Take a random political issue with two sides A and B. Suppose that exactly one of the following would be true for me given my moral framework and unlimited time to process all public information about the issue:
A is undoubtedly correct and (in a manner proportional to its importance) I should expend time/money/energy supporting A.
A is probably correct, but it’s not so clear that it’s worth doing more than just voting in the direction of A.
It’s unclear whether A or B is correct and anyone who claims otherwise is either not doing good epistemics or taking a moral framework that isn’t acceptable to me.
B is probably correct, but it’s not so clear that it’s worth doing more than just voting in the direction of B.
B is undoubtedly correct and (in a manner proportional to its importance) I should expend time/money/energy supporting B.
Let’s also say that:
Foreign actors will attempt to push people on twitter/reddit/etc. towards either (1) or (5), even if the answer is really (3) for them. Everyone I interact with is either partially influenced by these actors or discusses their opinions with people who are influenced by these actors.
I have limited time to seriously explore a given issue.
I would like to err on the side of approaching the center, but not drastically so.
The major issue to me here is (1), which might only get worse over time. I am aware of the post on epistemic learned helplessness by Scott Alexander, but I have become a little wary of certain academic fields. I have generally liked using Wikipedia to quickly explore issues, even though there are occasional biases (which have hurt this website in the past). I have also enjoyed reading blogs and opinions from people who appear highly educated and intelligent, but there are natural biases there as well.
If possible, the best defense is learning about the topics before they become controversial. Also, don’t jump directly into the controversial part, but learn the fundamentals of the field first.
For example, the actual reason why I don’t believe in homeopathy is not because I found the “anti-homeopathy” side more convincing in the debate than the “pro-homeopathy” side. I actually suspect that most doctors do not understand half of the stuff they do, and that a large part of medical best practice is simply placebo effect.
Instead, it is because at the elementary school I learned about atoms. How water is composed of molecules of H2O, how being liquid means that those molecules bounce around randomly. Homeopathy working would require this model to be completely wrong. But that model doesn’t seem to be made by someone with an anti-homeopathy agenda, because it is used in so many unrelated contexts. Therefore, homeopathy is wrong.
Another example, evolution. Instead of jumping to the deep end (trying to make My Own Opinion™ on whether something could or couldn’t have evolved, without actually understanding how biology works), I start simple: Things are made out of atoms, yes or no? Atoms make molecules, yes or no? DNA is a molecule, yes or no? DNA encodes the traits of the organism, yes or no? (Don’t just say “yes”, think about it. How specifically can different cells do different functions if all of them have the same DNA?) Is it plausible that sometimes the DNA copies incorrectly? It is plausible that sometime an error in copying provides an advantage to the organism? (Is that a frequent or a rare thing to happen? How would the organism with the magically improved DNA reproduce with the ones that have the original DNA?) Etc. Now if someone claims that evolution is not real, I can ask them which specific step of this chain was wrong.
Similarly, there are some controversial(?) topics in mathematics. Instead of engaging with them directly, I have downloaded a few university textbooks on topics that are prerequisites for that, and I am going through them step by step, actually doing the exercises, and probably being way more paranoid about them than an average student. That will take a lot of time. But I believe it is a time better spent than trying to address the controversies directly without having solid fundamentals.
Learning the fundamentals requires a lot of time, but it is a limited amount of time; I assume that at some moment I will know enough to make an expert judgment. Merely debating the topics may require less time in short term, but it is an unending process; there will always be yet another clever argument or yet another internet debate. Also, by learning the field I can become a (kind of) expert on the field, but by debating a controversial topic I become only… an expert on debating this one specific topic, in best case.
One thing that works in your favor, epistemically, is that in democracy it is not necessary to convince everyone; you just need to convince the majority. Most people are kinda stupid, so the arguments designed to convince them are usually not too complicated. If you actually listen to both sides, it is often possible to find the mistake. (Don’t bother telling them, no one is going to listen.) Sometimes you find that both sides believe stupid things. Not in the “truth is exactly in the middle” way, but sometimes one side is like 90% right but really strongly insists on the one absurdity they hold dear, which the other side is happy to expose… and then connect to their own absurdities. Basically, don’t assume that just because two people are arguing, one of them has to be right; you might be observing two idiots arguing for two different wrong things.
My other heuristic is to have a list of people I trust and ask about their opinion. Explaining how to make such list would be quite complicated, but similarly to the “learn the fundamentals” advice, those people should be experts on something related to the controversy, but not solely on the controversy itself. (You want people good at modeling things, not just good at arguing for/against a side of a controversy.)
The first line of your answer is something I hadn’t thought of before and strikes me as really good advice.
I don’t really agree with your point on fundamentals. I’m a big “fundamentals” guy—I did a Math Ph.D. and despite coming in with a big head start, it took me a disproportionately long time to even start research because I had to build up everything from scratch in my own words (which is just not feasible nowadays). I say this to indicate that I already err on the side of being overly-focused on fundamentals. (Unrelated but out of curiosity—which specific mathematical controversies are you referring to?)
But using fundamentals for anything more than addressing fringe theories (like homeopathy and flat earth) would strike me over-extrapolating from partial knowledge of a system. For example, I don’t believe questions of “how will X affect Y aspect of the economy/ a person’s health/ the global climate” can be fully addressed by fundamentals, but people (not saying you) will often make them seem like they can be by using some simple model or assuming that we we know is all there is to know.
Yes, it takes a crazy amount of time, so I choose my battles. In case of homeopathy and evolution I actually got the background knowledge regardless of controversy, as I was already interested in natural science. (Also, my wife is a biochemist, so I often defer to her expertise.)
For political/economical things, my rule of thumb is to listen to people who mostly do the “boring” work. Such as, collecting information on corruption, which 99.99% of time everyone ignores, and 0.01% explodes into a huge political scandal. When the scandal happens, I trust the opinion of the guy who worked on all the non-scandalous stuff over anyone who only pays attention to the “cool” stuff.
Basically, you need to know what is “the business as usual”, and compare to that. For example, most people enter politics in order to make some kind of personal profit. But most of them stay within certain lines, and some of them go way beyond them. So instead of “did X embezzle money at Y”, a better question is “did X embezzle the usual amount of money at Y, or did something extraordinary happen here”? If you ask the right question, you will see the greatest criminals. If you ask the wrong question, your attention will go where the media want it to go. Yeah, in a perfect world all crime would be prosecuted, but we don’t live in that world. (For example the problem with Trump is not that he is bad, but that he is bad beyond usual. Some people believe that introducing random change to the system is good. I believe most of the time it only makes the system worse.)
With math… well, there are topics that other people consider controversial, such as Cantor’s diagonal argument or the Axiom of Choice. My approach is that instead of “joining a side”, I want to get a better insight into how these things work, on the mechanical level. (LOL, you probably know about these things much more than I do, but telling me the answer wouldn’t help me much unless I can derive it myself. And that’s kinda my point: I wouldn’t spend my effort on trying to agree or disagree with you, but rather on trying to get to your level, at least in some very narrow area.)
The method of “put the numbers (that you can enumerate) in a table and invert the diagonal” provides a number that is outside the original set, which can be used in multiple ways. Like, if you put the rational numbers in the table, the inverted diagonal will be an irrational number. If you put the computable numbers in the table, the inverted diagonal will be an uncomputable number. So even if someone claims to be coming from a finitist or whatever other perspective, my intuition would be like “you guys basically redefined ‘number’ to mean X, and I am not going to argue definitions here, but anyway, when you put all Xs in the table, the inverted diagonal is going to be a non-X”.
The real fun, from my perspective, is Skolem’s paradox. I think I approximately understand the point. The first-order logic cannot express certain concepts (even quite simple ones, such as standard natural numbers). So you should not think of the axioms as describing “the Platonic world”, but rather as applying to different models. (Feel free to think about the Platonic world as containing models of sets, rather than the sets directly.) Then instead of “wow, this is a mysterious paradox”, you should approach it as a hacker and say “wow, there seem to be malicious models that technically follow the letter of the axioms, while completely ignoring the original intentions of their authors… sounds like a lot of fun”. And then, whenever you hear a statement about something, you should be like “I wonder how this statement works in one of those malicious models”. -- And, specifically, I wonder how exactly Cantor’s diagonal argument works in one of those malicious models, but I am not there yet. I am reading a textbook that I have already read previously, except this time, I am like a hacker looking for a possible exploit. Like, when it says “natural numbers”, I go like “I wonder what happens if those are nonstandard natural numbers”.
(And I plan to approach the axiom of choice the same way. Like, the axiom is neither “true” nor “false”, there are simply models that are compatible with it, and models that are incompatible, and I want to get an intuitive understanding of both.)
This will take me a lot of time, and perhaps I will never finish it in my lifetime, but that’s okay because I enjoy math. :)
I’ll PM you about the math stuff when I have a chance. I would guess that the “devil” in Cantor diagonalization that you’re unearthing is closely related to the impossibility of semantic closure in a mathematical language. I’m not a set theorist but I also spent some time thinking about these things and getting partial answers that I was okay walking away with.
Do you have any sources you’d be willing to share for politics and economics?
I suspect this is all connected somehow: set theory, first-order logic, Gödel’s incompleteness theorem, etc. I plan to read a textbook on logic next. Then model theory.
Sorry, my sources for politics are local, so unless you are interested in the political situation of Slovakia (short version: it sucks; slightly longer version: some people believe that voting for populists is relatively harmless because they are all talk no action, well this is mostly true until suddenly it’s not and then all competent people just scream helplessly) I don’t have anything to offer. And even here, the source were the people (the kind that does the boring stuff) I spend a lot of time talking to, not any written source.
One detail maybe: some people in politics may be easier to approach than they seem. (Then again, that’s my local experience, maybe not true in USA.) For example, once I successfully invited our member of parliament to our local Less Wrong meetup, to tell us about some then current cause. It was surprisingly simple: I just messaged her on Facebook like “hey, we have a meetup of some smart people who like to discuss various things, and we would be happy to hear your opinion on X”, and she was like “actually, I have a free evening that day, so unless something unexpected happens, I would be happy to meet you”.
In fact,
diag-a1. if you put the computable numbers in the table, and
diag-a2. pretend that the assignment is computable also, and
diag-a3. (optionally) pretend that procedure for looking up the row of specific number is computable also,
then
diag-l1. the inverted diagonal is computable by explicit construction,
diag-l2. the inverted diagonal does not belong to the table,
thus
diag-t1. we have the contradiction (based on diag-l1 and diag-l2),
diag-t2. (if diag-a3 holds) the contradicting place is computable as well.
I agree with your view but that specific example was wrong!
The inverted diagonal differs from every element in the table for any ordering of the computables (by construction). Try to actually pseudocode a program to get the nth digit of the nth computable in your arrangement without invoking a halting oracle.
Retrieve I-th computable from table: computable by assumption.
Get K-th digit from a given computable: computable by definition.
Get I-th digit of I-th computable: computable as composition of (1) and (2).
Invert given digit: trivially computable.
Get an inverted I-th digit of I-th computable: computable as composition of (3) and (4).
I’ve actually written formal refutation of any bijection between N and 2N in Idris 2.
Demonstration
totalstands for functions which are defined everywhere on their stated domain (as opposed topartial), and computations for which are proven to always halt (if there’s no such guarantee, function iscovering).%default totalmeans that all functions below must be total.Voidtype means that a contradiction was obtained from given arguments.I interpreted your algorithm for listing computables to be something like “enumerate the Turing machines that output ‘.’ then 0s and 1s and list what they print”, without worrying about the fact that some computables repeat. This technically lists all computables even though some machines will get stuck in some non-halting behavior that prints nothing after printing finitely many 0s and 1s. But you can’t figure out the nth digit of an arbitray thing in the list because you don’t always know if a machine will continue to print 0s or 1s or get indefinitely “stuck”.
It seems that you actually meant that you could have an algorithm that begins by enumerating the Turing machines that print computables and never get stuck in some non-halting configuration. This can’t be done.
If you have any surjection: N→S⊂(N→{0,1}) and diagonalize against it, you know the result is not in S. This fact doesn’t depend on the actual nature of the surjection N→S, just that S is the image. Here S is the computables.
I’m pretty sure my argument did not mention how computables are listed at all, rather proving that for any specific listing the inverse-diagonal is computable as well.
Yes. However, it’s the specific choice of set “computables” which creates the contradiction: I agree with “inverse-diagonal for rationals is an irrational number” and like.
Once again: for any “user-provided” computable table of computable digit sequences, I can, in finite time, get value for any specific position in table; therefore, each digit of inverse sequence is computable; therefore, I conclude that the inverse-diagonal sequence is itself computable (if I’m not mistaken in definitions).
My claim is that such a table does not exist because it leads to a contradiction. If you add it as an assumption, you can obtain a false conclusion because the assumption itself can never hold.
I think it’s often the case that neither A nor B are true. Common opinions are shallow, often simplified and exaggerated or even entirely besides the point.
Now, you’re asking what a good way to form opinions is, well, it depends on what you want.
Do you want to know which side you should vote for to bring the future towards the state that you want?
Do you want to figure out which side is the most correct?
Do you want to figure out the actual truth behind the political issue?
Do you want to hold an opinion which won’t disrupt your social life too much or make you unpopular?
I expect that these four will bring you to different answers.
(While I think I understand the problem well, I can’t promise that I have a good solution. Besides, it’s subjective. Since the topic is controversial, any answer I give will be influenced by the very biases that we’re potentially interested in avoiding)
By the way, personally, I don’t care much what foreign actors (or team A and B) have to say about anything, so it’s not a factor which makes a difference to me.
Edit: I should probably have submitted this as a comment and not an answer. Oh well, I will think up an answer if you respond.
It seems to me that you might not have read the question/premise carefully. If you did and stand by this answer/comment, let me know and I’ll respond when I have time
I misread a small bit, but I still stand by my answer. It is however still unclear to me if you value truth or not. You mention moral frameworks and opinions, but also sound like you want to get rid of biases? I think these conflict.
I guess I should give examples to show how I think:
Suppose that climate change is real, but that the proposed causes and solutions are wrong. Or that for some problem X, people call for solution Y, but you expect that Y will actually only make X worse (or be a pretend-solution which gives people a false sense of security and which is only adopted because it signals virtue)
Suppose that X is slightly bad, but not really worth bothering about, however, team A thinks that X is terrible and team B thinks that A is the best thing ever.
Suppose that something is entirely up to definition, such that truth doesn’t matter (for instance, if X is a mental illness or not). Also, suppose that whatever definition you choose will be perceived as either hatred or support.
I don’t think it’s good to get any opinions from the general population. If actual intelligent people are discussing an issue, they will likely have more nuanced takes than both the general population and the media.
Lets say that X personality trait is positively correlated with both intelligence and sexual deviancy. One side argues that this makes them good, another side argues that this makes them bad. Not only is this subjective, people would be confusing the utilitarian “good/bad” with the moral “good/bad” (easy example: Breaking a leg is bad, but having a broken leg does not make you a bad person).
I think being rational/unbiased results in breaking away from socities opinions about almost everything. I also think that being biased is to be human. The least biased of all is reality itself, and a lot of people seem really keen on fixing/correcting reality to be more moral. In my worldview, a lot of things stop making sense, so I don’t bother with them, and I wonder why other people are so bothered by so many things.
I might be unable to respond for a little while myself, sorry about that
To clarify the question: I’m taking as an axiom that there are just two options A or B. So this isn’t some big issue like “are democrats right on climate change” but something specific like “Is the climate changing”. Then conditional on that being yes, “is a significant portion of this change human-induced” would be a separate A vs. B. Then conditional on that being “yes”, we could get to “is X solution proposed going to do more harm than good according to my moral framework”.
About valuing truth or not: the idea is that one of those 5 options would hold for me if I was able to process all available “truth”, but my goal is to approximate the correct option without spending that much time. Does that clarify things?
For your bullet points:
addressed above
This is what I mean by “proportional to its importance” but an additional degree of uncertainty would be “how important is it”.
This would not fit the axioms posed, but it’s good that you brought that up. Arguing over definitions and semantics with edge cases is something that I’m only interested in if the question is if a certain law applies or not.
I overused the word bias in different settings. What I meant by “my intellectual sources could be biased” is that they could be biased in the same direction by hidden variables that I would want to control for. For instance my personal intellectual influences in a lot of areas are disproportionately Jewish and most pro-Palestine people I know are not people I look up to.
I hoped to get around this issue by fixing a moral framework. Do you think that doesn’t suffice?
If you don’t have time to reply for an arbitrarily long amount of time, I’d still be happy to continue the conversation (even if that’s like months from now)
While you could format questions in such a way that you can divide them into A and B in a sensible manner, my usual reaction to thought experiments which seem to make naive assumptions about reality is that the topic isn’t understood very deeply. The problem about looking at the surface (and this is mainly why average people don’t hold valuable opinions) is that people conclude that solar panels, windmills and electric cars are 100% “green”, without taking into account the production and recycling of these things. Many people think that charging stations for electric cars are green, but they don’t see the coal powerplant which supplies power to the charging station. In other words “Does X solution actually work?” is never asked. Society often acts like me when I’m being neurotic. When I say “I will clean my house next week” I allow my house to stay messy while also helping myself to forget the manner for now. But this is exactly like saying “We plan to be carbon neutral by 2040″ and then doing nothing for another 5 years.
And yes, that does clarify things!
Valid, but knowing what’s important might require understanding the problem in the first place. A lot of people want you to think that the thing they’re yelling about is really important.
Then the axioms do not account for a lot of controversial subjects. I think the abortion debate also depends on definitions “at how many weeks can the child said to be alive?” “When is it your own body and when is it another body living inside you?”
I’m afraid it doesn’t. I believe that morality has little to no correlation with intelligence, and that truth has little to do with morality. I’d go as far as to say that morality is one of the biases that people have, but you could call these “values” instead of biases.
To actually answer your question, I think understanding human nature and the people you’re speaking to is helpful. Also the advantages of pushing certain beliefs, and the advantages of holding certain beliefs.
If somebody grew up with really strict parents, they might value freedom, whereas somebody who lacked guidance might recognize the danger of doing whatever one feels like doing. And whether somebody leans left or right economically seems influenced by their own perceived ability to support themselves. Ones level of pity for others seems to be influenced by ones own confidence, since there’s a tendency to project ones own level of perceived fragility.
If you could measure a groups biases perfectly, then you could subtract it from the position they hold. If there’s strong reasons to lean towards X, but X is only winning by a little bit, then X might not be true. You can often also use reason to find inconsistencies. I’d go as far as saying that inconsistencies are obvious everywhere unless you unconsciously try to avoid seeing them. Discrimination based on inherent traits is wrong, but it’s socially acceptable to make fun of stupid people, ugly people, short people and weirdos? The real rule is obviously closer to something like “Discrimination is only acceptable towards those who are either perceived to be strong enough to handle it, or those who are deemed to be immoral in general”. If you think about it enough, you will likely find that most things people say are lies. There’s also some who have settled on “It’s all social status games and signaling” which is probably just another way of looking at the same thing. Speaking of thinking, if you start to deconstruct morality and questioning it, you might put yourself out of sync with other people permanently, so you’ve been warned.
But the best advice I can give is likely just to read the 10 or so strongest arguments you can find on both sides of the issue and then judging for yourself. If you can’t trust your own judgement, then you likely also can’t trust your own judgement about who you can trust to judge for you. And if you can judge this comment of mine, then you can likely judge peoples takes on things in general, and if you can’t judge this comment of mine, then you won’t be able to judge the advice you get about judging advice, and you’re stuck in a sort of loop.
I’m sometimes busy for a day or two, I don’t think I will have longer delays in replying than that
The idea that either A, B or something in between has to be right is for many political issues wrong. It’s possible that both A and B are wrong. I don’t see why would would start with a different assumption.
For most issues, you are not required to have an opinion and it’s often better to focus your energies on issues where you have unique insight or power to affect the issue than focusing on national level political issues where you have neither unique insight nor power to influence them in a meaningful way.
Why do you consider it better to be manipulated by domestic actors than foreign actors? Why does it matter whether the actors are foreign?