Kids Should Be Taught to Think Logically
scientificamerican.com
scientificamerican.com
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.
What would be on that list?
> 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.
"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.
"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.
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.
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.
In general, look into the analytic-synthetic distinction: https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_dis...
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.
Critical, creative, analytical, abstract, concrete, divergent/lateral, convergent/vertical.
Or
Synthesist, idealist, pragmatic, analytic, realist.
There are lots of options. My point was really about awareness of the different styles and their advantages/disadvantages.
Reason > Logical reasoning methods and argumentation: https://en.wikipedia.org/wiki/Reason#Logical_reasoning_metho...
Critical Thinking > Logic and rationality > Deduction, abduction and induction ; Critical thinking and rationality: https://en.wikipedia.org/wiki/Critical_thinking#Deduction,_a...
Logic: https://en.wikipedia.org/wiki/Logic :
> 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 reasoning: https://en.wikipedia.org/wiki/Logical_reasoning
An argument can be Sound or Unsound; or Cogent or Uncogent.
Exercises I recall:
Underline or Highlight or Annotate the topic sentence / precis sentence (which can be the last sentence of an introductory paragraph),
Underline the conclusion,
Underline and label the premises; P1, P2, P3
Don't trust; Verify the logical form
If P1 then Q
P2
therefore Q
If P1, P2, and P3
P1 kinda
we all like ____
therefore Q
"Pete, it's a fool that looks for logic in the chambers of the human heart.", money x3, posturing
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
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.
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.
I think you might be right in some situations but wrong in most others.
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"
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.
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.
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.
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.
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.
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.
Do we choose the authority of the hour? An older tradition? Come up with our own ideas? Lots of options there.
A culture where people think it’s ok to believe in made up nonsense will always work against rational thinking.
Even stuff like crystals, tarot cards, and astrology contribute to this.
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.
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.
> 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.
This is semantics, not logic.
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.
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
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
Hmm, is this something that you can prove with logic though?
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.
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".
If people think it’s ok to have irrational beliefs, you give their brain an escape hatch to ignore logic and reason if it feels good.
Not to mention this can and does get exploited by bad actors.
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.
Charlotte Thomson Iserbyt's "The Deliberate Dumbing Down of America" may be a case in point.
https://deliberatedumbingdown.com/ddd/
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.
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.
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.
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.
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.
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.
i'd argue that the more common problem is a deficiency in assessing reasonableness or plausibility of facts and claims.
if you feed garbage data into your logic-machine, you'll get garbage results.
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.
Is it the most common claim of naysayers? I very much doubt it. Do you have any proof of this?