In what follows the distinction bewteen Islam and Islamism is used, though the distinction is debateable – Islamism = political Islam, but Islam is a political-judicial-religious expansionist ideology by design, so where is the distinction? It can be convenient to identify some Muslims as being not particularly political, but when push comes to shove, in the earshot of more ‘serious’ Muslims, you may find they are Islamists too.

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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, both not empty. 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 such that all members have property X, then all members of A (and therefore all 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.

More complex combinations of sets may be difficult to show in simple Venn diagrams, where there are many properties, and where the properties may or may not be changeable in individual members over time. But this does not detract from the basic principles.

Examples follow where this is misunderstood.

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. (*2024 – Twitter seems to have cleaned up its act since this was written. Oddly, these hyper-sexualised accounts were availably to everyone, including children, at a time when Twitter’s owners at the time were consoring pretty much anything they disagreed with.)

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, but dishonestly

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 rediculous claim by Jenkinson, “Transwomen are not women they are transwomen”. But that relies on Ash’s false presupposition that Transwomen are women. Jenkinson is right, transwomen are not women (they are not a subset of women), they are transwomen (a subset of men).

So, of course, Ash’s “Tall men are not men they are tall men” is false, as she knows, but “Transwomen are not women they are transwomen” is true, because transwomen are a subset of all men.

To think transwomen are women is to confuse innate characteristics with adaptable identities, 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, dead-naming.

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 misogyny of transwomen TRAs against women is far greater than is the bigotry 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.

Innate Characteristics v Changeable Identities

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

1 – 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. The sets are distinct.

2 – 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. The difference here though is that skin colour, and race, are ALL mixes, from pareant to child, within and outside human ‘races’, because all decend from a small number of original humans. Therefore it is far easier for ‘mixed race’ (mixed in the recent past when previously disparate groups began to mix more often) to identify as black or white or neither or both. The problem with race is not the variety of races, but the fact that some people use morphological differences to discriminate against people that don’t “look like us” – i.e. actual racism. The sets are actually complex in this case. Isolated peoples could be put into distince sets based on morphology that would have a correspondence in DNA. However, after so much mixing (and there was always some mixing except in rare very isolated cases) it is impossible to put individuals into distinct sets – even the whitest of white supremacists would have a hard time explaining away some of their genetic heritage.

3 – Christian/Muslim – Changeable 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 that were believers 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. The sets and subsets are clear, though people may swtich between them.

4 – Transman/Transwoman – Changeable identities – You get a choice, whether to be a man, or a trans woman; or to be a woman, or a trans man. Note how committed many Transmen and Transwomen 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. So, as in 1, you can act out as if you can change from a man into a woman, but that does not make it innate or real. The innate characteristics are being a man or a woman, the ‘feeling’, the adapted identity, trans woman, trans man, is not innate. The sets are clear, and even rare intersex cases do not refute this.

5 – Being Jesus – Mistaken identity – It’s clear to most sensible people that any person today claiming to be Jesus the returned Messiah is in fact deluded and mentally ill. Along with many other delusions, including many forms of paranoia, sufferers need help to overcome their condition, not affirmative support. The sets of mental illness are not so clear because we can all suffer degrees of delusion, which may change over time. But, in many specific cases there is enough information available to classify someone as suffering an illness, rather than genuinely being Jesus returned.

6 – Religious Belief – The God Delusion. Enough said. Distinct sets and subsets. There may be some ‘spiritual’ outer set that includes many people that can’t decide on a particular religion, but profession to one religion usually excludes all others, except to the extent that there are subsets, sects, or religions that are ostensibly the same religion at the core: Christian (Catholic, Protestand, Baptist, …) ; Muslim (Sunni, Shia, …). It’s laughable that the religious, which for expansionist purposes call themselves ‘inclusive’ are pretty good at letting you know which other scsts of the same religion are no ‘proper’ Muslims or Christians.

7 – Somatoparaphrenia – “Somatoparaphrenia is a type of monothematic delusion where one denies ownership of a limb or an entire side of one’s body. Even if provided with undeniable proof that the limb belongs to and is attached to their own body, the patient produces elaborate confabulations about whose limb it really is or how the limb ended up on their body.” Clearly, in these cases the problem is one of a sufferer of a mental condition caused cognitive impairments. The set of sufferers of somatoparaphrenia form a subset of people with mental issues**.

8 – Body Disphoria – “Body dysmorphic disorder (BDD), or body dysmorphia, is a mental health condition where a person spends a lot of time worrying about flaws in their appearance. These flaws are often unnoticeable to others. People of any age can have BDD, but it’s most common in teenagers and young adults. It affects both men and women. Having BDD does not mean you’re vain or self-obsessed. It can be very upsetting and have a big impact on your life.” – On the other hand we have this arbitrary claim from a group that supports the affirmation of trans identities, “A transgender person experiences distress because their body does not reflect their true gender. Conversely, a person with body dysmorphia experiences distress because they perceive flaws in their body or weight that do not exist.” This is extreme gaslighting. As far as I’m aware there is no genuine research that shows “in the wrong body” compared to one’s “true gender” is a meaningful distinction from a delusion. People suffering body dysphoria form a subset of people suffering mental issues.

9 – Homosexuality/Bisexuality – These are sets based on what one’s sexual attraction is. This is not a mental illness**. There is no dysphoria regarding one’s own body. Some homophobes may like to classify it as a mental illness because sexual preference is traditionally and mostly heterosexual, and heterosexuality is evolutionarily required for the propagation of the species, at least prior to current advances such as artificial insemination. But, heterosexuality is not required across all members of the species. Many heterosexual couples choose not to have children and the species survives – though if this occurs in enough people it would not. So, the Human species (and others) can survive some proportion being homosexual – and bisexuality need have no impact on reproduction at all.

*Don’t let the arguments from ‘intersex’ confuse the issue. Most trans people are not intersex, they are straight forward biological male or female.

**There is a genuine question of what counts as a mental illness, as opposed to something that is contrary to a societies customs and moral attitudes.