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子曰：「工欲善其事，必先利其器」(《論語•衛靈公10》)；「器」在這裏指的大概是工具。但是，要把一件事「做對」，「工具」之外，還得講究「方法」。「雖不中不遠矣」 (《大學章句10》)，講的應該是「態度」；這個道理用在「方法」上也可以說得通。這是「科學基礎論」中「科學方法」研究的對象。
大概在初中時，家父給了我一本討論「科學方法」的書；書名已經忘了。這是我第一次接觸到這個主題；自然印象深刻。後來成長過程中，我對它一直非常注意。「邏輯學」之外，我還讀過笛卡爾和波普的書。本部落格過去登過不少這方面的評論。
循此處各《開欄文》之意，另立此欄。
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非文學類的7個寫作小心得 -- Mental Garden
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7 Harsh Writing Lessons I Learned After 300 Articles — So You Don’t Waste Years
How to dramatically accelerate your growth
Mental Garden, 11/21/25
I want you to know this: I wish I had read this when I first started.
If you want to start writing and you feel like your words could go further — that they lack impact or fail to resonate with anyone… I’ll share with you 7 keys I’ve learned and applied during more than 500 days of writing and over 300 published articles.
Here are the 7 keys you can use right now to strengthen your writing.
1. Ignore the word count
A text isn’t better because it has 800, 1,000, or 2,000 words.
The only thing that matters is: Did you answer what the reader came looking for?
A title is nothing more than a promise. It tells the reader what they’ll find once they begin reading. Your only real job is to deliver that valuable information as clearly as possible.
* A Twitter thread won’t have 20,000 words, but it might have 200.
* A newsletter won’t have 200 words, but it might have 1,200.
* A book won’t have 1,200, but it might have 50,000.
The medium you write for defines what’s acceptable — nothing more.
Just write within that range; it doesn’t matter if today’s newsletter is 700 or 1,500 words. When I started writing on Substack, I’d think: “Too short, it should have at least 800 words.” Now I tell myself: “If the idea is resolved in 700, then it’s 700; if it needs 1,500, then it’s 1,500.”
The metric is not the word count.
The metric is: Did the reader leave with what they came for?
If yes, they’ll come back.
2. Make an “anti-list”
People are tired of hearing the same things.
* The perfect diet.
* The perfect study routine.
* The 10 secrets of productivity.
They’re always the same clichés: sleep 8 hours, drink water, plan, meditate. Everyone repeats them. And when everyone repeats the same thing, you add nothing.
Imagine your writing is a fruit shop.
Apples are the typical advice: easy to sell, everyone likes them. But here’s the problem: there are fifty fruit shops on the same street selling the exact same apples. No one will remember yours.
The solution is simple: offer something different.
Yes, sell apples — every fruit shop needs some clichés — but add the specialized fruit that makes you unique: passion fruit, dragon fruit, lychee, papaya. Those unexpected fruits make customers say: “I haven’t seen this anywhere else — I’ll try it!”
Want to stand out as a writer? Do the opposite of what everyone else is doing.
Example: If you want to write “The perfect productivity routine,” you think of waking up early, organizing schedules, taking breaks, drinking coffee, sleeping 8 hours. Sound cliché? Good. Now the interesting part: you can’t use any of that.
That’s your anti-list.
What else can you offer? When you eliminate the obvious, the unexpected emerges. This technique comes from option suppression — look it up if you want to go deeper. For example, you could start your real productivity list like this:
* Batch errands into a single day: groceries, pharmacy, paperwork.
* Decide your weekly menu on Sunday: no more “What do we eat today?”
* Write your tasks on paper, not your phone: avoid digital distractions.
These productivity tips are far less common.
That’s the power of the anti-list.
Want an example from me? Please See：How aerodynamic drag in Formula 1 applies to productivity.
3. Start strong and end strong
The first and last lines are the two pillars of the text — if they’re weak, everything collapses.
Readers mostly remember what grabbed them at the beginning and what you concluded at the end. What’s in the middle matters, of course, but the introduction and the ending carry the maximum tension; the middle is just the development. This applies both at the article level and within each block.
That’s what makes the text effortless to read and brings key ideas to the foreground.
If you look back at what you just read, you’ll see the structure: first a striking statement — “The first and last lines are the two pillars of the text” — then the development that expands it, and finally an unforgettable closing: “That’s what makes the text effortless to read and brings key ideas to the foreground.”
You’ve just seen how effective this structure is.
When you write online — where attention is fragile and readers can close your article in a second — writing this way ensures they stay. This is due to the “F-pattern effect.” Look it up to understand how we read on the internet and how to adapt your text to that reading pattern.
Then you’ll understand why this “strong start and strong finish” is so effective.
4. Don’t write only long paragraphs
Not everything has to be dense text blocks.
Newsletters are read on small screens, amid distractions, sometimes standing on the subway or bus. Readers need breathing room and text that’s effortlessly legible.
Give them exactly that.
* Use lists when you enumerate ideas, descriptions, or steps.
* Don’t hesitate to include visuals, images, or supporting elements.
* Insert short sentences when you want to emphasize something — like in tip #3.
This makes your writing more readable and aligned with how people read online.
5. Delete the “I…”
“I think…”, “I believe…”. These openings are redundant.
You’re the author — obviously the ideas are yours, you don’t need to clarify it constantly. I realized this after re-reading my articles many times: those filler phrases became stones in the path. They tired the reader and added nothing.
Deleting “I…” makes the sentence stronger.
Instead of “I think writing is a muscle,” write: “Writing is a muscle.” The second hits harder, more directly.
The exception? When quoting others.
If I mention Hemingway, García Márquez, or a scientific study, I clarify. That’s where attribution matters. In all other cases, readers already know the voice is yours. Anything not attributed to someone else is yours.
Clear the stones and weeds from the reader’s path.
6. Warm up before you start
No one walks into the gym and lifts 100 kilos without warming up.
Why do we do that when we write?
Julia Cameron recommended what she called “morning pages,” meaning writing pages about anything that comes to mind to wander, generate ideas, and prepare the mind for focused writing. Spend 10 minutes writing freely. Write about what you dreamed, what you think of the day, what you ate for breakfast. It doesn’t matter.
The result doesn’t matter; the goal is to clear mental noise and enter flow.
Press enter or click to view image in full size
7. Use few adverbs — avoid the ones ending in -ly
Hemingway knew it and García Márquez said it clearly:
“Adverbs ending in -mente are an impoverishing vice. I haven’t used any in my books for a long time. I force myself to find richer, more expressive ways of writing.” — Gabriel García Márquez, Living to Tell the Tale
Every time you write quickly, subtly, delicately, the text loses strength.
A good verb does the job better than any adverb. Don’t say “walked slowly,” say “ambled.” Don’t say “spoke passionately,” say “exclaimed.”
The message becomes clearer — therefore more memorable.
When revising your text, do this exercise: look for adverbs and delete them.
You’ll be surprised how little you needed them.
Writing better is having the right tools for each situation:
* Ignore the word count
* Make an anti-list
* Start and end strong
* Don’t rely only on long paragraphs
* Delete the “I…”
* Warm up before writing
* Use few adverbs — avoid the -ly ones
Small practices that, together, make your writing resonate and leave an impression.
Nothing more to add.
Your turn: What other writing key has worked for you and deserves to be on this list?
Quote of the day: “Writing as a poet is one thing; writing as a historian, another.” — Miguel de Cervantes, Don Quixote.
Here I plant ideas. In the newsletter, I make them grow.
Daily insights on self-development, writing, and psychology — straight to your inbox. If you liked this, you’ll love the newsletter. Join 43.000+ readers: Mental Garden
See you in the next letter, take care!
References
Márquez, G. G. (2002). Vivir para contarla.
Written by Mental Garden
Productivity and psychology inisghts in useful life lessons +3M monthly views and +300 articles
Published in Change Your Mind Change Your Life
Read short and uplifting articles here to help you shift your thought, so you can see real change in your life and health.
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讀書務必使用「根基法」 ---- Mental Garden
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請參見拙作《淺談「讀書方法」》(本欄2025/03/18)，以及此文(該欄2025/03/17)。
The Root Method: How to Absorb Books Like a Genius (Without Highlighting a Single Page)
Stop collecting information — start crafting your own knowledge
Mental Garden, 04/30/25
We immerse ourselves in books because we seek to understand the world, to develop new skills, to change the way we think. But if you’re like me — or like so many voracious readers — have you ever finished a book that inspired you, that you even talked about with a friend, but a few weeks later…
You can barely remember anything.
Maybe you feel like you could get more out of your reading — all those hours and all that wisdom that end up going nowhere, unorganized, not put into practice… Today, I want to share with you the most effective minimalist method I know to fix this.
The Root Method.
You’ll retain more, understand better, and most importantly: you’ll start connecting ideas across books, authors, and disciplines. Same readings, deeper learning.
What is the Root Method?
It’s based on a fundamental principle: shifting from passive reading to active learning.
1. Before starting a book, take a blank sheet of paper and write down everything you already know about the topic you’re about to read about. Even if you think you know very little.
2. During your reading session, add what you learn in a different color.
3. Before your next session, review your sheet. During the session, return to step 2.
4. Store the sheets in a binder and study them periodically.
That’s it.
But what happens inside you while you do this… that’s where the magic lies.
Let’s break down each of the 4 steps:
Step 1: Before starting a book
Take a blank sheet of paper and write down everything you know (or think you know) about the topic. It doesn’t matter if it’s just three words or half a page. The important thing is to force your brain to recall and organize your ideas before consuming new ones.
Don’t know anything? Perfect.
Write down the questions you have. Or create a mind map with scattered words. The key here is to establish your starting point. It’s a quality filter to see what beliefs you hold, what preconceptions you carry, and it opens you up to the possibility of correcting them later.
Step 2: During your reading session
After reading a section of the book (a chapter, a block of ideas, or even just a dense page), return to your sheet and add what you learned — using a different color.
This detail is crucial.
Each color represents a different reading session. Visually, you can see how your knowledge evolves. It’s not just “read and turn the page.” It’s about extracting the best from each session. Documenting your growth. Building a structure of ideas you didn’t have before.
Never copy a paragraph or idea word for word.
You must explain it in your own words, in a summarized form.
This forces you to process the information, not just store it. And while doing so, you’ll likely notice errors in what you wrote at the beginning or in previous sessions.
Awesome, right?
Correct them, cross things out, jot down the updated version. This comparison makes you think critically about what you wrote, sharpening your learning more and more.
Step 3: Before your next session
Before starting your next reading session, review your blank sheet.
It’ll only take a few minutes, but this simple act refreshes your memory about what you’ve already learned and prepares you to connect the new ideas with what you already know. It transforms every learning into building blocks, session after session, allowing you to see connections that previously seemed invisible.
* Recurrent keywords or technical terms.
* Core ideas that structure the whole topic.
* Cause-effect patterns or parallels.
In other words: you read more deeply.
Step 4: After finishing the book
You’ve finished the book and now have several sheets filled with colors, ideas, corrections, and notes.
Store them in a folder. That sheet is a map of your learning. A valuable resource you can review later. I recommend rewriting it neatly. Doing so forces you to synthesize again, organize your ideas definitively, and filter out the essential now that you have the full perspective.
Then, every few months, review it. Spend a few minutes.
This simple, repeated act embeds the information into your long-term memory — it’s called spaced repetition, and it’s the most effective technique for retaining knowledge for years.
Why does it work so well?
Because it combines 3 powerful learning principles in one simple action: writing.
1. It naturally applies the Feynman Technique
When you write and structure what you learn in your own words, you force yourself to explain it clearly. You don’t just repeat — you truly understand what you read.
And that’s harder than regular note-taking… but also far more effective.
Every connection between concepts, every outline, every review is an opportunity to detect mistakes or gaps. Rewriting is learning because it pushes you to make sense of what’s inside you, just as Feynman recommended.
2. It leverages spaced repetition
Spaced repetition is the most effective way to memorize long-term.
Every time you review your sheet before a new session, you’re refreshing your memory right when you need it. You fight the forgetting curve with small doses of active recall. And when you rewrite the sheet cleanly at the end, you create a distilled version of the essentials — a synthesis your mind can retain.
That’s knowledge you’ve worked for, connected, and internalized.
3. It avoids the collector’s fallacy
The collector’s fallacy is the idea that hoarding PDFs, highlighting everything, and taking endless notes equals learning.
No.
That just fills your folders with unprocessed data. With the blank sheet method, you can’t hide. You only write down what you truly understand, and you only keep what makes sense to you. You store less information, but you learn more. You don’t just collect ideas: you craft them. And that extra effort makes each sheet packed with real knowledge.
That’s why it works. Because it simplifies, repeats, and refines.
It’s not enough to know: you have to understand.
The Root Method isn’t just for books; it works for any learning process: courses, conferences, YouTube videos, podcasts. You don’t need complicated apps or anything fancy — just paper and colored pens.
Don’t stay at the surface of knowledge — dig down to the root of every topic.
You’ll notice the change instantly.
Your turn: What methods do you use to learn from your reading?
Quote of the day: “The skill I was learning was crucial: the patience to read things I could not yet understand.” — Tara Westover, Educated: A Memoir.
Here I plant ideas. In the newsletter, I make them grow.
Daily insights on self-development, writing, and psychology — straight to your inbox. If you liked this, you’ll love the newsletter.
Join 11,000+ readers: Mental Garden
See you next time!
Written by Mental Garden
Productivity and psychology inisghts in useful life lessons +3M monthly views and +300 articles
Published in Change Your Mind Change Your Life
Read short and uplifting articles here to help you shift your thought, so you can see real change in your life and health.
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推理過程的演繹法與歸納法 -- David Kyle Johnson
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Deductive vs. Inductive Reasoning
Dr. David Kyle Johnson, 10/10/25
Why Aristotle (and your science textbook) is wrong about deduction and induction — and why it matters.
A common misconception about the nature of deductive and inductive reasoning
請至原網頁觀看一般人對「演繹法」與「歸納法」誤解之處的說明圖
It’s commonly said that deductive reasoning goes from the universal to the particular, while inductive reasoning goes from the particular to the universal. You’ve probably seen these definitions in a science textbook; indeed, this notion was endorsed by “the rogues” on episode 1055 of my favorite science podcast, the Skeptics Guide to the Universe. But this understanding of deduction and induction is inaccurate — or, more specifically, outdated. (The SGU graciously had me on to correct the record.) And the point is not just semantic; the philosophical development of our understanding of the difference between induction and deduction completely changed the world, and is vitally important for understanding the nature of science (and debunking pseudoscience).
The Common “Aristotelian” Understanding
The common understanding of deduction and induction is usually attributed to Aristotle. A classic example of the kinds of arguments that he said, in the Prior Analytics (e.g., I.1 (24b18–20)) capture deduction, goes like this:
All men are mortal. (Universal)
Socrates is a man.
So, Socrates is mortal. (Particular)[i]
In the Posterior Analytics (II.19 (99b35–100b5)), as an example of induction, he gives us “posing the skilled pilot is the most effective, and likewise the skilled charioteer, then in general the skilled man is the best at his particular task.” In the Rhetoric, Aristotle offers an even clearer example:
Socrates was wise and just. (Particular)
So, all wise men are just. (Universal).
Based on these examples, it looks like deduction reasons from universals, while induction reasons to universals. But this is not how modern logicians define these terms — and for very good reason.
What’s Wrong with the “Aristotelian” Understanding of Deduction?
The first problem is this. Aristotle does not actually define deduction in this way. He says that deduction captures “syllogistic reasoning,” which he defined (in the Prior Analytics) as “a discourse [logos] in which, certain things being stated, something other than what is stated follows of necessity from them.” In other words, deduction happens when one statement (or statements) guarantees another. Now, many of the examples of this kind of reasoning Aristotle gave went from the universal to a particular, but there are other kinds of syllogistic reasoning that does not. For example:
Obama was president from 2009 to 2017. Therefore, all persons born during his presidency were born in the 21st century.
This actually goes from a particular (fact about when Obama was president), to a universal (a statement about when a whole category of people were born). Yet, in this example, the premise guarantees the conclusion.[ii]
What’s more, one can reason from the universal to the particular without the conclusion being guaranteed. For example, in 2019, someone might have said:
“All the previous seasons of Game of Thrones were good. Therefore, the last season will be good.”
While that conclusion, given the evidence, was likely — as we all know, it was not a guarantee.[iii]
What’s more, there are many more kinds of syllogisms — arguments where the premises guarantee the conclusion. There are hypothetical syllogisms, like modus ponens (If P then Q. P. Therefore Q) and disjunctive syllogisms (Either A or B. Not A, Thus B.). And these don’t have to go from universals to particulars, or from particulars to universals, at all.
If the alarm is armed, then the light will be red. The alarm is armed. Thus the light is red.
Either the light is on or off. It’s not off. So it’s on.
So “from universals to particulars” doesn’t fully capture the kind of syllogistic “the conclusion is guaranteed” reasoning that Aristotle was trying to describe.
What’s Wrong with the “Aristotelian” Understanding of Induction?
Interestingly, Aristotle didn’t really conceive of induction as a method of reasoning; for him, it was more of a psychological or epistemic process by which we come to grasp universal truths from particular experiences — the way we learn what he called “first principles.” To paraphrase a famous passage from his Posterior Analytics, “the soul sees the universal through induction.” Since this is a habit of mind, rather than an argument form, or even a form of reasoning, it’s obviously not very useful for classifying arguments or kinds of reasoning.
What’s more, something that Aristotle seems to have failed to recognize (at least in places) is what sets induction apart from deduction. The important difference is not that it is “a passage from individuals to universals,” but that it is not syllogistic; it doesn’t guarantee its conclusion. Sure, Socrates being wise somewhat raises the probability that all men are wise. But it by no means guarantees it. While Aristotle recognized this fact about this argument, he seemed to fail to recognize that this was induction’s defining feature (not the fact that it went from the particular to the universal).
But there are lots of different ways to raise the probability of conclusions. Arguments from analogy do this.
Thing 1 has properties A, B and C.
Thing 2 has properties A and B.
So Thing 2 has property C as well.
In certain circumstances, such a conclusion can be likely — but is never guaranteed; yet this kind of reasoning does not involve going from the particular to the universal.
Or consider inference to the best explanation. You take two or more explanations, compare them to certain criteria — criteria that explicate what good explanations are supposed to do — and then accept the explanation that adheres to them best. By no means is such a conclusion guaranteed — although, if done correctly, it can be beyond all reasonable doubt — but it does not involve reasoning from the particular to the universal.
Arguments from authority raise the probability of their conclusion but don’t always argue to the universal. Statistical arguments raise the probability of their conclusion but don’t always argue to the universal. Again, it seems Aristotle’s understanding of induction — or at least what is commonly thought to be Aristotle’s understanding of induction — is shortsighted.
The Modern Definitions
Although I am taking a shortcut through the work of Francis Bacon, David Hume, John Stuart Mill, C.S. Peirce (Purse), John Maynard Keynes, Hans Reichenbach, Rudolf Carnap here — what modern logicians eventually realized was that the following was a better understanding of the distinction at which Aristotle was seemingly pointing:
Deduction: Reasoning that guarantees its conclusion.
Induction: Reasoning that (merely)[iv] supports its conclusion.
To summarize this, we might say that deductive arguments are those with premises that guarantee their conclusion, while inductive arguments are those with premises that raise their conclusion’s probability. And if you are looking for a “short takeaway” from this article, that is it.
A Nuanced Point
That can’t be the whole story, however. Why? Because, if we accept the italicized phrases above at face value, we run into a problem: there can’t be “bad” deductive or inductive arguments (e.g., a deductive argument which fails to guarantee its conclusion).
For example, most people consider arguments which deny the antecedent to be deductive. “If P then Q, not P, therefore not Q.” When people give this argument, they often think the conclusion necessarily follows. But it doesn’t; denying the antecedent is a fallacy. Sure, if I am in Philly then I am in PA. But the fact that I am not in Philly does not guarantee than I am not in PA — I could be in Pittsburg, for example. So, although such an argument is clearly deductive, it does not guarantee its conclusion.
Likewise, someone could give a bad inductive argument. “Bob is blonde and plays football. Steve is blonde. So Steve probably plays football too.” The premises don’t raise the probability of the conclusion at all — yet clearly the argument is inductive (it’s an argument from analogy and analogies aren’t deductive).
To avoid this problem, modern logic textbooks usually suggest that whether an argument is deductive or inductive is determined by the intentions of the one who gives it. If the speaker intends for the premise of their argument to guarantee its conclusion, it is considered deductive; if they merely intend for it to provide probable support, then it is inductive. Once such intentions are clear, we can categorize the argument and bring the appropriate logical tools to bear to determine whether the argument does what the speaker intended for it to do.
Same Form, Different Categorization
Interestingly, this means that two arguments which take exactly the same form could fall under different categories. One can be deductive and the other inductive even though they look the same. For example, another classic deductive but invalid form of reasoning is affirming the consequent. (If P then Q. Q. Therefore P.) “If I am in Denver, then I am in Colorado. I am in Colorado. Therefore I am in Denver.” Obviously, this is not guaranteed; there are ways of being in Colorado without being in Denver. But clearly this argument is deductive.
But now consider a scientist running an experiment to test a hypothesis; they will consider an experimental result that a hypothesis predicted to be evidence for that hypothesis. (If H then R. R. Thus H.) Clearly, this follows the same pattern — yet we would not consider this form of reasoning deductive. Indeed, the good scientist will know and admit that the experimental result doesn’t prove the hypothesis true — it merely supports it or raises its probability. So this is an example of inductive reasoning. And we wouldn’t consider it “fallacious.” If the experiment is done correctly, it could provide a good amount of support for the hypothesis. So whether an argument is deductive or inductive can be sensitive to context too; it depends on the intentions of the person giving it.
Why This Is Important
There are two reasons you should care about this.
First, this issue is not just semantic; it’s not just about the definitions of words. Logicians replacing the old interpretation laid the groundwork for formal logic (like propositional logic and predicate calculus), the system that can mathematically determine whether the premises of an argument guarantees its conclusion. And formal logic laid the groundwork for all modern computing. You can’t build logic gates with categorical logic. Everything that uses a computer — which, today, is practically everything — is impossible without realizing that deduction is reasoning that guarantees its conclusion (rather than reasoning that argues to universals).
Second, science is inductive. Both scientists and philosophers of science recognize that, given the very nature of what scientific reasoning is, science never guarantees its conclusion. Although it can involve many kinds of reasoning, some of which are deductive, they are all in service of finding the best explanation — and inference to the best explanation is an inductive form of reasoning.
This is important to realize because one of the most common arguments of pseudoscientists, and those that deny what science has revealed, is rooted in what science has and has not “proven.”
“You can’t 100% prove how much damage climate change will do, so we don’t have to worry.”
“You can’t prove that vaccines don’t cause autism, so they do.”
As any good logician will recognize, these arguments commit a fallacy called “appeal to ignorance.” The fact that you can’t 100% prove something true doesn’t mean that it is false. But understanding that the nature of science in inductive reveals clearly why such arguments, especially when leveled against science, are fallacious. They are asking science to do something that, by definition, by its very nature, it cannot do. Science is inductive, so it doesn’t deal in proof. It, instead, raises the probability of certain theories and statements; it shows them to be more likely to be true. So, if we hold out for proof; it will never come. When deciding what we should believe regarding scientific matters, we must simply, as David Hume put it, proportion our belief to the evidence.
Or, to paraphrase a point Aristotle made in Book I, paragraph 3 of the Nicomachean Ethics: “It’s the mark of an informed mind to be satisfied with the degree of precision that the nature of the subject admits; it does not to seek for exactness where only an approximation to the truth is possible.” When something is beyond any reasonable doubt, we should accept it — and science can and does, quite often, establish things beyond any reasonable doubt.
The vast majority of scientific evidence suggests that climate change will be catastrophic and that vaccines are safe and effective. Those who refuse to believe such things are simply holding onto straggling threads of evidence, thinking that gives them the “right” to just believe whatever they want, because of a fundamental misunderstanding of what science is.
A Final (Unnecessary) Note on Einstein
In a somewhat famous essay, Einstein decried induction and praised deduction as the method by which physicists established new physical theories (like relativity). This makes it sound like perhaps he was contradicting some of the points I am making here. So was he? And was he right?
Not exactly.
First of all, he wasn’t working with the same definitions of the terms. When he said induction, what he had in mind was Aristotelian “particular to universal” reasoning, and he was arguing that that is not how physicists come up with theories. They don’t make observations of particulars and generalize about the entire universe; instead, he argued, they generate new theories through acts of inspiration. The process of theory creation is a bit like art.
While the latter may be how he came up with relativity, I’m not convinced that is how all physicists (and certainly not all scientists) generate new theories. I think generalizing from particular observations can and does play a role in some cases. Now, clearly, particular to universal reasoning doesn’t prove anything; it doesn’t even help establish it. It’s just a way of coming up with a hypothesis. But it doesn’t matter how theories are generated; what matters is whether they survive being tested and turn out to be better than competing theories. Which brings me to my second point.
What Einstein meant by “deduction” is actually what I and other modern logicians would call an inductive reasoning process. Once a theory is hypothesized, Einstein argued, physicists gather support for them by “deducing” (deriving) what the theory would entail (what one would expect to observe if the theory were true), and then performing experiments to see if those observational predictions are correct. Does what the theory say would happen actually happen? (A famous example of relativity being confirmed in this way is when relativity correctly predicted where astronomers would observe stars in the Hyades Cluster during the famous 1919 eclipse.)
But notice that, while it does involve what we might call a “deduction” (by yet another definition of the word), if this whole process is actually deductive reasoning, it is invalid. “If my theory is right then I should expect result R. Result R did happen. Therefore my theory is true.” (If H then R. R. Therefore H.) That’s the fallacy of affirming the consequent! But as an inductive argument, this reasoning is strong. Relativity correctly predicting where stars in the Hyades Cluster would be observed during the 1919 eclipse is what made many physicists realize that relativity was correct.
So, while Einstein was pretty accurately describing the reasoning process behind physics, he was using the wrong terminology. Perhaps he can’t be blamed for this; the logic textbooks (e.g., by Copi) that made non-philosophers aware of the updated more accurate deduction/induction distinction were still a few decades away. But still, recognizing the distinction that Einstein missed is important: Deduction is reasoning that guarantees its conclusion; induction is reasoning that provides conclusions with probable support.
Notes:
[i] Aristotle did not give this example himself, but it is a classic example (given by medieval scholars) to demonstrate what he had in mind.
[ii] I believe Aristotle actually recognizes this basic fact in the Prior Analytics when he says “Similarly too, if the premise is particular. For if some B is A, then some of the As must be B. For if none were, then no B would be A. But if some B is not A, there is no necessity that some of the As should not be B; e.g. let B stand for animal and A for man. Not every animal is a man; but every man is an animal.”
[iii] Aristotle may have also recognized this when he said, in Rhetoric, “The other kind of Sign, that which bears to the proposition it supports the relation of universal to particular, might be illustrated by saying, ‘The fact that he breathes fast is a sign that he has a fever’. This argument also is refutable, even if the statement about the fast breathing be true, since a man may breathe hard without having a fever.”
[iv] I put the world “merely” in parentheses here because I do not wish to imply that inductive reasoning is less powerful or valuable; indeed, most knowledge is acquired through inductive reasoning. But since guaranteeing a conclusion is one thing providing support is another, a distinction needs to be made between how inductive and deductive arguments support their conclusions. (** 此段文字的原文似有錯簡。淺藍色字體為編者所做修正，以求文從字順。)
Written by Dr. David Kyle Johnson
I am a philosophy and Great Courses (Wondrium) professor who publishes on religion, metaphysics, logic, and the intersection of philosophy with popular culture.
本文於 修改第 1 次
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淺談「讀書方法」：《增強閱讀記憶的七個方法》讀後
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0. 前言
讀了卡羅史先生的大作後(該欄03/17/2025，下稱《記憶》)，我不禁想起我十多年前經常看書時所用的一些「方法」。它們跟《記憶》推薦的「方法」有不謀而合之處；不過，當時我並不知道那樣做能幫助我記住書中內容。下面談談我做法和這七個方法相近的三個，給年輕網友們參考；括號裏的數字對應於《記憶》中七個方法的序號。
本文子標題為「《增強閱讀記憶的七個方法》讀後」；由於該文在「自我提升篇」之下，而本文主旨實屬「科學基礎論」下的「方法論」；故刊於此欄。
1. 「寫下書中有趣的點子」(方法3)
23歲到49歲之間我在美國唸書和工作，不容易買到中文書。因此，這段時間我讀的書大概80%以上是英文。回國後，由於成了習慣，看書還是以英文為主。為了確定自己讀懂，我會把術語、關鍵詞、重要概念、甚至一整段話翻譯成中文，寫在頁緣。當時雖然不知道這會幫助記憶，現在回想起來，它的確有這個作用。
2. 「跟作者對談」(方法4)
《記憶》方法4中的兩個建議也是我的做法。我用黃色和粉紅色的螢光筆來顯示我認為重要的文字；用星形、菱形、或三角形等來標示重要的段落和關鍵詞。我當時這樣做，並不知道它會加強記憶，而是為了日後要引用這些想法或概念時，容易找到它們。
此外，當我認為作者前後用不同方式陳述/強調同一個觀點，或作者前後說法不相容，我會在頁緣處做兩者相對照的註記；例如，「見102頁的星號」，或「比較69頁的三角形」。
我還有一個習慣跟這個方法相近。當我看到一個概念或理論時，我會回想一下：在我讀過的中國典籍和其他學者著作裏，是不是有類似或相反的說法。我不敢說自己每讀一本書都試圖「融會貫通」，但在幫助了解書本內容上，「比較」是一個非常有效的方法；它可以視為「跟作者對談」的方式之一。
3. 「活學活用」(方法5)
這一點我可以舉出三個實例：
1) 《我說「不」時，會覺得難為情》(1975)
看完這本書後，我常常把「不」掛在嘴邊；直到有一天我發現自己「不」過了頭。然後做了些修正；此之謂：「盡信書，不如無書」。
2) 《看人如看書》(1973)
讀過這本書後，我開始注意自己手、腳、胸、和肩膀等等的「位置」和坐姿、站姿等等。中國人說的：「賊眉鼠眼」和「誠於中，形於外」 (《大學章句7》)，大概跟「肢體語言」有幾分近似。
3) 《打招呼以後該說什麼》(1973)
這本書幫助人們了解一些溝通時可能遇到的障礙；我1983讀它，過了40多年，現在還偶而還會有用到「互動分析」理論的機會。
由於寫文章時以「言之成理」和「言必有據」期許自己；從而，我常常要引用自己讀過的概念、觀點、和理論。這是「活學活用」到思考，而不是日常生活的行為。但它應該也有加深記憶的作用。我用學到的概念和理論建立了一些自己的「觀點」；例如，《唯物人文觀》、《「自由意志」的討論》、和《交換價值和資源分配》。
4. 儒家學習方法
以上三個方法是我自己摸索而來，當時目的不在加強記憶；而在幫助我了解書本的內容。下面是我認為值得我們實踐的儒家「學習方法」。
1) 「博學之，審問之，慎思之，明辨之，篤行之。」《禮記•中庸22》
2) 「學而時習之」《論語•學而1》；「溫故而知新」《論語•為政11》
3) 「學而不思則罔」《論語•為政15》
這三個方法跟上面討論的「跟作者對談」、「活學活用」、以及「溫習！溫習！溫習！」(方法7)都相通；不在此多所著墨。
各位在此不妨實踐「活學活用」和「跟作者對談」兩者；比較一下以上三個「土法學習」和《記憶》的七個方法；然後自行評判我認為它們「相通」的看法能不能成立。
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