind of reasoning isn’t too crazy. We’re not always trying to provide a serious theory or being ultra rigorous and in such instances we tend to use generic generalisations like “Chickens lay eggs”. Most philosophers of language, and most people in general, think that I can truthfully utter “Chickens lay eggs” even though it’s not the case that all chickens lay eggs. We can even say “Birds lay eggs” when we know that male birds don’t lay eggs. Everyone has a decent idea of what we mean and it would be pedantic to reply “But not all birds lay eggs!”

It would be false, however, to say that all chickens or all birds lay eggs. If I have a theory of chickens that says all chickens lay eggs, then my theory has already been disproven by the existence of non egg-laying chickens. That’d still be the case in a world where 99.99% of chickens laid eggs. I can’t just say that those chickens are exceptions and that means they don’t count as genuine counterexamples. That’s obviously bullshit. If you’re proposing a genuine explanatory theory, then you can’t just dismiss exceptions.

Sometimes people like to respond by saying that all concepts and means of classification have exceptions. To demand otherwise is to demand perfect science from an imperfect world. Cambridge Dictionary defines a chair as ‘a seat for one person that has a back, usually four legs, and sometimes two arms’, yet we know that this excludes some chairs and includes some things that obviously aren’t chairs. Nonetheless, this does not threaten our concept of chair.

A chair and a not-chair

But Cambridge Dictionary isn’t trying to give us a theory of chairs. If you complained to the lexicographers then they’d tell you that you don’t understand what dictionary definitions are supposed to do. They’re giving us a useful description of what ‘chair’ often means. They’re not telling us that this description applies to all chairs and excludes everything that isn’t a chair. Whereas Dawkins really is saying that “Sex really is binary. You’re either male or female, and it’s absolutely clear you can do it on gamete size.”

And there are obviously concepts and means of classification that don’t have exceptions, like “All positrons have the same mass and spin as electrons but they have positive charge” or “The mass of an electron is 9.1093837 × 10⁻³¹ kg.” It’s true that we do run into a lot more “All Xs are Ys, except when they’re not” claims in biology, but those claims need to be appreciated for what they are. They serve an important purpose but they are not exhaustive theories. “All Xs are Ys, except when they’re not” does not imply “All Xs are Ys”.

All this is to say that you can discount exceptions, but only if you’re speaking generally or you have some clear and transparent reason for doing so.² It’s fine to come up with a useful rule or heuristic and admit that, while there are exceptions, it’s just simpler or easier to ignore them in this case. It’s not fine to come up with a theory of something and then, when someone brings up an exception, to say that the exception somehow doesn’t count because it’s rare. “Sex is binary except for the rare exceptions, so it’s not a very successful theory of biological sex” is more honest and compelling than “Sex is binary and there are exceptions to this theory but they’re really rare so they don’t count because I said so”.

Addendum: For what it’s worth, there is a way one could claim that biological sex is binary but not all human beings are either male or female. Paul E. Griffiths argues that “the biological definition of sex is not based on an essential quality that every organism is born with, but on two distinct strategies that organisms use to propagate their genes.” Unfortunately for Dawkins, an explicitly minimalist and domain-specific approach like this one won’t allow him to have his cake and eat it too.

1. The claim seems to originate from this commentary paper authored by Leonard Sax, though it doesn’t seem to be popular in the medical literature or among intersex rights activists.

2. Occasionally there are social/pragmatic reasons to avoid generalising or using generalisations to inform our behaviour regarding other people. You’re obviously up to something if you walk around saying “People are either male or female” like you’re innocently uttering a generic.