There is a principle in systems of formal logic called the principle of explosion. Without getting all technical what it says is that if you introduce into your logic two contradictory statements, which are both assumed to be true, then you can use them to prove that any other statement is also true (or false, if your preference takes you that way).

While the principle of explosion has a fancy name, and a formal proof, and even italics, it’s basically saying something that anybody older than, say, 10 could work out; that if you assume something false is true then all of your logic from there on in is fucked into a tin hat (10 year-olds may not say it exactly like that, depends where they’re from, I guess).

Which brings us to 2019’s most controversial axiom, “Trans-women are women”

As a slogan it has a lot going for it. It sounds a lot like it means, “Trans-women should be treated as women” or “Trans-women have the same rights as women” or “It would be incredibly rude to point out that trans-women aren’t women”.

But it doesn’t mean any of those those defensible and rational points. It means, literally, that trans-women are women.

You can go onto social media and see people arguing that this is the case. There are hundreds of blogs you can read stating it as fact. It is already accepted as such in some of the mainstream media. More and more organisations are accepting it as an article of faith.

Thousands of words are poured into studiously ignoring a million years of human evolution, with one class of people who give birth and one class who do not, instead, advancing edge cases and unwillingly co-opt those with disorders of sexual development to prove that there is no meaningful biological difference between men and women.

All that is allowed to remain to separate the classes of ‘male’ and ‘female’ is a belief in an un-testable, un-falsifiable, un-scientific innate sense of gender, a gendered soul.

This is the principle of explosion in action. When it is axiomatic that males are female then biology must be irrelevant, so the relevant difference must be something outside of the realms of biology.

By assuming something contradictory we have proved that souls exist, ex contradictione sequitur quodlibet.

It doesn’t stop there, of course. As we’ve seen, the contradictory axiom drags the idea that homosexuality is a choice out of its last refuges in golf clubs and fundamentalist churches, provides a proof that it’s true, and then frames any voices raised in objection as those of  bigots.

It makes it OK to prevent women from meeting and speaking, because the train of logic shows that you are doing so to protect the rights of women to meet and speak. Women must be willing to give up their spaces where men are not allowed so that women can continue to have men-free spaces.

And, of course, it allows you to draw parallels with the struggle for gay rights, or black civil rights. Because when you have constructed an increasingly tall tower of pure imagination you could draw parallels with the Apollo Moon missions, or the history of glass-making, or the story-arcs of the characters in Friends. When everything is based on a fundamental flaw then it can look and feel like whatever you want.

Most damaging of all, it legitimises of abuse towards, threatening of, and violence to women, because it allows those guilty of such actions to say that their ultimate goal is the protection of women.

You start with “A=B and A≠B” and end up with a man punching a women in the face, yelling, “This is for your own good!”

Trans-rights activists have proved fond of suggesting that “Trans-women are women” is no different to stating that “Black women are women”. Looking at it through the lens of the principle of explosion shows this to be false. Stating that black women are women does not require long threads about albinism or getting lesbians to renounce their sexual preferences, or for broad restructuring of the language, to make it inclusive.

What that lens also shows is that most of the arguments one sees are, sadly, pointless. Lord knows how many millions of words have been argued, from both side, about the biological difference and similarities between males and females, and chromosomal abnormalities, and other edge cases, in the mistaken belief that these are the pillars supporting the argument that trans-women are women. Rather, they are the logical consequences of it. They are the grappling hooks thrown out by those defending a fundamentally illogical position to shore up only their own refusal to abandon it, not to support the argument itself.

Which is a shame. There are undoubtedly men who suffer from genuine dysphoria, and others who desperately want to be female, and undoubtedly they need support, acceptance and allyship – and can be inspirational, brave and pioneering.

Those things cannot be at the expense of not only a willingness, but a demand, that facts are ignored, logic is trampled and reasonable dissent is seen as abuse, because the principle of explosion says that just one contradiction is enough to prove anything and everything, and women – actual natal women – have lengthy experience of where giving men the power to determine everything leads.