Knowing you were wrong


From time to time we can be on the wrong side of a argument or just lack the facts we needed to make the right statement but how can we be sure we are wrong? How can we be sure the answers we’re getting are correct?


Mathematics seems to be something that has been working quite well to refine knowledge. The weight of proof is heavy and a single counter-example is enough to defeat a theory.

So when I come up with an idea, say that every even integer greater than 2 can be expressed as the sum of two primes, then it’s just an idea (the stage before a theorem). It fits the data. Everything I know about primes and even numbers makes me think this is reasonable. I have something I think of as a good idea. I can, by constructing a proof (do not attempt at home for the above), lean on other concepts that I am confident of, to build a framework that explains why this idea is true, a theorem (starting with axioms I take to be core and building a chain of proofs at each stage that show each theorem is consistent with those axioms).

But, and this is the huge but, one counter-example is enough to show my proof was invalid and the theorem fails. It doesn’t matter if there is a lovely proof for the above idea as long as someone has found a single even integer that cannot be expressed as the sum of two primes. That’s game over. So knowing we have the right answer is very hard and should always be considered to be the best match we have for everything we currently know, but often we can know very quickly we have the wrong answer.

This comes up again and again. The scientific method is extremely similar to this process, but focused on observations and refining theories on top of a mathematical framework - something that can deal with the slightly more messy and imprecise real world rather than pure mathematics. I also see some parallels to P vs NP in computer science - we have an open question of if we can quickly solve problems that we can quickly verify. This shows the unequal path again where, for a huge range of problems, if you tell me X is a solution to a problem Q then I can very quickly test it and verify but if you ask me for a solution to Q then I may not have a fast/scalable algorithm with which to find you an answer. Knowing you are wrong is easy vs finding the right answers (yes, this isn’t identical as verification of right answers is also easy for these problem classes but I think it’s worth bringing up the comparison).

We can never be sure the answer we get are correct, but we may be able to quickly know when the answers are wrong. Lots of it is based on access to both information to validate and a huge mountain of domain understanding already built up by generations of thinkers.


While the answer to that question will always be a complicated matter, I think the best you can do is to seek out people of different opinions. From there you can get a better look at the topic as a whole and hopefully attain some information to fortify your argument or change it entirely.


Technically if your proof is an actual one and does not contain mistakes of any sort, you would know that there cannot in fact be an even integer that can’t be expressed as the sum of two primes. Once a theorem is proven nobody would be able to provide a contradictory example because none could exist.
Not many fields are as clear cut and accurate as Mathematics though, so they might not be the best example to use in response to OP’s question…


I mean, technically you’re correct that the proof was not valid and the counter-example just makes that more obvious but also mathematics is built on axioms and proof chains that we’re pretty confident are all valid but all are up for being taken down. That’s the thing, even with something like pure mathematics then it’s far from easy to see a tricky flaw, especially if the proof isn’t valid but the idea is in fact a theorem (ie the thing you’re trying to prove is true, but you just haven’t actually proved it - there cannot be a counterexample but also someone can show your proof is incorrect).

I should probably have been clearer that ease of disproval is relative and non-uniform. Some things are incredibly easy to disprove via a trivial example and so there are lots and lots of things we know are not true. But as we slowly build these towers of ideas then counterexamples become rarer and even being certain about a flaw in a proof becomes the effort of years of work a lot of the time. Sometimes counterexamples are wrong, but it’s somewhat rarer because they usually make it easy to understand how the idea cannot be true (but to do so you probably want a minimal counterexample and then we’re into a whole other area of hard work).

I think mathematics is a great example when discussing knowledge/the scientific method/understanding (partially because 15 years ago I was doing it at university so still haven’t quite forgotten everything I knew back then) because it is held up as something so pure and always building. It’s only when we move to things like climate change that bad actors attempt to “teach the controversy” in a way that goes against the scientific method. But we don’t need to start there as mathematics has plenty of examples of how it’s not a perfect straight path and sometimes things need to be re-evaluated even without competing ideas.

The greater point is that a lot of ideas are easy to know are bad and that doesn’t take away from how grindingly slow progress is and how everything we do know is not perfect so there are areas of valid debate. But those areas do not include things which can easily be shown to be false - areas where someone without domain expertise may not know enough about the terrain to even know the difference between something obviously false and an actual point of academic dispute. There is a huge issue with people who do not know enough to know what they do not know being considered important voices needed for debate (simply because conflicts make for good theatre) - this runs counter to everything we have achieved in building these towers of knowledge. The understanding of the variable difficulty of proof, disproof, etc helps to prepare us to spot when we are sold controversy (and a claim of potentially equal validity) rather than good ideas.


Fundamentally this gets down to some real heavy philosophy, how can we truly know anything except our own mind? and the answer, I think, is that basically we can’t ever be entirely sure of anything,. all we can do is try to be open to changing our mind and willing to investigate honestly, and if you do that then I don’t think anybody can fault you for sometimes coming up short.


I think therefore I am.


I think this is a good answer - and I would add to that that it’s a good idea if trying to investigate honestly to become aware of the numerous ways in which minds are fallible.


Critical thinking is a vitally important skill and one which I think is in short supply these days. Researching facts and knowing how to distinguish opinion from a researched conclusion is difficult, but necessary. You have to take care to not only research your problem, but also the researchers or entities providing what you use to research your point. In the end though, as others have mentioned, always keep in mind that you can’t know anything for certain unless you embody that thing, so keep an open mind, consider dissenting viewpoints for their validity based on what facts you can find, and always frame your responses in a way that does not declare someone else as wrong, but simply ask for more information and their sources and provide your own if requested.

Some places this approach won’t work, but I’d posit that those people aren’t really looking for answers or the truth anyway.


The problem is we have great examples of where that absolutely doesn’t work. New Atheists flowing into modern Rationalists and journalists who pick science as their beat is a textbook example of where even what may be a genuine desire for elevated critical thinking turns into weird cults and anti-science screeds wrapped up as if they support science (with no more validity than climate change denial). It’s one of the oldest issues in the book for science itself: failure to account for our own biases creates a distorted understanding of everything and skews the data we gather. Phrenology, eugenics, early psychology (a field so great we had to put in place exhaustive ethics panels to prevent our hubris harming volunteers and producing invalid results at the same time). All of this is an ongoing process of trending towards fixing our mistakes (guess who still gets published most easily? Straight White men) but it’s also something that’s gone into fully blown toxicity on the fringes of academia and into the areas that feed on Dawkinism and similar.

When atheists decide they are suddenly some perfect rational machines and that what the world really needs is to adapt Nazi ideology to target a different minority religion (Islamophobia) then it absolutely needs to be pointed out that they have constructed a faith around hatred. When that same group are defending literal calls to implement the same eugenics arguments made 100 years ago to “purge the species of disability” then it cannot be left as if it was a reasonable discussion and a font of critical thinking. When journalists and TWEFs decide to ignore the body of science and weaponise transphobia via fringe studies and discredited scientists who abuse children then we must stand up and call out how science is being misused - that a blind faith in some inward rationality is being used to ignore a severe domain-specific knowledge deficit from the proponents of these ideas. These are extremely dark paths which many people may not even realise they are being led down by some fetishisation of a mythical human rationality combined with common societal biases and a few actively evil participants who have crossed lines in what they have decided is acceptable.

When it comes to people promoting eugenics, denying the very humanity of marginalised and oppressed populations then we absolutely have a duty to declare things wrong: morally, ideologically, and factually. That these abhorrent ideas have taken hold in communities claiming to be all about open debate and the pursuit of truth (via such things as evaluation of research, critical thinking, and asking for sources) serves as a major warning to us all that even good intentions cannot save us from the darkest paths through collective ignorance.


I got so sick of those Facebook memes going round “Solve this problem: GENIUS LEVEL” and then it’s a simple arithmetic puzzle that I made one of those using Goldbach’s Conjecture, which actually was genius level. As far as I know nobody solved it…


In most cases outside mathematics and formal logic it is relatively hard to know you were wrong except when it has been revealed by time - that one lottery ticket I was sure would win, well, it didn’t. Once it had happened there was no question.

Usually, though, the times that it matters, there probably won’t even be a definite answer. I’ve used the internet, so I’ve seen people argue pretty much every ass-backwards point of view you can imagine and a lot that you probably wouldn’t until you saw it right there. A lot of them have some kernel of maybe not-completely-wrong in a massive ocean of yes-completely-wrong. So for example, my friend didn’t really believe that male privilege was a thing, because he’s a white man and he tries to treat other people fairly. It was only after talking it through at length with other people who see it in action or have a more difficult life as a result that he started to grasp that it was a real thing and that whether or not he was conscious of it, he benefits from it. Looking back how, he would say he was wrong before because he now has more perspectives on it and understands it differently. In my experience talking something through with people who know about it is the most useful way of discovering you are wrong, but also it never becomes easy. You always held a belief or did a thing for what seemed to you a sufficiently good reason - even if that reason was no more than a habit of thinking - and getting yourself over the bump to let go of that is hard.


i feel like a lot of the time people with bad opinions get off a little too easily actually

lot of sympathy for those who’ve had their personalities shaped by whoever they’re dependent on and / or surrounded by but there is also a line. looking at constant overwhelming awfulness and telling the people who live it “well there sure are some problems it’d be nice if someone fixed them” but also that this is ~as good as you get~ is, like, objectively awful, and i don’t believe they should be excused for just not being hashtag woke enough (hey kids, remember that people saying all the right things doesn’t always mean they believe them), because if you’re not capable of basic human sympathy then what are you even doing

i didn’t really start this post meaning to write a dang manifesto but: it’s really important to constantly expose yourself to new people and experiences (note: this does not mean “let fascists speak”; this means “shut up about things that other people live and listen to them instead”) and i don’t want to sound like i’m resting on my queen of wokeness laurels here but at the same time: there’s a baseline level of humanity that you should hopefully know you measure up to

everything else, to a greater or lesser degree, follows from there


I understand the anger. I’ve done my fair share of yelling at people on Facebook for being ignorant or spreading lies, but in my experience meeting their hate filled lies with aggressive retorts no matter how factual, never results in them changing their minds and indeed it actually makes them dig in harder because I am meeting their anger with more anger and emotion gets involved which then causes them to bristle and defend their statement no matter what, or devolve it to name calling.

I have seen people on all sides abandon civilised discourse for name calling and refusing to even try and understand how the other side might have come to their opinions or beliefs.

I too have labeled others as awful human beings or ended friendships based on other’s opinions of a certain topic simply because I felt they were wrong, and because of our stubbornness neither side would try to understand the other.

Now I always try to remember a story Joe Biden told from when he was new on the Hill. He was told “you can question a man’s judgement, but never question his motives.”. Too often we assume we know why someone did something or feels a certain way, without bothering to actually ask them.


It is just really goddamn easy to fall into an escalation cycle. You don’t give in and I won’t either. Complete descent into baseline beliefs. Nuance is lost. And when nuance is lost, so is everyone in the discussion. At some point you’re not talking with someone, you are fighting them with words.
It’s a ridiculous thing but endemic that through all our advances and knowledge we will find a way to devolve any encounter if it pushes us enough. The old joke of ‘what happens if the unstoppable force hits the immovable object’ comes to mind.
Frankly I have lost enough sleep trying to prove to people i shouldn’t have to prove anything to that me being trans doesn’t make me a "deviant"
It has become tiresome because, to answer the thread title question, when it concerns fundamental parts of my existence i do not know if I am at fault for not handling the conversation any better than I should. Understanding very likely never comes out of confrontation. And confrontation has been distilled in the internet age to be sharper, more frequent (due to the inpersonality of it all) and ultimately bereft of its visible consequences.
Living in an age where bubbles are formed around certain people and the propagation of misinformation makes this feel like, frankly, a complete nightmare of a headache.


So here’s the thing: this is still that corrupted view that pushes civility and lack of emotions (note this is gendered, “you’re being/getting emotional” is a phrase used to perpetuate patriarchy as well as also being used in racist framings) as it if was somehow closer to a truth or has more inherent value and some secret path to rationality. This is the path down which people are told to “let the neo-Nazi speak”, totally ignoring that doing so denies the very humanity of many of those who “disagree” with neo-Nazis. That there are well-studied examples of how this is another tool that defends power imbalances.

Someone is not being civil when they deny my bodily autonomy, no matter how softly they speak that toxic idea. A lack of emotions around topics is a great indicator that someone is playing with a topic that doesn’t significantly affect them, they are not talking of something which is linked to constant microaggressions and larger oppressions. Something which they lack domain-specific understanding of because it is not a power vector that opposes their right to exist.

It is not my job to understand why someone else has decided they deserve to control my body and take that autonomy from me. That statement is already violence. That is one of the most aggressive things you can say, to assert ownership over someone else’s body; no matter how calm and friendly the tongue. This is not a case of needing mutual understanding. It is not a case where I need to just put up with his boot upon my neck for a bit longer while we all understand one another, to give up my own “stubbornness” so we can find somewhere to meet in the middle. Oppressors are raised to understand they simply have what is rightfully theirs, that this is the way of the world, that any benefit they may get from that continued oppression is actually earned and just.

I’m White; I benefit from systemic racism and the continued effects of historic racism; I will have absorbed a host of racist biases by growing up in a White supremacist society. But undoing that is my problem, one for which there are already bountiful tools to assist me. I can never become a domain expert because this is an oppression I will never truly understand (from the inside), but I can become less ignorant by reading and listening. But that cannot start until I am willing to begin. None of that process involves a person of colour needing to be more civil to me, to give up on any stubbornness, to understand me (as if being oppressed doesn’t quickly teach the mind of the oppressor), to never swear over the effect of that oppression for them. I am not owed their time or patience to ask questions or demand debate to spoon-feed me - in fact my desire to understand and do my own reading is critical to the process and builds upon the huge existing effort of those people of colour who have already written and spoken about this extensively.

It’s like the issue with middle class White cishet dudes (some even in academia, plenty who have regular columns) who are constantly talking about “SJWs/Lefties in their echo chambers”. What that says is that person is so privileged that they do not have to deal with daily microaggressions, with people attempting to deny their humanity on the regular, of publications endlessly attacking them. They don’t realise that simply living is a constant act of defiance and there is no chance of an echo chamber for the oppressed. That is a privilege only offered to the oppressors. It’s the same as a fetishisation of the idea of needing “debate”, meaning that privileged want to deny oppression without facing consequences for their views. Because for the privileged it’s just talk, it’s not actually a reflection of the daily power vectors they have to navigate to survive.


To wrap that long post back to the original question and my initial response: how did I realise I was wrong?

Because I slowly unlearned my ignorance and became more aware of the White supremacist society I was living in and the long history of that oppression. We can never be sure I’ve got a perfect view of the complex & intersectional power dynamics involved in society (in fact I doubt anyone does) but I can be pretty certain that any talk of achieved equality/equity or “post racial society” is absurd. The mountain of evidence is undeniable and we only don’t see it more clearly because of the blinkers of bias we are fitted with growing up, the way our lives are better if we don’t consider how we benefit from systemic issues and a history of privilege.

And that required me to want to be less oppressive (a never-ending incremental process). Like, racism doesn’t harm me; it cost me basically nothing to be ignorant. It takes me wanting to start learning the domain-specific knowledge before anything can happen.


My point is that what seems so self evident and obvious to you, may not be how others see the world or have experienced it. It is exactly when we allow emotions to control us, that the Neo Nazis gain power, because as we all know, there is nothing factual in their belief that one race deserves to be here or have more rights than any other.

Declaring that someone does not have the right to speak simply because they have a different view point, as radical as it may be, is 100% the problem. How we can claim to be all about equal rights and free speech, then turn around and say someone doesn’t deserve to speak because we don’t agree with what they believe only serves to increase tensions between people of differing views and does absolutely nothing to solve anything or prove them wrong. In fact, it only furthers their agenda because it paints those who seek to silence their voices as the oppressors.

Since joining this forum, I have at times felt that I am being told I don’t get to comment on things or share my views simply because my profile picture is a white man.

Yes, I don’t have the same experiences, none of us can know what any of us have gone through unless we talk about it and learn. I can no more help what color skin or gender I have or sexual orientation than any one else here, so forgive me if being told I my thoughts or opinions don’t matter because of who I am sounds more like the Neo Nazis and less like the Dalai Lama to me.

Getting back to the original post, being open to discourse and constantly reexamining our own beliefs in light of new evidence is the only way forward for civilization. Everyone, know matter how flawed their reasoning, believes they are right. We should help them discover that they are wrong by engaging with them and by upholding the ideals of a fair and just society instead of devolving into chaos and declaring war on each other.

I have family who voted differently than I did in this election, and I immediately labeled them as racist, masoginistic bigots who sold our children’s’ future for tax breaks and misguided hatred of immigrants. I was so confused and angry because this didn’t make sense based on who I thought they were before the election. Turns out, after a while had passed, that I had been wrong in my knee jerk reaction about WHY they voted for candidate X, and after listening to their reasons, which I think are still short sighted and wrong ultimately, I am now relieved because they aren’t flaming racists and white supremacists. In fact they felt that their voice had been ignored and saw the government as being corrupt.

I learned that I can’t assume motivations. Just like Joe says.


I don’t mean to be rude so please don’t take this the wrong way.

From a generalized point of view I absolutely understand where you are coming from however the key point here might just be experience in marginalized spaces. I’m gonna be 28 soon and I have spent an exhaustive amount of time either debating, conversing or outright arguing with people of different viewpoints. Whether it be about my views on gender identity, sexuality, gender equality or race.
There was always a spectrum of open-mindedness. From people declaring I would go to hell to people who were just genuinely curious what my experiences are and such.
The issue, i believe as far my observations go, is that we are tired.
Years upon years of debate. Having to over and over defend our position as a marginalized people who really only want to be participants in society without marginalization is tiring.
At some point I personally would like us to all have a baseline understanding that the underlying issue is not who is right or wrong but that we all just would like to enjoy our lives without having to defend our existence, however mild or innocent the discussion may be.

I fully understand and agree that you cannot push progress by force into everyone’s head - that’s a paradox.
However I also understand why many are just really exhausted of having to retreat the same ground ad infinitum and as a result get annoyed or combative. A whole heap of issues grow from that frustration, really.

But this, I would like to very much empathize is something specific to an issue such as the one I mean but has applicability to any other issues where there is often times a divide. Us vs. Them breeds in such environments.

Ideal world scenario is that we can all consider every viewpoint and find ways to coexist without stepping on anyone’s toes but given a climate of mutual antagonism and just pure exhaustion (on any side mind you!) leads to the aforementioned frustration and the subsequent decline of an open minded discussion regardless of intentions.


Yes I understand. I don’t claim to have any or all the answers, but just from my own life experiences, which I added some examples to my previous post, I find my emotions steered me wrong, and that if I had asked them and listened to them instead of getting angry and assuming motivations, I would have saved myself and my family alot of grief.

There is no doubt we are at a crossroads, and I believe we here are all on the side for equality for everyone and no discrimination, I just don’t think that meeting irrational hatred with violence or more anger will do much to help us in the end.