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Ask HN: Any resources to learn the fundamentals of critical thinking?
86 points by febin on June 9, 2018 | hide | past | favorite | 49 comments

Do a web search for “trivium”.


> ”Our teachers of the last generation have divided knowledge into relatively isolated “subjects” without emphasizing the interconnection of all knowledge. We have learned “subjects” without actually learning how to tackle these subjects—we have not learned how to learn. We might say that we have been set to work hammering, chiseling, planing and carving without ever being taught how to use the tools. We have picked up what we could as we went along, incidentally.

> The classical educators started from the other end and emphasized the importance and use of those master tools that could be widely applied. Of course in order to learn the use of these master tools (grammar, logic and rhetoric), it is necessary to apply them to some piece of wood, to some subject—and so actual subjects must be studied (English, Latin, History, etc.). But note that the chief goal was to master the tools—for in mastering the tools, the subject (any subject) would soon be mastered as well. We encounter a paradox: classical educators favor tool over content and therefore help students to master more content than ever. They have taught their students how to learn.“

(warning: above PDF has a specific worldview)

It's a lack of critical thinking that requires a disclaimer about the PDFs world view.

Totally, but there will be less noise if I state that upfront to decrease the chances that someone will take offense. Your comment, for example, is much more interesting :)

Studying math is the most direct and easiest route to get the human tendency to believe what's psychologically expedient beaten out of you. Any rigorous intro to math (abstract algebra, analysis, topology, whatever) book will do. But the easiest, most varied and funnest would be intro to discrete math or the so called "transition" books. For example, check out [1] Discrete Math by Susanna Epp, [2] Transition to Advanced Math by Gary Chartrand et al, [3] How to Think about Analysis by Lara Alcock, [4] Learning to Reason by Nancy Rodgers

[1] https://books.google.com/books?id=PPc_2qUhXrAC&pg=PA1&source...

[2] https://www.amazon.com/Mathematical-Proofs-Transition-Advanc...

[3] https://books.google.com/books?id=n0tuBAAAQBAJ&pg=PA4&source...

[4] https://books.google.com/books?id=J9RLuhDRWGQC&pg=PR6&source...

If you're on a budget, check out the free ones like [1] Book of Proof by Richard Hammack, [2] Math Foundations of Computing by Keith Schwarz

[1] https://www.people.vcu.edu/~rhammack/BookOfProof/

[2] https://web.stanford.edu/class/cs103/notes/Mathematical%20Fo...

I've been doing the book of proof front-to-back, all the odd problems and finished like 30% of it. Been doing it for about 1.5 months so far before I go to sleep.

Its made me realize that critical thinking is just breaking down logic to its smallest component form. And having some means of expressing different ways of organizing those components. Logic applies to all things, so time spent learning math is always useful.

I'm trying to make math derivations / critical thinking something I can do without trying, so its easier for me to pick up more complex topics and actually understand what's going on.


Two general principles that have helped me a lot:

1) Resist attaching my ego to my thoughts and ideas, whenever possible (sometimes it is unavoidable).

2) Avoid having a strong opinion on something without really good reason [1], especially if it is a serious issue.

This makes it easier to deeply look at a difficult issue from multiple angles, and perhaps get a better understanding. Something that is difficult but very rewarding is the practice of taking some idea or belief that you disagree with, and trying very hard to imagine what the world would look like if it was true.

[1] Such as significant time researching and studying multiple sides of an issue. And even then, we have to be careful. How do we know our research was actually sufficient? The world is incredibly complex.

Here are two books I've enjoyed

Systems Thinking: https://amzn.to/2y43BaO

. Shows how most situations in life we face require a larger perspective, to see them as a complicated system. Contains many good references to systems thinking

How to Solve it: https://amzn.to/2sR1Jw4

A book by a mathematician (Polya), which tells you how to think about problems in a way that you can generalize to any type of life situation

Edit: Sorry, fixed the second link

Critical Thinking: Tools for Taking Charge of Your Professional and Personal Life was part of my degree, I wound up buying it. https://smile.amazon.com/dp/B00ER86QOU/ref=cm_sw_r_cp_apa_i_...

Both links point to the same book. Do you mind posting a link for the second book?

I believe that there is no one-fits-all recipe for critical thinking, because its more of a personal thing.

It depends on your motivation for starters. Ever caught yourself thinking "Why do I need to question everything?"? Well, there you have it. Are you just curious, or is it mistrust that drives you? Are you able to question your own thoughts and motivation? Can you identify and fix your own errors? Are you able to answer these question? Observe your own thoughts and examine ideas that come to your mind, as if in argument with yourself.

Critical thinking is an endless stream of: Why, why why? So its not really about finding the answers, but rather asking the right questions.

@dschuetz's answer is pretty good.

I would add that it helps to hang around people who are themselves critical thinkers. Not the negative cynical kind, mind you, but those who like to explore new ideas, question old ones, and are not afraid to admit that some new ideas ended up sucking (after some consideration) and that the old ones weren't too bad with which to begin. Surrounding yourself with people like these help expand perspective and avoid group think.


This site has great information on how to think. The above post is particularly excellent.

As someone who wanted to ask a similar question to the OP, and didn't specifically know how to word it, the link on mental models really hit the nail on the head.

Make sure that whatever resource you find doesn't prescribe the results of your critical thinking. There are plenty of ideologues that try to prove to you that with critical thinking and rationality you will come to the same conclusion as the ideologues and that this is the only valid way of thinking.

If you read one thing and one thing only, it should be this. It's overwhelmingly long, but it's really, really, really worth it.

I think one of the fundamental aspects is self-awareness and meta cognition. Think about your thinking process, in comparison to those you interact with, and you will learn about your assumptions/biases (and theirs). Use that awareness to compare with people whose judgement you respect (and those you don’t), and how they frame their opinions. These might even be fictional/idealized characters—the point is that they provoke meta cognition in you. As you become aware of different mental models, start practicing applying them to matters you encounter, and learning from feedback. Most resources take a short cut to this stage, but the art of choosing which mental models to apply when is an intensely personal matter, and can’t be obtained by reading about mental models.

Further, as a useful rule of thumb: On any controversial topic, you’re not allowed to hold a strong opinion till you can clearly articulate the reasons for both/all sides of the matter (such that a person advocating the respective side would consider it a fair representation of their views/thought process)

The highest roi I ever found for critical thinking enhancement was LSAT prep.

Specifically, the logical reasoning section has you evaluate a series of arguments and answer (often tricky) questions about the argument--analogizing, finding flaws, etc.

Formal books etc are fine, but if this were programming, I'd say dive in and write code. Imo LSAT prep is the 'write code' in this instance.

If you define "critical thinking" as the ability to reason correctly, ie to identify the truth value of a statement or idea, given certain assumptions, then you're talking about logic.

It baffles me that -- at least in the U.S. -- we don't include logic per se in the core curriculum of a liberal arts college (let alone high school) education.

As an undergraduate I took an "Intro to Formal Logic" course, found I really enjoyed it, and was invited to become a tutor in subsequent semesters. At the time (circa 1995) we used the 7th edition of a classic textbook, "Logic & Philosophy: A Modern Introduction"[1]. Doing logical proofs in sentential and predicate logic is a lot more fun than it sounds, and results in improved instincts and ability to determine the logical validity and veracity of any set of statements. This skill is profoundly useful, and has incredibly broad applicability. It helped me ace my LSATs, and enabled my transition to software engineering. I think logic per se should be a core requirement for any kind of decent education. And if you're looking to improve your critical thinking skills, this is the foundation. It's reason, distilled.

[1] https://www.amazon.com/Logic-Philosophy-Introduction-Alan-Ha...

[Edited to add intro / context]

While not disagreeing with your thesis, I took "Argument and Applied Logic" in college and found it to be a low-point in my academic career. It was less fun than it sounds.

Logical thinking is the absence of illogical thinking. Therefore, one way to learn logical thinking is to learn the common patterns of illogical thinking, and avoid them.

Here is a list of the most common ways that humans think illogically:


In all seriousness, the comedian Gallagher started me on the path. He would point out a lot of flaws in our language, society, a lot of odd things, but the bit of wisdom that rung in my ears:

"What is the truth? And what does it mean to be true to the truth?"

A full exploration of that question is its own education.

My personal advice is patience.

Patience is the key to so many things! I break into three steps:

- Faith: in your methodology or approach

- Determination: to actually follow through

- Courage: to act when the time is right or to admit you were wrong

If courage fails you lack determination if determination fails you lack faith. Such is patience.

Now what should you believe? Cause that is the question you are trying to have answered here, when you ask to learn 'critical thinking' you are asking for a method to believe in.

I don't think that makes much sense, you already have a method and it is your raison d'être. Now what you need is introspection, but approach the task of incremental improvement patiently (i.e. explicitly / scientific method-y) and you won't go in circles.

Math is a fine place to start but just study whatever is relevant and do it well.

It's not as easy as one would think, no pun intended.

For way too long I have lamented the steep decline of critical thinking in everyday life, and yet - outside for Academic circle - there's very little discussion and education on the matter. In my ever-long TO-DO list there's a project to write a Critical Thinking 101 book, alas it's probably not going to happen.

Good comments and resources in this discussion, I'd like to add http://criticalthinking.fsu.edu/news/ted-talks/ and also the usual suspects at Amazon.com.

P.S.: If someone has a good resource/book for Critical Thinking for kids, please post it.

'The Fall of the Human Intellect'

Study it critically: https://www.amazon.com/Fall-Human-Intellect-Parthasarathy/dp...

Strive to become comfortable with uncertainty and doubt. At first your instinct is to arrive at certainty, to hang onto “facts” and put things in boxes. It can cause anxiety to leave things in some state of either-or-maybe, but it’s a critical too. I’m not arguing for global intellectual relativism, but a lot of what people settle on with certainty isn’t certain. Ask endless questions, and assign weights to answers, but even when one is 99.9% likely, don’t totally ignore the other 0.1%. Take opportunity reevaluate what you “know” based on new information, and try to avoid traps like groupthink or contrarianism.

Above all, accept this as an ongoing process that only ends when you die.

"Structure of Magic, Vol. I" by Bandler

The "Meta-Model" is a set of questions based on Chomsky's Transformational Grammar that are designed to elicit"hidden" information by detecting and "surfacing" the deep structure of linguistic models in a therapeutic context.

For example, a statement of the form, "Foo shouldn't bar." omits the reason or motive, and can be met with a question of the form, "What would happen if foo did bar?"

You can use the Meta-Model to guide your own introspection and elicit thoughts or beliefs that you might not even be aware you hold.

Not an external resource but I've identified that there are thought tools I continually apply in my own thinking to gain new perspective. I started writing them down and organizing them which has immediately benefited me and maybe one day I'll have distilled them clearly enough to share with others. Kind of like a toolbox for the mind.

Anyway, my advice is write down your own thoughts and discoveries. You'd be surprised how much content there is when you start collecting it all in one place and it will help you be more critical of your inner workings

Always look for the hidden agenda.

Believe none of what you hear and only half of what you see and still will believe twice too much.

Rationalism over emotionalism.

Get facts only from respected, objective, primary sources.

Extraordinary claims need extraordinary evidence.

As Sharyl Attkisson warns, essentially everything in the mainstream media is paid for by someone who wants to influence your opinion.

Remember the statement of Nazi Minister of Propaganda, J. Goebbels "If you tell a lie often enough, then people will believe it. Eventually even you will come to believe it.". A lot of people out there are pushing propaganda in just that way.

Measure twice and saw once.

In many circumstances, people are permitted to lie and commonly take advantage of that fact.

At dawn, a lie can circumnavigate the globe while the truth is still getting its shoes on.

I think for me, the key was reading books by authors who were exceptionally good at it. Here are a few off the top of my head from the political domain that opened my eyes:

Gaddis: The Landscape of History

Bazerman & Watkins: Predictable Surprises

Kuperman: The Limits of Humanitarian Intervention

You simply cannot read enough material by people who think well.

Daniel Dennett [philosopher] Presents Seven Tools For Critical Thinking

I can't remember who said this, but it was something along the lines of "mastering the use of an abstraction means one must understand what's happening one layer deeper". So in essence, always ask why something works.

The Philosopher's Glove http://www.jesus-eucharistie.org/wisdom

the book The Pyramid Principle: Logic in Writing and Thinking is a fantastic resource. The first part of the book discusses how to structure your ideas in writing to communicate them well. The second half of the book addresses logical thinking


Critical thinking, one of the two most important skills IMHO, is not a defined set of skills but more an undefined set of principles applied in different ways by different fields and, of course, by different people. Probably the best resources, IMHO, are university courses and their cirriculums.

* Most importantly, surround yourself with the very best. As much as possible, read the best thinkers. Stop reading Reddit, blogs, op-eds, Internet rants etc. as much as possible; they will drag you down. If you want to write well, you read the best writers; their high standards and abilities become your norm and you absorb their techniques and ideas; if you read average writers, they become your norm and you absorb average techniques and ideas. It's the same for critical thinking; the best are not perfect - they are not prophets and they don't write scripture; they are flawed and we all should read them that way - but for flawed humans, they build amazing things. Thanks to the wonders of written language and the efforts of endless generations of scholars, you can read some of the very best thinkers over the history of humanity. The cirriculums of university courses can be a great starting point.

* Study with experts: You don't know what you don't know. Amateurs in any field often have enormous blind spots. They ask the wrong questions, based on the wrong assumptions, and have the wrong answers to those questions. There are other critical questions they simply have no idea to ask. Again, expertise shouldn't be taken uncritically, but someone who has spent a lifetime studying the field knows more than you do. The obvious solution here is to take classes, online or in person, or at least utilize some of their work product, their curriculums.

Also, going a step beyond the (brief) question, I'd especially make an effort to learn critical thought from a variety of perspectives and fields, to using variety of tools. Off the top of my head,

* Scientific method, and the philosophy behind it (post-positivism, etc.). Actually designing, implementing, and writing up an experiment is an invaluable experience.

* The difference between the Enlightenment, the birth of modern critical thought, reason and science, and the Middle Ages (and really all of human history) which came before it.

* Quantitative reasoning, including statistics: how they can be applied and misused, and how to think critically about them. I don't mean learning all the quantitative tools (though that can be helpful too).

* Post-modernism, in the critical literary sense: The fact that so many respond so angrily to it should tell you how powerful and challenging it is, as well as the fact that those same people use it without seeming to realize it.

* Anthropology: I've always wanted to study this, as it steps outside the culture, and all cultures, and views them from a different perspective.

* Radical / revolutionary thought: I'm not at all saying to become a radical or revolutionary. But in this field are tools to step outside and think critically about social norms, which is one of the hardest things for humans to do - most people can't even imagine the universe is larger than their norms.

* Historiography: You can't understand history unless you can think critically about the sources of your knowledge of it.

* Economics: This set of tools is very powerful, extremely influential, and widely applicable.

Descriptive knowledge:

* The psychology of perception: All critical thinking begins with inputs of observation and communication, which necessarily are processed through human perception. The psychology of it is both critical and not at all what most people expect.

* The psychology of reasoning and decision making: How people actually make decisions, which is not at all how they think they do.

In my view, the best way to learn critical thinking is to practice it. For example, let's analyze this part critically for a moment:

> * Post-modernism, in the critical literary sense: The fact that so many respond so angrily to it should tell you how powerful and challenging it is, as well as the fact that those same people use it without seeming to realize it.

Some of the most devastating criticism of postmodernism consists of incidents like the Sokal affair [1]. I don't see how this would count as 'using' postmodernism, though, when it is merely pointing out that the theory is indistinguishable from word salad. I suspect you had other criticism in mind, but this specific criticism could only be seen as 'using' it if you privilege postmodernism itself as the overarching framework under which to understand everything else. Such a viewpoint which would be quite ironic in postmodernism, though, and should therefore be rejected as self-contradictory.

The other bit of reasoning employed here seems to be pretty much the 'denial is proof' trap, which should also be understood to be an inherently self-refuting argument. This is true even if one wishes to say that it 'uses' the argument in some sense while playing the thing against itself to arrive at a contradiction.

After all, one cannot both accept that denial is some kind of proof, while denying the rest of the above logic and thereby providing proof for it.

[1] https://en.wikipedia.org/wiki/Sokal_affair

As I said, read the best, not the Internet forums. There are problems with post-modernism just like there are with everything else, but not those described above. Read the best criticisms of it.

> devastating

The same way cold fusion 'devastated' physics, the Piltdown Man 'devastated' archeology, and nonsense comments 'devastate' Hacker News. I have no idea of the facts of the event in question - not the claims endlessly repeated as a dramatic gimmick, but the reality - and I don't really care because it amounts to very little either way.

Read about actual post-modernism; you might find some of yourself in it. It would make you a heretic in some circles, I know.

It's been repeated multiple times, not targeting the weak low quality journals (which, I agree, can likely be done to any field) but the top journals. If the Piltdown man had been published in the journal Science, that'd be more analogous.

Some of the criticisms levied by post-modernism are valid, but if the best journals can't distinguish between it and a Markov chain, we have a problem of low information content.

It's a minor point, but since you mentioned the scientific method and the Enlightenment, the way the field of anthropology operates is still based to some extent on those cultural specifics so they aren't completely stepping outside of all cultures.

Good for you for wanting to think more critically.

Sorry if this is anecdotal babble, but when I was in junior-high they put all of us that were ‘ahead’ (I.e. those that read too much instead of going outside and socialising) in a Critial Thinking class.

I loved it, thought I was a great critical thinker, and then ended up getting a D in the final exam. My teenage hubris was a double-edged sword. Nevertheless, some of the concepts we were taught over a decade ago still stick with me as great heuristics that crop up all the time in poorly constructed arguments.

A few of my favourites that I recommend you read-up on (Wikipedia or otherwise) are:

- Tu-Quoque

- Ad Homeneim

- Straw Man

- CRAVEN for Credibility of Evidence

Apologies if you already know these, just thought they may help you on your journey to more critical everyday thought. :)

Critical thinking is really easy. Just take something that is self-evident or obvious and start thinking about why you believe that thing. Doubt it for a moment and come up with evidence for (or against) the thing. If you get into the habit of doing that, you will be a great critical thinker. Especially do this to new information that enters your system. Critical thinking is not a difficult concept to grasp at all.

One that's currently on the front page is playing games like The Incredible Machine. I credit games - and to some extent, the fiddlefucking that was involved to get them running in the MSDOS days, for most of my critical thinking skills.

You learn to question the published truth, and get down to the bare, hard facts of reality, which often doesn't match. And you learn to try things, and how to iterate if things don't work, in a relatively low stakes environment.

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