Trouble With Set Containment and Defining Properties

Within a few days I’ve seen the shocking failure of Western education systems even in the basics. From religious nuts to Woke evangelicals there seems to be an inability to grasp the basic containment principle of proper subsets, and of their defining properties.

Define two sets, A and B. If B is a proper subset of A then ALL members of B are also members of A, but not all memebrs of A are members of B.

If A is defined as having property X, then all memebrs of A (and therefore of B) have property X.

If B has a distinguishing property Y that distinguishes its members from other memebrs of A, then all memebrs of A that are not in B do not have property Y.

Islamists are Muslims and are Islamic

This diagram illustrates the principle of containment and defining properties of proper subsets.

Here is an exchange on Twitter that shows that Sara might not know what a proper subset is – or that she really thinks being Islamic and being an Islamist are mutually exclusive:

She either doesn’t know that Islamists are a proper subset of Muslims and are therefore by definition Islamic, or she doesn’t understand the meaning of the terms Islamic and Islamist. It may well be the latter – as a matter of wishful thinking. She wasn’t alone. Between them Sara and Chris are simply not getting it.

The only way to interpret these responses is:

  • They are just dishonest. They know full well that Islamists are Muslims.
  • They really think there are two mutually exclusive sets of Muslims – Islamic Muslims and non-Islamic Muslims (Islamists) – but they would still have to understand they are both Muslims. You know they know this by rejecting my suggestion they are playing “Nothing to do with Islam”
  • They actually think Islamists are not Muslims at all. But “Islamists are comparable to Christian terrorism … or the violence perpetrated by Christian fundamentalists” indicates that they really do know that Islamists are Muslims. So, what do they think Islamic means? Just ‘Nice Muslims’? That judgement would require them to know something of Islam, which if they did they’d know it’s a nonsensical judgement.

Other respondants show similar misunderstandings.

Ash Sarkar: Tall Men are not Men

Ash seems very confused about the application of descriptions to the various sets. By definition there are biological males and biological women. Not shown on the diagram are some of the nuances of how to classify people that are biologically male or female at the edges – but this is not what Trans identity is about.

If you doubt this last claim search Twitter for #trans and you’ll be inundated with tweets of people who are very clearly biological males engaged in sex acts, and most are obviously male, with male penises and fake boobs – these are not the the people born with ambiguous genitalia.

If you want further evidence of the male nature of many transwomen, look up #sissy on Twitter and you’ll see more men. This time they are projecting – it’s simply a more committed version of men imagining themselves as ‘slutty’ women, which these guys are acting out.

Good luck to them. Each to their own. Back to Ash’s points.

The diagram below illustrates Jenkinson’s point, and includes Ash’s addition of the characteristic of being tall.

Of course Ash does understand the point that Tall Men ARE a subset of Men. That’s why she’s using it, sarcastically.

In fact Tall Transwomen are also a subset of Men, the intersection of Transwomen and Tall Men – we love a bit of intersectionality. Ash’s intention is to try to illustrate what she thinks is Jenkinson’s error. She thinks that saying “Transwomen are not women” is the same kind of error as “Tall men are not men” because she thinks that Transwomen are actually women, as if there is no significant difference.

Ash’s use of “Tall men are not men they are tall men” is specifically trying to point out what she thinks a reduculous claim by Jenkinson, “Transwomen are not women they are transwomen”. But that relies on Ash’s false presupposition that Transwomen are women. Jekinson is right, transwomen are not women (they are not a subset of women), they are transwomen (a subset of men).

To think transwomen are women is to confuse innate characteristics with adaptable identifies, which becomes a problem every time Ash thinks she’s spotted a White Supremacists – she may well have dead-skinned a Transblack Black Supremacists, to use an adaptation of a favourite notion of Trans ideology.

After so many advances against bigotry the TRA ideologues are not only blurring that issue, but they are engaging in their own bigotry – as you can see by the many abusive TRA messages that appear in the social media of women. This also illustrates the fact that transwomen are not women but men, the misoginy of transwomen TRAs against women is far greater than it is against men, and is also greater than the abuse from transmen (women) against men or women. The most abuse you see is from TRA transwomen and their ‘allies’, against actual women.

There are innate characteristics, and then there are changeable identities and behaviours:

Man/Woman – Innate – You don’t get a choice. You can act out as if you can change, but that does not make it innate or real.

Black/White – Innate – You don’t get a choice. You can act out as if you can change, but that does not make it innate or real.

Christian/Muslim – chanegable identities – You get a choice. Note how committed many Chrisians and Muslims are. They see it as a core aspect of their identity. But many atheists look back and acknowledge that no matter how committed they felt in their religion they were at the time, it was not the actual biological nature that identified them but their mental attitude to their chosen (or indoctrinated) identity.

Transman/Transwoman – chanegable identities – You get a choice. Note how committed many Transman and Transwoman are. They see it as a core aspect of their identity. But many de-transitioners look back and acknowledge that no matter how committed they felt they were at the time, it was not the actual biological nature that identified them but their mental attitude to their chosen (or indoctrinated) identity.