Types of Wrong

I know two ways to be wrong very well, but people have more ways to be wrong, and I don't know the rest very well at all. But I'd like to.

The first way to be wrong - and the most wrong someone can be - is to make a contradiction. People do this when they get their sums wrong, miscounting how much money to give to a shopkeeper; or when they make contradictory statements, claiming that a politician they dislike has no right to do something, then claiming that everyone has a right to do the thing the next day, because their own political party's members did the thing.

People who study types of wrong call this first type 'analytically wrong'.

The second way to be wrong is saying something is the case when it isn't. People do this kind of wrong all day, and we judge the wrong by degrees (when you're only a bit wrong), or justification (when you had good reason to think something, overlooking a subtle detail) or intentions (because saying 'you'll be fine' is fine, but saying 'I think we ate the last cake already' with the intention of checking the fridge later, alone, isn't).

People who study types of wrong call this second type 'synthetically wrong', and focus on how universities and corporations can avoid being wrong, but almost never discuss the messy little allowances and unstated rules of being wrong-about-facts.

People have many more ways to be wrong.

This VPN uses military-grade encryption!

People say this about VPNs, which gives uninformed listeners the impression that:

• encryption comes in grades (it could, but it doesn't),
• one of the highest is 'military grade', which is therefore 'good encryption' (unlike the standard encryption you buy at the shops),
• so this extra encryption must make you safer.

These statements are all synthetically wrong, but the original sentence? Is it wrong? The 'military' (whether that means Italian soldiers who look at Tik-Tok, or Chinese generals who want to transfer plans across China, or any other meaning), all use standard encryption, like TLS certs, mostly on their outdated Android phones and Windows 10 PCs. So is the sentence right? It seems about as right as saying 'I eat military-grade breakfast cereal'.

For now, I'm calling this 'presumptuously wrong'. It's possible to show someone has a presumption, and to show it's wrong when they're making making short inferences. I have a Polish friend who noticed someone checking up on her, to make sure she didn't steal anything, moments after learning she's Polish. There's only one difference to make the difference, so the check-up clearly came from bigotry. And more than clearly, her thinking was analytic.

• Premise 1: This person is Polish.
• Premise 2: Redacted
• Conclusion: Therefore, we must check she's not trying to steal anything.

The missing step is as plain as x + 2 = 4. People may obfuscate this process, objecting 'no, in fact:'

    0!
x = ───
    0.5

...and the assumptions around theft were not concerned with being Polish, but 'simply that they were concerned about certain things, after reading certain reports, and taking certain facts into account...' et c. ad obfuscatium. However it goes, following this thread just means taking the long-way around.

But that little trick-of-the-Maths works rarely. Mostly, people degenerate quickly into mind-reading accusations. Most people don't act on a single piece of information simply because they have a lot more information. Give the aforementioned bigot another day, and he would have plenty of other facts he could plausibly have taken into account. Or if not 'plausibly', we could not deduce the bigotry from clean (not 'pure', but still 'clean') Mathematics. Likewise in the case of people advertising Nord VPN's 'military-grade encryption', I can't see any room for good motivations, but I can't Mathematically verify bad intentions.

This kind of presumptuously wrong might just be the regular wrong but inferred, but it has sharp differences. It often looks like someone holding a world-view that's wrong, and the statements are more of an indicator of the wrong than actually wrong themselves.

I found myself being presumptuously wrong a while ago while watching a CGP Grey video with a slippery question.

Which planet is closest to Earth?

The 'gotcha' here is that Earth and Mars revolve around the Sun, so they spend some time far away from each other. Once you start looking at how close other planets are to Earth on average, the answer turns out to be Mercury. But the video's not about getting the question wrong, it's about the underlying world-view that makes us think in terms of planets in a line.