I agree with the article. But I'd go further and say that children should be introduced to, and taught, multiple styles of thinking. And they should understand the strengths and weaknesses of those styles for different tasks and situations.
But logical thought is definitely important. Judging by some people I encounter, even understanding the concepts of "necessary but not sufficient" or "X is-a Y does not mean that Y is-a X" would make a big difference.
> It emphasises how logic alone might not lead us to the right conclusions, because there are more things at play in reality than in our mental models.
> It suggests that we choose actions by carefully studying outcomes rather than based on what ought to yield the best outcome.
> It tells us that differences in outcomes may not be a signal of differences in controllable antecedents: it is often just the natural variation of the process.
As a statistician, perhaps the most useful feature of statistical thinking is an explicit rejection of point estimate. Always, always, always, give an interval estimate, or a five point summary if you have that. This was the one lesson that was drilled into me repeatedly.
Ofcourse, you head out into the real world & it is full of point estimates! The article gives a very good example of real-world statistical illiteracy - "If the gas mileage of a car is 40 miles per gallon, and I drive 20 miles, I will have used half a gallon of gas". While I'm sure that the HN audience prides itself on statistical literacy, they will certainly have trouble coming up with a good interval estimate for that scenario.
I think the comment is alluding to the scientific method, more or less. Some kinds of knowledge are simply not accessible through logic alone. Facts about the world have to be obtained through observation. We then create mental models based on logic that can often explain and predict more facts about the world, but these mental models themselves often turn out to be incomplete or based on faulty assumptions. If we make observations contrary to the prediction of the model, we then have to revise the model.
I'll give a rather silly example: I recently saw a couple of people debating whether betting odds should give more accurate predictions of the outcomes of sporting events than other predictions. One person claimed that people are more risk-averse when their money is on the line and therefore should be expected to consider the probabilities more rigorously, while the other person claimed that it shouldn't matter whether one is putting up money. In other words, they were both making a priori arguments for why betting odds would or would not be most predictive. But in fact it is empirically verifiable that betting odds are more predictive than other models; no amount of a priori reasoning will lead you to the correct answer, only observation will.
The downside to logical reasoning is that it only deals with absolutes. If you mistake an uncertain trend in the world for an absolute fact then logical reasoning also suffers from garbage in garbage out.
All models have prerequisites, and logic requires propositions, which are either true or false. If you are trying to talk about models themselves (which is what most of math is), then logic is useful because it's easy to come up with propositions about models, and then you can explore what else must be true, or what else can't be true.
Probability and statistics are much more useful for explaining the world than logic. But we use logic to prove things about the models that we use in probability and statistics.
Logic is correct, you aren't going to find something logically true and then see it violated empirically. You are going to instead discover that the real world thing can't be neatly modeled as propositions. The error will be in producing the inputs to the model, not the model itself.
"They have a really good startup idea so they will be successful."
"We need to fire a salesperson so we'll pick the one with the lowest total contract value."
"The bus trip takes 43 minutes so I will be there at 12.17."
You'll note that these are not failures of logic (which is somewhat self-consistent and cannot fail) but rather of small-ish world views that don't allow for uncontrolled factors, which I think is a distinguishing factor of statistical thinking.
As you intimated, none of these are logically provable. They seem like sound logical conclusions on their face but, if someone has studied logic, they know that further evidence is required to make these deductions.
You're going off a very strict "logically provable" definition which is generally incompatible. We use "logically provable" like this in cases for math equations and algorithms (which has a lot of value!) but not for every day things.
"My cat is sad" is not logically provable, but we feel comfortable that this idea is basically real enough. "vorpalhex has an internal monologue" is not logically provable, but we feel comfortable that it's probably true if I say it's true.
To go back to your original ask, for something that can be shown via Bayesian thinking but not logical deductive reasoning: "Intelligent alien life has never visited Earth". This can't be logically proven because of the observer paradox - the strongest statement we could defend logically would be "There is no known evidence that intelligent alien life has ever visited Earth" (which is a weaker claim). If we allow Bayesian reasoning, then we can defend that the likelihood that intelligent alien life has visited Earth and never left behind evidence is much, much smaller than the likelihood that intelligent alien life has simply never visited us.
> Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language.
Logical thinking is a good foundation, but one of its main problems is that it is rapidly overwhelmed in the real world by massive amounts of data and the need to make decisions even if you can't logic through the problem for a variety of reasons. So: probabilistic thinking. Logical thinking is a foundation here, probabilistic thinking done correctly still involves the basics of logic, but you may have to take what is in logic a huge net of propositions and data and collapse it down to a single number.
Statistical thinking, which I will draw a for-this-message-only distinction (that is, don't reply with some angry denunciation of this difference, I'm not globalizing it) as when you have high-quality data and statistics can draw out some non-obvious conclusion. The previous paragraph is about very real-world situations where you don't even have high quality data and has its own flavor to it. This can generally be more specialized to people going into a science or engineering track; for most people what I am thinking of in the previous paragraph is already more than they are currently operating with.
Financial thinking. Time value of money, investments, compound interest and the much less common understanding of why you can't just model it as "8% a year" in the real world because the black swans happen on large enough time frames, investment, information about basic business. This dips into politics as well with the ever-important question qui bono? There's also some generalized "planning thinking" that goes into this, like, if you want to be in a particular place in 10 years, how do you get there? e.g., in a particular job, in a particular relationship state, in a particular financial position, etc. I witness so many people who clearly have goals or desires for these sorts of things yet simply have no idea how to take such things down to "what do I do this year, this month, this week, today to advance that goal" with the result that progress is never made except by accident and the goals are so frequently missed as they just live day-by-day without advancing their goals. (Note I am not critiquing day-by-day living itself. I am not Type-A and don't plan obsessively. But I do try to make sure that if I have long-term goals I make progress towards them at a pace that means I'll get there.)
Mathematical thinking; another specialized one that not everyone needs, but the basics of "starting from these axioms where can we go" and "given this real world thing how can I reformulate it into this mathematical system"? This is, by and large, not what is already being taught in school. Which is not necessarily bad on its own terms, but grinding through quadratic equations isn't really what I mean here.
Not intended as an exclusive list. The main point is, to quote a great philosopher, "Logic is the beginning of wisdom, not the end." - https://www.youtube.com/watch?v=A4XPTmmvVow
Are you going to teach children to be independent thinkers? To do anything but follow the consensus like a bird in a flock? I don't see that happening.
They should at least be able to identify good sources of trends (parents, siblings, close community networks) and buck bad sources of trends (everyone else)
Except that your country needs blue collar workers. You don't get them by creating smart people. You also don't want intelligent people that recognize emotional manipulation, politicians cannot have that!
Also a lot of people including kids are stupid. No amount of trying will change it.
Those are the lessons I learnt coming from your position in my youth.
> children should be introduced to, and taught, multiple styles of thinking
I agree with this as a descriptive fact about what a good education looks like, but I may disagree with the motivation. Thinking is for predicting the world, understanding which parts you can control, and then using that control to make progress towards goals.
Multiple styles isn't an end on it's own as if they were different essential nutrients. Different models will give more or less predictive value in different cases, which is maybe what you were saying here:
> understand the strengths and weaknesses of those styles for different tasks and situations.
The goal is still to produce the single best model for predicting the world. The best will depend on cost to evaluate as well as accuracy. That will be a hybrid of these different ways of thinking, but it's still one coherent model, not separate ones that we respect for no reason.
the way things are headed in the US, “kids should be taught” is itself an aspirational goal. “think logically” would be icing on a nonexistent cake. my state is unwilling to pay more than $21 per hour to a teacher. every attempt to add even a dollar to this figure has been overturned. first “congress should be taught” what a reasonable wage is.
In my state, they proposed a list of words that can no longer be used in public school classrooms. To align the tests to the new mandate, there is also a proposal to remove those words from any of the tests taken to evaluate the students at the end of the year. So the goal, apparently, is for children to not even be able to define the words.
In schools nationally, kids can take advanced physics classes and never get an intro to quantum theory, or even special or general relativity. Why? It's not on the tests at the end of the year and the teachers run short of time. So preference is given to the content that the students will be tested on.
And on and on and on.
We could all give a million examples I'm sure. But the hard part is what to do about it?
After 8 years in a public school, I've decided enough is enough. I've attended numerous school board meetings. Written to teachers. Given generously to the teacher funds. Voted. Nothing works. So we've saved up some money. We'll be putting our kid in a private school starting next Fall. It's hard, yes. It's hard on him - he's going to miss his buddies. It's hard on us - $40000 per year for high school, thanks America! I honestly don't know what else to do. There's a second private school in the area that charges $65000 per year, so perhaps I should console myself that I'm being responsible by saving $25000 per year.
We have a choice between the blackboard and the phone screen.
The screen has already won. I think everyone is worried about AI takeovers but until they have hands and feet we'll just have to live with Human-assisted AIs. That should take care of a lot of jobs.
Look up the total expenditure on education per student in your state, then do a rough calculation of how much of it is actually going to teaching students (facilities, teacher salaries, school supplies). It's usually not that much and school districts spend it on nonsense instead. There's probably enough money already so adding more won't help.
I live in Arizona, which regularly places last in education. We also happen to place 49th in spending, at about $10k per student vs $15k on average nationally.
I think you might be right in some situations but wrong in most others.
AZ average students per class is 18. $21/hr for 2000 hours is $42k. Double it to overaccount for total cost of employee. Where's the $96k remaining going?
I'm not going to analyze further, I don't live in AZ. But you should check out the actual answers. Teachers could make more without spending more on education. Or rather spending more on education and less on "education"
Teacher salary is only one cost of educating students. You also need to have school buildings, maintenance staff, administrative staff, etc. Stingy states like Arizona are not overspending on education. They need to minimize waste AND spend more to adequately educate their children.
Thinking critically is in direct contradiction with the notion that everyone's opinion is equally valid. Our society does not promote critical thinking as a useful life skill, it's more about appeal to authority and belonging. Our culture would need to change to make this a life skill worth having.
>Thinking critically is in direct contradiction with the notion that everyone's opinion is equally valid
Democratic societies tend to follow the model that truth comes out of conflict in the marketplace of ideas: the best idea wins, and everyone’s opinion is equally valid as spoken, until it is shown to be unfit through competition.
Authoritarian movements tend to follow the more religious model that the truth is only knowable by a learned/privileged class in a society, and those not in this group should support them and leave them to discover it, then accept it.
So, I would say critical thinking is necessary for democracy and anathema to authoritarianism, or perhaps the democratization of critical thought is necessary for healthy democracy.
> Democratic societies tend to follow the model that truth comes out of conflict in the marketplace of ideas: the best idea wins, and everyone’s opinion is equally valid as spoken, until it is shown to be unfit through competition.
And like most ideas most people have about marketplaces, it's wrong. The marketplace of ideas is like most marketplaces in that it, by virtue of being built of people, inherits all the flaws present in those people: emotional thinking, biases (conscious and unconscious), and all the mental frailties that plague us as beings: concerns about social status, fitting in, and the desire to flex.
As a result, again like any other marketplace, simply "having the best product" is a distant last place to far more effective strategies to ensure your success in the market: good branding and advertising, collusion with other participants, vertical integration and of course, bullshitting the consumers on an industrial scale. And, failing all that, litigation.
That an idea succeeds in a marketplace of ideas is no different than a product which succeeds in a marketplace: it doesn't mean anything intrinsic about the idea/product, it just means that idea/product did well in this market, at this time, with these consumers, and if any of those circumstances were changed, it is entirely possible that product would then lose.
Since critical thinking is performed by humans, surely the same human ‘flaws’ apply.
I would think that having characteristics of humanity is not necessarily bad for a human oriented system, and I can also point to any number of atrocities that were the ‘perfectly rational’ course of action for a statesman, nation or movement at some point in time.
> Since critical thinking is performed by humans, surely the same human ‘flaws’ apply.
Oh absolutely. And that's just accounting for actual critical thinking in which human flaws enter the equation and muck things up. Huge swathes of public intellectuals claim to be rational, objective, critical thinkers all the time when they're spouting complete nonsense, usually for a paycheck.
> I would think that having characteristics of humanity is not necessarily bad for a human oriented system, and I can also point to any number of atrocities that were the ‘perfectly rational’ course of action for a statesman, nation or movement at some point in time.
I would also add to that, that a purely rational worldview or thought isn't even necessarily a good thing. We will never escape the foibles of our human limitations (at least, probably) but in the same way, we must always retain our humanity too.
That seems like a very naive view of markets. More idealistic than realistic and to a degree that’s frankly harmful as quite often bad actors abuse markets while using the idealism as propaganda to confuse, gaslighting, and distract.
Symbolic logic is already taught as part of the common core, just not in the distinctly programatic way it exists in writing code. Logical thinking in mathematics has been pushed down to elementary school. What the author thinks ought to be already mostly is.
But let's say you're an activist and expect the world to reflect your view...
The National Governors Association and the Council of Chief State School Officers are the two governing bodies that pushed for it. You can either lobby them or the Department of Education to force states to teach what you want them to teach.
My wife teaches second grade and for some time they had a common-core math curriculum that encouraged writing about math, how you solved this problem, and discussing that with the class. It was interesting to me to see this in person, because children often solve problems in different ways which work for them, discussing it as a class disseminated that knowledge to someone else who may find it useful. The end result is second graders who are good at math but also understand why X+Y=Z, not just that it does.
It is hard to teach this and requires a lot of work from the teacher's side to become good at it and to pull the right information from the children. In a state that criminally underfunds public education, many teachers didn't want to learn this and when the time came, discontinued this curriculum for something that required no writing (also a mandate from our worthless state department of education) and did offer more color-by-numbers, which my wife describes as "pre-k stuff".
Rant aside, I was astounded to watch how much 2nd graders understood about math when given the opportunity to approach problems like this.
Not a fan of this article. I agree with the premise, but I don't think the conclusions are sound. We live in a society of imperfect information, and logic can give rise to conspiracies just as easily as dispel them. "Jet fuel can't melt steel beams," for example. I think it's a fallacy to assume the root of our political divide is a lack of logic.
> For example, many naysayers to global warming present the evidence of cold weather on a particular day as a proof that global warming is a conspiracy. A logical thinker is quick to spot that weather is what happens on any given day, while climate is what is happening across the globe over decades.
I concur. Logic is rarely the problem. The problem is nearly always what you're applying the logic to.
The article, and the HN discussion, conflates "logic" with "critical thinking". They are in fact quite different. Logic is a mechanical process, which can be done by computers. "Critical thinking" is how we come up with the premises to which we apply the logic.
Garbage in produces garbage out. It would be nice to teach kids to recognize garbage, but you're going to have a hard time getting adults to agree on what "garbage" is. It would be nice to be able to make statements like "If effectively every single relevant scientist agrees on something, it's far more likely to be true." But even if you did get schools to teach that, many parents will loudly contradict it.
I don’t agree,
We can learn to apply thought process.
We learn by heart patterns and recognize them in new situations.
Learning that a -> b doesn’t mean that b-> a.
I would be able to say it for a few cases intuitively but knowing this pattern exists I’m able to apply it to all construct not a few cases
I also allow me to formally prove or disprove something I have an intuition for
I disagree. All humans can be taught to think critically. It's a learned skill. Logic is rather rigorous i.e. just learning a few basic rules and applying them can falsify the bulk of claims made in typical discourse. Everyone can learn to sniff out bullshit without having to become a Descartes.
Maybe that's true, I might've been wrong. But still I don't think that it's that straightforward, human brain and intelligence are things we don't fully understand yet.
Also, Basic statistical reasoning is required. And some core facts about our physical world. What about an open curriculum listing the most important things in a teachable order?
> For example, many naysayers to global warming present the evidence of cold weather on a particular day as a proof that global warming is a conspiracy.
Look, if they're trying to bring in symbolic logic to prove something about global warming, namely, that humans are causing it, that's fundamentally misguided because causality is not provable. I'm not saying that I don't believe that humans are causing it, just that talking about causal relationships is outside the scope of what logic is meant for
You can have a logically consistent worldview that the author would immediately discount as conspiracy garbage. Logical inconsistency is not the issue here. The issue is that the author doesn't like the set of assumptions that other people are making
As an aside, expecting people to have completely consistent and justified sets of beliefs is completely out of touch with how people actually are. Anyone who's read some dostoevsky knows this
You’re correct that logical thinking falls short of proving human-caused global warming in and of itself, but you couple that with empirical evidence. Under all thinking roots logical thinking. Data and research only go so far: At some point, you have to try to take the evidence you have and apply it using logic. Indeed you need logic to even construct the studies in a way that they will yield useful results.
I understand the example is contrived, but the point is you have a framework for making conclusions. All of the data in the world won’t help you if you can’t arrange its into a way to make a conclusion from it. This is how logic underpins everything.
It’s sort of like physics. Everything is just physics at its basis.
The issue with disinformation, conspiracies and everything similar is that it's not very simple to logically prove one or the other. There are so many unknown factors, and different base truths that people would have to agree on.
Usually it's the way where someone forms a belief for whatever reason. It could be because it's just beneficial for them. E.g. someone who likes gas guzzlers might want to reject climate change just because they want to keep doing what they are doing guilt free. So then whatever logic skills they have, they would only apply it to argue against climate change. Not try to figure out whether there actually is climate change. It would just make them more skilled in finding logic around areas with many unknown factors.
Then - the article says to warn about potential conspiracy theories that might be arising. But if someone is prone to consider conspiracy theories, wouldn't that possibly have the counter effect, the Barbara Streisand effect. Wouldn't they think that "that's exactly what people behind the conspiracy would do, try to convince us of it not being there".
Adults should be taught to think logically first, then they can teach the children.
The problem with the idea that logical thinking will dispel conspiracy thinking is that conspiracy is the norm. Of regime changes in the 21st Century more than half were the result of a coup. Crypto AG was a CIA front. Cigarettes are bad for you. (I could go on giving examples all day. All. Day.)
Symbolic logic will not save us from conspiracy for the simple reason that conspiracy is everywhere. Those that think otherwise are ignoring evidence or non-rational.
- - - -
Application of symbolic logic to human psychology reveals that human motivations form a DAG (Directed Acyclic Graph) that tops out in deep and profound spiritual states. (E.g. I do A to achieve B which results in C that in turn engenders profound bliss.)
It turns out that most human activity is yak-shaving and, strictly speaking, unnecessary.
That's how you use symbolic logic to defeat misunderstanding and make life better.
Logical and critical thinking would be a challenge to those in power, apparently the Trivium had been removed from a classical liberal education some time ago. I learned about the Trivium in an online school long after I left college...
Charlotte Thomson Iserbyt's "The Deliberate Dumbing Down of America" may be a case in point.
Conspiracy surrounds us, "conspiracy theory" seems to be a tactic first used by an "intelligence" agency to discourage those who question the "authorized" narrative.
Free thinking is a gift, that can also be a challenge when it goes counter to main stream culture.
> To combat conspiracy thinking, the most promising approach has been found to be prevention. We must either warn people ahead of time about a particular conspiracy theory or explicitly teach them how to spot shoddy evidence. Symbolic logic provides rigorous training to spot inconsistencies and flaws in reasoning. For example, many naysayers to global warming present the evidence of cold weather on a particular
I like the effort. But it is done very poorly. Term "global warming" was replaced by "global climate change". There are valid scientific reasons and nuances for that change.
I like symbolic logic, but does it actually make people better citizens / resistant to conspiracy thinking / ... as the author hopes? Is there any evidence for that?
This is my question too. Is this a proven thing, or is it just the author's opinion or intuition? How do you even measure "better citizens"?
Lots of drivers will say we should build more and wider roads, more motorways, and so on. But there are some arguments for not doing that. The obvious thing or the intuitive thing is not always the right thing to do.
While better understanding of logic and reason are certainly not harmful, they are not the solution to the problems the article describes, because it is not the lack thereof that is causing these problems in the first place:
Fighting conspiracy theories and disinformation, educating the next generation to vote more thoughtfully and independently, etc. "responsible citizenship" as the article puts it.
What I observe over and over again is that people are quick to draw the conclusion that everybody who arrived at a different worldview than them must be lacking logical reasoning abilities, thus be stupid. Because, how else would you not arrive at the only "logical" worldview? And the article makes the same mistake.
(For the record, I am not saying that there are multiple subjective truths, no, there is only one objective truth. However, nobody can truly claim to know knowing it.)
Furthermore, this misunderstanding about the problem perpetuates the problem. It is like treating an infectious disease by draining blood from the patient.
In a functional society everybody only verifies a small part of the truth, which they have expertise in. These parts then overlap and form the whole. No single individual has to be able to reason through its entirety and prove everything, as that is impossible. Instead, the system relies on trusting the partial results of others. And that is exactly the attack surface is.
Conspiracy theories, disinformation and populism are nourished by completely different mechanisms independent of thought and reasoning. Attacking them on that level is futile. Even if they superficially look like manipulation of the though process, they are instead emotional manipulation. Typically the erosion of trust with fear as replacement.
I don’t disagree with the premise that this is a worthy goal to strive for, but I do find it odd to tie it to the need to combat “outlandish conspiracy thinking” and linking to a three year old NPR article about Trump.
I already knew it was going to be something like this just from the title. Kids should be taught to think for themselves, not just logically. We are growing a generation of people who offload their critical thinking to authority or actors/actresses or pop culture.
I agree. Learning symbolic logic might help (in that it might make if easier to recognise fallacies), but it is a small part of what is needed. If you just teach it, it will just be another bit of theoretical knowledge from school people never apply.
At the risk of sounding a bit conspiracy theorist myself I would say "authority" is quite comfortable with people not thinking themselves. People aim to be in authority because they think they know what is best for everyone - no thinking required of the hoi polloi.
Edit: I think it would be rather like maths. A lot of people (not around here, but say, business people on LinkedIn) say "I never use the maths I was taught in school so its pointless teaching it" because they do not know how to apply it.
To be fair, every generations is "a generation of people who offload their critical thinking to authority or actors/actresses or pop culture."
This didn't start with the generation currently under 18 years of age. I mean not to put too fine a point on it, but the outlandish conspiracy theories everyone is concerned about came from Boomers, Millennials, X'ers and older GenZ'ers. Frankly, the evidence points to all of us having questionable critical thinking skills.
My suspicion is that not only those under 18, but those over 18 as well could use a bit of a refresher on symbolic logic. Also a refresher on assessing the verifiability and relative value of facts.
I think you could describe the main alternative as 'institutionally mandated thinking' which ironically tends to be the approach used by school systems.
The main alternative is obviously emotional thinking, or "motivated reasoning." It is a factor in every decision made by anyone about anything, and has far greater reach than whatever bugbear you're pointing to here.
> For example, many naysayers to global warming present the evidence of cold weather on a particular day as a proof that global warming is a conspiracy.
This is quite rare and the opposite is in fact more common. “Hottest day since xx” is the most common claim.
Even in an article about logic, they can’t help but gaslight.
But logical thought is definitely important. Judging by some people I encounter, even understanding the concepts of "necessary but not sufficient" or "X is-a Y does not mean that Y is-a X" would make a big difference.