I’ve been off Twitter for a few days and realise I missed out on the great ‘2 + 2 = 5’/’trans women are women’ debate. As someone who has written and talked about both topics, I feel the need to wade in! https://twitter.com/wtgowers/status/1290219053286658048

First, credentials. Here’s me last October questioning whether 2 + 2 = 4, before it was cool:

And here’s me on sex and gender and why it’s important to have a word to pick out the class of female people: https://medium.com/@mary.leng/where-metaphysics-meets-politics-in-gender-critical-feminism-1fe565e2093a

Now let’s put 2 and 2 together. As I say in my talk on 2 + 2 = 4, and as Tim @wtgowers says in his thread, in mathematics there’s a strong sense in which it’s up to us what’s going to count as ‘true’.

If we define ‘2’ ‘+’, ‘=’, and ‘4’ using one set of axioms and definitions, then 2 + 2 = 4 just is true – true in the story where the words have the meanings given in our definitions.

But we could pick a different set of definitions – a different story to tell about ‘2’, ‘+’, ‘4’, ‘=’ - and it could be true in that story that ‘2 + 2 = 5’.

We could do that, but then again as Tim says, given what we want to do with mathematics, we’d probably still be much more interested in the ‘2 + 2 = 4’ story than the ‘2 + 2 = 5’ one.

What matters in picking definitions here is not so much which is ‘really true’, but which one is ‘fit for purpose’. If we’re wanting to count and compare sizes of collections of medium sized dry goods, then ‘2 + 2 = 4’ is what we need.

And our choices matter politically too – if we want to track inequality using statistics, we’d better make sure the maths we’re using is fit for this job.

Similarly, Tim points out, with the definition of ‘woman’. We could define the term in multiple different ways, but what’s really at issue is not so much the metaphysical: “what is a woman, really?”, but the political, ...

... “What is the political import of using the term this way rather than that way, and are there good political reasons to do so?” (Philosopher Sally Haslanger makes the case for this kind of approach here: http://www.mit.edu/~shaslang/papers/WIGRnous.pdf)

And Tim points out that here, unlike with the dummy system where we define 2 + 2 to equal 5, there are some good political reasons for adopting an inclusive definition of women that classes trans women in the category with which they identify.

(Philosopher Katharine Jenkins makes the political case for adoption of an inclusive definition here: https://www.journals.uchicago.edu/doi/abs/10.1086/683535 )

Tim thinks this is an important disanalogy between ‘2 + 2 = 5’ and ‘trans women are women’ – i.e., in order to find a use for definitions on which the former claim comes true we have to involve ourselves in some ridiculous mental contortions, whereas ...

...there’s a perfectly good way of thinking of the term ‘woman’ according to which trans women are women in the same kind of way that adoptive parents are parents.

Given that Tim thinks that there are good reasons for adopting a trans inclusive concept of ‘woman’, he ends his thread here: “it isn't hard to use the word "woman" in that way, and there are good reasons to do so".

However, I think Tim is too quick to drop his analogy. Because suppose we found ourselves regularly in contexts where his ‘break counting’ method, on which a 2 break session plus a 2 break session equals a 5 break session, was useful for us to adopt.

Suppose, that is, that we found that it wasn’t hard for us to use ‘plus’ in that way, and we had good reasons to do so.

Nevertheless, the old concept of addition would still be important to hang on to. When we weren’t involved in break counting and structurally similar contexts, we’d still want to use plain old addition to do the kinds of things it’s useful for.

So we might agree to say “OK, when it’s clear that you’re involved in break counting, it’s fine to use ‘plus’ in your way, but when we’re trying to work out who owes what for dinner, we’ll use the other version, the one on which ‘2 + 2 = 4’.”

In pure mathematics, where we’re used to the same symbols and terms being defined differently in different contexts, this would be an utterly trivial move.

In applications, one word meaning two things might be more complicated, but so long as we’re careful to disambiguate and say which one we are working with, we won’t get into too much trouble.

But suppose two avid break counters went for lunch and were presented with a £50 bill. If on splitting the bill they decided that they each owed 2 x £10, the restaurant would have grounds for complaint if they handed over the cash: "Here you are: 2 x £10 + 2 x £10 = 5 x £10".

Now imagine that not only do the break counters refuse to rectify the error when the server complains. Suppose further that they complain that their server is a bigot for insisting that 2 + 2 = 4, insisting ‘2 + 2 = 5: get over it’?

Mightn’t the restaurant quite reasonably respond, "look, we recognise that your counting method is useful for some purposes, but it’s useless for bill calculation and if we agree to adopt it, we’ll quickly go out of business"?

This, unfortunately, is where we find ourselves with proposals to define ‘woman’ in a way that includes trans women. There may well be some really good reasons for adopting a categorisation that puts trans women in the same category as females who are not trans.

But if we do so, we also need to recognise that the term ‘woman’ has previously been used to pick out female people.

And we need also to recognise that many of what we call women’s rights have been fought for on the basis of the needs of female people. I talk about the examples of women’s sport and all women’s shortlists here: https://medium.com/@mary.leng/harry-potter-and-the-reverse-voltaire-4c7f3a07241

More generally, the point of that piece is that there are good political reasons to retain a term to talk about the class of female people, a class whose members are still subject to particular kinds of discrimination and oppression in a sexist and patriarchal society.

If we agree to adopt a term ‘woman’ according to which ‘trans women are women’, then it should not be automatic, as a result of definition, that trans women belong in women’s sports (for example).

We may reasonably suggest that in this and other contexts, when we use the term ‘women’ we mean ‘female people’, even if we accept that the term can be used with a broader meaning elsewhere.

After all, one word meaning two things can be complicated, but shouldn’t get us into trouble if we’re careful to disambiguate where the need arises.

But women who make this suggestion are met with accusations of bigotry and transphobia. They are regularly on the receiving end of rape threats and worse. They are told "Trans women are women: get over it".

But we can’t get over it. Because we need the words to recognise and respond to the facts of our oppression just as surely as we need to be able to say that 2 + 2 = 4.